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A System of Logic, Ratiocinative and Inductive Flashcards

John Stuart Mill · Public domain edition · 431 cards · 116 chapters

Mill argues that logic should be grounded in experience and induction rather than intuition, and defends a systematic theory of reasoning against skeptics. The deck covers Mill’s account of propositions, language, inference, and logic’s scope, using the preface and introduction to frame his aims and replies to critics.

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Chapter 1 · Question

According to the Preface to the First Edition, what is the book's claim to originality?

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Section 14 cards

According to the Preface to the First Edition, what is the book's claim to originality?
Mill states the book does not offer a new theory of the intellectual operations. Its claim rests on attempting to embody and systematize the best existing ideas, cementing detached fragments of the subject and harmonizing the true portions of discordant theories. He allows only the originality required to connect and disentangle these, denying any revolution in the theory of investigating truth.
Chapter 1
How does Mill respond to writers who pronounced a general theory of induction impossible?
Mill says eminent writers, including Archbishop Whately and the author of a celebrated article on Bacon in the Edinburgh Review, had recently pronounced it impossible. He endeavors to combat their theory in the manner Diogenes confuted the skeptical reasonings against motion, noting that Diogenes's argument would remain conclusive even if his perambulations never extended beyond his own tub.
Chapter 1
What does Mill say in the third and fourth edition preface about responding to critics?
Mill says he reconsidered all points on which his conclusions were assailed but announces no change of opinion on any matter of importance. He corrected minor oversights, sometimes silently and sometimes merely to remove a stumbling-block. He replies at length to some arguments because truth on these subjects is militant and establishes itself by conflict, and he wishes the book had been attacked more.
Chapter 1
What does Mill say about the diversity of definitions of logic in the Introduction?
Mill observes there is as great diversity among authors in defining logic as in treating its details, which is expected when writers use the same language to deliver different ideas. Ethics and jurisprudence share this liability. Almost every writer takes a different view of particulars, framing his definition to indicate his own tenets and sometimes to beg the question in their favor.
Chapter 1

Section 24 cards

According to Mill, how are truths known to us?
Mill distinguishes two ways truths are known: some are known directly and of themselves, as the subject of Intuition or Consciousness; others are known through the medium of other truths, which is Inference. The truths known by intuition are the original premises from which all others are inferred, since we could never arrive at knowledge by reasoning unless something were known antecedently to all reasoning.
Chapter 2
What example does Mill use to show inference mistaken for intuition?
Mill cites the perception of distance by the eye. It seems like direct intuition, but what the eye perceives is at most a colored surface; the estimate of distance results partly from rapid inference from muscular sensations of focal adjustment and partly from unconscious comparison of apparent size and faintness of color. It is thus an inference grounded on experience, learned and improved with experience, though so rapid it seems on a par with perceptions of color.
Chapter 2
What does Mill say is the proper province of logic?
Mill restricts logic to the portion of knowledge consisting of inferences from truths previously known, whether those antecedent data be general propositions or particular observations. Logic is not the science of Belief but the science of Proof or Evidence; it supplies a test for whether a belief founded on proof is well grounded. With claims resting on the evidence of consciousness, logic has nothing to do.
Chapter 2
How does Mill describe logic's role as ars artium?
Mill calls logic the common judge and arbiter of all particular investigations: it does not find evidence but determines whether it has been found; it neither observes, invents, nor discovers, but judges. It does not tell the surgeon what appearances accompany a violent death, but judges whether his observation and rules justify his conduct. In this sense it is the science of science itself, pointing out relations that must subsist between data and conclusions.
Chapter 2

Section 34 cards

Why must the study of language precede the study of logic, according to Mill?
Mill argues that reasoning usually proceeds by means of words and in complicated cases can occur in no other way, so anyone lacking insight into the signification of words will almost certainly reason incorrectly. Logicians have therefore always treated an inquiry into language, as far as needed to guard against its errors, as a necessary preliminary to logic.
Chapter 3
What three parts make up every proposition, and what does each denote?
Mill states every proposition consists of Subject, Predicate, and Copula. The predicate names that which is affirmed or denied; the subject names the person or thing something is affirmed or denied of; the copula is the sign showing there is an affirmation or denial, distinguishing a proposition from other discourse. In 'The earth is round,' 'round' is predicate, 'the earth' the subject, 'is' the copula.
Chapter 3
Why does Mill say 'the sun' alone cannot be believed or disbelieved?
Mill argues that a bare name like 'the sun' has meaning and suggests it to a listener, but there is as yet nothing to believe or disbelieve, so no answer can be given. Only when a second object of conception is added, as in 'the sun exists,' does belief become possible; existence is distinct from the sun, since the sun may be conceived as no longer existing.
Chapter 3
Why does Mill reject the advice to dismiss words and look directly into things?
Mill calls this advice something no one has the power to follow, since it would discard all fruits of predecessors' labors and treat the inquirer as the first ever to examine nature. Beginning with names brings before us distinctions recognized by all inquirers together, not just one; we must first recognize ordinary language's distinctions, abridging them later only if close examination shows they are not fundamental.
Chapter 3

Section 44 cards

How does Mill define a general name versus an individual name?
A general name is capable of being truly affirmed, in the same sense, of each of an indefinite number of things, such as man affirmed of John, George, and Mary. An individual or singular name is capable of being truly affirmed, in the same sense, of only one thing, such as John, or 'the king who succeeded William the Conqueror.'
Chapter 4
What distinguishes a collective name from a general name?
A general name can be predicated of each individual of a multitude separately; a collective name can only be predicated of all taken together. 'The 76th regiment' is collective and individual, since it cannot be said of each soldier, while 'a regiment' is both collective and general, being affirmable of each individual regiment.
Chapter 4
How does Mill define concrete versus abstract names?
A concrete name stands for a thing; an abstract name stands for an attribute of a thing. John, the sea, and this table are concrete; whiteness, humanity, and old age are abstract. Mill follows the schoolmen's usage and rejects applying 'abstract' to all general names, as Locke's followers did.
Chapter 4
What makes a name connotative rather than non-connotative?
A non-connotative term signifies a subject only or an attribute only, like John or whiteness. A connotative term denotes a subject and implies an attribute, like white, which denotes white things and connotes whiteness. Mill argues all concrete general names, such as man, are connotative.
Chapter 4

Section 54 cards

According to Mill, where does the meaning of a name reside?
Mill argues that whenever names convey information and have proper meaning, the meaning resides not in what they denote but in what they connote. The only names that connote nothing are proper names, which strictly speaking have no signification. Connotative names are significant marks, a kind of livery in which an attribute clothes all objects recognized as possessing it.
Chapter 5
What does Mill's chalk-mark analogy illustrate about proper names?
Mill compares imposing a proper name to the robber chalking a house to recognize it again. The mark serves distinction but conveys no information about the house. Similarly, a proper name is an unmeaning mark connected in the mind with the idea of an object, letting us identify it when spoken of, not when seen. Morgiana defeated the scheme by chalking all houses alike, erasing the difference.
Chapter 5
Why does Mill say knowing what a name denotes isn't knowing its meaning?
Mill argues that many names may apply to the same individual while differing in meaning. Sophroniscus can be called 'Sophroniscus' and 'the father of Socrates': same individual, different purposes and meanings. Likewise 'a man,' 'a Greek,' 'a sculptor' each apprise one of distinct facts. One might know every individual a name applies to and still not know its meaning, as a child knows its siblings before understanding 'brother' or 'sister.'
Chapter 5
What problem does Mill identify with indeterminate connotation in general names?
Mill says it is often unclear how much a word connotes, as with 'man,' where the required external form and lowest degree of rationality are unsettled. This vagueness is tolerable only with strict precautions. Using connotative terms without distinctly ascertained connotation is a chief source of lax thought; names creep from subject to subject until common meaning disappears, and even scientific writers have aided this perversion.
Chapter 5

Section 63 cards

According to Mill, what makes a name relative?
A name is relative when, besides denoting an object, its signification implies another object that derives its denomination from the same fact grounding the first name. Equivalently, its meaning cannot be explained without mentioning another thing, or it cannot be used meaningfully unless another thing's name is expressed or understood. Mill says all these definitions are equivalent.
Chapter 6
How does Mill distinguish univocal from equivocal names?
Mill argues these are not two kinds of names but two modes of employing names. A name is univocal when predicated of things in the same sense, equivocal when predicated in different senses. An ambiguous word is really two names accidentally coinciding in sound, like 'file' (instrument) and 'file' (line of soldiers), no more one word than 'grease' and 'Greece'.
Chapter 6
Why does Mill criticize Aristotle's ten Categories?
Mill argues the Categories are a mere catalogue of distinctions from familiar language, with little philosophic analysis, and are both redundant and defective: some objects omitted, others repeated under different heads. He notes Relation should include action, passivity, and local situation; Quando and Ubi overlap; Situs is merely verbal. Crucially, feelings and states of mind fit neither substances nor attributes.
Chapter 6

Section 74 cards

How does Mill classify so-called perceptions of external objects?
Mill classes perceptions among feelings or states of mind, specifically as cases of belief that claims to be intuitive or independent of external evidence. When a stone lies before me, he says, I have sensations, and in saying they come from an external object I intuitively believe an external cause exists. The laws of intuitive belief belong not to logic but to the science of the ultimate laws of the human mind.
Chapter 7
What two things does Mill say constitute an action?
Mill argues an action is not one thing but a series of two: the state of mind called a volition, followed by an effect. The volition or intention to produce the effect is one thing; the effect produced in consequence is another; together they constitute the action. His example: I form the purpose of moving my arm, and my arm, not being tied or paralytic, moves in obedience.
Chapter 7
How do school logicians distinguish substance from attribute?
School logicians say an attribute must be the attribute of something: color must be color of something, and if that something ceased to exist the attribute would end. A substance is self-existent; we need not put 'of' after its name. A stone is not the stone of anything. Mill finds this unsatisfactory, since 'of' itself needs explanation, and we can no more imagine substance without attributes than attributes without substance.
Chapter 7
What definition of body do modern metaphysicians give, and what objection follows?
Mill reports the received doctrine that a body is the external cause to which we ascribe our sensations; the sensations are all we are directly conscious of, but we consider them produced by something external to mind and organs. He then notes philosophers who argue that if an orange lost every sensible quality nothing would remain, so a body is only a set of sensations, or possibilities of sensation, joined by a fixed law.
Chapter 7

Section 84 cards

According to Mill, what do we really assert when we say snow has the quality whiteness?
Mill says we assert only that when snow is present to our organs we have a particular sensation called the sensation of white. We know snow is present only by the sensations it gives us, and ascribing whiteness means that the sensation of white color is one of the sensations composing that group or series.
Chapter 8
What alternative view of qualities does Mill describe before setting it aside?
The alternative holds that while sensations are the sole evidence for ascribing a quality, evidence and thing are not identical. On this view whiteness is not the fact of receiving a sensation but a power inherent in the object, something in virtue of which it produces the sensation. Mill says logic need not decide between the views.
Chapter 8
How does Mill ridicule the notion of qualities as entities per se?
Mill says he sees no foundation for a peculiar species of entities called qualities except a mental tendency to suppose that two non-synonymous names must name two different things. He compares it to Molière's physician who explained opium's sleep-inducing effect by saying it has a soporific virtue—merely reasserting the fact, not explaining it.
Chapter 8
What is the fundamentum relationis, and how does Mill define a relation?
Mill says the fundamentum relationis is some fact or phenomenon into which the two related things both enter as parties concerned. Just as a quality is grounded on sensations produced in us by an object, a relation is an attribute grounded on some fact into which the object enters jointly with another object. Such facts resolve into states of consciousness.
Chapter 8

Section 104 cards

According to Mill, does the circumstance of time attach to the copula or the predicate?
Mill argues that past, present, and future are designations belonging to the event asserted, not different kinds of rising. They affect the applicability of the predicate to the particular subject, not the predicate itself. What is affirmed as past, present, or future is what the predication signifies, expressed only by the proposition as such. Therefore time properly attaches to the copula, the sign of predication, not to the predicate.
Chapter 10
How does Mill analyze propositions like 'Cæsar may be dead'?
Mill says such modality modifications fall under another head: they are properly assertions not about the fact itself but about the state of our own mind regarding it, namely our absence of disbelief. Thus 'Cæsar may be dead' means 'I am not sure that Cæsar is alive.' The assertion concerns our mental state, not any attribute of Cæsar or of the event.
Chapter 10
Why does Mill deny that 'Cæsar is dead, and Brutus is alive' is a compound proposition?
Mill holds it is not a proposition at all but several propositions held together by a conjunction. The words are equivalent to: Cæsar is dead; Brutus is alive; it is desired that the two be thought of together. With 'but' a fourth proposition is added, asserting a contrast. Particles like 'and' and 'but' are abbreviations of propositions, so calling this a complex proposition is like calling a street a complex house.
Chapter 10
What is the real subject and predicate of a hypothetical proposition like 'If the Koran comes from God, Mohammed is his prophet'?
Mill argues nothing is affirmed of the Koran or Mohammed themselves; neither simple proposition need be true for the hypothetical to be true. What is asserted is the inferribility of one proposition from the other. The real subject is the entire proposition 'Mohammed is the prophet of God,' and the predicate is a general relative name meaning 'an inference from so and so.' So subject and predicate are names of propositions.
Chapter 10

Section 114 cards

What does Hobbes say a proposition signifies, and when is it true?
Hobbes holds that every proposition signifies the speaker's belief that the predicate is a name of the same thing the subject names; the proposition is true if the predicate really is such a name. Thus 'All men are living beings' is true because 'living being' names everything 'man' names, while 'All men are six feet high' is false.
Chapter 11
Why does Mill reject Hobbes's theory as a full account of predication?
Mill concedes Hobbes's analysis states a property all true propositions share, and is the whole meaning of some. But it is only a minute fragment of meaning for most propositions. It fully explains only predications of proper names, like 'Tully is Cicero,' because proper names are mere marks for individuals. Hobbes, like other Nominalists, ignored connotation and looked only at denotation.
Chapter 11
According to Mill, what does 'All men are mortal' really assert?
Mill argues its meaning is that all beings possessing the attributes connoted by 'man' also possess the attributes connoted by 'mortal.' The class inclusion follows from that conjunction of attributes; it is not the proposition's fundamental meaning. Connotative names follow the attributes they connote rather than preceding them.
Chapter 11
What logical error does Mill attribute to the class-inclusion theory of predication?
Mill calls it ὕστερον πρότερον, explaining a thing by something that presupposes it. When judging 'snow is white,' I think of snow as a class but not of white objects as a class; thinking of white things as a class follows such judgments rather than preceding them. The theory explains the cause by the effect and rests on a misconception of classification.
Chapter 11

Section 124 cards

According to Mill, what does a proposition like 'All men are mortal' actually assert?
Mill argues that such a proposition asserts that one phenomenon always accompanies another: wherever the physical and mental phenomena connoted by 'man' are found, the phenomenon called death will occur. It does not specify when death occurs, since 'mortal' connotes only that the phenomenon happens at some time or other.
Chapter 12
What five kinds of matter-of-fact does Mill say every non-verbal proposition asserts?
Mill gives an exhaustive five-fold classification: Existence, Co-existence, Sequence, Causation, and Resemblance. One or other of these is asserted or denied in every proposition that is not merely verbal. He presents this as covering all things that can be believed, all questions propounded, and all answers returned to them.
Chapter 12
Why does Mill deny that class-membership propositions merely assert resemblance?
Mill argues class terms connote common peculiarities, and propositions assert those attributes, not resemblance. 'Gold is a metal' would keep its meaning even if no other metals existed, just as 'Christians are men' holds without non-Christian men. Resemblance is asserted only in exceptional cases, such as anomalous borderline species admitted by courtesy, or simple sensations classed by unanalyzable likeness.
Chapter 12
How does Mill analyze 'A generous person is worthy of honor'?
Mill treats it as asserting co-existence between two complicated phenomena. Generosity is ascribed on the ground of mental states and conduct, both phenomena; 'worthy of honor' connotes an approving, admiring emotion followed by outward acts, plus our approval of showing honor. The proposition affirms that wherever generosity's inward feelings and outward facts occur, honor and approval would follow.
Chapter 12

Section 134 cards

According to Mill, what do merely verbal propositions assert, and what proof can they have?
Mill holds that merely verbal propositions do not relate to any matter of fact but to the meaning of names. Since names and their signification are arbitrary, such propositions are not strictly susceptible of truth or falsity, only of conformity or disconformity to usage; the only proof they admit is proof of usage, showing that words have been employed in the acceptation the speaker intends.
Chapter 13
How does Mill redefine the essence of a thing, such as man's rationality?
Mill argues that the essence of man simply means the whole of the attributes connoted by the word, and any single one of those attributes is an essential property. The supposed impossibility of conceiving man without rationality is only an impossibility in the conventions of language: the thing could be conceived and perhaps exist, but would not be called a man.
Chapter 13
Why does Mill say essential propositions are identical propositions conveying no information?
Mill argues that when a predicate connotes only part of what the subject's name connotes, the universal affirmative is true because whatever possesses the whole set of attributes must possess any part of it. Such a proposition conveys no information to anyone who already understood the whole meaning of the terms; thus every man is rational, corporeal, or a living creature adds nothing.
Chapter 13
Why does an accidental affirmation imply the real existence of its subject while an essential one does not?
Mill explains that the copula ambiguously connotes existence, so essential predication only apparently implies the subject exists; one may say a ghost is a disembodied spirit without believing in ghosts. But an accidental affirmation does imply real existence, since with a non-existent subject there is nothing for the proposition to assert, as with a ghost haunting its murderer.
Chapter 13

Section 144 cards

According to Mill, does predication presuppose classification?
No. Mill argues general names mean attributes independently of being names of classes; whether many, one, or no objects answer to a name is accidental. 'Dragon' and 'ghost' are as much general terms as real names. Employing a name to connote attributes creates a class ipso facto, but in predicating the name we predicate only the attributes, not class membership.
Chapter 14
What are the five Predicables, and what kind of division are they?
Genus, species, differentia, proprium, and accidens—a fivefold division of general names handed down from Aristotle and Porphyry. Unlike ordinary divisions, it is not grounded in the attributes a name connotes but in the kind of class the name denotes. The distinctions express the relation a predicate bears to the subject on a given occasion.
Chapter 14
Why are genus and species called relative terms?
Because the same name is a genus or species only relative to a given subject. Animal is a genus with respect to man but a species with respect to substance; rectangular is a differentia of a geometrical square but an accidens of the table. No name is exclusively a genus or species; the label depends on the class denoted and its place in a classification.
Chapter 14
How do classes differ in the properties they share beyond the defining attribute?
Mill holds the power of framing classes is unlimited, since any difference can ground a division. But some classes, like white things, share little beyond the connoted attribute; others, like animals, plants, sulphur, or phosphorus, share inexhaustible common properties. The author argues this difference marks a more radical distinction between classifications.
Chapter 14

Section 153 cards

Why did Aristotelians reject 'cooking animal' as man's differentia?
Mill says the Aristotelians held the differentia, like genus and species, must be of the essence of the subject. Since rationality is connoted by the name 'man' but cooking food is not, rationality counted as differentia while cooking was relegated to accidental properties. Mill argues this distinction rests not on the nature of things but on the connotation of names.
Chapter 15
How does Mill distinguish Proprium from Accidens?
Both are accidents in the wide sense, forming no part of the essence. But Proprium is predicated accidentally yet necessarily: it flows from the essence and is inseparably attached to the species, like properties of a triangle that follow from its definition. Accidens has no connection with the essence and may come and go while the species remains what it was.
Chapter 15
Why may a species have different differentiae in different classifications?
Mill argues the differentia varies with the principle and purpose governing a particular classification. A naturalist may divide animals by warm-bloodedness, lungs versus gills, or diet, creating classes for scientific convenience. Even where classes are real Kinds, practical convenience warrants marking distinctions by whichever properties it most recommends—so 'man' may connote rationality ordinarily but teeth and posture in Linnaeus's system.
Chapter 15

Section 164 cards

According to Mill, what is the definition of a connotative name?
Mill holds that for connotative names the meaning is the connotation, so a definition is the proposition declaring that connotation. It may be done directly, stating the name connotes such and such attributes, or indirectly by predicating another name or names connoting the same aggregation of attributes. The direct form is most precise but too technical and not brief enough for common discourse.
Chapter 16
Why does Mill say a definition can be called an analysis, citing Condillac?
Mill says a complete definition is the sum total of essential propositions framed with the name as subject, all implied in the name and evolvable from it without other premises. Replacing one word connoting a set of attributes collectively by two or more connoting them singly or in smaller groups resolves a complex whole into elements—which is analysis. He therefore says it is not without reason that Condillac and others affirmed definition to be analysis.
Chapter 16
How are names of single attributes like eloquence defined, per Mill?
When an abstract name expresses a single attribute, Mill says every attribute is grounded on some fact or phenomenon, its foundation, from which alone it derives meaning. To define the attribute, analyze that phenomenon into its parts. Eloquence, though one attribute, is grounded on complicated external effects; resolving the causation into cause and effect yields the definition: the power of influencing the feelings by speech or writing.
Chapter 16
What two kinds of imperfect definition does Mill distinguish, and what makes each imperfect?
Mill distinguishes Essential but incomplete definitions, which define a connotative name by only part of its connotation—like 'Man is a rational animal,' which would include Houyhnhnms—and Accidental Definitions or Descriptions, which define by something forming no part of the connotation at all, such as 'Man is a featherless biped.' Both arise from accepting anything that marks out the denotation, and descriptions need only be convertible with the name.
Chapter 16

Section 174 cards

What does Mill claim all definitions are definitions of?
Mill argues that all definitions are of names, and of names only. He rejects the Aristotelian distinction between nominal and real definitions, holding that no definition ever 'unfolds the nature of a thing.' Some definitions merely explain a word's meaning, while others also imply that a corresponding thing exists—but that implication is not part of the definition itself.
Chapter 17
How does Mill analyze the definition of a triangle?
Mill says the definition of a triangle comprises two distinguishable propositions: 'There may exist a figure bounded by three straight lines' and 'this figure may be termed a triangle.' The first is a postulate, susceptible of truth or falsehood and able to ground reasoning; the second is a mere nominal definition, which can be neither true nor false, only conformable or not to ordinary usage.
Chapter 17
What does Mill conclude from the 'dragon' syllogism?
Mill constructs a syllogism from 'A dragon is a serpent breathing flame' that yields true premises but a false conclusion, which he calls an absurdity. He concludes that definitions cannot be the real premises; the real premises tacitly assume a really existing dragon, which is false. Substituting 'means' for 'is' yields only a conclusion about words.
Chapter 17
Why does Mill say geometrical postulates are not exactly true?
Mill notes that it is not true that a circle exists, or can be described, with all radii exactly equal; such accuracy is ideal only, not found in nature or realized by art. He says this apparent paradox will be examined under Demonstration, where he will show that as much of the postulate is true as is required to support as much as is true of the conclusion.
Chapter 17

Section 183 cards

According to Mill, how does a name come to denote a confused huddle of objects?
Mill argues that language "is not made, but grows": a name is first applied to one thing and then extended by successive links of resemblance to other objects. Eventually it may be applied to things having nothing in common with the original, yet the name is not dropped, so it denotes a confused huddle and connotes nothing, making it unfit for thought or communication until stripped of part of its denotation.
Chapter 18
What four questions does Mill identify in defining an abstract name like justice?
Mill says the first question is whether mankind agree sufficiently on which actions they call just, making the inquiry possible; this alone concerns usage and convention. The other two concern matters of fact: whether the actions really share a common quality, and what it is. If no common class exists, a fourth, often harder question remains: how best to form a class artificially for the name to denote.
Chapter 18
Which examples does Mill give of apparent but not real inference?
Mill lists three cases: equivalent rewordings, as "No man is incapable of reason, for every man is rational"; inferring a particular from a universal, as "All A is B, therefore Some A is B"; and affirming of a subject something already connoted by its predicate, as "Socrates is a man, therefore Socrates is a living creature." He says these repeat rather than prove, and that logic manuals often use such trivial examples.
Chapter 18

Section 194 cards

How does Mill distinguish Induction from Ratiocination by generality?
Mill says Induction infers a proposition from premises less general than itself, while Ratiocination infers a proposition equally or less general than its premises. When the conclusion is more general than the largest premise, the argument is called Induction; when less or equally general, Ratiocination. He notes these popular labels are brief rather than precise.
Chapter 19
What does Mill claim is essential to a legitimate syllogism?
Mill states a legitimate syllogism must have exactly three propositions—the conclusion and two premises—and exactly three terms: the subject and predicate of the conclusion plus a middle term found in both premises. The major term is the conclusion's predicate, the minor term its subject; the major premise contains the middle and major terms, the minor premise the middle and minor terms.
Chapter 19
How are syllogistic figures distinguished, and how many does Mill recognize?
Figures are distinguished by the position of the middle term: subject in both premises (third figure), predicate in both (second), subject of major and predicate of minor (first), and subject of minor and predicate of major (fourth). Mill notes some logicians count three figures, folding the fourth into the first. Moods are then divided by quantity and quality of propositions.
Chapter 19
Why does Mill say every valid ratiocination can be put in the first figure?
Mill holds that all correct ratiocination admits of being stated in syllogisms of the first figure alone, since every mood of the second, third, and fourth figures can be reduced to a first-figure mood by converting one or both premises. He notes some arguments fall more naturally into other figures and are more obviously conclusive there, but reduction remains possible.
Chapter 19

Section 204 cards

What error does Mill say keeps returning in new phrasing?
Mill argues that an error once refuted often returns disguised in new terminology and is accepted unquestioned for ages. He claims the scholastic doctrine that universals are the only stable objects of knowledge, though nominally rejected, persisted under Locke's Abstract Ideas, Hobbes's and Condillac's nominalism, and later German ontology, continuing to corrupt philosophy.
Chapter 20
What does Mill say about Condillac's aphorism that a science is a well-made language?
Mill rejects Condillac's claim that a science is little more than une langue bien faite, i.e. that naming things properly is the sufficient rule for discovering their properties. He argues the reverse: we cannot name things properly unless we already know their nature and properties. Names only help us remember and communicate thoughts, functioning as an artificial memory, not as a source of new knowledge.
Chapter 20
How does Mill analyze the syllogism in terms of attributes rather than classes?
Mill holds that every informative proposition asserts a matter of fact about attributes, not mere class membership. In 'All men are mortal; Socrates is a man,' the major asserts the attributes connoted by 'man' never occur without mortality; the minor asserts Socrates has the attributes of man; the conclusion asserts he has mortality. A negative major asserts incompatibility of attributes instead.
Chapter 20
What two axioms does Mill substitute for the dictum de omni et nullo?
Mill replaces the dictum with two principles resembling mathematical axioms. The affirmative principle: things co-existing with the same thing co-exist with one another (if A co-exists with B and B with C, then A with C). The negative principle: a thing co-existing with another that does not co-exist with a third is not co-existent with that third. These concern facts, not conventions.
Chapter 20

Section 214 cards

Where does Mill say the inference resides in concluding the Duke of Wellington is mortal?
Mill argues the inference is finished once we assert that all men are mortal; the subsequent descent from the general proposition to the Duke of Wellington is merely deciphering our own notes. The individual cases of John, Thomas, and others are the whole evidence, and interpolating a general proposition adds nothing to the proof.
Chapter 21
What does Mill say about Archbishop Whately's view that syllogizing is the mode in which all men reason?
Mill respectfully disagrees, saying the vulgar notion is more correct. If we are entitled to conclude all human beings are mortal from instances like John and Thomas, we could have concluded directly that the Duke of Wellington is mortal. The individual cases are all the evidence; no logical form makes it greater, so we may take the shortest cut from premises to conclusion.
Chapter 21
What example does Mill give of reasoning from particulars to particulars in a child?
A child who has burned his fingers avoids the fire again, having reasoned from the remembered particular case without ever forming the general maxim 'Fire burns.' He believes in each case without looking beyond the present one; he is not generalizing but inferring a particular from particulars. Mill adds that brutes reason the same way: the burned dog dreads the fire.
Chapter 21
What does Mill say about the skilled dyer who could not teach his method?
The Scotch manufacturer hired a dyer famous for fine colors, but the man proportioned ingredients by handfuls rather than weighing. Asked to convert his handling system into an equivalent weighing system so the principle could be ascertained, he found himself unable to do so and could impart his skill to nobody. He had established connections between tactual perceptions and color effects without ever generalizing them in language.
Chapter 21

Section 224 cards

On Mill's view, what does the syllogism actually accomplish in reasoning?
The author argues the syllogism is not a correct analysis of the inference process; real reasoning runs from particulars to particulars, authorized by a prior induction. The syllogism's function is to interpret a memorandum of our previous belief, maintaining consistency between general directions and particular conclusions, much as a judge interprets a law to avoid departing from the legislator's intention.
Chapter 22
What does Mill say is the true ground for believing the Duke of Wellington will die?
The author argues the real premises are the observed deaths of his fathers, our fathers, and all contemporaries—not any necessity of avoiding verbal inconsistency. There is no contradiction in supposing those persons died while Wellington lives forever; the contradiction arises only if we first make a general assertion covering his case and then refuse to stand to it in the individual instance.
Chapter 22
How does stating an inference as a general proposition help detect bad evidence?
The author argues a general proposition presents a larger object to the imagination, prompting more careful weighing of the experience. More importantly, if the premises are insufficient, the general conclusion may include some fact we already know to be false, exposing the error by reductio ad impossibile. His example: expecting Commodus to be just would collapse under 'all Roman emperors are just rulers,' since Nero and Domitian refute it.
Chapter 22
What are the benefits and drawbacks of general language that Mill identifies?
The author argues general propositions let inductions be made once for all and registered, so bulky experimental details can be forgotten while their knowledge is retained in available form. The countervailing inconvenience is that inferences made on insufficient evidence become consecrated into general maxims, and the mind cleaves to them from habit after forgetting the particulars, not thinking to revise. Mill judges this a small set-off against the immense benefits.
Chapter 22

Section 234 cards

According to Mill, into what elements is every reasoning process resolvable?
Mill argues all reasoning resolves into: certain individuals have a given attribute; other individuals resemble the former in certain other attributes; therefore they resemble them also in the given attribute. This type of ratiocination does not claim, like the syllogism, to be conclusive from mere form, since whether one fact proves another depends on other considerations—a question of Induction.
Chapter 23
How does Mill divide the logical operation, and what does he call each part?
Mill divides the operation into two steps: first, ascertaining what attributes are marks of mortality; second, whether given individuals possess those marks. He calls establishing the general proposition Induction, and interpreting the general proposition Deduction. Every inference about an unobserved case consists of an Induction followed by a Deduction, though the process need not always be carried on in that form.
Chapter 23
What is Mill's reply to critics who say the major premise affirms the sufficiency of the evidence?
Mill admits the major premise affirms the sufficiency of the evidence and says that is the essence of his theory. But he denies this recognition is part of the induction itself, calling that false psychology. The conclusion is inferred from the evidence, not from recognizing the evidence's sufficiency—as one infers a friend approaches because one sees him, not because one recognizes one's eyes are open.
Chapter 23
How does Mill distinguish Formal Logic from Logic in the widest sense?
Mill conceives Logic as the entire theory of ascertaining reasoned or inferred truth. Formal Logic, which Hamilton and Whately treat as the whole of Logic proper, is really a subordinate part, concerned with the equivalence of modes of expression and rules for when assertions imply others. Its end is not truth but consistency; it is a necessary auxiliary to the logic of truth and can be studied earlier in education.
Chapter 23

Section 244 cards

How does Mill describe complex deductions in advanced sciences?
Mill argues that in complex branches of knowledge, deductions seldom consist of a single chain where a is a mark of b, b of c, and c of d. Instead, they consist of several chains united at the extremity: a is a mark of d, b of e, c of f, and d, e, f together are a mark of n, so a, b, c together are a mark of n. He illustrates this with reflected rays and a parabolic surface.
Chapter 24
What is the difficulty in recognizing the angles in Euclid's fifth proposition?
The angles at the base of an isosceles triangle do not obviously fall under any of the eight formulas for equality or inequality. On examination they are found to be the differences of equal things, but each angle is the difference of innumerable pairs of angles. The difficulty is imagining the base angles as remainders made by cutting one pair of angles out of another, requiring a happy contrivance to select the right pairs.
Chapter 24
Why does Mill say geometry is a Deductive Science?
Mill argues that all inductions in geometry are comprised in the simple axioms and a few definitions, which are obvious and familiar. The rest of the science consists of processes for bringing unforeseen cases within these inductions, or proving the minors necessary to complete syllogisms. Since the marks are few and the inductions obvious, the connecting of several together forms the whole difficulty and bulk of the science.
Chapter 24
What distinction does Mill draw between deductive and experimental sciences?
Mill argues the opposition is not between deductive and inductive, but between deductive and experimental. A science is experimental in proportion as every new case with peculiar features needs fresh observations and experiments. It is deductive in proportion as it draws conclusions about new kinds of cases by processes bringing them within simpler inductions. Every step in deduction is still an induction, and sciences tend to become more deductive without being less inductive.
Chapter 24

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According to Mill, why is the science of number the grand agent for making sciences deductive?
The author argues that number's properties are, in the most rigorous sense, properties of all things whatever: all things are not colored, ponderable, or even extended, but all things are numerable. Because the science of quantity is altogether deductive, when variations of quality correspond regularly to variations of quantity, the theory of those qualities becomes deductive too.
Chapter 25
What revolution in geometry does Mill credit to Descartes and Clairaut?
Mill calls it the most striking historical instance: to every variety of position in points, direction in lines, or form in curves and surfaces (all qualities) there corresponds a peculiar relation of quantity among two or three rectilineal co-ordinates. If the law of their variation is known, every other geometrical property can be inferred, so every geometrical question reduces to an algebraical one.
Chapter 25
Why does Mill say the necessity ascribed to mathematics is an illusion?
The author argues geometry's definitions assume real things conformable to them, but no points without magnitude, lines without breadth, or perfectly equal radii exist. The necessity consists only in conclusions correctly following from suppositions that are not even true and purposely depart from truth; they are hypotheses, not necessary truths.
Chapter 25
How does Mill respond to the claim that geometrical objects exist merely in our conceptions?
He calls this doctrine psychologically incorrect. Our ideas of points, lines, and circles are copies of things known in experience; a point is the minimum visibile. A line without breadth is wholly inconceivable, though we can attend to part of a perception rather than the whole. Geometry concerns really existing figures, with definitions as first generalizations only nearly true.
Chapter 25

Section 264 cards

According to Mill, what is the status of the axiom that two straight lines cannot inclose a space?
Mill argues it is an induction from observation, not an a priori truth. He notes that even if evident independently of experience, it is also confirmed by experience in almost every instant of life, since intersecting straight lines visibly diverge. The burden of proof, he contends, lies on those who claim a different origin for this knowledge.
Chapter 26
What is Bain's psychological explanation for why axioms seem knowable from the idea alone?
Bain argues that in acquiring the idea we have already learned the fact. To grasp the notion of whole and part requires concrete experience that implies the whole is greater; to master the notion of straightness requires comparisons yielding that two straight lines cannot inclose a space. Thus the same knowledge that makes a first principle understood suffices to verify it.
Chapter 26
What is the second main argument for axioms being a priori, and how does Mill respond?
The argument holds that axioms are conceived as universally and necessarily true, which experience cannot supply, since it consists of limited observations and shows only what happens, not what must happen. Mill answers that mental diagrams of lines and angles exactly resemble realities and serve as fit subjects of geometrical experimentation, so the conclusion remains an induction from observation.
Chapter 26
Why does the impossibility of tracing lines to infinity not defeat Mill's account?
Mill argues that if two lines ever meet after diverging, they must do so at a finite distance, not infinity. We can transport ourselves there in imagination and form a mental image of the appearance, which resembles reality. Experience then tells us that a line which begins to approach after diverging produces the impression of a bent line, not a straight one.
Chapter 26

Section 274 cards

What does Mill say about the inconceivability of two straight lines inclosing a space?
Mill argues that even if our belief in this axiom comes from experience, its negative would still be inconceivable to us, since we have no analogous experience to help us conceive it. Our impressions of form exactly resemble their prototypes, so merely imagining two straight lines to try to conceive them inclosing a space repeats the very experiment that disproves it.
Chapter 27
What does Mill urge those who agree with Whewell to study, and why?
Mill urges them to study the general laws of association, confident that moderate familiarity with those laws will dispel the illusion that our earliest inductions from experience have a peculiar necessity. He contrasts this with Whewell's advice to study geometry, which Mill says he has conscientiously fulfilled.
Chapter 27
How does Mill use Whewell's own words against the inconceivability theory of axioms?
Mill quotes Whewell saying the essence of scientific triumphs is leading us to regard rejected views as not only false but inconceivable. Mill argues this concedes that inconceivableness is accidental, depending on mental history rather than the phenomenon itself, so it cannot be grounds for rejecting a proposition as impossible.
Chapter 27
What does Mill say about Whewell's claim that the laws of chemical composition are beyond mere experiment?
Mill calls it a reductio ad absurdum of the inconceivability theory. Whewell claims we cannot conceive elements combining in other than definite proportions, so the laws have evidence beyond experiment. Mill replies that Whewell, meditating on a truth whose discoverer was still living, made the association so familiar he could not conceive one fact without the other.
Chapter 27

Section 284 cards

According to Mill, what is the true nature of deductive or demonstrative sciences?
The author argues that deductive or demonstrative sciences are all, without exception, inductive sciences whose evidence is that of experience. They are also hypothetical sciences, because their conclusions are only true on certain suppositions that are or ought to be approximations to truth but are seldom exactly true. Their supposed peculiar certainty is ascribed to this hypothetical character.
Chapter 28
What nominalist theory of arithmetic does Mill examine, and what difficulty does he say is fatal to it?
The theory holds that propositions of number are merely verbal, and algebra is just substituting equivalent expressions, so 'two and one is three' is a definition of the word three. Mill says this cannot explain how, after such translations, the fact itself comes out changed, as when a new geometrical theorem is demonstrated by algebra—a difficulty fatal to the theory.
Chapter 28
Why does Mill say algebraical symbols need not raise ideas of particular things?
Mill argues all numbers must be numbers of something, but may be numbers of anything, so numerical propositions concern all things whatever. Algebraical symbols represent all numbers without distinction, and algebraical truths like 2(a+b)=2a+2b are co-extensive with all nature. Since they are true of all things, the symbols need not excite ideas of any particular thing.
Chapter 28
How does Mill answer the claim that 'two and one is three' is a merely identical proposition?
Mill says the expressions denote the same objects but connote differently: three pebbles in two parcels and three in one parcel make different impressions on the senses. The assertion that the same pebbles can by rearrangement produce either set of sensations is not identical but an inductive truth known by early and constant experience, and such truths are the foundation of the science of Number.
Chapter 28

Section 294 cards

What does Mill say actually forces assent in a correct syllogism, if not reductio ad absurdum?
Mill argues no one is ever forced to a contradiction in terms; a denier of the conclusion can only be pushed to deny a premise by another ratiocination, which he may equally reject. What he violates is the fundamental maxim of ratiocination: whatever has a mark has what it is a mark of, and whatever is a mark of a thing is a mark of whatever else that thing marks.
Chapter 29
How does Herbert Spencer define the test of whether a belief invariably exists?
Spencer holds that we can have no stronger ground for a belief than that it invariably exists, and that the criterion for deciding this is our inability to conceive its negation. The inconceivability of the negative is thus, on his view, the test by which we ascertain whether a belief invariably exists, and he treats it as the ultimate ground of all assured beliefs.
Chapter 29
What two arguments does Mill attribute to Spencer in support of the inconceivability test?
Mill distinguishes a positive and a negative argument. The positive one claims every such belief represents the aggregate of all past experience, with universal uniformities in nature producing inconceivable negations. The negative argument answers that occasional failures of the test no more vitiate it than mistaken inferences vitiate logic, since our most certain beliefs admit no better guarantee.
Chapter 29
What counterexamples does Mill give against uniformity of experience as a criterion of truth?
Mill cites two: that all metals sink in water was uniform experience until Sir Humphry Davy discovered potassium, and that all swans are white was uniform until the discovery of Australia. He also notes the inconceivability of antipodes and of the sun's motion, which reflected no real experience but only a mistaken supposition of experience.
Chapter 29

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What two meanings of 'inconceivable' does Mill distinguish?
Mill distinguishes between 'unbelievable' and the proper sense: a proposition whose terms cannot be brought before consciousness in the asserted relation, offering insurmountable resistance to union in thought. He argues the argument from inconceivableness usually turns on alternately substituting one meaning for the other, and questions whether Spencer consistently maintains the proper sense.
Chapter 30
Why does Mill say Spencer's test fails for objective beliefs?
Mill argues that beliefs about an external world, extension, space, and time are not invariable, since many thinkers have disbelieved them. Their negations are therefore believable, because they are actually believed. The test of inconceivableness thus fails precisely in the cases where it would be needed, leaving the existence of matter a question of argument.
Chapter 30
What sunrise/sunset example does Mill use against Spencer?
Mill notes that educated persons believe the earth moves, yet habitually conceive the phenomenon as the sun's ascent or descent, and cannot easily conceive otherwise. He argues this parallels Spencer's doctrine about belief in matter: if inconceivability proved truth, we would have to believe the sun moves. Mill says Spencer does not make that claim.
Chapter 30
What limitation does Spencer claim for his test, and how does Mill respond?
Spencer limits the test to simple propositions assented to on simple inspection, not complex ones requiring mediate proof, and notes users may err through incapacity or carelessness. Mill accepts the limitation but says it still excludes marked cases once thought inconceivable, such as the sun moving at sunset, gravitation without a medium, and antipodes.
Chapter 30

Section 314 cards

How does Mill define Induction for his inquiry?
Mill defines induction as "the operation of discovering and proving general propositions." He notes that indirectly ascertaining individual facts is also inductive, but not a different kind: generals are collections of particulars, and evidence justifying one unknown case justifies a whole class of similar cases. Thus a complete logic of the sciences would also be a logic of practical business and common life.
Chapter 31
What is Mill's view of the Principle of Contradiction?
Mill partly agrees with the Nominalists: that if the negative is true the affirmative must be false is a mere identical proposition, since the negative asserts only the falsity of the affirmative. But he goes no further with them, denying it is merely verbal. He considers it a generalization from experience, founded on Belief and Disbelief being distinct, mutually excluding mental states, and on contrasted phenomena like light and darkness.
Chapter 31
Why does Mill say Excluded Middle is not absolutely true?
Mill argues a proposition must be either true or false only provided the predicate can intelligibly be attributed to the subject. Otherwise there is a third possibility, the Unmeaning: "Abracadabra is a second intention" is neither true nor false. He says this undermines Hamilton's extension of the maxim to Noumena, since divisibility may not be predicable of Matter in itself.
Chapter 31
What does Mill say about the practical inquirer's chief difficulty?
Mill says the practical inquirer, such as an advocate or judge, faces a difficulty induction cannot help with: not making inductions but selecting them—choosing from true general propositions those that furnish marks for tracing whether the subject has the predicate. Skill lies in bringing the case under trite principles; success depends on sagacity and knowledge, and invention cannot be reduced to rule.
Chapter 31

Section 324 cards

Why does Mill deny that summing up circle, ellipse, parabola, and hyperbola properties is induction?
Mill argues there is no inference because the conclusion merely sums up what was asserted in the various propositions from which it is drawn. Since a cone demonstrably cannot be intersected by a plane except in one of these four lines, there is no room for generalization beyond the proposition, so it may be called a generalization but not an induction.
Chapter 32
What does Mill call the geometrical proof by diagram, and why is it not induction?
Mill suggests the name "induction by parity of reasoning" but denies it is induction properly. The truth obtained, though really general, is not believed on the evidence of particular instances. We do not conclude all triangles have the property because some do, but from the ulterior demonstrative evidence that was the ground of conviction in the particular case.
Chapter 32
According to Mill, what was the only real induction in Kepler's discovery of Mars's elliptical orbit?
The real induction was inferring that because the observed places of Mars were correctly represented by points in an imaginary ellipse, Mars would continue to revolve in that same ellipse, and that intermediate positions coincided with the curve. These were facts not directly observed. But astronomers had long known planets return to the same places, so Kepler made no further induction.
Chapter 32
How does Mill distinguish colligation of facts from induction, against Whewell?
Mill agrees with much of Whewell's account of colligation, the descriptive operation summing up details in a single proposition, but thinks Whewell errs in setting it up as the type of induction generally. Mill argues the general proposition is not something added to the facts: the ellipse was in the facts before Kepler recognized it, as the island was an island before being sailed round.
Chapter 32

Section 333 cards

What distinction does Mill draw between colligation and induction?
Mill argues colligation is merely describing observed facts under a general conception, while induction is inferring something unobserved from something observed. Colligation is not always induction, but induction is always colligation: once an induction is made, it also connects the same facts under a new conception, serving as a new bond of classification.
Chapter 33
What does Mill say about Kepler's elliptical orbit statement regarding induction?
Mill argues Kepler's statement that Mars moves in an ellipse was not induction, because it did not extend an observed truth to new cases or widen the subject of the proposition. Kepler changed the predicate, summing up already-observed successive places as points in an ellipse. It took in no cases beyond those observed or inferable beforehand.
Chapter 33
How does Mill respond to Whewell's view that induction requires a new mental conception?
Mill argues Whewell confounds Invention with Proof. Introducing a new conception belongs to invention, which may be required in any operation but is the essence of none. Induction is proof, inferring the unobserved from the observed, and requires a test of proof; most inductions need no conception beyond what was present in each particular instance.
Chapter 33

Section 344 cards

What is the ultimate major premise of every inductive argument, according to Mill?
Mill argues that the immediate major premise of an inductive syllogism is a proposition like 'what is true of John, Peter, etc., is true of all mankind,' which is not self-evident. Tracing the proof of that premise back through further syllogisms, one arrives at an ultimate syllogism whose major premise is the axiom of the uniformity of the course of nature.
Chapter 34
How does Mill regard the axiom of the uniformity of nature?
Mill states he regards the uniformity of the course of nature as itself a generalization from experience. He notes others hold it to be a principle we are compelled by the constitution of our thinking faculty to assume as true antecedently to experience. He defers fuller discussion of this controversy, saying he has already combated a similar doctrine regarding mathematical axioms.
Chapter 34
What is induction by simple enumeration, and why is it insufficient?
Mill describes it, following Bacon's phrase, as ascribing general truth to propositions true in every instance we happen to know of, without seeking contrary cases. He argues we may only conclude something universally true from unvarying experience if we have reason to believe contrary instances would have been known to us. This assurance is usually unavailable, so science needs a surer instrument.
Chapter 34
Why does one instance sometimes suffice for induction while myriads do not?
Mill contrasts a chemist's conclusion from a single experiment, accepted as universally valid, with the proposition that all crows are black, which myriads of instances cannot establish against one credible report of a gray crow. He says whoever can answer why a single instance suffices in some cases but not others has solved the problem of induction.
Chapter 34

Section 354 cards

Why does Mill reject Descartes' precept of beginning by doubting everything?
Mill argues that many uniformities are so constant and open to observation that they force themselves on us involuntarily, like expecting food to nourish or bodies to fall. The first scientific inquirers rightly assumed such known truths and set out to discover others, subject to later revision when knowledge reveals limits or hidden conditions. Any other mode, he says, is rigorously impracticable.
Chapter 35
Why is the black swan claim more credible than men with heads under their shoulders?
Mill says it is because there is less constancy in animal colors than in general anatomical structure, and we know this from experience. Experience must be consulted to learn in what cases arguments from experience are valid; we make experience its own test, trusting uniformities more in classes where they have hitherto been more uniform.
Chapter 35
What happens when a weaker induction is deduced from stronger ones?
It acquires the strength of those from which it is deduced and even adds to their strength, since the independent experience supporting the weaker one becomes additional evidence for the better-established law. Mill's example: the generalization that uncontrolled power is often abused gains assurance when shown to follow from facts about human character and education.
Chapter 35
What ends belief in comets as omens, oracles, and astrology, according to Mill?
Not the sheer number of failures, since such faith survives many failures if nourished by casual coincidences. What really ends these insufficient inductions is their inconsistency with stronger inductions later obtained by scientific inquiry about the causes of terrestrial events; where those truths have not penetrated, similar delusions still prevail.
Chapter 35

Section 364 cards

For Mill, what is the true cause of a phenomenon?
The author argues the real cause is the whole set of antecedents—the sum total of positive and negative conditions—whose concurrence invariably produces the effect. Singling out one antecedent as "the cause" and calling the rest mere conditions is, philosophically speaking, incorrect; all conditions are equally indispensable, and any statement of the cause is incomplete unless it introduces them all.
Chapter 36
Why does common usage single out the last condition as cause?
The condition that completes the set of conditions is an event—a change—while the other conditions are often pre-existing states of indefinite duration. Since the effect begins immediately once this final event occurs, it appears more closely connected to the effect. Mill notes this tendency explains why people name the proximate event the cause, though it has no closer relation than the others.
Chapter 36
What example shows the cause-label is capricious?
Mill analyzes a stone falling to the bottom of water. Each condition—the earth's existence, the stone being within the earth's sphere of attraction, its specific gravity exceeding the fluid's—can with equal propriety in common parlance be called the cause. This shows no scientific ground exists for distinguishing a phenomenon's cause from its conditions; selection depends on which condition is most conspicuous or being insisted on.
Chapter 36
How does Mill treat negative conditions in causation?
Mill argues negative conditions, like a sentinel being off his post, are not producing causes but the mere absence of a preventing cause; from a negation no consequences proceed. All effects connect by the law of causation to some set of positive conditions. Since causes counteract one another by their own laws, all negative conditions can be summed up as the absence of counteracting causes.
Chapter 36

Section 373 cards

Why is night not the cause of day, despite their invariable succession?
The author argues that invariable sequence is not causation unless it is also unconditional. Night is followed by day only provided the sun rises; if the sun ceased to rise, night might be eternal. The true cause of day is the existence of a luminous body with no opaque medium between it and us, since that combination would produce day whether or not night had preceded it.
Chapter 37
How does Mill answer the objection that unconditional causation is a belief not derived from experience?
Mill replies that experience itself teaches which uniformities are conditional and which unconditional. Twice daily, when the sky is clear, we have an experimentum crucis showing the sun causes day. Experimental knowledge of the sun justifies concluding that if the sun were always above the horizon there would be day even without prior night. Thus experience, not mere observation of sequence, grounds the belief.
Chapter 37
Does a cause always precede its effect, or can they be simultaneous?
Mill says a distinction must be drawn. Conditions necessary for a phenomenon's first production are occasionally also necessary for its continuance, though more commonly continuance requires only negative conditions. Most things, once produced, continue until something changes them, as a plowshare remains after the hammering stops. Some effects, like the pressure sustaining mercury in a tube, do require the continued presence of their producing agency.
Chapter 37

Section 384 cards

According to Mill, what determines the co-existences observable among effects?
The author argues that uniformities of co-existence among effects are never independent laws; they result either from the identity of their causes or from the causes' co-existing. Since primeval causes cannot be reduced to a universal law of co-existence, there are no unconditional uniformities of co-existence between effects of different causes. The only independent, unconditional co-existences are between different properties of the same natural agent.
Chapter 38
What two stages does Mill identify in the Conservation of Force doctrine?
Mill distinguishes one stage of ascertained fact from another containing a large element of hypothesis. The factual stage shows heat, electricity, chemical action, nervous and muscular action, and momentum are interchangeable in fixed numerical equivalents, with the same quantity reappearing when the process is reversed. The hypothetical stage reduces conservation of force to conservation of motion, invoking molecular motions and a subtle ether pervading space.
Chapter 38
What is Mill's true definition of Force, and why reject 'matter in motion'?
Mill rejects defining Force as matter in motion, because the matter need not be in actual motion: the coal in the earth and the stone resting on a height hold force without moving. The true definition is Potentiality of Motion. The doctrine amounts to this: the possibilities of motion are limited to a definite quantity that cannot be added to but cannot be exhausted, and all actual motion is a draft on that stock.
Chapter 38
Does Mill think the Conservation of Force theory requires modifying his view of Causation?
Mill answers no. He argues that the manifestations the theory regards as modes of motion remain as much distinct and separate phenomena when referred to a single force as when attributed to several. Whether a phenomenon is called a transformation of force or the generation of one, it still has its own set or sets of antecedents, connected to it by invariable sequence.
Chapter 38

Section 394 cards

What does Mill claim about a volition's causal status?
Mill argues a volition is not an efficient cause but simply a physical cause. The will causes bodily action in the same sense that cold causes ice or a spark causes gunpowder to explode: the volition is the antecedent mental state, the limb's motion the consequent. The connection between them is learned by experience, not given in consciousness.
Chapter 39
What does Mill say we would know without experience of moving our bodies?
Mill argues that if our motor nerves were paralyzed or muscles stiff from birth, we would never know volition as a physical power, nor be conscious of any tendency of mental feelings to produce bodily motion. We might still feel a sensation of effort, but would experience it only as uneasiness accompanying desire, not as aiming at an end.
Chapter 39
How does Hamilton argue against consciousness of volition causing movement?
Hamilton argues that between the mental determination and the bodily movement lies a long series of intermediate agencies—muscles, nerves, solid and fluid parts—of which we are not conscious. So no one is immediately conscious of moving an arm by volition. The paralyzed person learns only after willing that the limb does not obey; the healthy person likewise learns obedience only after the fact.
Chapter 39
What is Mill's account of the origin of the volitional theory of causation?
Mill argues the theory rests on a spontaneous tendency of the intellect to explain causation by assimilating it to intentional acts of voluntary agents. This original fetishism, as he calls it, treats our own volitions as the type of all causation. It persists beneath scientific habits and draws strength not from argument but from an obstinate tendency of the infancy of the human mind.
Chapter 39

Section 404 cards

What did Mill argue against Dr. Tulloch and his reviewer regarding Thales and Anaximenes?
Mill argues that Tulloch and his reviewer wrongly claim the Greek philosophers recognized νοῦς (Divine Intelligence) as the efficient cause above material sources. Mill counters that Thales and Anaximenes held only material causes, citing Aristotle's Metaphysics, which states most early philosophers recognized only the material cause and credits Anaxagoras with first introducing νοῦς as efficient cause.
Chapter 40
According to Mill, what did Aristotle say about early philosophers and the efficient cause?
Mill cites Aristotle's Metaphysics: most early philosophers recognized only the material cause (τὰς ἐν ὕλης εἶδει). Aristotle names Thales as leader of this view, then Hippon, Anaximenes, Diogenes, Hippasus, Heraclitus, and Empedocles. Anaxagoras taught a different doctrine, introducing an efficient cause to explain change, since material cannot originate its own changes. Aristotle notes these philosophers felt no difficulty about this.
Chapter 40
What did Mill say about Aristotle's inclusion of Chance and Spontaneity as efficient causes?
Mill says Aristotle mentioned τύχη (chance) and τὸ αὐτόματον (spontaneity) as other possible efficient causes besides intelligence. Aristotle did not reject them as incapable of any effect, only as unworthy of producing the universe's order. Mill argues this shows Greek philosophers did not feel compelled to conceive volition as the sole origin of force, undermining the Volitional theory.
Chapter 40
How does Mill use Leibnitz and Malebranche against the Volitional theory?
Mill argues Leibnitz and the Cartesians held that finite minds cannot act on matter at all—only an omnipotent Divine Mind can. Leibnitz's Principle of Sufficient Reason made the inconceivability of mind-matter interaction equivalent to its impossibility. Malebranche argued no created spirit can move a body; only omnipotence makes it conceivable. Mill says this is the precise reverse of the Volitional theory, exposing inconceivability as worthless evidence.
Chapter 40

Section 414 cards

What distinguishes the Composition of Causes from the heteropathic case?
In the Composition of Causes, joint effects equal the sum of separate effects, and each cause exerts full efficacy by its own law. In the heteropathic case, the agencies cease entirely and a wholly different set of phenomena arises, as when two liquids mixed in certain proportions become a solid mass. The author argues the former is the general rule and the latter special and exceptional.
Chapter 41
According to the author, why need we not despair of making chemistry deductive?
Though chemical laws arise from a breach of the Composition of Causes, heteropathic laws can themselves compose with one another. The author argues chemical truths cannot be deduced from simple elements, but may be deducible from laws commencing at moderate combinations. He cites the law of definite proportions, Berthollet's law of double decomposition, and the law of isomorphism as partial generalizations encouraging this hope.
Chapter 41
Where does the supposed axiom of proportionality of effects to causes fail?
It fails precisely where the Composition of Causes fails: when the concurrence of causes changes the properties of the body generally and subjects it to new laws. If a certain heat merely increases bulk, double heat melts, and triple decomposes, these heterogeneous effects admit no ratio. The author argues the proportionality principle is superseded by the more comprehensive Composition of Causes, which implicitly asserts as much of it as is true.
Chapter 41
What does the author call the main business of Induction?
The author states that ascertaining the laws of causation in nature—determining the effect of every cause and the causes of all effects—is the main business of Induction, and pointing out how this is done is the chief object of Inductive Logic. Since uniformities are either laws of causation or consequences deducible from them, knowing causes and effects would acquaint us with the whole course of nature.
Chapter 41

Section 424 cards

Why does Mill say artificial production of a phenomenon aids inquiry?
Mill argues that when we can produce a phenomenon artificially, we bring it among circumstances we accurately know. Knowing the simultaneous state of everything else within the phenomenon's influence, we need only observe what alteration its presence makes. He contrasts knowledge gained from electrical experiments with what mere observation of thunder-storms could have yielded.
Chapter 42
What does Mill say about studying phenomena we cannot produce, like a human mind?
Mill argues that when we cannot fabricate a phenomenon, we must discover its concomitant circumstances rather than choose them, which is next to impossible beyond simple cases. A human mind always comes with a body, a vast complication of physical facts rarely identical and mostly beyond exploration. For a society or State, the same difficulties recur in greatly augmented degree.
Chapter 42
Why can artificial experimentation only start from causes, not effects?
Mill explains we can take a cause and try what it produces, but cannot take an effect and try what produces it; we can only watch for it or produce it by accident. Since we must travel from known to unknown, we start at whichever end is more familiar. When the cause is obscure but the effect familiar, we must begin from the effect.
Chapter 42
What does Mill conclude observation without experiment can and cannot establish?
Mill argues that observation without experiment, supposing no aid from deduction, can ascertain sequences and co-existences but cannot prove causation. Finding an antecedent invariably connected with an effect is not enough until we produce the antecedent and the effect follows. Otherwise the succession might, like day and night, be stages of an ulterior cause.
Chapter 42

Section 434 cards

What does Mill's Second Canon (Method of Difference) state?
If an instance where the phenomenon occurs and one where it does not have every circumstance in common save one, that one occurring only in the former, then that differing circumstance is the effect, or the cause, or an indispensable part of the cause, of the phenomenon. The method compares an occurrence with a non-occurrence to find what differs, rather than comparing agreeing instances.
Chapter 43
Why does Mill say the Method of Difference suits artificial experiment better than spontaneous nature?
The method requires two instances exactly alike except for one circumstance (ABC and BC). In nature, Mill argues, such complication and obscurity prevail that a spontaneous experiment of this kind is commonly not found. In artificial experiment, by contrast, we introduce a definite change into a known prior state, so a suitable pair of instances is obtained almost as a matter of course.
Chapter 43
What is the Method of Agreement's chief limitation compared with the Method of Difference?
Mill argues that only the Method of Difference can, by direct experience, arrive with certainty at causes. The Method of Agreement yields only laws of phenomena—uniformities that may not be causal laws, or whose causation remains undecided. It is chiefly useful for suggesting applications of the Method of Difference, or as an inferior resource when artificial experimentation is impossible.
Chapter 43
What is the Indirect Method of Difference (Joint Method), and how does it fall short?
It uses the Method of Agreement twice: instances where the phenomenon occurs share A, and instances where it is absent share the absence of A, supplying positive and negative instances the direct method needs. But Mill says it is not equivalent to direct difference, since we can never be sure each set agrees in nothing but A or its negation; it extends Agreement without its cogency.
Chapter 43

Section 444 cards

Why can't the first three experimental methods determine heat's effects?
Mill argues we can never exhaust a body of all its heat, nor perceive heat not emanating from a body. Since Body and Heat cannot be separated, we cannot produce the variations the Methods of Agreement, Difference, and Residues require. Any attempt to subtract what is due to a body's other properties would be illusory, because effects of its contained heat might be part of what we subtract.
Chapter 44
How does the Method of Concomitant Variations establish heat as a cause?
Though heat cannot be expelled entirely, it can be modified in quantity—increased or diminished. Mill notes that such increase or diminution is followed by expansion or contraction of the body. Since we can produce the variation in heat ourselves, we conclude that one effect of heat is to enlarge bodies' dimensions, or widen the distances between their particles.
Chapter 44
What is Mill's Fifth Canon of the Method of Concomitant Variations?
Whatever phenomenon varies in any manner whenever another phenomenon varies in some particular manner, is either a cause or an effect of that phenomenon, or is connected with it through some fact of causation. The last clause is added because two phenomena may be joint effects of a common cause; this method alone cannot decide which supposition is true.
Chapter 44
How is the doubt between cause and joint effect resolved under Concomitant Variations?
Mill says the only solution is to try to produce one set of variations by means of the other. Increasing a body's temperature increases its bulk, but increasing its bulk does not increase its temperature—it generally diminishes it, as in rarefaction of air under an air-pump. Therefore heat is a cause, not an effect, of increase of bulk. If we cannot produce the variations, we seek nature producing them under known circumstances.
Chapter 44

Section 454 cards

According to Mill, what are the only possible modes of experimental inquiry?
Mill states that the four methods he has described are the only possible modes of experimental inquiry—of direct induction a posteriori, as distinguished from deduction—and he says he knows not, nor can imagine, any others. He adds that even the Method of Residues is not independent of deduction, though because it requires specific experience it may be included among methods of direct observation and experiment.
Chapter 45
How does Liebig explain the fatal action of metallic poisons?
Mill reports that Liebig connected known facts by a higher induction: arsenious acid and salts of lead, bismuth, copper, and mercury combine with animal substances such as albumen, milk, muscular fibre, and membranes, forming compounds resistant to decomposition. Since organic life consists in continual decomposition and recomposition, whatever incapacitates tissues for this destroys life. Mill treats this as the proximate cause, established as far as the Method of Agreement can establish it.
Chapter 45
How does Mill test Liebig's poison theory by the Method of Difference?
Mill compares cases resembling the poisonous ones but without the effect: insoluble basic salts of arsenious acid and alkargen are not poisonous and do not combine with tissues. He notes these are different substances, so the method is not rigorously satisfied. Antidotes supply better instances: peroxide of iron with arsenic, sugar with copper salts, and sulphuric acid lemonade preventing painter's colic, all acting by forming insoluble or non-combining compounds.
Chapter 45
Why does nitrate of silver not poison despite its antiseptic power?
Mill calls this an apparent exception that yields the theory's strongest confirmation. Soluble silver salts stiffen decomposing animal substances and act as caustics externally, so they ought to be poisonous, yet can be given internally with impunity. In the stomach, common salt and free muriatic acid combine with the nitrate, converting it into slightly soluble chloride of silver, incapable of combining with the tissues, though it retains a medicinal influence.
Chapter 45

Section 464 cards

Why can't the Method of Agreement determine whether coldness causes dew or dew causes coldness?
The Method of Agreement establishes only an invariable connection between dew deposition and a surface colder than the external air. It cannot determine which is cause and which is effect, or whether both are effects of something else. Mill says a more potent method is needed: collecting more facts, varying circumstances, and especially noting negative cases where no dew is produced, to bring the Method of Difference into play.
Chapter 46
What does the Method of Concomitant Variations establish about dew deposition and heat?
By diversifying polished surfaces, Mill finds substances that conduct heat worst are most strongly dewed, while good conductors resist dew. Since all substances conduct heat somewhat, the method is used from necessity. The conclusion is that ceteris paribus dew deposition is proportional to the power of resisting heat passage, making this (or something connected) at least one cause. A second application shows dew is also proportional to the power of radiating heat.
Chapter 46
How does the deductive argument explain exceptions like no dew in a very dry summer?
Mill reasons deductively from known laws: only a limited quantity of water vapor can remain suspended at each temperature, and this maximum decreases as temperature falls. Contact with a colder body lowers the air's temperature, condensing some vapor onto the surface as dew. But if the air is so under-supplied with vapor that even after cooling it can still hold all its vapor, no dew forms—hence dry summers have no dews and dry winters no hoar-frost.
Chapter 46
How does the cloudy-night observation serve as a natural experiment for the Method of Difference?
Dew is never copiously deposited in situations screened from open sky and not at all on cloudy nights; if clouds withdraw even briefly, dew begins and increases, and dew may evaporate when sky becomes overcast. Since a clear sky is merely absence of clouds, and clouds radiate heat to raise surface temperature, the disappearance of clouds cools the surface. Nature thus introduces a single definite change, satisfying the Method of Difference.
Chapter 46

Section 474 cards

According to Mill, what determines whether cadaveric rigidity sets in early and briefly?
Mill summarizes that when muscular irritability at death is slight—due to bad nutrition, exhaustion from overexertion, or convulsions from disease or poison—cadaveric rigidity sets in and ceases soon, and putrefaction appears and progresses quickly. The contrary case, high irritability, produces late and prolonged rigidity with slow putrefaction.
Chapter 47
Why does Mill say the lightning case requires experiments with galvanism rather than lightning itself?
Lightning cannot be commanded at pleasure, but galvanism is the same natural agency in manageable form. Galvanism can reproduce only one of lightning's possible modes of action—producing muscular convulsions—so if galvanized bodies show shortened rigidity and accelerated putrefaction, the effect can reasonably be ascribed to that shared property rather than the others.
Chapter 47
How does Mill use the Method of Concomitant Variations in Brown-Séquard's galvanism experiments?
Brown-Séquard galvanized animal bodies with charges of varying strength and found that the more powerful the charge, the shorter the rigidity and the speedier the putrefaction; with the strongest charge rigidity lasted only fifteen minutes. Mill infers that the duration of rigidity depends on the degree of irritability, and a lightning-strength charge might abolish rigidity altogether.
Chapter 47
What defect of the Joint Method of Agreement and Difference does Mill identify, and how is it overcome here?
Mill says the Joint Method, like the Method of Agreement, cannot by itself prove causation. Here causation is already established: death is beyond doubt the cause of rigidity and putrefaction, resting on familiar observations falling under the Method of Difference. Whatever varies with the effect must then be the particular feature of death on which it depends.
Chapter 47

Section 483 cards

Why does Mill say his examples dissatisfied Whewell?
Mill says he chose examples only to illustrate and make the Methods conceivable through concrete instances, not to convince anyone that observation and experiment yield knowledge. Had his aim been to justify the methods as investigation, simple cases like "Dogs bark" (Method of Agreement) or "Fire burns" (Method of Difference) would have sufficed.
Chapter 48
What is the Method of Agreement's characteristic imperfection?
Plurality of Causes makes Agreement uncertain. Two instances agreeing only in A may have produced the effect by different causes (e.g., C in one, E in the other), so A need not be the cause. The conclusion is valuable only when instances are multiplied and varied, or when it leads to a Difference test or deductive verification.
Chapter 48
How does Plurality of Causes affect the Method of Difference?
It does not diminish reliance on Difference, nor require more observations: one positive and one negative instance still suffice for rigorous induction. If adding A to B C turns b c into a b c, then A was the cause or an indispensable part of it in that instance, even if other causes produce the effect elsewhere.
Chapter 48

Section 493 cards

Why does Mill say experimental methods struggle with the Composition of Causes?
In composition, the separate effects do not terminate but persist, intermingled and disguised by homogeneous effects of other causes. They become quantities that partly cancel and partly merge into one sum, so no fixed relation between result and causes can be traced by observation. Mill calls this far harder for direct induction than the chemical case, where the new phenomenon stands out undisguised.
Chapter 49
What is 'transformation' and why does Mill call chemical composition incomplete transformation?
Transformation is when two phenomena are reciprocally cause and effect, each generated by the other's destruction, as water comes from oxygen and hydrogen and they are reproduced from water. Mill argues chemical composition is incomplete transformation: we still suppose oxygen and hydrogen present in water as such, a supposition grounded solely on the fact that water's weight equals the sum of the ingredients' weights.
Chapter 49
Why can't heteropathic mental effects be investigated like chemical compounds?
Mill says the product is generated by its factors, but the factors cannot be reproduced from the product — as a youth can grow into an old man, but not the reverse. So we cannot make a complex mental state generate its simple feelings as we decompose a compound. We must instead study simple feelings and experiment synthetically on their combinations to learn what they generate.
Chapter 49

Section 504 cards

Why does Mill say simple observation fails to establish mercury's efficacy?
Mill argues the Method of Agreement fails here because of Plurality of Causes: many natural and artificial causes also tend to cure the disease, so recoveries will occur without mercury and failures with it. At best, hospital returns might show slightly more recoveries with mercury—secondary value for practice, almost worthless for theory.
Chapter 50
How does Mill distinguish the Empirical Method from deduction?
Mill says the Empirical Method experiments directly on the complex case, seeking a direct answer to whether mercury cures the disease, and must abstract entirely from knowledge of mercury's simpler modi operandi. Trying mercury on healthy people to derive general laws and then reasoning to the diseased case is, by contrast, deduction, not the empirical method.
Chapter 50
Why can't the Method of Difference be applied to test mercury experimentally?
Mill holds that we cannot know all pre-existing circumstances in a living being, and other influencing circumstances disguise mercury's effect. Comparing the same case before and after fails because other causes operate during the transition; comparing two cases similar in all respects but one is chimerical, since such cases likely never occur and we could not know they were identical.
Chapter 50
What does Mill say about experimental reasoning in politics and history?
Mill argues politics and history involve Plurality of Causes in boundless excess, with effects like public wealth and security affected by nearly every social fact. He calls the vulgar notion that Baconian induction is the safe political method a mark of a low speculative state, and mocks arguments like asking how an institution is bad when the country prospered under it.
Chapter 50

Section 514 cards

Why does Mill think physiology faces greater natural difficulties than social science?
The author argues that physiological agencies cannot be separated and observed apart without destroying the very phenomena under investigation, whereas it is possible to study one human mind apart from other minds much less imperfectly than one organ or tissue apart from the rest of the body. He therefore inclines to the view that physiology may be susceptible of a lesser degree of ultimate perfection than social science.
Chapter 51
How do pathological facts serve as a substitute for experimentation in physiology?
Diseases often exhibit a definite disturbance in one organ or function while others remain initially unaffected, giving an equivalent to proper experimentation. But because organs act and react on one another, a prolonged disturbance eventually involves many others and the experiment loses scientific value. Everything depends on observing the earliest, least marked stages; and if the original derangement was constitutional rather than local, cause and effect cannot be distinguished.
Chapter 51
What is Verification and why is it essential to the Deductive Method?
Verification is the third essential component of the Deductive Method, without which its results are little more than conjecture. Conclusions reached by deduction must be found, on careful comparison, to accord with direct observation wherever it can be had. If a predicted effect fails to follow where the combination existed, we must show or plausibly surmise what frustrated it; and the verification is incomplete unless some confirming cases are at least as complex as any case where the theory would be applied.
Chapter 51
What role do mathematics and geometry play in the second stage of the Deductive Method?
The second stage is a ratiocination or calculation determining what effect a given combination of causes produces. Where causes are known to exact numerical laws, the theorems of number enter as premises, and geometry where effects involve motion and extension. But Mill notes even the three-body problem admits only an approximate solution, and in highly complex phenomena these laws apply, if at all, only on a scale where precision of detail is unimportant.
Chapter 51

Section 524 cards

When a remote cause A acts through intermediate B to produce C, which laws are more general?
The author argues the two laws into which the sequence resolves—A produces B, and B produces C—are both more general than the law that A produces C. The law A produces B holds whether or not B is followed by C, and B may have causes other than A, so B produces C covers more instances. The remote-cause law is thus less general and more liable to limitation.
Chapter 52
How does Mill illustrate remote causation with touch and sensation?
Mill notes people knew touching an object causes a sensation, but later discovered a change occurs in a nerve before the sensation. Touching is only the remote cause—the cause of the cause—while the nerve's change of state is the real, proximate cause. The sequence resolves into two laws: contact produces a nerve affection, and nerve affection produces sensation.
Chapter 52
Why is a complex law of combined causes less general than the laws of the separate causes?
The author argues a complex law only holds when the causes are combined, while each separate cause's law holds both in combination and apart. Every contingency defeating any one cause defeats the complex effect, like rust in a machine. Also, altering only the proportions of the same causes can change the effect in kind, as with planetary orbits.
Chapter 52
What is the third mode of resolving laws, and what is Mill's prime example?
The third mode is subsumption: gathering several laws under one more general law that includes them all. Mill's splendid example is bringing terrestrial gravity and the central force of the solar system under the general law of gravitation, after showing the moon's tendency to the earth matched terrestrial weight in quantity as well as quality.
Chapter 52

Section 534 cards

How does Newton's law of gravitation explain astronomical phenomena?
The author presents Newton's generalization as the most striking example of resolving special uniformities into a simpler law. A single tendency of every particle toward every other, varying inversely as the square of the distance, explains falling bodies, planetary and satellite revolutions, cometary motions, elliptical orbits and their variations, the relation of solar distances to orbital periods, the precession of the equinoxes, and the tides.
Chapter 53
What did Dalton's atomic theory accomplish for chemical proportions?
Chemists knew bodies combine in fixed proportions, but expressed them as percentages, obscuring relations between an element's combinations. Dalton saw that a unit weight per substance, with combination in that unit or a low multiple, yields all the percentage proportions. Taking hydrogen as 1 and oxygen as 8, water and peroxide of hydrogen follow from one-to-one and one-to-two combinations; a table of atomic weights then explains all combining proportions.
Chapter 53
How did Graham's colloid/crystalloid distinction explain taste and digestion?
Graham distinguished crystalloid and colloidal states of matter. Colloids are inert chemically, gelatinous in water, and poorly penetrate one another, enabling dialysis. Because soluble crystalloids are sapid while colloids are insipid, Graham reasoned the palate's nerve endings are probably protected by a colloidal membrane impermeable to other colloids. Similarly, stomach coats dialyse food, absorbing crystalloids and rejecting colloids, so vegetable gum is not digested.
Chapter 53
What is reflex nervous action, and what phenomena does Brown-Séquard say it explains?
Reflex nervous action is action of one part of the nervous system on another without intermediate brain action, hence without consciousness, or at least independent of will. Experiments show irritation in one place excites action elsewhere, such as saliva secretion from food in a divided œsophagus. Brown-Séquard uses it to explain tears from eye or nose irritation, sympathetic eye inflammation, neuralgia-caused blindness or cataract, sudden death from cold water or abdominal blows, and remote organ inflammation after burns.
Chapter 53

Section 544 cards

What does Mill say about the direction of scientific method's shift, and how does it compare to Bacon?
The author argues that scientific investigation is destined to be dominated by the Deductive Method, reversing Bacon's change from deductive to experimental. Unlike Bacon's rejected deductions from hastily assumed premises, the new deductive method requires premises established by experimental inquiry and results tested by verification through specific experience.
Chapter 54
Why can ultimate laws of nature never be fewer than our distinguishable sensations?
The author argues that ultimate laws cannot be fewer than the distinguishable feelings of our nature that differ in quality, not merely degree. Since color is a phenomenon sui generis, intrinsically unlike heat, odor, or motion, any explanation of color must always retain a law of color as its final link, even if chemical or mechanical actions precede it.
Chapter 54
What is the ideal limit of explaining natural phenomena, and why is motion the best case?
The ideal limit would be showing each distinguishable sensation has only one sort of cause. Science has succeeded most in explaining the propagation of phenomena through space, especially mechanical motion, because motion differs only in degree—duration, velocity, direction—so it may all be produced by one kind of cause, as when falling bodies and planetary motions were unified under mutual attraction.
Chapter 54
How does Mill respond to Comte's claim that explaining specific color is illusory?
The author argues Comte's objection fails: although a color always remains different from a weight or a sound, varieties of color might still follow or correspond to given varieties of weight, sound, or other phenomena. Mill distinguishes the question of what a thing is from the question of what produces it, so specific color may still admit of explanation.
Chapter 54

Section 553 cards

What does the Hypothetical Method suppress, and what does it retain?
It suppresses the first of three steps, the induction to ascertain the law, and contents itself with ratiocination and verification. The law reasoned from is assumed instead of proved. This is legitimate only if the final verification amounts to a complete induction, i.e., if no false law could lead to the same true results.
Chapter 55
How does Mill analyze Newton's verification of the central force?
Mill argues the verification conforms to the Method of Difference: A B C, a b c versus B C, b c, where A is central force and a is equal areas in equal times. The instances came by prior deduction rather than experiment, which Mill says is immaterial. Newton also showed no other direction of force would produce equal areas.
Chapter 55
When can the negative instance not be obtained, according to Mill?
Mill argues it cannot be obtained when the assumed cause is an unknown cause imagined solely to account for the effect. The negative instance is obtainable when determining the precise law of a cause already ascertained, or distinguishing which of several known agents is the cause. Newton's case was the first kind, since the existence and direction of a force were already known.
Chapter 55

Section 564 cards

What does Mill say about Dr. Whewell's claim that no two conflicting hypotheses equally explain numerous phenomena?
Mill notes that Whewell, despite his knowledge of scientific history, contradicts himself: a few pages earlier Whewell argued that even exploded hypotheses like the vortices could be modified to match the phenomena. Mill therefore treats Whewell's denial of such cases as undermined by his own admission, and rejects the claim that inability to imagine an alternative justifies accepting a hypothesis.
Chapter 56
Why does Mill reject assuming a hypothesis is true merely because no alternative can be imagined?
Mill argues there is no necessity that the true explanation be one we could imagine with present experience. An unknown cause other than an elastic ether might produce effects identical to undulations of an ether. To assume no such cause can exist is, the author argues, an extreme case of assumption without evidence, and he criticizes Whewell for recognizing no induction except trying hypotheses until one fits.
Chapter 56
How does Mill distinguish legitimate geological inference from mere hypothesis?
Mill says geology legitimately infers a past cause from present effects, using known laws and known agents, much like a judicial inquiry reconstructing a murder from circumstantial evidence. It does not invent unknown agencies to explain classes of phenomena. Where effects are far larger than any now produced, geologists may conclude the causes were more intense or operated over enormous time, without hypothesis.
Chapter 56
Why does Mill rank Laplace's nebular theory below geological theories in evidence?
Mill says Laplace's theory introduces no unknown substance or law, reasoning from the sun's cooling and contraction to abandoned rings that became planets. But he holds it inferior in evidence to geology: even granting the ring conditions, assuming the laws of nature at the solar system's origin were the same is a greater risk than presuming they lasted through a few transformations of one body.
Chapter 56

Section 573 cards

What makes cases of a cause continually added to its own effects suited to deductive treatment?
The author argues that when a cause continues acting and adds to its effect by equal quantities in equal times, the result can be computed mathematically, since it involves infinitesimal increments—the very case the differential calculus was invented to meet. Such blending of effects with causes makes experimental treatment chimerical, so these cases are peculiarly amenable to the deductive method.
Chapter 57
How does the sun's summer warming illustrate a progressive effect with changing circumstances?
The author's example: as the sun nears the zenith and stays longer above the horizon, warmth accumulates. Even if the sun came no nearer, mere continuance would raise temperature once it exceeds the earth's radiation. Additionally, changing diurnal positions increase the effect. After the solstice the change reverses, but accumulated continuance still exceeds it, so temperature keeps rising.
Chapter 57
Why does Mill deny that spring is the cause of summer, or the seedling the cause of the tree?
Mill holds that the unconditional invariable antecedent is termed the cause, not the conditional one. Spring might continue forever without producing summer; both are successive effects of solar heat. Similarly, the seedling resembles the tree and grows gradually, suggesting both are terms in a series produced by continued nutrition, not cause and effect.
Chapter 57

Section 584 cards

According to Mill, what is the utmost the Method of Agreement can establish?
Mill argues the Method of Agreement can only ascertain the whole of the circumstances common to all cases in which a phenomenon is produced. This aggregate includes the cause but also collateral effects and co-existing causes, so it cannot distinguish laws of causation from derivative laws. Thus all its results are empirical laws until confirmed by the Method of Difference or explained deductively.
Chapter 58
What is Mill's first sign that a law of causation is derivative rather than ultimate?
The first sign is evidence of some intermediate link between antecedent and consequent—a phenomenon whose existence can be surmised though its precise nature cannot be ascertained. If such an x exists, then a causes b resolves into at least a causes x and x causes b. Mill illustrates with chemical composition: the unseen corpuscular action behind water's formation.
Chapter 58
What is Mill's second sign that an observed law of causation is derivative?
The second sign is when the antecedent is an extremely complex phenomenon, so its effects are probably compounded of the effects of its elements. Mill notes the Composition of Causes is the ordinary case, not the exception. He illustrates with weight (made up of particles' weights) and meteorology, where a barometer fall followed by rain involves both air and aqueous vapor.
Chapter 58
Why does Mill say unresolved uniformities not known to be laws of causation are unreliable beyond their observed limits?
Mill argues that so long as such uniformities remain unresolved, we cannot tell on how many collocations as well as laws their truth depends. Therefore we can never extend them with confidence to cases where we have not assured ourselves by trial that the necessary collocation exists. This property of being unfit to be relied on beyond time, place, and circumstance belongs to this class alone in all strictness.
Chapter 58

Section 594 cards

How does Mill test whether rain is connected to a particular wind?
Mill argues we must compare observed coincidence against what mere frequency of each phenomenon would produce. In England westerly winds blow about twice as often as easterly; if rain occurs only twice as often with westerly winds, no law is inferred. More than twice suggests a connection; less suggests repugnance, so rain would actually be linked to the less frequent easterly wind.
Chapter 59
What numerical example does Mill give for expected chance co-existence of A and B?
Mill supposes A exists in one case out of two and B in one case out of three. If there is neither connection nor repugnance between them or their causes, both should co-exist in one case out of six. Finding more co-existence than this indicates some cause producing conjunction; less indicates repugnance. The residual above chance proves a law.
Chapter 59
How does Mill propose eliminating the effects of chance?
Mill argues we repeat trials while holding cause A invariable, letting indeterminate modifying causes vary. If results oscillate about a stable mean rather than progress, and additional trials do not materially alter that average, the mean is the effect due to A and the remainder is chance. He calls this the Elimination of Chance, exemplified by averaging repeated experiments to cancel individual errors.
Chapter 59
How can a small constant cause be discovered amid larger variable ones?
Mill argues that if an effect were wholly due to changeable causes, a sufficient aggregate would cancel to zero. If instead the average settles at a nonzero value after enough trials, that residual reveals a constant cause. He cites loaded dice, where a preponderance for a particular throw exposes the loading, and the barometer's diurnal variation, later explained by daytime air rarefaction.
Chapter 59

Section 603 cards

In the two-color ball case, why is drawing black or white an even chance even if the box holds 99 of one color?
Because we are not told which color is the majority. The author argues that when we have no ground for expecting one color over the other, our conduct is the same as if the balls were equally divided; the draw is an even chance to us. This holds even if we know by authentic information that the box contains ninety-nine of one color and one of the other.
Chapter 60
What axiom underlies probability when we know only the number of possible cases?
The obvious principle that when existing cases are shared among several kinds, each kind cannot be a majority of the whole; there must be a majority against each kind except one at most. If any kind exceeds its proportional share, the others collectively must have less. Assuming no ground to select one kind as more likely to surpass the average, we cannot rationally bet in its favor at less than the ratio of the other kinds.
Chapter 60
Why does Mill say probability from causes is a better basis than probability from mere frequency?
The author argues that probability calculated from mere frequency in past experience is only an empirical law, resting on the Method of Agreement. When we can ascend to the causes on which occurrence depends and estimate the comparative frequency of favorable and unfavorable causes, we obtain data of a higher order that either correct or confirm the empirical law, giving a more correct measure of probability.
Chapter 60

Section 614 cards

How does Mill solve the third case, where causes differ in both frequency and likelihood of producing M?
Mill argues the probability that M was produced by a given cause equals the cause's antecedent probability multiplied by the probability it would produce M if it existed. His example: A is twice as frequent as B, A produces M twice in four times, B thrice in four times; the ratios 2:1 and 2:3 multiply to 4:3, giving probabilities 4/7 and 3/7.
Chapter 61
What rule does Mill give for the probability that a casual coincidence repeats n times in succession?
If the probability of a casual coincidence is 1/m, the probability of its repeating n times in succession is 1/m^n. Mill's example: throwing ace with a die is 1/6, twice in succession is 1/36, and three times is 1/216, occurring on a large average only once in two hundred and sixteen throws.
Chapter 61
Why can't we precisely compare the probability of chance versus an unknown law of nature?
Mill holds that while the chance of a casual coincidence is appreciable, the antecedent probability of an undiscovered law of nature is not susceptible of even approximate valuation. It would require knowing what proportion of all natural sequences are law versus coincidence, which we cannot conjecture. So we conclude causation only when accidental coincidence would be extremely uncommon.
Chapter 61
Why does Mill say derivative uniformities are contingent on collocations, and how does that affect predicting sunrise?
Derivative uniformities between effects of different primeval causes hold only where the same collocation of causes exists; if it varies, different derivative uniformities result. Day follows night only because both are effects of the earth's rotation and the sun's light. We expect sunrise tomorrow because those causes persist, and no counteracting cause has appeared in five thousand years.
Chapter 61

Section 624 cards

When may an empirical law of conjunction be extended beyond observed local boundaries?
When effects always found conjoined can be traced with probability to an identical (not merely similar) origin, the empirical law may be extended to all places within the extreme local boundaries of observation, subject to possible counteracting causes. Confidence increases when the law is not merely empirical but resolvable into ascertained causes, since extension then follows the boundaries of the causes' influence.
Chapter 62
How does Mill illustrate extending a derivative law beyond observation?
Mill uses the succession of day and night: we know it holds for all bodies of the solar system except the sun, but only because we know the causes. Without that causal knowledge, we could not extend the proposition beyond the orbits of the earth and moon, at both extremities of which we have observational evidence.
Chapter 62
What is analogy in the primitive mathematical sense, per Whately?
Analogy as resemblance of relations: a colony is called a mother country's child because colonies stand in the same relation to the country as children to parents. Mill notes such arguments have no inherent inferiority of conclusiveness—they may amount to nothing or be a perfect induction, depending on whether the shared circumstance is material.
Chapter 62
What does analogical reasoning amount to when no invariable conjunction is established?
Since no Method of Difference or Agreement has been applied, the argument concludes only that fact m, true of A, is more likely true of B if B shares properties with A—even without known connection between m and those properties. It requires that shared properties not be known to be unconnected with m, or the analogy is put out of court.
Chapter 62

Section 634 cards

What does Mill say about the metaphysical claim that universal causation is an instinct?
The author argues that treating the universality of causation as an instinct or law of belief is no proof of a fact in external nature. Belief is not proof and does not dispense with the need for proof; evidence is what the mind ought to yield to, not whatever produces belief. A mere disposition to believe, even if instinctive, is no guarantee of truth.
Chapter 63
How does Mill respond to the charge that induction by simple enumeration is inconsistent with rigorous induction?
He says the inconsistency is only apparent. If simple enumeration were invalid, no process grounded on it could be valid, just as telescopes fail if eyes cannot be trusted. But it is a fallible process, fallible in different degrees, so substituting a less fallible form for more fallible ones is a material improvement. Scientific induction does exactly this.
Chapter 63
According to Mill, how does the precariousness of simple enumeration relate to the size of a generalization?
The author argues the precariousness is in inverse ratio to the largeness of the generalization. The method is delusive exactly in proportion as the subject-matter is special and limited. As the sphere widens it misleads less, and the most universal truths, such as the law of causation and principles of number and geometry, are satisfactorily proved by that method alone.
Chapter 63
When does the distinction between empirical laws and laws of nature vanish, according to Mill?
It vanishes when a generalization's subject-matter is so widely diffused that no time, place, or combination of circumstances fails to afford an example of its truth or falsity, and it is never found otherwise than true. Its truth then cannot depend on contingent collocations or be frustrated by counteracting agencies, making it an empirical law co-extensive with all human experience.
Chapter 63

Section 644 cards

Why does Mill think the law of causation can only be held provisionally?
Mill argues that in matters of evidence we neither require nor can attain the absolute. We must hold even our strongest convictions with an opening left for facts that contradict them, and only then may we act with complete confidence when no contradiction appears. Whatever has been found true in innumerable instances and never false after due examination may be acted on as universal provisionally, provided a real exception could scarcely have escaped notice.
Chapter 64
How far does Mill say the law of causation extends?
Mill argues it must be received not as a law of the universe but only of that portion within the range of our means of sure observation, with reasonable extension to adjacent cases. In distant stellar regions, where phenomena may be entirely unlike those we know, it would be folly to affirm confidently that this general law prevails, any more than the special laws found on our own planet.
Chapter 64
What are the two kinds of propositions asserting uniformity of co-existence?
Mill says either the properties depend on causes or they do not. If they depend on causes, the proposition is a derivative law of co-existence between effects, and until resolved into the laws of causation it is an empirical law. If they are ultimate properties, then if they invariably co-exist they must all be ultimate properties of one and the same Kind.
Chapter 64
Why can't co-existence uniformities get rigorous scientific induction?
Mill argues the basis is wanting: there is no general axiom standing to uniformities of co-existence as the law of causation does to those of succession. The Methods of Induction rest on the principle that everything which has a beginning must have some cause, and that among circumstances existing at its commencement some combination is unconditionally consequent. No parallel axiom exists for co-existence.
Chapter 64

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According to Mill, what status do uniformities of co-existence have, even when ultimate?
The author argues that uniformities of co-existence, whether they are consequences of laws of succession or ultimate truths, must be ranked for logic among empirical laws. They are not to be presumed true beyond the limits of time, place, and circumstance in which observations were made, or in strictly adjacent cases, and are subject to the same rules as unresolved uniformities known to depend on causation.
Chapter 65
Why is it harder to establish an exception to a more general empirical law?
The author argues that as empirical laws rise in generality they become more certain. If they result from causation, greater generality shows many causes cannot affect them; if they are ultimate co-existences, they rest on more experience, so exceptions would likely have appeared. Hence more evidence is needed to establish an exception to a general law than to a special one.
Chapter 65

Section 664 cards

How does Mill say an approximate generalization can be replaced by a certain indication?
Mill argues that when we can actually recognize the cause or mark of an attribute, the uncertain approximate generalization can be replaced by a certain indication. In the witness example, instead of relying on "most persons speak truth," we consider whether the witness is honest, an accurate observer, or has an interest to serve—facts knowable directly or through marks like reputation or past conduct.
Chapter 66
When may an average like "nine of ten A are B" be applied to a particular case?
Mill states it applies only to cases of which we know nothing except that they fall under class A. If we know the instance's species or variety, or that particular circumstances influence it, applying the genus average will generally mislead. Averages suit large numbers—life tables help insurance offices but barely inform one's own life chances, since almost every life is better or worse than average.
Chapter 66
How do two approximate generalizations combine by Addition versus by Ratiocination?
By Addition, each proposition applies separately to the case, and the combined probability exceeds either—as with two independent witnesses, or concealment plus bloodstained clothes. By Ratiocination, only one proposition applies directly, the second through the first, and probability decreases at each step—as with hearsay, or washing clothes to suggest they were stained. Bentham called these self-corroborative and self-infirmative chains.
Chapter 66
What two exceptions let approximate generalizations be reasoned with like universal laws?
First, when the only obstacle is inconvenience, not impossibility, and we know the distinguishing character of exceptions, we may convert the proposition into a universal with a proviso—e.g., all persons with uncontrolled power employ it ill, provided they lack unusual judgment and rectitude. Second, when premises hold of nearly all their subjects, chains may continue several steps, though error accumulates at each step.
Chapter 66

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According to Mill, what does the existence of a phenomenon mean?
Mill argues that the existence of a phenomenon is but another word for its being perceived, or for the inferred possibility of perceiving it. When beyond present observation, its existence is inferred from other phenomena connected to it by inductive laws of succession or co-existence. Thus we prove a thing exists by proving it is connected by succession or co-existence with some known thing.
Chapter 67
Why are general propositions affirming bare existence easy to prove?
Mill states such generalizations are sufficiently proved by a single instance. If it were positively ascertained that ghosts, unicorns, or sea-serpents had even once been seen, their existence would be fully established. Whatever has once happened is capable of happening again; the only remaining question concerns the conditions under which it happens.
Chapter 67

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On what inductive law does Mill ground all arithmetical calculation?
Mill argues that arithmetic rests on the inductive law that "the sums of equals are equals," or, more characteristically, whatever is made up of parts is made up of the parts of those parts. Being true of all phenomena that admit of numbering, he calls it a law of nature of the highest order, and every arithmetical operation applies it or laws deducible from it.
Chapter 68
What is the general problem of the algebraical calculus, and what answers it?
Mill states the general problem as: F being a function of a given number, find what function F will be of any function of that number. For example, (a+b)^n is a function of the binomial; the binomial theorem shows how that number may be formed directly from a, b, and n without repeated multiplication. All theorems of the science of number assert the identity of results of different modes of formation.
Chapter 68
Why does Mill reject defining equal magnitudes as those that coincide?
Mill argues that equality of geometrical magnitudes cannot differ fundamentally from equality of weights, heat degrees, or durations, none of which can be superposed to coincide, yet we understand them as equal. Things are equal in magnitude when felt to be exactly similar in the compared attribute; superposition, like balancing on scales, is only a means of letting the senses detect deficiencies of exact resemblance.
Chapter 68
Why can geometry be deduced from so few premises, according to Mill?
Mill explains that all questions of position and figure resolve into questions of magnitude: a point's position is fixed by three rectangular co-ordinates. Geometry thus reduces to measuring magnitudes, i.e., ascertaining equalities. Since one axiom makes any equality evidence of many more, and another multiplies equalities through addition, a science conversant about equality yields a copious supply of marks of marks.
Chapter 68

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How does Mill distinguish disbelief from mere absence of belief?
Mill says the ground for abstaining from belief is simply the absence or insufficiency of proof. Disbelief, by contrast, is the state in which we are fully persuaded that some opinion is not true—so much so that even apparently strong evidence (testimony or our own perceptions) would make us conclude the witnesses lied or that we ourselves were mistaken.
Chapter 69
When is an alleged fact called 'impossible' rather than merely 'improbable'?
If the affirmative evidence rests only on approximate generalizations and the negative evidence does too, it is a comparison of probabilities, and a proposition is called improbable and disbelieved provisionally. But if the alleged fact contradicts a completed generalization grounded on rigorous induction, it is called impossible and disbelieved totally.
Chapter 69
What does Mill say Hume's doctrine about miracles really amounts to?
Mill argues Hume's celebrated doctrine—that nothing is credible which contradicts experience or the laws of nature—is merely the plain proposition that whatever is contradictory to a complete induction is incredible. He adds that Hume only established that no evidence can prove a miracle to someone who did not already believe in supernatural beings with power over nature.
Chapter 69
Why does Mill say a miracle is not a contradiction to the law of cause and effect?
Mill argues the allegation must be that a cause operated without its effect in the absence of any adequate counteracting cause. In a miracle, the claim is the opposite: the effect is defeated in consequence of a counteracting cause, a direct interposition of a will with power over nature. So a miracle is a new effect from a new cause, not a contradiction of causation.
Chapter 69

Section 704 cards

Why does Mill say an improbable event is not thereby incredible?
Mill argues that the unusualness of a fact is no reason to disbelieve it if the case makes it certain that either that fact or something equally improbable had to happen. In throwing a fair die, ace comes up once in six throws on average, yet some number equally rare must occur; likewise a man certain to die must die on some particular day, though chances are great against each specific day.
Chapter 70
What error does Mill attribute to Dr. Campbell's reply to Hume?
Mill says Campbell and others answered Hume by noting we do not disbelieve things merely because chances were against them, since such things conform to experience. Mill replies that whatever observation or natural law shows to occur in some proportion of cases is not contrary to experience, yet we are still right to disbelieve it if another supposition involves a smaller departure from the ordinary course of events.
Chapter 70
How does Mill explain why regular coincidences seem more improbable than irregular ones?
Mill holds the common impression is merely grounded on the fact that scarcely anyone remembers seeing such a coincidence, because no one's experience extends to the number of trials within which a given combination can be expected. Ten successive sixes with two dice is likely only once in 3,656,158,440,062,976 trials, yet any other fixed succession of ten throws is exactly as unlikely.
Chapter 70
Why does Mill say Laplace's black-and-white ball argument is faulty?
Laplace argued a witness's false announcement of white would occur far more often than a false announcement of ticket No. 79, since white is one of only two possible reports. Mill objects that this assumes equal accuracy across cases, which is unwarranted: a person with only one form of error to guard against is far less likely to mistake than one with 999 errors to avoid.
Chapter 70

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According to Mill, what is the sole condition for an observation to be reliable?
Mill states the sole condition is that what is supposed to have been observed must really have been observed—it must be an observation, not an inference. He argues observation and inference are blended in almost every act of perception, with perhaps one-tenth observation and nine-tenths inference. The logic of observation consists in correctly discriminating what was actually perceived from what is inferred.
Chapter 71
Why does Mill say errors called 'errors of sense' are not really errors of sense?
Mill argues there are no proper errors of sense; they are erroneous inferences from sense. The sensations themselves are genuine—as with the multiplying glass, kaleidoscope, or crossed fingers—but the judgment that infers an external arrangement from those sensations is mistaken. The habit of inferring becomes so powerful it is confounded with intuitive perception, though it is really acquired, not instinctive.
Chapter 71
Why does Mill claim a general proposition may be more certain than any singular premise it was inferred from?
Mill explains that each singular proposition used in induction involves an inference from the sensory impression to the fact causing it, and that inference may be erroneous in any one instance. But it cannot well be erroneous in all instances if their number is sufficient to eliminate chance. Therefore the general conclusion may deserve more complete reliance than any single inductive premise.
Chapter 71
What does Mill say is always implied when we describe an observation in words?
Mill argues we cannot describe a fact without implying more than the fact. Describing something as 'white' asserts a resemblance between it and all things called white—it classes the sensation. Every description is inherently a statement of resemblance, introducing a conception common to the phenomenon and others, an operation preceding induction and supplying its materials.
Chapter 71

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Why did the ancients fail to discover the laws of mechanics, per Mill citing Whewell?
Because they lacked, or lacked clearly, the ideas of pressure and resistance, momentum, and uniform and accelerating force. Mill asks whence they could have obtained these ideas except from the very facts of equilibrium and motion. Similarly, Whewell ascribes the slow development of optics, electricity, magnetism, and higher chemistry to the absence of the Idea of Polarity—opposite properties in opposite directions.
Chapter 72
What is Mill's objection to the phrase 'connecting facts' by a conception?
Mill says the technical phraseology means only comparing facts and determining in what they agree. The facts are not connected except metaphorically; only our ideas of them become connected, which any casual association could produce. He argues 'Comparison' expresses what really happens more philosophically, since the conception is both obtained and applied by comparison.
Chapter 72

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What habits does Mill say produce clear conceptions?
Mill holds that the principal requisites of clear conceptions are habits of attentive observation, extensive experience, and a memory that retains an exact image of what is observed. He adds the indispensable habit of never using general names without a precise connotation, which he says naturally results from those other endowments.
Chapter 73
According to Mill, when are general conceptions appropriate rather than merely clear?
A conception may be clear yet inappropriate. Mill argues conceptions are appropriate only when the properties they comprise are those of primary importance for the purpose in view — either going deepest into the nature of things, if understanding is the aim, or most closely connected with the particular property under investigation.
Chapter 73
Why does Mill say good general conceptions cannot be framed beforehand?
Mill argues we cannot frame good general conceptions in advance, because only completing the work reveals whether the conception is the one wanted. Premature conceptions are Bacon's 'notiones temerè à rebus abstractæ,' and they impede knowledge only when permanently acquiesced in — as the ancients did in physics and, the author argues, the world still does in morals and politics.
Chapter 73

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According to Mill, what does the vulgar actually express when applying a general name?
Mill argues that the vulgar—all who lack accurate habits of thought—seldom know what common property they mean to express. The name conveys only a confused feeling of resemblance between the object and other things previously denoted by that name. They do not ask in what respect it is like, or what degree of resemblance authorities require. The logician's business is to analyze this vague impression into the particular circumstances of resemblance that produced it.
Chapter 74
How does Mill explain the origin of abstract names like Civilization?
Mill argues that the abstract name arises when people assume the concrete name must convey a meaning, so they name the supposed common property. But since most people never compare the things called by the concrete name, each falls back on his own vague marks and hearsays. These differ in every person and every time, so the abstract word conveys scarcely the same idea to any two minds, and no one knows precisely what it asserts.
Chapter 74
What constraint does Mill place on defining a term already in use?
Mill insists the meaning of a term in use is not an arbitrary quantity to be fixed but an unknown quantity to be sought. A definition should agree as far as possible with existing associations, so that generally received propositions remain at least as true as before. The precise connotation should not deviate from but agree with the vague connotation the term already had. Hence defining a name in use is a matter of discussion, not choice.
Chapter 74
Why does Mill say definitions improve as science progresses?
Mill argues that framing a good definition of a name in use is not choice but discussion—about the properties of things, even their origin. We select from common attributes those on which many others depend, or which are sure marks of them. Every enlargement of knowledge may suggest an improved definition, so no perfect set of definitions is possible until the theory of the subject is perfect; definitions progress with science.
Chapter 74

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According to Mill, what happens when a transition of meaning rests on a virtually indissoluble association?
The transitive meanings coalesce into one complex conception, and each new transition becomes a more comprehensive generalization of the term. Mill calls this a law of mind and says ignorance of it causes perplexity in detecting transitions of meaning. Where the association is slight and casual, by contrast, the several meanings stay distinct and may seem capricious uses of the same sign.
Chapter 75
How does Mill use Plato and Bacon to illustrate ignorance of this law of mind?
Mill says Plato, in defining general moral terms, often wasted his logical powers because the phenomena he compared had no common properties. Bacon likewise, in speculating on heat, confounded under the name 'hot' classes of phenomena with no property in common. Mill credits Bacon with calling Plato's inquiries near to a true inductive method, yet both fell into the same error.
Chapter 75
What does Mill say about the word 'Beautiful' and whether it has a fixed connotation?
Mill, agreeing with Stewart, doubts 'beautiful' connotes the same property for a color, face, scene, character, and poem. It likely spread from objects of sight by resemblance of the emotions they excite. The only common property may be agreeableness, but many agreeable things are never called beautiful. So it cannot be given a fixed connotation covering all current uses, and without one it is unfit as a scientific term.
Chapter 75
What rule of terminology does Mill draw from the case of 'Beautiful'?
When fixing a vague term's connotation, we must not discard any part of the connotation it previously carried, unless advisedly and from deeper knowledge. Otherwise language loses its function as conservator of ancient experience. Mill argues it is better to restrict the term's denotation than to extend it, since people calling something beautiful think they assert more than mere agreeableness.
Chapter 75

Section 764 cards

According to Mill, what two counter-movements are always occurring in language?
Mill identifies a double movement: Generalization, by which words continually lose portions of their connotation and become less meaningful but more general in acceptation; and Specialization, by which words take on fresh connotation, acquiring additional meaning by being restricted to only part of the occasions on which they might properly have been used before. He treats this twofold phenomenon as important enough in the natural history of language to justify dwelling on it further.
Chapter 76
How did the word 'pagan' come to mean a heathen exclusively?
Paganus originally meant villager, the inhabitant of a pagus. At a particular era of Christianity's spread over the Roman empire, adherents of the old religion and country people were nearly the same body, since towns were converted earliest. This casual coincidence made the word suggest worship of the ancient divinities so forcibly that the place-of-residence circumstance was eventually disregarded, and pagan came to mean heathen exclusively.
Chapter 76
What does Mill say about the word 'gentleman' and dictionary definitions?
Mill argues the word gentleman originally meant simply a man born in a certain rank, then came to connote qualities and circumstances usually found in persons of that rank. This explains why in one vulgar acceptation it means anyone who lives without labor, in another without manual labor, and in its elevated sense it signifies conduct, character, habits, and appearance expected of persons born and educated in high social position. He uses this to show dictionaries are imperfect guides.
Chapter 76
What does Mill say about the Coleridge school's view of language?
Mill says the Coleridge school's doctrine that the language of an old-cultured people is a sacred deposit no age should alter borders on extravagance, but is grounded on a frequently overlooked truth: while each age adds truths, a counter process of losing truths already possessed constantly goes on. Language is the depository of accumulated experience, so we should be careful not to let any of our forefathers' premises slip away.
Chapter 76

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How does Mill explain generic terms becoming limited to a single species?
Mill argues a generic term is liable to become limited to one species or individual when people have occasion to think and speak of that thing much oftener than of anything else in the genus. His examples: a stage-coachman understands 'cattle' as horses, agriculturists use 'beasts' for oxen, and some sportsmen use 'birds' for partridges only.
Chapter 77
What does Mill say about the connotation words acquire from pleasure and pain?
Mill argues the ideas most liable to cling by association to anything are those of our pleasures and pains. So the additional connotation a word most readily takes on is agreeableness or painfulness, being good or bad, desirable or to be avoided. He says hardly any name expressing a moral or social fact lacks such connotation, producing 'question-begging names' — a fallacy Bentham noted.
Chapter 77
What practical rule does Mill give logicians about changed word meanings?
Mill says the logician cannot prevent usage from transforming significations, so should submit with good grace when changes are irrevocably effected, and if a definition is needed, define the word according to its new meaning, retaining the former as a second signification if needed. Logicians cannot make the meaning of non-scientific terms; the collective human race makes them.
Chapter 77
What is the first requisite of a philosophical language Mill discusses in Chapter VI?
Mill says language must not only give every word a determinate meaning but also have no important meaning without its word: whatever we think of often, and for scientific purposes, ought to have a name. He calls the first head an accurate Descriptive Terminology, needed to record individual observations so the words exactly show what fact was observed.
Chapter 77

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Why does Mill say naming an abstract result matters beyond perspicuity?
Mill argues a compact, specific name fixes attention on an abstract result and keeps it before the mind. Names are remembered and suggest their definition, whereas a loose combination of words already used for other purposes has nothing to make itself remembered. He claims apt words nail down original thoughts so they take hold in the mind, even for their inventors.
Chapter 78
What examples does Mill give of names aiding discovery?
Mill says if mathematicians had to say 'that to which a quantity is always approaching nearer but never exactly equal' instead of 'the limit of a quantity,' most truths about limits would probably have long remained undiscovered. Likewise, without the word momentum for the product of velocity and mass, many dynamical truths would probably have escaped notice for want of ready recall.
Chapter 78
How does Mill define a Kind, and what is not a Kind?
Mill defines a Kind as a class distinguished not by one or a few definite properties but by an unknown multitude of them, the known combination being an index to indefinite further attributes. Horse and animal are Kinds; no definition of animal could exhaust its properties. White horse is not a Kind, since horses agreeing in whiteness share nothing else beyond qualities common to all horses.
Chapter 78
How does Mill distinguish nomenclature from terminology?
Mill credits Dr. Whewell with first regularly assigning different meanings to the two words. A nomenclature is the collection of names of all the lowest Kinds with which a branch of knowledge deals; terminology covers names for properties and descriptive characters. Lavoisier's chemical reform was a new nomenclature; 'linear' or 'serrated' leaves belong to botany's terminology, while 'Viola odorata' belongs to its nomenclature.
Chapter 78

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Why does Mill say algebraic notation is a poor model for other sciences?
Mill argues that algebraic notation is perfect for subjects already reduced to relations between numbers, but its very virtues make it unfit as a general model. In other sciences we should want contrivances ensuring we never lose sight of the meaning of signs, rather than contrivances preventing attention from being distracted by that meaning.
Chapter 79
What does Mill recommend for constructing scientific words, and which languages does he praise?
Mill says as much meaning as possible should be put into the word itself, using derivation and analogy to keep its signification alive. He praises languages forming compounds from native roots, like German, over those using foreign or dead roots, as English, French, and Italian do, and ranks Greek above German except for prepositional compounds, which are often anomalous.
Chapter 79
What happens to a thinker who lives only among formulae, according to Mill?
Mill warns that anyone content to live among formulae, without keeping acquaintance with the realities from which the laws were collected, will continually fail in practice because he won't consider whether other laws modify or supersede his formula. Worse, the formulae themselves progressively lose meaning, until he cannot even recognize with certainty whether a case falls under them.
Chapter 79
What makes a classification scientific rather than technical, for Mill?
Mill says scientific classification groups objects so that the greatest number of important general propositions can be made about them. The properties chosen should be causes of many other properties, or at least sure marks of them; since causes are seldom usable as diagnostics, we generally select prominent effects. Such a natural arrangement is recommended, though not required, to match the mind's spontaneous groupings.
Chapter 79

Section 804 cards

For Mill, what determines whether an object belongs to a natural class?
Mill argues natural groups are determined by characters, not by resemblance to a type. The class is defined by possessing all universal characters and most characters admitting exceptions; a plant may lack one or more rose characters and still be included, since it likely resembles the class in undiscovered properties too.
Chapter 80
What does Mill mean by distinctions of Kind?
A Kind is a distinction running through the whole nature of things, not just a set number of properties plus their effects. Knowledge of a Kind is never complete; we expect new properties to be discovered, and inference from things not connected by Kind counts only as faint analogy.
Chapter 80
How does Mill limit the doctrine of Types in classification?
Mill credits Whewell with stating the type principle but says types only suggest groups; they do not determine membership. Groups are framed with reference to characters, with near-matching species added as an appendix. A mental standard specimen illustrates the definition rather than replacing it.
Chapter 80
What two modes can give a Kind's name significance?
A Kind's name is defined by enumerating distinctive characters. Beyond that, a name may convey information by its formation, indicating the very properties it connotes; but since many characters are needed to distinguish a species, a name cannot etymologically indicate more than a very small number without becoming too cumbrous for use.
Chapter 80

Section 812 cards

Which Method of Experimental Inquiry does such a series correspond to, and what is its principle?
Mill says arranging instances in order of degree is implied by the fourth Method, that of Concomitant Variations. Its principle: facts that increase or diminish together, and disappear together, are either cause and effect or effects of a common cause. Once the relation between variations is established, a connection may be laid down as a law of nature or only an empirical law, according to circumstances.
Chapter 81
Why is a type-species indispensable, and which species serves as the type?
Mill argues recognizing the same phenomenon in minute or obscure forms requires assuming a type-species: the Kind exhibiting the class's constitutive properties in the highest degree, with other varieties conceived as degeneracy from it. Every phenomenon is best studied where it exists in greatest intensity. In man, both animal and organic life exist in the highest degree, so he is the type.
Chapter 81

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What two principles does Mill use to classify things mistaken for evidence?
Mill says apparent evidence can be classified either by the cause that makes it appear to be evidence though it is not, or by the particular kind of evidence it simulates. He states that the Classification of Fallacies attempted in the next chapter is founded on these two considerations jointly.
Chapter 82
What distinguishes Fallacies of Inference from Fallacies of Simple Inspection?
Mill divides fallacies by whether the supposed connection between facts is a conclusion from evidence or admitted without such ground, as self-evident. Fallacies of Simple Inspection include beliefs held with no extrinsic evidence and cases where simple inspection creates a presumption that dispenses with strict induction. Mill calls these Natural Prejudices or Fallacies a priori and places them first.
Chapter 82
What are Fallacies of Confusion, and why does Mill say almost all fallacies could fall under them?
Fallacies of Confusion, a phrase Mill borrows from Bentham, arise when premises are not conceived with due fixity: one conception is formed when evidence is collected and another when it is used, or premises are unconsciously substituted. Mill says bad reasoning rarely states all links, so the error often lurks in suppressed premises, making strict classification doubtful.
Chapter 82
How does Mill subdivide Fallacies of Inference?
Mill first separates Fallacies of Confusion from the rest. Remaining fallacies divide by whether apparent evidence is particular facts or foregone generalizations, simulating Induction or Deduction, and by whether that evidence is false or true but inconclusive. This yields Fallacies of Observation and Generalization under Induction, and Fallacies of Ratiocination under Deduction.
Chapter 82

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What fallacy does Mill say underlies many popular superstitions about omens?
Mill argues that superstitions arise from a tacit assumption that the order among our ideas must match the order among things in nature: if a thing makes us think of another, that other is supposed to follow in fact. Thus talking of the devil supposedly brings him, and speaking of misfortune is thought unlucky. He notes such fallacies often cluster with malobservation and false generalization.
Chapter 83
What two axiomatic maxims does Mill identify as embodying the a priori fallacy?
Mill identifies two maxims claiming axiomatic truth: things we cannot think of together cannot co-exist, and things we cannot help thinking of together must co-exist. He says he is unsure the maxims were ever expressed in these exact words, but both philosophy and popular opinion abound with exemplifications of both forms.
Chapter 83
How does Mill criticize Descartes' use of clear and distinct conception as a test of truth?
Mill says Descartes built his system on the maxim that whatever is clearly and distinctly conceived must exist, inferring geometrical figures really exist because they can be distinctly conceived. Mill objects that the idea, being a result of abstraction, ought to conform to facts, not make facts conform to it. He claims this fallacy caused two-thirds of bad philosophy, especially metaphysics.
Chapter 83
What examples does Mill give of the error that whatever is inconceivable must be false?
Mill cites the long-held belief that Antipodes were impossible because people could not conceive persons with heads in the same direction as our feet, and the objection to Copernicanism that the supposed void space in the celestial regions was inconceivable. He argues people wrongly mistook the limitation of their own faculties for a limitation on possible modes of existence.
Chapter 83

Section 844 cards

What does Mill identify as the essence of Mysticism?
The author argues mysticism, whether in the Vedas, Platonists, or Hegelians, is ascribing objective existence to the subjective creations of our own faculties—ideas or feelings of the mind—and believing that by contemplating these self-made ideas the mind can read what takes place in the world without.
Chapter 84
What is the Principle of the Sufficient Reason and how does Mill judge it?
It is the principle that a phenomenon must follow a certain law because we see no reason why it should deviate in one way rather than another. Mill calls this reasoning entirely fallacious, arguing it secretly assumes what it sets out to prove, as Dr. Brown also showed.
Chapter 84
How does Mill criticize the a priori proof of the law of inertia?
He says it begs the question by assuming only external force counts as sufficient reason for motion in one direction. If spontaneous motion were admissible, so would be motion toward the sun, earth, or zenith—or a horse's natural state being to amble rather than stand still.
Chapter 84
What prejudice did Greek philosophers show about language and nature?
Mill says they assumed differences in nature must correspond to received distinctions in language, so effects called by different names must have different natures and causes. Knowing only their own language, they treated its classifications as natural and others as arbitrary, making science a sifting of common-language notions.
Chapter 84

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What a priori fallacy does Mill call the most deeply-rooted natural prejudice?
Mill identifies the assumption that the conditions of a phenomenon must, or at least probably will, resemble the phenomenon itself. He calls it the most deeply-rooted of the a priori fallacies, noting it reigned supreme in the ancient world and still holds dominion over many cultivated minds, with examples drawn even from recent thinkers.
Chapter 85
How did belief in principles of heat, cold, dryness and moisture lead to alchemy?
Mill argues the ancient assumption of principles of heat, cold, dryness and moisture led directly to belief in transmutation. Each property of gold has its forma or essence; if discoverable and realizable, that property could be superinduced on wood, iron or clay. Since fire and water daily change sensible properties, transmutation seemed possible and practically hopeful.
Chapter 85
What is the Doctrine of Signatures, and what examples does Mill give?
Mill cites Dr. Paris describing it as the belief that every natural substance with medicinal virtue indicates by an obvious external character the disease it remedies. Examples: fox lungs for asthma due to the animal's respiration, turmeric's yellow color for jaundice, poppies for head diseases, Lithospermum's stony seeds for gravel, and eyebright's black spot for eye complaints.
Chapter 85
How does Mill illustrate the resemblance fallacy in perception theories?
Mill says the Epicurean species sensibiles and the modern doctrine of perception by ideas both assume the phenomenon in us when we see or touch an object must closely resemble the outward object. The Epicureans posited impalpable images projected from objects; moderns substituted a mental image as direct object. Mill credits Dr. Reid with arguing sensations need not resemble their causes.
Chapter 85

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Why does belief in almanac weather prophecies persist despite frequent failures?
Mill cites the uneducated agricultural classes' faith in almanac-makers' weather predictions. Every season brings many completely erroneous predictions, yet each season also yields some fulfilled ones, which keeps the prophet's credit alive among people who fail to reflect on the number of instances needed for the Elimination of Chance, since casual coincidences must occur between unconnected events.
Chapter 86
What does Coleridge's 'Fortune favors fools' discussion illustrate about memory?
Coleridge, quoted by Mill, explains that unforeseen coincidences helping a clever man excite little attention, since his success seems natural, while the same happening to a weak man is dwelt on and remembered. Likewise a fool's failure, being expected, is forgotten. So we accumulate one sort of facts and never collect the other, putting a part for the whole.
Chapter 86
How did the Copernican controversy exemplify non-observation from preconceived opinion?
Opponents argued that if the earth moved, a stone dropped from a tower would land away from its foot, likening it to a ball dropped from a ship's mast. Copernicans could have refuted them by actually trying the mast experiment, which shows the ball falls at the foot, but instead they admitted the spurious fact and argued the stone was part of the earth.
Chapter 86

Section 874 cards

What fallacy does Mill identify in the common argument against free trade?
Mill says the protectionist argument is a Fallacy of Non-observation: it sees only that buying British silk encourages British industry, overlooking that purchasing any foreign commodity causes, directly or indirectly, an export of equivalent home production. This cannot always be verified by specific observation, but no observation can contradict it, and the reasoning is irrefragable.
Chapter 87
How does Mill define mal-observation, and what is its root error?
Mal-observation is when the error is not that something is unseen but that something seen is seen wrong. Since perception is infallible evidence of whatever is really perceived, the error arises by mistaking inference for conception—treating a conclusion drawn from appearances as if it were direct sensory evidence. Mill says we may mingle inference with observation but must know which part is which.
Chapter 87
What celebrated example does Mill give of mistaking inference for sense evidence?
Mill cites resistance to the Copernican system on grounds of common sense: people fancied they saw the sun rise and set and the stars revolve around the pole. They actually saw only appearances equally reconcilable with either theory; the motion was a false inference of judgment, not testimony of the senses. Mill says this should have inspired bigots of common sense with modest distrust.
Chapter 87
Why does Mill hold that generalizations resolving radically different phenomena into one element are necessarily false?
Mill says theories like those of Thales and Democritus, resolving all things into one element, are necessarily false. Resolving motion into motion, as with gravity or electricity, can be legitimate induction. But resolving heat, light, or sensation into motion confuses conditions with explanation: however many motions are interpolated, there remains a motion antecedent and a color consequent, and the law of color stays peculiar.
Chapter 87

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What is the fallacy of post hoc, ergo propter hoc?
It is inferring causation from mere casual conjunction, without due elimination or any presumption from known properties of the supposed agent. Mill's examples include inferring England owed her industrial pre-eminence to restrictions on commerce, or that the national debt caused national prosperity. Such a single instance has value only as verification by specific experience if other evidence already renders the supposed tendency probable.
Chapter 88
What distinguishes bad a priori generalization from bad a posteriori generalization?
Bad a posteriori generalization, or empiricism properly so called, infers causation from casual conjunction without elimination. Bad a priori generalization, or false theory, deduces conclusions from properties of one known agent while overlooking all other co-existing agents. Mill says the former is the error of sheer ignorance, while the latter especially afflicts semi-instructed minds attempting to explain complicated phenomena by a simpler theory than their nature admits.
Chapter 88
According to Mill, what is an argument from analogy and how much probative force does it have?
It infers that what is true in one case is true in a somewhat similar case not known to be exactly parallel. An object has property B; another resembles it in property A, not known connected to B; the conclusion is that the second object also has B, as when planets are inferred inhabited because Earth is. Analogy yields only a small, non-assignable increase of probability; if any real connection between A and B were suspected, the argument would no longer be analogy.
Chapter 88
Why does Mill call the paternal-government defense of despotism a false analogy?
The argument says paternal government works well, so despotic government in a state will work well. Mill replies that parental government's benefit depends not on irresponsibility, the only point it shares with political despotism, but on the parent's affection for the children and superiority in wisdom and experience. Neither property can be reckoned on between a political despot and his subjects, so the analogy fails.
Chapter 88

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According to Mill, what is the logical status of a metaphor or analogy in argument?
Mill argues a metaphor is not itself an argument but an assertion that an argument exists—a claim of parity between the two cases. The applicability of the metaphor is the very thing to be proved, since contrary analogies and conflicting metaphors are easy to raise. Its use is to aid apprehension and sometimes to suggest the proof, as with the uncultivated-soil argument for education.
Chapter 89
Why does Mill reject Bacon's river metaphor about time preserving only worthless ancient writings?
Mill says there is no parity of cause: the levity by which objects float on a stream and the levity meaning worthlessness share nothing but the name. He notes that swapping in the word buoyancy turns the semblance of argument against Bacon. So even if the illustrated assertion were true, the metaphor would be no good illustration.
Chapter 89
What is the most fertile source of Fallacies of Generalization, and how does Bacon's 'Humidum' illustrate it?
Mill says bad classification is the most fertile source: grouping under one name things with no common properties, or none important enough to support valuable general propositions. The misleading effect is greatest when a word with a definite common meaning is stretched to slightly resembling cases. Bacon's 'Humidum' exemplifies this, since flame, air, dust, and glass are called wet or not under shifting senses.
Chapter 89
What error does Mill identify in converting a hypothetical proposition, and how does it relate to accepting conclusions as proof of premises?
Mill says the proper converse is: if the consequent be false, the antecedent is false. But inferring that if the consequent be true the antecedent is true is an error, corresponding to simple conversion of a universal affirmative. Yet people constantly reason this way, treating a doctrine's leading to acceptable conclusions as presumption of its truth, when it amounts only to absence of evidence of falsehood.
Chapter 89

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What defines Mill's fifth class of fallacies, Fallacies of Confusion?
Mill groups here fallacies where the error is not a false estimate of the probative force of known evidence, but an indistinct, indefinite, and fluctuating conception of what the evidence is. The leading case is ambiguity of terms: something true in one sense of a word is reasoned on as if true in another, so there is evidence, but to a different point.
Chapter 90
How does the fallacy of ambiguity enter ratiocination, according to Mill?
Mill says it occurs in two ways: when the middle term is ambiguous, or when one of the terms of the syllogism is taken in one sense in the premises and in another sense in the conclusion. He notes it is committed more often in ratiocination than in direct induction, since there we decipher notes rather than have the things themselves present.
Chapter 90
What does Whately's example of 'projector' versus 'project' illustrate?
Whately offers it as a case of the fallacy built on grammatical structure: people assume paronymous words of the same root have precisely corresponding meanings, which is not universally true. 'Projectors are unfit to be trusted; this man has formed a project, therefore he is unfit' assumes one who forms a project must be a projector, though the bad sense of 'projector' is not implied in 'project.'
Chapter 90
How does Mill use the 'scarcity of money' phrase to illustrate verbal ambiguity?
Mill says 'money' in commerce means either currency, the circulating medium, or capital seeking investment, especially on loan—the sense used of the 'money market' and the 'value of money,' meaning the interest rate. So when loans are hard to get and interest is high, people conclude the circulating medium must have shrunk or should be increased. Mill admits the facts themselves offer some apparent support, but the ambiguity blocks all light on the subject.
Chapter 90

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What does Mill say is the real fallacy in Achilles and the Tortoise?
Mill argues the fallacy lies in the ambiguity of the word "infinite." The argument's "forever" in the conclusion means for any supposable length of time, but in the premises it means any number of subdivisions of time. An unlimited number of subdivisions may be made of something itself limited, so the argument proves only infinite divisibility, not infinite duration—a distinction Hobbes had already seen.
Chapter 91
How does Mill distinguish the two senses of having a "right" to do something?
In one sense, you have a right to do a thing if all persons are morally bound not to hinder you. In another sense, having a right means the opposite of having no right—that you may do it without breach of duty, and others have no cause to think worse of you. Mill says these distinct propositions are perpetually confounded, as when someone claims a right to publish opinions.
Chapter 91
What is the Fallacy of Composition and Division, and what example does Mill give?
It occurs when a term is collective in the premises and distributive in the conclusion, or vice versa. Mill's example: because any one great man might have been replaced by another, the argument concludes all great men could be dispensed with. "Great men" is distributive in the premises but collective in the conclusion. Mill also cites lottery players and the spendthrift who can afford each expense but not all together.
Chapter 91
What is petitio principii, and how does Mill explain its disguises?
Petitio principii, or begging the question, is using a premise that is the same as the conclusion, proved from it, or only provable by it. Mill says it is common because people forget how they came by their opinions. It often hides by stating the same proposition in abstract terms as proof of the concrete version, as with the physician's "dormitive virtue" of opium.
Chapter 91

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Why does Mill call the argument from upper and under surfaces a petitio principii?
The argument claimed every portion of matter, however small, must have an upper and under surface, to prove infinite divisibility. Mill says it assumes the very point in dispute: the impossibility of a minimum of thickness. If a minimum exists, its two surfaces would be one, so it would be a surface only. The premise seems more obvious than the conclusion but is really identical with it.
Chapter 92
What circularity does Mill find in ethical writers' appeal to natural sentiments?
Mill describes writers who take the general sentiments of mankind as their standard of moral truth, then explain away divergent cases as "unhealthy" perceptions. When someone reports no such sentiment in himself or in other countries and ages, the reply is that his feelings were sophisticated and unhealthy. Mill calls this reasoning in a circle.
Chapter 92
How does Mill criticize Hobbes's social compact argument?
Mill sets aside whether the compact is fictitious and asks why we are bound by a promise made for us by ancestors, or by any promise at all. The only satisfactory ground is the mischievous consequences of absent faith and mutual confidence — the interests of society. Yet those same interests are not admitted as sufficient justification for government and law.
Chapter 92

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What does Mill say Philosophical Necessity actually means?
Mill argues that Philosophical Necessity means only that, given a person's motives and character, their conduct could be unerringly inferred and predicted with the same certainty as a physical event. It is a statement of universal experience, not a mysterious constraint. He denies it conflicts with the feeling of freedom, since being predictable by someone who knows us is compatible with acting freely.
Chapter 93
What error does Mill say most necessitarians share with free-will opponents?
Mill argues that most necessitarians, despite accepting Hume's and Brown's analysis of causation, secretly imagine a stronger tie between volitions and their causes than mere uniformity of order and predictability. They thus commit the same mistake as their opponents and may suffer the depressing consequences wrongly imputed to the doctrine itself.
Chapter 93
How does Mill distinguish a fatalist from a necessitarian?
Mill says a fatalist believes whatever will happen must happen no matter how we struggle against it. A necessitarian holds only that actions follow from character, and character from organization, education, and circumstances. Mill argues the fatalist conclusion is a grand error: we can partly form our own character by willing the requisite means, since the desire to change is itself one influential circumstance.
Chapter 93
Why does Mill object to the word Necessity for human actions?
Mill argues Necessity in ordinary use implies irresistibleness, causes too powerful to be counteracted. Human actions are never, except in some cases of mania, ruled by one motive with absolute sway; other motives can counteract. So calling them necessary uses the term in a sense almost amounting to a play on words, and its associations breed fatalism in feeling.
Chapter 93

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According to Mill, why is meteorology already a science despite its imperfection?
Mill argues that any facts following constant laws can be a subject of science, even if those laws are undiscovered or undiscoverable by present resources. Rain and sunshine depend on laws derived from heat, electricity, vaporization, and elastic fluids. Meteorology is imperfect only because of the inherent difficulty of observing the facts it depends on, not for lack of natural requisites.
Chapter 94
What distinguishes an exact science from an inexact one, using astronomy and tidology?
Mill says astronomy became exact once all causes influencing its phenomena, great or trifling, were brought under laws assigning each its true share of effect. Tidology remains inexact because only laws of major causes are accurately known; minor causes like ocean-bottom configuration, shore confinement, and wind are not sufficiently ascertained to be compounded into a complete law.
Chapter 94
Why can't human actions be predicted with scientific accuracy, according to Mill?
Mill states we cannot foresee all circumstances individuals will be placed in. Further, conduct results jointly from present circumstances and individual character, and the agencies forming character are so numerous and varied that no two cases are exactly alike. Even a theoretically perfect science could not make positive predictions or universal propositions, since data are never all given nor precisely alike.
Chapter 94
How does Mill define laws of mind, and how do they differ from laws of body?
Mill sets aside questions about the mind's own nature and means by laws of mind the laws of mental phenomena: thoughts, emotions, volitions, and sensations. A law of Mind applies when a state of mind is produced by another state of mind; a law of Body applies when a state of mind is produced directly by a state of body. Sensations, though proximately caused by nervous states, are themselves mental.
Chapter 94

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Why does Mill think mental chemistry's proof of association is incomplete?
Mill argues that showing certain associated ideas were present whenever a complex feeling occurred amounts only to the Method of Agreement, which cannot prove causation. To establish that association generates belief or moral reprobation, one must also apply the Method of Difference—testing whether that specific association, when attached to a previously indifferent action, produces the effect. He says this has been made extremely probable but not conclusively proved.
Chapter 95
Even if complex feelings derive from simpler ones, what study does Mill say remains necessary?
Mill holds that deriving one class of mental phenomena from another is an interesting fact in psychological chemistry, but it does not remove the need for experimental study of the generated phenomenon—just as knowing oxygen and sulphur does not let us deduce sulphuric acid without observation. So psychologists must still study beliefs, desires, and volitions by the canons of Induction, and association governs these complex states as it does simple ideas.
Chapter 95
What three causes may explain differing mental susceptibility among individuals?
Mill lists: first, differences may be original and ultimate facts; second, they may result from the individuals' previous mental history; third, they may depend on varieties of physical organization. He says prior mental history must play some part, and that bodily structure also co-operates—an opinion of all physiologists confirmed by common experience, though he regrets it has been accepted in the gross without analysis.
Chapter 95
How does Martineau's essay explain different types of mental character?
Martineau argues that simultaneous sensations associate into ideas of objects, successive ones into ideas of events. Whatever favors synchronous association yields a perceptive mind—taste for the beautiful and moral enthusiasm; whatever favors successive association yields a ratiocinative, philosophic intellect. Mill cites this to show that mere differences of intensity in sensations can produce different qualities of mind.
Chapter 95

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What does Mill call the science of character formation, and how does it relate to psychology?
Mill proposes the name Ethology, from the Greek ἦθος (character), for the science that determines what kind of character general laws of mind produce under any set of physical and moral circumstances. Psychology studies the elementary laws of mind through observation and experiment; Ethology is wholly deductive, deducing character-formation laws from those general laws. Ethology corresponds to education in the widest sense, including collective national character.
Chapter 96
What limits does Mill place on the practical power of Ethology?
Mill concedes we cannot accurately know all circumstances of a given case, so positive prediction of character is vain. But knowledge short of prediction has practical value: knowing that certain means tend to produce or frustrate an effect lets us shape circumstances under our control more favorably. This is the limit of our power, but within it the power is most important.
Chapter 96
Why does Mill say Ethology's propositions must be hypothetical and assert only tendencies?
Because character involves highly complex phenomena, Mill holds that exactness requires propositions affirming tendencies, not facts. They must not claim something always or certainly happens, but only that a given cause produces such an effect so far as it operates uncounteracted. His examples: bodily strength tends to make men courageous, interest tends to bias judgment, experience tends to give wisdom — universally true though the tendencies may be frustrated.
Chapter 96

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What does Mill call the science of forming individual character, and what is its task?
Ethology. Its problem is to deduce middle principles from the general laws of Psychology, determining from those laws and the general position of the species what combinations of circumstances promote or prevent qualities in human beings. Once so prepared, it becomes the foundation of the art of education, which transforms its principles into precepts adapted to individual cases.
Chapter 97
How must a priori deduction and a posteriori verification relate in Ethology?
They must proceed pari passu. Theory's inference about the character formed by given circumstances must be tested by specific experience of those circumstances whenever obtainable, and conclusions must be perpetually verified and corrected by common experience and history. Neither theory nor observation can be trusted alone; only their consilience grounds the science.
Chapter 97
Why can social science not predict society's future like astronomy, according to Mill?
The laws themselves need not be less certain; the difference lies in the data. Astronomy's causes are few and change little by known laws, so data are as certain as the laws. Social circumstances are innumerable and perpetually changing, defying calculation, and precise numbers cannot be applied to such facts.
Chapter 97
What error does Mill attribute to the Chemical or Experimental method in social science?
It overlooks that society's laws are just the laws of individual human nature, and that the Composition of Causes is universal in social phenomena. Its followers reject reasoning from principles of human nature as 'abstract theory' and demand specific experience in every case, producing arguments no chemist since Bacon would accept.
Chapter 97

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Why does Mill find the experimental argument for a restrictive system's prosperity inconclusive?
Mill argues national prosperity is always the collective result of many favorable circumstances. A restrictive nation may share some circumstances with one prosperous nation and others with another, uniting more favorable conditions than either, while each of those nations has only half. So the closest imitation of legitimate induction from direct experience gives only a specious semblance of conclusiveness, without real value.
Chapter 98
Why does the Method of Concomitant Variations fail for society?
Mill argues every attribute of the social body is influenced by innumerable causes, and the elements of society act mutually, so whatever affects one important element affects others directly or indirectly. Since effects of different agents are not different in quality while each quantity is a mixed result of all agents, variations of the aggregate cannot bear a uniform proportion to any one component.
Chapter 98
What does Mill say about Coleridge's use of the Method of Residues?
Mill says Coleridge, comparing great occurrences with past history and subtracting points of difference from likeness, no doubt employed the Method of Residues, weighing rather than merely numbering points. But Mill stresses this method is not pure observation: it presupposes causes already known by deduction from principles of human nature, with experience only supplementary, and it concludes from an instance compared with a previous deduction.
Chapter 98

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What does Mill say influences rulers' conduct besides personal interest?
Mill argues rulers are largely influenced by habitual sentiments and modes of thinking prevailing in their community, by the feelings and habits of their particular class, and by maxims and traditions inherited from predecessors—traditions that have retained ascendancy even against rulers' private interests. He grants private interest is a powerful constant force, but insists it cannot sufficiently explain all of rulers' conduct, including what makes their government good or bad.
Chapter 99
Why does Mill reject responsibility to the governed as the only cause of identity of interest?
Mill calls this claim even less admissible than the first. He notes cases where what serves the general interest—such as suppressing anarchy and establishing central authority in medieval Europe—is also prompted by rulers' strongest personal interest, consolidating power. Responsibility could not strengthen, and might weaken, those motives. He cites Elizabeth's reign and Peter the Great as cases where identity of interest was strong without responsibility.
Chapter 99
What is Mill's criticism of the geometrical school's method, and what concession does he make?
Mill argues their method was unscientific: they constructed a science from only a few agencies determining phenomena, leaving the rest to routine or conjecture, causing disproportionate attention to included factors. He concedes their mistake was more of form than substance—their premises were really the polemics of the day, not a complete theory—and that constitutional checks remain needed as security against rulers' selfish interests.
Chapter 99
What method does Mill say is proper to social science, and what remedy corrects its imperfections?
Mill says sociology is a deductive science, but after the model of complex physical sciences, not geometry: it deduces from many original premises, compounding the laws of all conjunctly influencing causes. Because complexity makes deduction precarious, the remedy is Verification—the third essential part of the Deductive Method—collating conclusions with concrete phenomena or their empirical laws, since confidence rests on agreement between a priori reasoning and observation.
Chapter 99

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Why must sociological inquiry be limited to facts under a few immediate causes?
The author argues that uncertainty grows at an accelerating ratio as more concurrent causes enter the calculation. Hypothetical combinations therefore cannot be made very complex without rapidly accumulating liability to error, which would deprive conclusions of all value. So this mode of inquiry, to avoid frivolity, must be limited to classes of social facts mainly under the immediate influence of a few agents.
Chapter 100
Why may different species of social facts be studied apart despite universal consensus?
The author holds that although all social phenomena are interconnected and the general state of civilization exercises paramount ascendancy, different species of social facts depend immediately and in the first resort on different kinds of causes. They therefore not only may but must be studied apart, like the physiology and pathology of separate organs, each acted on by the whole body yet shaped chiefly by local causes.
Chapter 100
What does Political Economy abstract from, and which two counter-motives does it retain?
The author argues Political Economy concerns only phenomena arising from the pursuit of wealth, abstracting from every other passion or motive except two perpetual antagonists to the desire of wealth: aversion to labor and desire for present enjoyment of costly indulgences. These are kept because they always accompany the pursuit as a drag, not merely occasionally conflict with it. It treats the wealth motive as sole end within its departments.
Chapter 100
Why are English political economy's distribution laws inapplicable elsewhere, and what remains universally valid?
The author notes English economists assume produce shared among three distinct classes—laborers, capitalists, landlords—all free agents. This fails in slave countries, where landlords are the only capitalists and laborers their property; in India, where the state is nearly universal landlord; in France and Ireland, with different ownership patterns. The conclusions need revision, but the method of investigation is universally applicable.
Chapter 100

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Why must deductive science oversee statistical and historical generalizations?
Because empirical laws of effects only give empirical laws of immediate causes, which depend on remote causes. Such generalizations can be trusted for unobserved cases only if no change has occurred in those remote causes. So we must know the remoter causes to avoid misapplying the law, and the deductive science must sanction every inference.
Chapter 101
Why can't specific experience yield empirical laws for single social causes like corn laws?
The effect of one cause is disguised by other simultaneous influences, so specific experience could at most show an average difference across many instances. But the number of instances needed to exhaust all combinations never can be obtained, since the world does not supply them within a given state of society.
Chapter 101
What is Mill's indirect verification of social theory?
Since direct verification of a prediction comes only in the very case predicted, too late for guidance, theory is verified indirectly by checking other conclusions drawn from the same laws. We must be able to explain and account for the existing state of the phenomena the cause influences; failure reveals either incomplete facts or an imperfect theory.
Chapter 101
How does Mill define a 'state of society' and its fundamental problem?
A state of society is the simultaneous state of all the greater social facts: knowledge and culture, industry and wealth distribution, occupations, class divisions and relations, common beliefs, tastes, government, laws and customs. Mill holds there are uniformities of co-existence among these elements, and the fundamental problem is finding the laws by which one state of society produces its successor.
Chapter 101

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Why does Mill say empirical laws of history need verification by psychological and ethological laws?
Mill argues that empirical laws of society rest on very few instances, since few nations have reached a high stage of social progress, and still fewer independently. If even one or two instances are poorly known or analyzed, a wrong empirical law is likely to emerge. Constant verification by psychological and ethological laws is the only check or corrective against erroneous historical generalizations.
Chapter 102
How does Comte distinguish Social Statics from Social Dynamics?
Mill reports that Comte divides empirical laws of society into uniformities of co-existence and of succession. Social Statics concerns co-existence: the conditions of stability in the social union and the mutual actions and reactions of contemporaneous social phenomena, provisionally abstracting from gradual movement. Social Dynamics is the theory of society in progressive movement, or the laws of progress.
Chapter 102
What does Mill call the necessary correlation between form of government and state of civilization?
Mill describes it as a natural law showing the necessary correlation between a society's form of government and its contemporaneous state of civilization. He says this stamps abstract discussions and theories of forms of government as fruitless and worthless, except as preparatory treatment of materials for constructing a better philosophy.
Chapter 102
What conditions does Mill identify as requisites of stable political union?
Mill says some circumstances appear in all societies and most where union is complete, and may count as conditions of a State when confirmed by psychological and ethological laws. Examples: no numerous society has held together without laws or equivalent usages, without tribunals and organized force to execute decisions, and without public authorities the community obeyed or was bound to obey.
Chapter 102

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What does Mill say empirical laws from history actually amount to?
Mill argues they are not the "middle principles" themselves but only evidence toward establishing such principles. They are general tendencies perceived in society, such as mental qualities prevailing over bodily ones as society advances. Most inquirers, including the Continental historical school, stop at these generalizations, which remain too distant from elementary laws of human nature to be direct corollaries.
Chapter 103
What must be combined to obtain better empirical laws of society?
Mill says we must not merely note progressive changes in separate elements of society. We must combine the statical view of social phenomena with the dynamical, considering both the progressive changes and the contemporaneous condition of each element. This yields empirically the law of correspondence between simultaneous states and simultaneous changes, which, verified a priori, becomes the real scientific derivative law of human development.
Chapter 103
Which social element does Mill identify as predominant in social progression?
Mill argues the state of the speculative faculties is predominant, including the nature of beliefs people hold about themselves and the world. Though speculation is relatively weak among human propensities, he argues its influence is the main determining cause of social progress, since other dispositions depend on it for the means of accomplishing their work. He cites the consilience of history and human nature as evidence.
Chapter 103
What three stages does Comte regard as the fundamental law of intellectual progress?
Mill reports that Comte conceives speculation to pass through three successive stages on every subject: first explaining phenomena by supernatural agencies, second by metaphysical abstractions, and third confining itself to ascertaining laws of succession and similitude. Mill says this generalization has high scientific evidence from the concurrence of history with the constitution of the human mind, though he rates Comte's predictions of the future as inferior to his appreciation of the past.
Chapter 103

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What mistake does Mill say Buckle and others made about moral qualities?
The author argues that Buckle and others inferred from statistical regularity that moral qualities are little capable of improvement or unimportant to social progress. Mill says this forgets that the averages come from narrow limits and few years, all under the same general causes. Comparing ages or countries differing in moral elements yields widely different crime totals, since crimes depend on collective moral qualities.
Chapter 104
How does Mill distinguish causation from fatalism in social progress?
Mill says the theory of invariable social laws is often wrongly combined with the doctrine that individual or governmental exertions cannot materially influence progress. Confusing causation with fatalism is the recurring error. He compares it to a shipwrecked person who, because annual deaths are constant, thinks saving his life is useless; but the average of such efforts is itself one of the causes of that annual number.
Chapter 104
What does Mill think of Macaulay's metaphor about great men and the sun?
Mill says Macaulay compares great men to people on a loftier height who catch the sun's rays earlier, implying that without Newton the world would have had the Newtonian system equally soon. Mill rejects this: if truths rose by their own motion without human effort, it would follow, but not otherwise. He believes the world must have waited for another Newton, and that eminent men evoke the light rather than merely reflect it.
Chapter 104
What does Mill say determines the order versus the celerity of progress?
Mill holds that the order of human progress may have definite laws, since certain truths cannot be discovered and certain social improvements cannot follow except after others, by the constitution of the human mind. But as to celerity, or whether progress happens at all, no general law can be made; only precarious approximations confined to the small portion of mankind with consecutive historical progress. Great men above all decide the celerity.
Chapter 104

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How does Mill distinguish art from science?
Mill distinguishes art from science by mood: science speaks in the indicative, asserting matters of fact, while art speaks in the imperative, expressing rules or precepts. Ethics or morality, as the knowledge of duties, is properly a portion of art corresponding to the sciences of human nature and society. Therefore the Method of Ethics can be no other than the Method of Art or Practice in general.
Chapter 105
How do rules of art relate to theorems of science?
Mill describes a division of labor: art defines an end and hands it to science; science studies it as an effect, investigates its causes and conditions, and returns a theorem of the circumstances producing it. Art judges whether those circumstances are in human power, and if so converts the theorem into a rule or precept. Art supplies only the major premise that the end is desirable; science supplies the proposition that certain actions attain it.
Chapter 105
Why must a scientific theory be complete before becoming a precept?
Mill argues a theorem is not ripe for conversion into a precept until the whole scientific operation is performed, including all negative conditions—circumstances that would prevent the effect. If a rule is framed prematurely and an overlooked counteracting cause occurs, the rule fails: means are employed but the end does not follow. No arguing about the rule helps; one must reopen the investigation and finish the science first.
Chapter 105
What error does Mill attribute to the geometrical school of politics?
Mill criticizes political speculators, especially in France, who reason downward from sweeping practical maxims as ultimate premises to particular applications, calling this being logical and consistent. He argues such maxims must rest on speculative grounds, and since no government produces all beneficial effects, an arrangement's not following from the government's general principle may be a stronger recommendation. He says this habit aggravates rather than alleviates a system's characteristic imperfections.
Chapter 105

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Does Mill claim happiness is the sole end of all actions?
No. Mill says he does not assert that the promotion of happiness should itself be the end of all actions or even of all rules of action. It is the justification and ought to be the controller of all ends, but not itself the sole end. Some virtuous actions sacrifice happiness in the particular instance, producing more pain than pleasure.
Chapter 106

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Why does Mill exclude the question of Noumena from Logic?
Mill says that as a metaphysician he has no quarrel with the opinion denying Noumena, but whether true or false it is irrelevant to Logic. Since all forms of language contradict it, introducing it unnecessarily would cause confusion, and every essential doctrine of Logic could stand equally well with the opposite accredited opinion.
Chapter 107
What rival doctrine does Mill call of greater practical moment, and where does he discuss it?
The doctrine of a direct perception or intuitive knowledge of the outward object as it is in itself, distinct from the sensations we receive from it. Mill says this is of far greater practical moment, but it depends on the nature and laws of Intuitive Knowledge and is not within Logic's province; he refers readers to An Examination of Sir William Hamilton's Philosophy.
Chapter 107
How does Mill respond to Whewell's mole objection about knowledge and instinct?
Whewell asks whether a mole cannot dig without an idea of the ground, snout, and paws. Mill replies he does not know what passes in a mole's mind or what mental apprehension accompanies instinctive actions, but a human being does not use a spade by instinct and certainly could not use it without knowledge of a spade and of the earth he uses it upon.
Chapter 107
What is Bain's distinction between definite and indefinite classes, and which does Mill adopt?
Bain says a definite class is an enumeration of actual individuals, like the Peers of the Realm or the known planets, while an indefinite class is unenumerated, like stars, planets, or men; in the latter sense class name and general name are identical. Mill assumes classes are indefinite because for Logic definite classes as such are almost useless, though often serviceable for abridged expression.
Chapter 107

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What does Bain's term 'Obversion' designate among equivalent propositional forms?
Bain uses 'Obversion' for one of the commonest changes of expression among Equipollent or Equivalent Propositional Forms: the change from affirming a proposition to denying its negative, or vice versa. Mill reports that Bain sets out these equivalent forms with some fullness in his Logic and calls this particular designation 'very happy.'
Chapter 108
How does Hamilton reformulate 'Some A is not B' as a convertible proposition?
Sir William Hamilton points out that 'Some A is not B' may be converted into the form 'No B is some A.' Mill's example: 'Some men are not negroes; therefore, No negroes are some men (e.g., Europeans).' This illustrates Hamilton's treatment of the quantity of the predicate, which ordinary logic leaves elided in expression.
Chapter 108
Why does Bain deny singular propositions a place in the syllogism?
Bain argues singular premises yield no real inference: if wise, poor, and man are part of the meaning of 'Socrates,' the conclusion merely repeats what was given. Even with real information, the conclusion only omits part of the premises, which Bain counts as equivalence or Immediate Inference, not genuine syllogistic deduction.
Chapter 108
How does Mill rebut Bain's objection to singular syllogisms?
Mill replies that Bain's first argument assumes proper names have meaning, contradicting Bain's own definition of a proper name as a 'single meaningless mark.' Against the second argument, Mill notes every syllogism's conclusion contains less than the premises, so the objection applies equally to universal propositions and is really an objection to the syllogism itself, not to singulars.
Chapter 108

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What misinterpretation of 'B coexists with A' does Mill say the practical maxim excludes?
Mill admits the coexistence form of the axiom may suggest, without warning, that two things are merely found together. He argues the practical form, Nota notae est nota rei ipsius, excludes this, since a mark of a thing never implies reciprocity: being in a confirmed consumption marks approaching death, but no one dies only from consumption.
Chapter 109
What does Mill say about the dictum de omni versus his proposed axiom?
Mill concludes both have value and a place in Logic. He would retain the dictum de omni as the fundamental axiom of the logic of mere consistency, or Formal Logic, and says he never proposed banishing it. But he argues his own axiom is the proper axiom for the logic of the pursuit of truth by way of Deduction.
Chapter 109
How does Mill respond to the objection that the major premise includes the conclusion?
Mill replies that the major premise does not individually specify all it includes; it gives only a description by marks, so the minor is still needed to compare a new individual with those marks. He contends both assertions are proved together by the same evidence, the grounds of experience, not the smaller by the larger.
Chapter 109
What does Mill say is the only minor premise necessary to reasoning in his example?
Mill says the only necessary minor is that Socrates is like A, B, C, and the other individuals known to have died. The formal minor predicating a class name is, he holds, no more necessary than the major; both are a precaution against erroneous reasoning rather than conditions of reasoning.
Chapter 109

Section 1104 cards

According to the chapter, what did Leibnitz give as his reason for rejecting Newton's solar system?
The author notes that Leibnitz, despite his great mental accomplishments, rejected Newton's scheme because he held that God could not make a body revolve around a distant centre except by an impelling mechanism or by miracle. Leibnitz argued that whatever is not explicable by the nature of creatures is miraculous, and that a free body given such a law would naturally fly off at the tangent unless angels or other bodies constrained it.
Chapter 110
What does the quoted writer argue about the origin of geometrical and mechanical axioms?
The quoted writer, cited approvingly by Mill, argues that axioms such as two straight lines cannot inclose a space, and that equal forces on equal lever arms balance, carry their inductive origin on their face. Their truth is forced on the mind by daily and hourly experience, including experience gained by contemplating inward pictures; what we call intuition here is only the vividness of such mentally summoned impressions.
Chapter 110
How does the quoted writer answer the paradox of universal propositions obtained by experience?
The writer argues there is nothing paradoxical in being led by observation to general propositions co-extensive with human experience. Truths pervading all objects of experience must be continually suggested by it; their truth ensures consistent, uncontradicted suggestion that commands implicit assent, and their simplicity secures admission by every mind. Such a sentiment must form part of the mental picture of the object whenever contemplated.
Chapter 110
What does Mill say about his chapter's relation to the Quarterly Review article on Whewell?
Mill states that the whole present chapter, except the last four pages added in the fifth edition, was written before he saw the Quarterly Review article of June 1841, most of it before publication. He says his object is not to claim originality but to recommend an opinion opposed to reigning doctrines through the striking concurrence of two independent inquirers, and he quotes passages in unison with his views.
Chapter 110

Section 1114 cards

What distinction does Mill draw between different Descriptions and different Inductions?
Mill holds that different Descriptions of the same fact can coexist, since they merely represent it, but different Inductions or explanations cannot both be true. He argues Whewell confuses holding contradictory opinions on a question of fact with merely employing different analogies to facilitate conceiving the same fact.
Chapter 111
Why does Mill say the vortex theory cannot be reconciled with Newton's?
Mill argues the vortices were not a mere aid to conceiving planetary motion but a supposed physical agent actively impelling the planets — a material fact that could be true or not, but not both. As explanation, Newton's theory ascribes motion to a law common to all matter, which absolutely excludes the vortex explanation.
Chapter 111
What does Mill say about the word 'inherent' in the theory of celestial virtue?
Mill replies to Whewell that if you leave out 'inherent,' nothing of the theory remains except that heavenly bodies move 'by a virtue,' i.e., by some power, or by their celestial nature — which directly contradicts the doctrine that terrestrial bodies fall by the same law. The word inherent is the theory.
Chapter 111
What condition does Mill say induction requires regarding uniformity of nature?
Mill says uniformity need not pervade all nature; it is enough that it pervades the particular class of phenomena the induction concerns. An induction about planets or magnets is not vitiated by supposing wind and weather are chance, provided astronomical and magnetic phenomena are law-governed. Induction implies uniformity either already known or now knowable.
Chapter 111

Section 1124 cards

How does Mill treat opacity as a possible exception to the general causation formula?
Mill notes that opaque bodies seem purely preventive, intercepting light without producing effects by the same law. He suggests opacity may only be an apparent exception, depending on unknown relations to light or structure. Crucially, he argues the formula including all negative conditions as "absence of counteracting causes" is not violated by such cases, though if all counteracting agencies were purely preventive, the formula would serve no purpose.
Chapter 112
What does Mill mean by "the constitution of things," and what example does he give?
Mill defines it as the ultimate laws of nature, whatever they may be, distinguished from derivative laws and from collocations. He illustrates with the earth's diurnal revolution, which is not part of the constitution of things because nothing can be so called which might possibly be terminated or altered by natural causes. So the constitution consists of laws not subject to possible alteration by natural causes.
Chapter 112
What does Mill say is really contradicted by consciousness regarding the human will?
Mill remarks that metaphysicians who deny the Law of Causation applies to the will ground their objection on consciousness. He argues they mistake what consciousness testifies against: what truly conflicts with consciousness is applying the ideas involved in the common term Necessity to human actions and volitions, which he agrees in objecting to. By causation here, he says, no more is meant than that a person invariably does act in conformity to his character.
Chapter 112
How does Mill respond to Bain's alleged exceptions to the Composition of Causes?
Bain cites cases like directing a gun, igniting gunpowder, and dosing medicine, where doubling a cause seems not to double the effect. Mill replies these are not real exceptions: the immediate effect is a collocation, and duplicating the cause doubles the collocation, though one collocation may suffice for the full effect. Doubling with difference of time and place does double the effect, and a double dose of aperient or laudanum does produce stronger or longer effects.
Chapter 112

Section 1134 cards

According to Bain, what are the limits of scientific explanation and induction?
Bain argues that scientific explanation and inductive generalization are the same thing, so the limits of Explanation are the limits of Induction. Induction supposes similarity among phenomena, and when similarity is discovered it reduces phenomena under a common statement. The limits to inductive generalization are the limits to the agreement or community of facts.
Chapter 113
Why does Bain say merging gravity and cohesion into one law is illusory?
Bain says gravity and cohesion agree only in attraction and differ widely otherwise. Gravity is common to all matter, equal in equal masses, follows the inverse square, extends unlimitedly, and is indestructible. Cohesion is special to each substance and decreases far more rapidly, vanishing at very small distances. They lack sufficient kindred, so the generalization is only nominal.
Chapter 113
What further limitation does Mill add to the explanation of laws of nature?
Mill adds that even when phenomena are not generically distinct, referring them to the same cause is legitimate only if the cause is shown capable of producing them according to the same law. Otherwise the unity of cause is a mere guess and the generalization only nominal, which even if admitted would not reduce the number of ultimate laws.
Chapter 113
Why does Mill defend Darwin's Origin of Species as a legitimate hypothesis?
Mill argues Darwin never claimed his doctrine was proved, so he was bound by the rules of Hypothesis, not the rules of Induction, which concern conditions of Proof. Natural selection is a vera causa shown capable of producing effects of the same kind, with the question one of degree. Mill says the rules of Hypothesis were seldom more completely fulfilled.
Chapter 113

Section 1144 cards

Why does Mill reject Taine's claim that abstraction guarantees universal laws?
Mill says he cannot see how any abstract conception elicited from experience can be evidence of an objective fact in universal Nature beyond what the experience itself witnesses, nor how the limitations of experience's testimony can be cast off in generalizing it. He admits he may not fully grasp Taine's meaning, but denies abstraction grants assurance of universality that experience cannot give.
Chapter 114
How does Mill answer Dr. Ward's argument that experience gives no knowledge of the future?
Mill sees no force in it, citing Priestley: we have had no experience of what is future, but abundant experience of what was future. The leap from past to future is no darker than from personally observed past to unobserved past. Bain's psychological presumption by the energy of the idea is not inconsistent with the logical truth that experience proves it, through invariable verification when the experience arrives.
Chapter 114
How does Mill classify miracles relative to the law of causation?
Mill admits no uniformity in nature other than the law of Causation, and holds a miracle is no exception to it. In every alleged miracle a new antecedent is affirmed—a counteracting cause, namely the volition of a supernatural being. So for anyone to whom beings with superhuman power over nature are a vera causa, a miracle is a case of Universal Causation, not a deviation from it.
Chapter 114
How does Mill respond to M'Cosh's claim that chemical composition laws fall outside causation?
Mill argues every case of chemical composition is a case of causation: saying water is composed of hydrogen and oxygen affirms that hydrogen and oxygen, acting on one another under certain conditions, generate the properties of water. Therefore the Canons of Induction laid down in the treatise apply, with only such special adaptations as the inductive methods may require.
Chapter 114

Section 1152 cards

Why does Mill prefer equidistance over non-intersection as the definition of parallel lines?
Mill argues that defining parallels as coplanar lines that never meet forces geometers to assume an extra axiom, which he calls the opprobrium of elementary geometry. Equidistance better captures what the name means: lines pursuing the same direction, neither approaching nor receding. Non-meeting is included in being everywhere equally distant, and a curve could otherwise be called parallel to its asymptote.
Chapter 115
What definition of impossibility does Mill propose, and why reject the cause-based one?
Mill rejects defining an impossibility as that for which no adequate cause exists, because it excludes cases like two and two making five, two straight lines enclosing a space, or anything beginning to exist without a cause. He proposes instead: an impossibility is that whose truth would conflict with a complete induction, the most conclusive evidence we possess of universal truth.
Chapter 115

Section 1163 cards

How does Mill defend Comte against Whewell's charge about theology?
Mill argues Whewell misreads Comte's theorem. The doctrine only implies that in advanced knowledge no Ruler is acknowledged except one ruling by universal laws, not producing events by special interpositions. Mill notes Comte himself thought theology would cease, but says this is not implied by the fundamental theorem.
Chapter 116
What does Comte mean by the metaphysical stage, per Mill?
Mill says Comte means the stage where abstractions are treated as active forces producing effects: Nature does this or forbids that, Nature's horror of a vacuum, vis medicatrix, vital force, and qualities mistaken for entities dwelling in things. Abstract names of phenomena are mistaken for causes of their existence.
Chapter 116
What did Buckle's friend say Buckle really intended about great men?
The friend states Buckle intended only to affirm emphatically that the greatest men cannot effect great changes unless the general mind has been considerably prepared by the age's general circumstances. Buckle also used abstraction like a political economist, treating intellect as the determining element and omitting other sentiments for method, not as fact.
Chapter 116

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All questions and answers

According to the Preface to the First Edition, what is the book's claim to originality?

How does Mill respond to writers who pronounced a general theory of induction impossible?

What does Mill say in the third and fourth edition preface about responding to critics?

What does Mill say about the diversity of definitions of logic in the Introduction?

According to Mill, how are truths known to us?

What example does Mill use to show inference mistaken for intuition?

What does Mill say is the proper province of logic?

How does Mill describe logic's role as ars artium?

Why must the study of language precede the study of logic, according to Mill?

What three parts make up every proposition, and what does each denote?

Why does Mill say 'the sun' alone cannot be believed or disbelieved?

Why does Mill reject the advice to dismiss words and look directly into things?

How does Mill define a general name versus an individual name?

What distinguishes a collective name from a general name?

How does Mill define concrete versus abstract names?

What makes a name connotative rather than non-connotative?

According to Mill, where does the meaning of a name reside?

What does Mill's chalk-mark analogy illustrate about proper names?

Why does Mill say knowing what a name denotes isn't knowing its meaning?

What problem does Mill identify with indeterminate connotation in general names?

According to Mill, what makes a name relative?

How does Mill distinguish univocal from equivocal names?

Why does Mill criticize Aristotle's ten Categories?

How does Mill classify so-called perceptions of external objects?

What two things does Mill say constitute an action?

How do school logicians distinguish substance from attribute?

What definition of body do modern metaphysicians give, and what objection follows?

According to Mill, what do we really assert when we say snow has the quality whiteness?

What alternative view of qualities does Mill describe before setting it aside?

How does Mill ridicule the notion of qualities as entities per se?

What is the fundamentum relationis, and how does Mill define a relation?

According to Mill, does the circumstance of time attach to the copula or the predicate?

How does Mill analyze propositions like 'Cæsar may be dead'?

Why does Mill deny that 'Cæsar is dead, and Brutus is alive' is a compound proposition?

What is the real subject and predicate of a hypothetical proposition like 'If the Koran comes from God, Mohammed is his prophet'?

What does Hobbes say a proposition signifies, and when is it true?

Why does Mill reject Hobbes's theory as a full account of predication?

According to Mill, what does 'All men are mortal' really assert?

What logical error does Mill attribute to the class-inclusion theory of predication?

According to Mill, what does a proposition like 'All men are mortal' actually assert?

What five kinds of matter-of-fact does Mill say every non-verbal proposition asserts?

Why does Mill deny that class-membership propositions merely assert resemblance?

How does Mill analyze 'A generous person is worthy of honor'?

According to Mill, what do merely verbal propositions assert, and what proof can they have?

How does Mill redefine the essence of a thing, such as man's rationality?

Why does Mill say essential propositions are identical propositions conveying no information?

Why does an accidental affirmation imply the real existence of its subject while an essential one does not?

According to Mill, does predication presuppose classification?

What are the five Predicables, and what kind of division are they?

Why are genus and species called relative terms?

How do classes differ in the properties they share beyond the defining attribute?

Why did Aristotelians reject 'cooking animal' as man's differentia?

How does Mill distinguish Proprium from Accidens?

Why may a species have different differentiae in different classifications?

According to Mill, what is the definition of a connotative name?

Why does Mill say a definition can be called an analysis, citing Condillac?

How are names of single attributes like eloquence defined, per Mill?

What two kinds of imperfect definition does Mill distinguish, and what makes each imperfect?

What does Mill claim all definitions are definitions of?

How does Mill analyze the definition of a triangle?

What does Mill conclude from the 'dragon' syllogism?

Why does Mill say geometrical postulates are not exactly true?

According to Mill, how does a name come to denote a confused huddle of objects?

What four questions does Mill identify in defining an abstract name like justice?

Which examples does Mill give of apparent but not real inference?

How does Mill distinguish Induction from Ratiocination by generality?

What does Mill claim is essential to a legitimate syllogism?

How are syllogistic figures distinguished, and how many does Mill recognize?

Why does Mill say every valid ratiocination can be put in the first figure?

What error does Mill say keeps returning in new phrasing?

What does Mill say about Condillac's aphorism that a science is a well-made language?

How does Mill analyze the syllogism in terms of attributes rather than classes?

What two axioms does Mill substitute for the dictum de omni et nullo?

Where does Mill say the inference resides in concluding the Duke of Wellington is mortal?

What does Mill say about Archbishop Whately's view that syllogizing is the mode in which all men reason?

What example does Mill give of reasoning from particulars to particulars in a child?

What does Mill say about the skilled dyer who could not teach his method?

On Mill's view, what does the syllogism actually accomplish in reasoning?

What does Mill say is the true ground for believing the Duke of Wellington will die?