whately’s revolution john p. mccaskey stanford university

Whately’sRevolution

John P. McCaskeyStanford University

Whately’s 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. . . .

”“

{

“Why can’t a woman

be more like a man?

“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 can’t induction

be 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 deductions—deductions that do not quite make the grade.”

Canonical History of Induction

Aristotelian epagōgē, or the “From-Induction

Deduction”

Cicero Coins

inductio

Scholastic Recovery

Francis Bacon’s

New Organon

Humean Problem of Induction

Mill’s Methods

Correct History of Induction

Socratic Scholastic Humanist Whatelian

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Socratic Induction

Prosecuting a wrongdoer, even if your own father.What is piety?

That’s 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 don’t know which.

Let’s start over. Isn’t 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

Mentions of epagogein Aristotle’s Works

1

12

5

14

11

4

3

27

2

0

13

2

Categories

On InterpretationPrior Analytics

Posterior Analytics

Topics

Sophistical RefutationsRhetoric

Physics

Metaphysics

Eudemian Ethics

Nicomachean 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.

“

”

Properties “Primitively Universal,” aka “Distinguishing by Nature”

Three sidesThree anglesAngles sum to 2R

Computer image by Anil Sabharwal

Property that causes changeProperty with respect to which change takes place

GoodnessFitness for function

Lack bileLong-lived

ContrarietyMaximum differenceComplete difference

In Greek: proton katholou; idion kata hauto

1

Guidelines for IdentifyingPrimitively Universal Properties

Categories


Posterior AnalyticsTopics

Sophistical RefutationsRhetoric

Physics

Metaphysics

Eudemian Ethics

Nicomachean Ethics

. . .

Book V

• Ensure 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

Epagōgē & Inductioin Antiquity

1

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

“

”

Topics

On Invention

Socrates

Aristotle

Cicero

GalenStoicsEpicureansQuintilian

Socrates

Aristotle

Cicero


The Neo-Platonic Reinterpretation

Aristotle 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.

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2

[Definition is the] summation resulting from Division.

“”Socrates

Aristotle

Cicero


Neo-Platonists

Clement

Alexanderof Aphrodisias

Simplicius

Philoponus

Prior Analytics B 23

Late 13th century Byzantine manuscript. Princeton MS. 173.

Induction then is—or rather, the from-induction deduction— deducing one extreme [to belong] to the middle through the other extreme.

Ἐπαγωγὴ μὲν οὖν ἐστι καὶ ὁ ἐξ ἐπαγωγῆς συλλογισμὸςτὸ διὰ τοῦ ἑτέρου θάτερον ἄκρον τῷ μέσῳ συλλογίσασθαι.

”“

”“

2

“ 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.

2

Socrates

Aristotle

Cicero


The Neo-Platonic Reinterpretation

Aristotle 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.

“”

2

Neo-Platonists

Clement


Simplicius

Philoponus

Socrates

Aristotle

Cicero


al-Farabi AverroesAvicenna

Peter ofSpain

Boethius

Neo-Platonists

Clement


Simplicius

Philoponus

WilsonAldrich

Zabarella

AlbertAquinasScotus

Ockham

Scholastic Transmission

210

27

0

13

0

1

Isagoge

Categories


Posterior Analytics

Topics

Survived in Boethius’s

translations and commentaries

Largely replaced by B’s

On Categorical SyllogismsFell out of use, then

lostReplaced by B’s

De Topicis Differentiis

Peter of Spain’s

Tractatus

B’s 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.

2

Scholastic Transmission

Socratic Scholastic

1

2



suppressed.

2


Peter ofSpain

Boethius

Neo-Platonists

Clement


Simplicius

Philoponus

WilsonAldrich

ZabarellaBuridan

AlbertAquinasScotus

Ockham

The Humanist Revolt

Cicero defines induction as follows . . . . Boethius, who followed a different school, disagrees . . .

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3

Boethius acts like one who has stolen a horse and tries to hide the theft by cutting and dyeing the horse’s hair.

• Increase in scope• Attention to the Topics• Interest in Cicero• Access to Platonic dialogues

Socrates

Aristotle

Cicero


RenaissanceHumanists

VallaAgricola

Socrates

Aristotle

Cicero



Peter ofSpain

Boethius

Neo-Platonists

Clement


Simplicius

Philoponus

WilsonAldrich

ZabarellaBuridan

AlbertAquinasScotus

Ockham

Baconian Induction

• Idols: Poorly defined notiones• Concepts, not propositions• Comparisons, not enumerations• The predicate, not the subject

• Ignited French gunpowder is hot.• Ignited German gunpowder is hot.• Ignited English gunpowder is hot.

Whewell

3

• Final Cause•Material Cause• Efficient Cause• Formal Cause

Harvey

Regula Socratis

“ ”

Bacon


VallaAgricola

Humanist

Humanist Induction

Socratic Scholastic

1

2

3

3

Induction:“Regula Socratis”

Scholastic Induction

Socratic Scholastic

1

2



suppressed.

2

Bacon Whewell

Socrates


Peter ofSpain

Boethius

Neo-Platonists

Clement


Simplicius

Philoponus

WilsonAldrich

ZabarellaBuridan


AlbertAquinasScotus

Ockham

VallaAgricola

Aristotle

Cicero


Whately’s Revolution

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.

* 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.


Barbara with the major premise

suppressed.

Whately

“As Bishop Whately remarks…”

Whately

Mill

4

Hamilton

HamiltonMill

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.

”

“De

Morgan

DeMorgan

Induction as Inference

Whately

Mill

4

Hamilton

DeMorgan

Jevons

Bain

Reasoning

Judgment

SimpleApprehension

Inferences

Propositions

Notions, Terms

Bacon

To be purged

Correct bad

notions

Whately

Better sense

Original and

strict sense

MillInduction

: Inferring general

propositions

Description is not

induction

DeMorgan

The original

andlogical sense

The sense

nowadays

Bain

Yes!

No!

Induction is a proceedingfrom particulars to a universal.

“”

Jevons

Derivative of

deduction

Every induction

ends with a

concept

Whewell

?

?

2 3 4

Keynes

Cassirer

VennHumeHumeWhere’s Hume?

David Hume & the“Problem of Induction”4

Whately

Mill

Hamilton

DeMorgan

Jevons

Bain

Whewell

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.

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Fowler

1843

Note 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).

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1870

Presumptions in any inference:• Sense perception•Memory•Uniformity of nature

In inductive inference:•Belief in uniformity of nature

Various defenses:•Mill’s•Reid’s•Hume’s•Venn’s own

1889

The 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.

Hume’s sceptical criticisms are usually associated with causality; but argument by induct-ion . . . was the real object of his attack. . . . Hume’s statement of the case against induction has never been improved upon.

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1921

— as Hume relentlessly insisted —

“ ”

1906

Whately’s Legacy

WhatelianSocratic Scholastic Humanist

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3

• Induction is about universal propositions, not universal concepts.

• It’s 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.

• It’s about propositional inference not abstraction.

“Why can’t induction

be more like deduction?

Correct History of Induction

Socratic Scholastic Humanist Whatelian

1

2

3

4

whately’s revolution john p. mccaskey stanford university

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