the other kind of induction john p. mccaskey history · philosophy · case study

The Other Kind of Induction

John P. McCaskey

History · Philosophy · Case Study

The Other Kind of Induction“Socratic Induction”

Two things may be ascribed to Socrates: inductive reason-ing and universal definitions.

Which kind of argument [is] called by the learned, “Socrates Induction”

has not yet been . . . tried except only by Plato . . . in settling on definitions

[Anatomist should proceed] according to the rule of Socrates.

Socrates made extensive use of it in his discussions

Particular & universal propositions

Particular things & universal terms

Two Conceptions of Induction

?Induction is a proceeding from particulars to a universal.

Man, horse, mule are long-lived.Bileless animals are man, horse, mule.Bileless animals are long-lived.

It is true of Father, Son and Holy Ghost.Father, Son and Holy Ghost are God.It is true of God.This animal chews by moving its lower jaw.That animal chews by moving its lower jaw.The other animal chews by moving its lower jaw.All animals chew by moving the lower jaw.What is true of the observed is true of all.This is true of the observed.This is true of all.

Scholastic Induction


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.This view takes inductions to be defective deductions—deductions that do not quite make the grade.An inductive inference can always be looked upon as an aspiring but failed deductive inference.



Particulars and universals are primarily propositions

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.





Two Conceptions of InductionParticulars and universals are primarily propositions


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 k ind of just ice. What k ind?

Socratic Induction

Two things may be ascribed to Socrates: inductive reasoning and universal definitions.

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.


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.


Socratic Induction

Ampliation takes place at the propositional level.

Ampliation takes place at the conceptual level.

Socratic Induction

Prosecut ing a w rongdoer, even i f your own f a ther.W hat i s p i e t y?

Tha t ’s an exam ple . W hat i s p i e t y i t se l f ?Do ing what p l eases t he gods .

Bu t gods d i sagree .

And t he re a re m any k i nds o f d i sagreem ent :

D i sagreem ent over wh i ch num ber i s g rea t er.

D i sagreem ent over wh i ch t h i ng i s l a rge r.

D i sagreem ent over wh i ch t h i ng i s heav ie r.

D i sagreem ent over j us t and un jus t .

D i sagreem ent over beau t i f u l and ug l y.

D i sagreem ent over good and bad.

P ie t y i s what p l eases a l l gods.Bu t i s i t p ious because i t p l eases t he gods or does i t p lease t he gods because i t i s p ious?

W hat i s l oved vs . what l oves .

W hat i s t he d i f f e rence?

W hat i s l ed vs . wha t l eads .

W hat i s seen vs . what sees .

So . . . wha t i s adm i red vs . what adm i res .

I don ’ t know wh i ch .

Le t ’s s ta r t over. I sn ’ t every th i ng p i ous a l so j us t bu t no t v i ce ve rsa?

Yes.

T h e n p i e t y i s a k i n d o f j u s t i c e . W h a t k i n d ?

Two things may be ascribed to Socrates: inductive reasoning and universal definitions.

Socrates

Categories

On Interpretation

Prior Analytics

Posterior Analytics

Topics

BookII

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

Induction then is—or the from-induction deduction—deducing one extreme to the middle through the other extreme.

Socrates

Of the two deductions, then, the “induction” one, that is the “from-induction deduction” is deducing that one extreme belongs to the middle through the other extreme.

Socratic Induction


Aristotle

Socratic Induction

Categories

On Interpretation

Prior Analytics

Posterior Analytics

Topics

Aristotle

Socrates

210

27

0

13

1

• 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 . . .

BookV

Socratic Induction

Aristotle

Socrates

Cicero

GalenStoicsEpicureansQuintilian

Aristotle

Socrates

Cicero



Neo-Platonists

Clement

Simplicius

Philoponus

Alexanderof Aphrodisias

Socratic Induction

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

Makes Prior Analytics B 23 the definitive text

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

al-Farabi AverroesAvicenna

Boethius

Neo-Platonists

Clement


Simplicius

Philoponus


6th c. → 12th c.

Study of the Organon

Isagoge

Categories

On Interpretation

Prior Analytics

Posterior Analytics

Topics

210

27

0

13

0

1

Peter ofSpain Zabarella

AlbertAquinasScotus

Ockham


Boethius

Neo-Platonists

Clement


Simplicius

Philoponus



AlbertAquinasScotus

Ockham

[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.


Boethius

Neo-Platonists

Clement


Simplicius

Philoponus



AlbertAquinasScotus

Ockham

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”

6th c. → 12th c.

Study of the Organon

Isagoge

Categories

On Interpretation

Prior Analytics

Posterior Analytics

Topics

210

27

0

13

0

1

Aristotle

Socrates

Cicero


Peter ofSpain

Boethius

Neo-Platonists

Clement


Simplicius

Philoponus


Zabarella

RenaissanceHumanists

AlbertAquinasScotus

Ockham

VallaAgricola

Nifo


Socratic Induction

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

Aristotle

Socrates

CiceroBacon Whewell



Socratic Induction

• Idols• Concepts, not propositions• Comparisons, not enumerations• The predicate, not the subject


Peter ofSpain

Boethius

Neo-Platonists

Clement


Simplicius

Philoponus

Zabarella

AlbertAquinasScotus

Ockham


Hume

Aristotle

Socrates

CiceroBacon Whewell



Socratic Induction


Peter ofSpain

Boethius

Neo-Platonists

Clement


Simplicius

Philoponus

Zabarella

AlbertAquinasScotus

Ockham


MillWhately

MillWhately

Every Tom, Dick, Harry, etc. is an animal.[ Every man is Tom, Dick, Harry, etc. ] Therefore, every man is an animal.

[Induction is] a Syllogism in Barbara with the major* Premiss suppressed.

* Not the minor, as Aldrich represents it.

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.

[ What is true of the observed is true of all. ] This is true of the observed. Therefore, this is true of all.

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



Socratic Induction


Peter ofSpain

Boethius

Neo-Platonists

Clement


Simplicius

Philoponus

Zabarella

AlbertAquinasScotus

Ockham


MillWhately

The Case of Cholera

1820s 1830s 1840s 1850s 1860s 1870s 1880s 1890s 1900s 1910s 1920s

18191829

C. accidentalisC. spontanea

C. spontaneaC. accidentalis

Epidemic C.C. Morbus=

1820s 1830s 1840s 1850s 1860s 1870s 1880s 1890s 1900s 1910s 1920s

1825


Epidemic C.C. Morbus ≠ ?

1820s 1830s 1840s 1850s 1860s 1870s 1880s 1890s 1900s 1910s 1920s

1832

=

Epidemic CholeraCholera Morbus

Broad Street Pump Epidemic

1820s 1830s 1840s 1850s 1860s 1870s 1880s 1890s 1900s 1910s 1920s

1854


1820s 1830s 1840s 1850s 1860s 1870s 1880s 1890s 1900s 1910s 1920s


Asiatic CholeraBilious CholeraEuropean CholeraCholera InfantumCholera Morbus

1870


1820s 1830s 1840s 1850s 1860s 1870s 1880s 1890s 1900s 1910s 1920s



Robert Koch Louis Pasteur

Cholera OutbreakCairo

1883


True cholera(wirklich, echt)

1820s 1830s 1840s 1850s 1860s 1870s 1880s 1890s 1900s 1910s 1920s



Asiatic Cholera Cholera:Cholera InfantumCholera Morbus

1910

1894

2013

1914

2013

Cholera is a malady characterized by vomiting, diarrhea, intestinal griping, lack of urination, and spasms in the leg.

Cholera is an intestinal infection caused by Vibrio cholerae.

Nominal Definition

Definition by Formal Cause

General Statements

Universal Statements

And if I ever found one that wasn’t _____ I wouldn’t call it a ____________

Tides are regular rising and falling of sea levels that occur twice a day.

Tides are regular rising and falling of sea levels caused by gravitational forces.

Dew is moisture on the ground after nights when there was no rain.

Dew is water in the form of droplets that appears on thin, exposed objects in the morning or evening due to condensation.

Electrical resistance is a material’s opposition to the passage of electricity.

The resistance of a device is the ratio of voltage across it to current through it.

Components of a Philosophy of Socratic Induction


1


General Statements

Universal Statements

All Ps are Q.All Ps are Q.

2



Synthetic a posteriori

Analytica posteriori








3



Formal Cause








4 Material and Efficient Causes


5

Boundaries can be changed.

Personal and discretionary

Good, bad, better, worse

Evolve and mature

Boundaries differ in stability.

Organic theory of concept-formation




Bacon Whewell


Aristotle

Socrates

Cicero


Socratic Induction


Peter ofSpain

Boethius

Neo-Platonists

Clement


Simplicius

Philoponus

Zabarella

AlbertAquinasScotus

Ockham


McCaskey

Popper Salmon RescherKeynesBain Jevons


MillWhately

All Ps are Q.

Analytica posteriori

FormalCauses

1

2

3

4

5

the other kind of induction john p. mccaskey history · philosophy · case study

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