myths in the history of induction john p. mccaskey stanford university

Mythsin the History

of InductionJohn P. McCaskeyStanford University

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

Prior Analytics B 23

Induction then is—or 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.

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

”“

”“

Conventional Reading of“a deduction from induction ”

(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.

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

. . .

”

We need to distinguish [1] how many kinds of dialectical reasoning there are. One kind is induction, another is deduction. [2] 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.

“

Mentions of epagogein Aristotle’s Works

All professions . . . “ ”All professions . . .All wise men . . .All irresponsible custodians . . .

“

”All causal interactions . . .All instances of contrariety . . .

“”

All instances of goodness . . .

“ ”

Categories


Posterior Analytics

Topics


Physics

Metaphysics

Eudemian Ethics

Nicomachean Ethics

. . .

A Non-Mention of epagogein Aristotle’s Works

Scalene triangles . . . Isosceles triangles . . .Equilateral triangles . . .

Therefore all triangles.

“

”

Categories


Posterior Analytics

Topics


Physics

Metaphysics

Eudemian Ethics

Nicomachean Ethics

. . .

A Deduction from a Middle

A Deduction from Induction

When the population is limited . . .

conversion is justified by an enumerated middle.

When the population is unlimited . . .

conversion is justified by induction.

(1) All C is A.

(2) All C is B.

(3) All B is C.

(4) All B is A.

Correct Reading of B 23

But how can an induction justify a conversion?

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.

“

”

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

Computer image by Anil Sabharwal

ContrarietyMaximum differenceComplete difference

Three sidesThree anglesAngles sum to 2R

Lack bileLong-lived

Property that causes changeProperty with respect to which change takes place

GoodnessFitness for function

In Greek: proton katholou; idion kata hauto

Guidelines for Identifying Characteristics Distinguishing by Nature

Categories


Posterior Analytics

Topics


Physics

Metaphysics

Eudemian Ethics

Nicomachean Ethics

. . .

• 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.• . . .

Book V

Use observations and comparisons to . . .

Two Conceptions of Induction

A kind of inference that gains force the more it is like a complete enumeration, an argument that can be rendered as a syllogism.

Prior Analytics B 23misunderstood

A kind of inference inferior to deduction.

Positive instances determine reliability.

Particulars and universals are primarily propositions

A compare-and-contrast process for discovering properties that characterize all members of a kind, some of which are unique to the kind, some of which even define the kind.

TopicsPosterior AnalyticsSocrates

Not an inference and not inferior to deduction.

Breadth and depth of comparisons determine reliability.

Particulars and universals are primarily things, concepts, or terms.

Transmission

Aristotle

Socrates

Cicero

Aristotle

Socrates

Cicero

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

Epagōgē & Inductio in Antiquity

Aristotle

Socrates

Cicero

GalenStoicsEpicureansQuintilian

The Neo-Platonic Reinterpretation

Aristotle

Socrates

Cicero


First to suggest that induction gains its force by a complete enumeration of particulars.

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 Neo-Platonists

Clement

Alexanderof Aphrodisias

Simplicius

Philoponus

Arabic Transmission

Aristotle

Socrates

Cicero


Neo-Platonists

Clement


Simplicius

Philoponusal-Farabi AverroesAvicenna

Isagoge

Categories


Posterior Analytics

Topics

Syriac & then Arabic study

of the Organon

6th c. → 12th c.

210

27

0

13

0

1

Boethius

Latin Transmission Through Boethius

Aristotle

Socrates

Cicero

And so there are two main species of arguing, one called syllogism, the other induction. Under these and, as it were, flowing from them are the enthymeme and the example. All these are drawn from the syllogism and obtain their force from the syllogism. For whether it is an enthymeme, induction or example, it takes its force as well as the belief [it produces] most of all from the syllogism; and this is shown in Aristotle’s Prior Analytics, which we translated. So it suffices to discuss the syllogism which is, as it were, principal and inclusive of the other species of argumentation.

“

”

Neo-Platonists

Clement


Simplicius


Boethius

Latin Transmission Through Boethius

Aristotle

Socrates

Cicero

Neo-Platonists

Clement


Simplicius


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

Aristotle

Socrates

Cicero

Boethius

Scholastic Textbooks

Neo-Platonists

Clement


Simplicius


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

Wilson

ZabarellaPeter of

Spain

Aristotle

Socrates

Boethius

Scholastic Textbooks

Neo-Platonists

Clement


Simplicius

Philoponusal-Farabi AverroesAvicenna Wilson

ZabarellaPeter of

Spain

Cicero

Induction is a progression from particulars to universal. For instance, Socrates runs, Plato runs, Cicero runs, et cetera; therefore every man runs. . . . [Induction is] an imperfect syllogism.

“

”

Induction . . . is of two types: perfect, which concludes necessarily, because it takes in all particulars; imperfect, which does not conclude necessarily, because it does not . . . . Peter, Socrates and Plato are biped; therefore every man is biped. . . . if we suppose that there are other men . . . this will be an imperfect induction.

“

”

Aristotle

Socrates

Boethius

Scholastic Philosophers

Neo-Platonists

Clement


Simplicius


ZabarellaPeter of

Spain

AlbertAquinasScotus

Ockham

Cicero

[In induction it] is required to suppose that he has listed all the things . . . . One cannot in virtue of the fact that Socrates and Plato and Cicero run, induce of necessity that every man runs.

“

” Devices for addressing the conflict between induction as a kind of defective syllogism and induction found elsewhere in the corpus:• Formal vs. material reduction to syllogism• Formally valid vs. materially valid• Regular induction vs. abstraction• Regular induction vs. demonstrative

induction• Use of “et cetera”

A perfect induction: true of the Father, Son, and Holy Spirit, therefore true of God.An imperfect induction: Socrates runs, Plato runs, etc., therefore all men run.

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.

“”

Aristotle

Socrates

Boethius

John Buridan: The First Challenge

Neo-Platonists

Clement


Simplicius


ZabarellaPeter of

Spain

AlbertAquinasScotus

Ockham

Cicero

Buridan

Aristotle

Socrates

Boethius

The Humanist Revolt

Neo-Platonists

Clement


Simplicius


ZabarellaPeter of

Spain

AlbertAquinasScotus

Ockham

Cicero

Buridan

RenaissanceHumanists

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

VallaAgricola

One asks whether it is admitted that the soul is better than the body. But this also must be built up from a Socratic induction. It must be asked whether the driver is superior to his chariot, the helmsman to his ship, the master to his house, and the ruler to his people, or in general whether he thinks that that which commands is superior to that which serves, and whether he thinks the body is ruled by the soul. Which if he concedes it, it will be necessary for him to concede that the soul is superior to the body.

“

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

“ ”

Aristotle

Socrates

Cicero

Baconian Induction

Neo-Platonists

Clement


Simplicius


ZabarellaPeter of

Spain

AlbertAquinasScotus

Ockham

Buridan

Boethius

• Idols• 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


VallaAgricola

Bacon

Aristotle

Socrates

Cicero

Whately’s Revival

Neo-Platonists

Clement


Simplicius


ZabarellaPeter of

Spain

AlbertAquinasScotus

Ockham

Buridan

Boethius

Whewell


VallaAgricola

Bacon

Whately

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

represents it.”

“

Mill

Aristotle

Socrates

Cicero

“ As Archbishop Whately remarks . . . ”

Neo-Platonists

Clement


Simplicius


ZabarellaPeter of

Spain

AlbertAquinasScotus

Ockham

Buridan

Boethius

Whewell


VallaAgricola

Bacon

Whately

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.

”

“

To the Deductive Method . . . the human mind is indebted for its most conspicuous triumphs in the investigation of nature.

“The Deductive Method . . . is destined to henceforth irrevocably to predominate in the course of scientific investigation.

”


Aristotle

Socrates

CiceroBacon Whewell

MillWhately

al-Farabi AverroesAvicenna

Peter ofSpain

Boethius

Neo-Platonists

Clement


Simplicius

Philoponus


Wilson

ZabarellaBuridan


AlbertAquinasScotus

Ockham

VallaAgricola

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

A kind of inference that gains force the more it is like a complete enumeration, an argument that can be rendered as a syllogism.

Prior Analytics B 23misunderstood

A kind of inference inferior to deduction.

Positive instances determine reliability.

Particulars and universals are primarily propositions


A compare-and-contrast process for discovering properties that characterize all members of a kind, some of which are unique to the kind, some of which even define the kind.

TopicsPosterior AnalyticsSocrates

Not an inference and not inferior to deduction.

Breadth and depth of comparisons determine reliability.

Particulars and universals are primarily things, concepts, or terms.

Does not depend on a principle whose own justification relies on induction.

Says ampliation occurs at the conceptual, not the propositional, level.

Treats concept-formation as a normative process.

Helps explain the remarkable scientific progress between Bacon and Whewell . . .

and the poor regard practicing scientists have had for philosophers of science ever since.


Aristotle

Socrates

CiceroBacon Whewell

MillWhately

al-Farabi AverroesAvicenna

Peter ofSpain

Boethius

Neo-Platonists

Clement


Simplicius

Philoponus


Wilson

ZabarellaBuridan


AlbertAquinasScotus

Ockham

VallaAgricola

myths in the history of induction john p. mccaskey stanford university

Documents

socratic induction

history of induction

prior analytics b

equilateral triangles

scalene triangles

isosceles triangles

bileless animals

correct reading of b