RelationshipHistory of the

ConceptsInduction&

John P. McCaskeyStanford University

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Induction is proceeding from particulars to a universal.

Topics 1.12

Two things may fairly be ascribed to Socrates:

Metaphysics 13.4

What sort of thing induction is,

Topics 8.1is obvious.

This one is blue.That one is blue.The other is blue. All are blue.

inductive reasoning and universal definition.

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On Interpretation

Prior Analytics

Posterior Analytics

Topics

Sophistical Refutations

Rhetoric

Physics

Metaphysics

Eudemian Ethics

Nicomachean Ethics

. . .

Mentions of epagoge

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Prosecuting a wrongdoer, even if it’s 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?

Socratic Induction

Ancient

Socratic

Scholastic

Scholastic

BoethiusPeter

AlbertAquinas

ScotusOckham

Zabarella

al-FarabiAvicenna

Averroes

ClementAlexander

Sextus EmpiricusThemistius

Ammonius HermiaeSimplicius

Philoponus

Father, Son and Holy Spirit are eternal.[God is Father, Son and Holy Spirit.]

Therefore, God is eternal.

An induction is a propositional inference made good by complete enumeration.

This man, or that man, et cetera, is an animal.[Every man is this man, or that man, et cetera.]

Therefore, every man is an animal.

An induction is a syllogism in Barbara

with the minor premise

suppressed.

Ancient

Socratic

Higginsian

This one is blue.That one is blue.The other is blue. All are blue. An induction is

a syllogism in Barbara

with the minor premise

suppressed.

Scholastic

Ancient Scholastic

Humanist

Sunlight

Sunlight through magnifier

Flame

Heated or boiling liquidsWet, compressed plantsFibrous fabricsQuicklime with waterAnimals

Horse dung

LightningMeteors

Volcanoes

Solids on fireNatural hot baths

Distilled spirits?

Presence Related Absence

MoonlightStarlight…magnifier turned around?Moonlt through magnifier?

Liquids in natural state“further inquiry is needed”“let an experiment be made”Quicklime with oil?Insects

Sheet lightningComets, aurora borealis

Rotting wood?“not enough investigations”

X

X

Degrees

Fish

Different parts of animals

Dung as fertilizer

Kinds of animals

Corpse right after death

SeasonsAltitude

Lightning hotter than fireMany kindsSmaller solids heat up faster

Three Tables1• Light? No: Dark things can be hot.• Something celestial? No: Heat can emerge from underground.• Something terrestrial? No: Heat can come from the heavens.• Expansion? No: Water does, but iron doesn’t expand when heated.• Rarity? No: Fire and hot air are rare, but dense things can be hot.• Motion? Not motion generally; some things move without getting hot,

but everything hot involves motion.

Candidates& Exclusions

2

Heat is a kind of motion.3 Genus

• Expansive motion—most apparent in flame, but also apparent in boiling liquids, combustible materials, metals melting, rocks softening when heated. Also consistent with opposite behavior in cold. For example, glass expands when heated then contracts and cracks when cooled.

• Motion is of the parts (maybe too small to see) not of the whole as a unit . . .

4 Differentia

Definition5 Heat is an expansive motion which is checked

and restrained, and acting through particles, expanding in all directions, . . .

. . . a true induction

Socratic

Humanist

Exploding French gunpowder is hot.Exploding German gunpowder is hot.Exploding English gunpowder is hot.

All exploding gunpowder is hot.

Heat is such-and-such motion.

All exploding gunpowder has heat.

Get definition by induction

By the nature of definition

They exhibit a certain motion.

Such-and-such motion is heat.Exploding gunpowder has such-and-such motion.

Humanist

Socratic

These things are hot.

Socratic

Ancient Scholastic

Humanist

Whatelian

Higginsian

Richard Whately

Scholastic

An induction is a syllogism in Barbara

with the minor premise

suppressed.

This, that and the other magnet attract iron.[All magnets are this, that and the other.]

Therefore, all magnets attract iron.

Henry Aldrich

1823

1826

* “Not the minor, as Aldrich represents it. The instance he gives will sufficiently prove this: . . . ‘All magnets are this, that and the other’. . . is manifestly false.”

* “Not the minor, as Aldrich represents it.”

“[Induction is] a Syllogism in Barbara

with the major* Premiss suppressed.”

Richard Whately

Observed tyrannies are short-lived.

Therefore all tyrannies are short-lived.

Therefore being short-lived is a property of all tyrannies.

Being short-lived is a property of observed tyrannies.

[A property of observed tyranniesis a property of all tyrannies.]

Minor

Conc.

Major

“[Induction is] a Syllogism in Barbara

with the major* Premiss suppressed.”

Therefore all magnets attract iron.

Therefore Socrates is mortal.

Therefore attracting iron is a property of all magnets.

Richard Whately

Therefore Socrates is mortal.

Therefore all magnets attract iron.

Major

MinorTherefore all tyrannies are short-lived.

Therefore being short-lived is a property of all tyrannies.

Observed tyrannies are short-lived.

Therefore all tyrannies are short-lived.

Therefore being short-lived is a property of all tyrannies.

Being short-lived is a property of observed tyrannies.

[A property of observed tyranniesis a property of all tyrannies.]

Minor

Conc.

Major

“[Induction is] a Syllogism in Barbara

with the major* Premiss suppressed.”

Richard Whately1828

“original”

“extremely important”

“[This] one remark would have sufficed to correct the erroneous notion the ancients had of induction, and to which Lord Bacon . . . [was responding]. They in fact mistook altogether the inductive syllogism, completing it by the addition of a minor, instead of a major.”

This, that and the other magnet attract iron.

[All magnets are this, that and the other.]

Therefore, all magnets attract iron.

An induction is a syllogism in Barbara

with the minor premise

suppressed.

“As Archbishop Whately remarks, every induction is a syllogism with the major premise suppressed; or (as I prefer expressing it) every induction may be thrown into the form of a syllogism by supplying a major premise. If this be actually done, the principle we are now considering, that of the uniformity of the course of nature, will appear as the ultimate major premise of all inductions.”

Observed tyrannies are short-lived.

Therefore all tyrannies are short-lived.

Therefore being short-lived is a property of all tyrannies.

Being short-lived is a property of observed tyrannies.

[A property of observed tyranniesis a property of all tyrannies.]

Minor

Conc.

Major

“palpably suicidal”

Socratic

Ancient Scholastic

Humanist

Higginsian

Whatelian

“ 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. ”

“ By Induction, we arrive at Propositions, . . . [It is not Induction] where what we arrive at is a Notion or Definition. ”

“ Hume’s sceptical criticisms are usually associated with causality; but argument by induction . . . was the real object of his attack. ”

Ancient Scholastic

Humanist

Whatelian

This one is blue.That one is blue.The other is blue. All are blue.

Higginsian

Socratic

• 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, not philosophers of mind, are in charge.

• It’s about propositional inference not abstraction.

Higginsian

Socratic

Higginsian

Socratic

• Ampliation occurs at the conceptual level, not at the propositional level.

• Ampliative propositional inference is grounded in quality of concepts.

• Universal statements are only as good as—but fully as good as—the constituent concepts.

• But isn’t this cheating?

• Definitions are normative and getting definitions right is the core project.

Synthetic Analytic

Nominal Definition

Causal Definition

Periodic rising and falling of large

bodies of water.

Periodic rising and falling caused

by gravity.

Definition by Shallow Causes

Definition by Deep Causes

Perceptual Associations

Impedance

Resistance

Referential Lockdown

VoltageCurrent

Resistance =

Cholera: an intestinal disorder characterized by such-and-such symptoms.

Cholera: an intestinal disorder caused by such-

and-such bacteria.

Tetracycline cured this case of cholera.Tetracycline cured that case of cholera.Will Tetracycline cure every case of cholera?

Synthetic Analytic

a priori

a posteriori

Socratic

Ancient Scholastic

Humanist

Higginsian

Richard Whately

Whatelian