whately’s revolution

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WhatelysRevolution

John P. McCaskeyStanford University

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Whatelys Revolutionary Footnote

[Induction is] a Syllogism in Barbara with the major* Premiss suppressed. * Not the minor, as Aldrich represents it.

As Archbishop Whately remarks . . .Every induction may be thrown into the form of a syllogism by supplying a major premise. . . .{2Why cant a womanbe more like a man?

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Induction takes its force from the syllogism. So it suffices to discuss the syllogism which is, as it were, principal.

Induction, therefore, so far as it is an argument, may, of course, be stated syllogistically.Induction and example are subsumed under syllogistic justification. Thus what we have said about them is enough.Induction takes its force from the syllogism. So it suffices to discuss the syllogism which is, as it were, principal.Why cant inductionbe more like deduction?An inductive inference can always be looked upon as an aspiring but failed deductive inference.. . . like social workers, providing under-privileged inductive inferences with the necessities enjoyed by valid deductions.This view takes inductions to be defective deductionsdeductions that do not quite make the grade.4Canonical History of InductionAristotelian epagg, or the From-Induction DeductionCicero Coins inductioScholastic RecoveryFrancis Bacons New OrganonHumean Problem of InductionMills Methods

5Correct History of InductionSocraticScholasticHumanistWhatelian123

46Socratic Induction

Prosecuting a wrongdoer, even if your own father.What is piety?Thats an example. What is piety itself?Doing what pleases the gods.But gods disagree.And there are many kinds of disagreement:Disagreement over which number is greater.Disagreement over which thing is larger.Disagreement over which thing is heavier.Disagreement over just and unjust.Disagreement over beautiful and ugly.Disagreement over good and bad.Piety is what pleases all gods.But is it pious because it pleases the gods or does it please the gods because it is pious?What is loved vs. what loves.What is the difference?What is led vs. what leads.What is seen vs. what sees.So . . . what is admired vs. what admires.I dont know which.Lets start over. Isnt everything pious also just but not vice versa?Yes.Then piety is a kind of justice. What kind?Two things may be fairly ascribed to Socrates: inductive reasoning and universal definition.1

7Mentions of epagogein Aristotles Works11251411432720132CategoriesOn InterpretationPrior AnalyticsPosterior AnalyticsTopicsSophistical RefutationsRhetoricPhysicsMetaphysicsEudemian EthicsNicomachean Ethics. . .1

We need to distinguish how many kinds of dialectical reasoning there are. One kind is induction, another is deduction. Now, what a deduction is has been explained earlier. Induction, however, is a proceeding from particulars to a universal. For instance, if the pilot who has knowledge is the best pilot, and so with a charioteer, then generally the person who has knowledge about anything is the best.8Properties Primitively Universal, aka Distinguishing by NatureThree sidesThree anglesAngles sum to 2R

Computer image by Anil SabharwalProperty that causes changeProperty with respect to which change takes place

GoodnessFitness for function

Lack bileLong-lived

ContrarietyMaximum differenceComplete differenceIn Greek: proton katholou; idion kata hauto1

9Guidelines for IdentifyingPrimitively Universal PropertiesCategoriesOn InterpretationPrior AnalyticsPosterior AnalyticsTopicsSophistical RefutationsRhetoricPhysicsMetaphysicsEudemian EthicsNicomachean Ethics. . .Book VEnsure property applies in individual cases.Test kinds broader and narrower.Identify linked contraries.Ensure the predicate can be applied broadly.Use terms that are unambiguous.Identify temporal qualifications.Identify dependencies.Use language that makes clear in what way exceptions are allowed.Check relationship of whole to parts.Be clear whether relationship is absolute or relative.. . .Use observations and comparisons to . . .1

Test broader and narrower If true of isosceles triangles, check if true of triangles. If true of triangles, check if true of various kinds of triangles. check if true of squares and circles also.

Linked contraries If you think good and evil are contraries, and good is the proper object of choice, and object of choice and object of avoidance are contraries check that evil is the object of avoidance.

Exceptions allowed? If you say man is biped, what are we to make of a man who gets his legs amputated? What about a head?10Epagg & Inductioin Antiquity1

This procedure, which arrives at its aim from several instances, may be named inductio, which in Greek is called epagg; Socrates made extensive use of it in his discussions.TopicsOn Invention

SocratesAristotle

CiceroGalenStoicsEpicureansQuintilian11

SocratesAristotle

CiceroGalenStoicsEpicureansQuintilianThe Neo-Platonic ReinterpretationAristotle discusses these types of justification [induction and paradigm] at greater length in the second book [of the Prior Analytics], showing how they differ from syllogistic justification, that they are useful, and how they are subsumed under syllogistic justification.

2[Definition is the] summation resulting from Division.

SocratesAristotle

CiceroGalenStoicsEpicureansQuintilianNeo-PlatonistsClementAlexanderof AphrodisiasSimpliciusPhiloponus

12Prior Analytics B 23

Late 13th century Byzantine manuscript. Princeton MS. 173.Induction then isor rather, the from-induction deduction deducing one extreme [to belong] to the middle through the other extreme. .

213 a deduction from induction is deducing . . . (1)Man, horse, and mule are long-lived animals.(2)Man, horse, and mule are bileless animals.(3)Bileless animals are man, horse, and mule.By conversion of (2):(4)Bileless animals arelong-lived.By (1) and (3):(1)C1, C2, C3 are A.(2)C1, C2, C3 are B.(3)B is C1, C2, C3.(4)All B is A.

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SocratesAristotle

CiceroGalenStoicsEpicureansQuintilianThe Neo-Platonic ReinterpretationAristotle discusses these types of justification [induction and paradigm] at greater length in the second book [of the Prior Analytics], showing how they differ from syllogistic justification, that they are useful, and how they are subsumed under syllogistic justification.The great Alexandrian synthesis: better known by nature vs. better known to us prior vs. posterior knowing the fact vs. knowing the reasoned fact deduction vs. induction deduction as a priori vs. induction as a posteriori [Definition is the] summation resulting from Division.

2Neo-PlatonistsClementAlexanderof AphrodisiasSimpliciusPhiloponus

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SocratesAristotle

CiceroGalenStoicsEpicureansQuintilian

al-FarabiAverroesAvicennaPeter ofSpain

BoethiusNeo-PlatonistsClementAlexanderof AphrodisiasSimpliciusPhiloponus

WilsonAldrich

Zabarella

AlbertAquinasScotusOckham

Scholastic Transmission2102701301IsagogeCategoriesOn InterpretationPrior AnalyticsPosterior AnalyticsTopicsSurvived in Boethiuss translations and commentariesLargely replaced by BsOn Categorical SyllogismsFell out of use, then lostReplaced by BsDe Topicis DifferentiisPeter of Spains TractatusBs Topics[In induction it] is required to suppose that he has listed all the things.Everything that is this man, or that man, etc. is an animal.Every man is this man, or that man, etc.Therefore, every man is an animal.Induction: an Enthymeme in Barbara with the minor premise suppressed.

216Scholastic TransmissionSocraticScholastic12

Induction: an Enthymeme in Barbara with the minor premise suppressed.

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The Humanist RevoltCicero defines induction as follows . . . . Boethius, who followed a different school, disagrees . . .3

Boethius acts like one who has stolen a horse and tries to hide the theft by cutting and dyeing the horses hair.Increase in scopeAttention to the TopicsInterest in CiceroAccess to Platonic dialogues

SocratesAristotle


RenaissanceHumanistsVallaAgricola18

SocratesAristotle




WilsonAldrich

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Baconian InductionIdols: Poorly defined notionesConcepts, not propositionsComparisons, not enumerationsThe predicate, not the subjectIgnited French gunpowder is hot.Ignited German gunpowder is hot.Ignited English gunpowder is hot.Whewell3

Final CauseMaterial CauseEfficient CauseFormal Cause

HarveyRegula Socratis

BaconRenaissanceHumanistsVallaAgricola

19HumanistHumanist InductionSocraticScholastic123

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Induction:Regula Socratis20Scholastic InductionSocraticScholastic12

Induction: an Enthymeme in Barbara with the minor premise suppressed.

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BaconWhewell

Socrates



WilsonAldrich

ZabarellaBuridanRenaissanceHumanists

AlbertAquinasScotusOckhamVallaAgricola

Aristotle

CiceroGalenStoicsEpicureansQuintilianWhatelys RevolutionEverything that is this man, or that man, etc. is an animal.[Every man is this man, or that man, etc.]Therefore, every man is an animal.* Not the minor, as Aldrich represents it.[Induction is] a Syllogism in Barbara with the major* Premiss suppressed. 4

[What belongs to the observed individuals belongs to all.]Being an animal belongs to this man, and that man, etc.Therefore, being an animal belongs to all men.Induction: an Enthymeme in Barbara with the major premise suppressed.

Whately22As Bishop Whately remarks

Whately

Mill4

Hamilton

Hamilton

Mill

Every induction may be thrown into the form of a syllogism by supplying a major premise. . . .The uniformity of nature will appear as the ultimate major premise of all inductions.

DeMorgan

DeMorgan23Induction as Inference

Whately

Mill4

Hamilton

DeMorgan

Jevons

BainReasoningJudgmentSimpleApprehensionInferencesPropositionsNotions, Terms

BaconTo be purgedCorrect bad notions

WhatelyBetter senseOriginal and strict sense

MillInduction: Inferring general propositionsDescription is not induction

DeMorganThe original andlogical senseThe sense nowadays

BainYes!No!Induction is a proceedingfrom particulars to a universal.

JevonsDerivative of deductionEvery induction ends with a concept

Whewell

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KeynesCassirer

Venn

Hume

HumeWheres Hume?David Hume & theProblem of Induction4

Whately

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Hamilton

DeMorgan

Jevons

BainWhewell

Why is a single instance, in some cases, sufficient for a complete induction, while in others myriads of concurring instances, without a single exception known or presumed, go such a very little way towards establishing an universal proposition? Whoever can answer this question . . . has solved the problem of Induction.

Fowler1843Note 2.Since the time of Hume, the nature of our conception of Cause has formed one of the principal topics of philosophical controversy. . . . (a controversy, however, which possessesa historical rather than a practical or scientific interest).1870Presumptions in any inference:Sense perceptionMemoryUniformity of natureIn inductive inference:Belief in uniformity of natureVarious defenses:MillsReidsHumesVenns own1889The very concept of an experimental inference involves a great petitio principii. Induction owes all its force to the premise that the future will be like the past, which is just what the induction itself seeks to infer.Humes sceptical criticisms are usually associated with causality; but argument by induct-ion . . . was the real object of his attack. . . . Humes statement of the case against induction has never been improved upon.1921 as Hume relentlessly insisted 190625

Whatelys LegacyWhatelianSocraticScholasticHumanist123

4SocraticScholasticHumanist123

Induction is about universal propositions, not universal concepts.Its a risky kind of inference to be understood with reference to the better kind, deduction.Uniformity principle is a presumed major premise.Logicians and mathematicians displace philosophers of mind.Its about propositional inference not abstraction.26Why cant inductionbe more like deduction?

27Correct History of InductionSocraticScholasticHumanistWhatelian123

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whately’s revolution

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