R elationship

1. History of the Relationship flickr: DrgnMastr between Concepts TripAdvisor: Groshen flickr: DigitalArt2 Induction & flickr: roch lasalle John P. McCaskey Stanford University flickr: garden beth flickr: Brian Scott

2. Induction is proceeding from particulars to a universal. Topics 1.12 This one is blue. That one is blue. The other is blue.  All are blue. DigitalArt2: CC George Goodnight DrgnMastr 1 Categories stevemallor1 Mentions of epagoge On Interpretation 0 Wendy’s Window What sort of thing induction is, Topics8.1 12 Prior Analytics is obvious. john.dart 13 Posterior Analytics 27 Topics 2 Sophistical Refutations 14 Rhetoric Two things may fairly be ascribed to Socrates: Metaphysics 13.4 5 Physics 11 Metaphysics inductive reasoning and universal definition. 4 Eudemian Ethics 3 Nicomachean Ethics 2 . . . flickr: Brian McStotts / mcshots.com

3. Socratic Induction What is piety? Prosecuting a wrongdoer, even if it’s your own father. 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 the difference? What is loved vs. what loves. 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?

4. Ancient Scholastic Socratic

5. Clement Boethius al-Farabi Alexander Peter Avicenna SextusEmpiricus Albert Averroes Themistius Aquinas AmmoniusHermiae Scotus Scholastic Simplicius Ockham Philoponus Zabarella An induction is a propositional inference made good by complete enumeration. Father, Son and Holy Spirit are eternal. • An induction is • a syllogism • in Barbara • with the minor premise • suppressed. [God is Father, Son and Holy Spirit.] Therefore, God is eternal. 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.

6. Ancient Higginsian Scholastic 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. Socratic

7. Ancient Scholastic Humanist

8. . . . a true induction Presence Related Absence Degrees 1 Three Tables Sunlight Moonlight Seasons Starlight Altitude • 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. …magnifier turned around? Sunlight through magnifier Humanist Moonltthrough magnifier? 2 Candidates & Exclusions Meteors Comets, aurora borealis Lightning Sheet lightning Volcanoes Lightning hotter than fire Flame X Many kinds Solids on fire Rotting wood? Smaller solids heat up faster 3 Genus Natural hot baths “not enough investigations” Heat is a kind of motion. Heated or boiling liquids Liquids in natural state Wet, compressed plants “further inquiry is needed” Fibrous fabrics “let an experiment be made” • 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 . . . Differentia Quicklime with water Quicklime with oil? 4 Animals Insects Fish Kinds of animals 5 Different parts of animals Corpse right after death Heat is an expansive motion which is checked and restrained, and acting through particles, expanding in all directions, . . . Socratic Definition Horse dung X Dung as fertilizer Distilled spirits?

9. Exploding French gunpowder is hot. Exploding German gunpowder is hot. Exploding English gunpowder is hot. All exploding gunpowder is hot. Humanist These things are hot. They exhibit a certain motion. Get definition by induction Heat is such-and-such motion. By the nature of definition Such-and-such motion is heat. Exploding gunpowder has such-and-such motion. All exploding gunpowder has heat. Socratic

10. Ancient Higginsian Scholastic Humanist Whatelian Socratic Richard Whately

11. Scholastic This, that and the other magnet attract iron. [All magnets are this, that and the other.] Therefore, all magnets attract iron. Henry Aldrich 1823 • An induction is • a syllogism • in Barbara • with the minor premise • suppressed. • “[Induction is] • a Syllogism • in Barbara • with the major*Premiss suppressed.” 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.” Richard Whately

12. Observed tyrannies are short-lived. [A property of observed tyrannies is a property of all tyrannies.] Being short-lived is a property of observed tyrannies. Major Therefore being short-lived is a property of all tyrannies. Therefore being short-lived is a property of all tyrannies. Minor Therefore all tyrannies are short-lived. Therefore all tyrannies are short-lived. Conc. Minor Major • “[Induction is] • a Syllogism • in Barbara • with the major*Premiss suppressed.” Therefore Socrates is mortal. Therefore Socrates is mortal. Therefore all magnetsattract iron. Therefore all magnets attract iron. Therefore attracting iron is a property of all magnets. Richard Whately

13. “[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.” Observed tyrannies are short-lived. [A property of observed tyrannies is a property of all tyrannies.] Being short-lived is a property of observed tyrannies. Therefore being short-lived is a property of all tyrannies. This, that and the other magnet attract iron. Major Therefore all tyrannies are short-lived. [All magnets are this, that and the other.] Minor Therefore, all magnets attract iron. Conc. “extremely important” 1828 “original” • “[Induction is] • a Syllogism • in Barbara • with the major*Premiss suppressed.” • An induction is • a syllogism • in Barbara • with the minor premise • suppressed. Richard Whately

14. Observed tyrannies are short-lived. “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.” [A property of observed tyrannies is a property of all tyrannies.] Being short-lived is a property of observed tyrannies. Therefore being short-lived is a property of all tyrannies. Major Therefore all tyrannies are short-lived. Minor Conc. “palpably suicidal”

15. Ancient Higginsian Scholastic “ Hume’s sceptical criticisms are usually associated with causality; but argument by induction . . . was the real object of his attack. ” “ 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. ” Humanist Whatelian Socratic

16. This one is blue. That one is blue. The other is blue.  All are blue. Ancient Higginsian Scholastic Humanist Whatelian Socratic

17. Higginsian • Induction is about universal propositions, not universal concepts. • It’s about propositional inference not abstraction. • 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. Socratic

18. Ampliation occurs at the conceptual level, not at the propositional level. Higginsian • Definitions are normative and getting definitions right is the core project. • 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? Socratic

19. Synthetic Analytic Nominal Definition Causal Definition Periodic rising and falling of large bodies of water. Periodic rising and falling caused by gravity. Referential Lockdown Perceptual Associations Definition by Deep Causes Definition by Shallow Causes Resistance Synthetic Analytic Impedance Tetracycline cured this case of cholera. Tetracycline cured that case of cholera. Will Tetracycline cure every case of cholera? a posteriori Cholera: an intestinal disorder caused by such-and-such bacteria. Cholera: an intestinal disorder characterized by such-and-such symptoms. a priori Voltage Resistance = Current

20. al-Farabi All men are mortal. The man, Socrates, was mortal. Cicero is a man. The man, Plato, was mortal. Cicero is mortal. The man, Aristotle, was mortal. The man, Cicero, is mortal. Synthetic Analytic The man, Boethius, is mortal. a posteriori a priori

21. Ancient Higginsian Scholastic Humanist Whatelian Socratic Richard Whately