Myths in the History of Induction

1. Mythsin the Historyof Induction John P. McCaskey Stanford University

2. 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

3. Prior Analytics B 23 “ Ἐπαγωγὴ μὲν οὖν ἐστι καὶ ὁ ἐξ ἐπαγωγῆς συλλογισμὸς τὸ διὰ τοῦ ἑτέρου θάτερον ἄκρον τῷ μέσῳ συλλογίσασθαι. ” “ Induction then is—or the from-induction deduction— deducing one extreme [to belong] to the middle through the other extreme. ” Late 13th century Byzantine manuscript. Princeton MS. 173.

4. Conventional Reading of“a deduction from induction ” (1) Man, horse, and mule are long-lived animals. (1) C1, C2, C3 are A. (2) Man, horse, and mule are bileless animals. (2) C1, C2, C3 are B. By conversion of (2): (3) Bileless animals are man, horse, and mule. (3) B is C1, C2, C3. (4) Bileless animals are long-lived. (4) All B is A. By (1) and (3):

5. Mentions of epagogein Aristotle’s Works “ 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. 1 Categories 0 On Interpretation 12 Prior Analytics 13 Posterior Analytics 27 Topics 2 Sophistical Refutations 14 Rhetoric 5 Physics 11 Metaphysics 4 Eudemian Ethics 3 Nicomachean Ethics 2 ” . . .

6. Mentions of epagogein Aristotle’s Works Categories “ ” All professions . . . On Interpretation Prior Analytics “ All professions . . . All wise men . . . All irresponsible custodians . . . Posterior Analytics Topics ” Sophistical Refutations Rhetoric “ All causal interactions . . . All instances of contrariety . . . Physics ” Metaphysics Eudemian Ethics “ ” All instances of goodness . . . Nicomachean Ethics . . .

7. A Non-Mention of epagogein Aristotle’s Works Categories “ Scalene triangles . . . Isosceles triangles . . . Equilateral triangles . . . Therefore all triangles. On Interpretation Prior Analytics Posterior Analytics Topics Sophistical Refutations ” Rhetoric Physics Metaphysics Eudemian Ethics Nicomachean Ethics . . .

8. Correct Reading of B 23 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. But how can an induction justify a conversion?

9. Socratic Induction What is piety? Prosecuting a wrongdoer, even if 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? “ Two things may be fairly ascribed to Socrates: inductive reasoning and universal definition. 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?

10. Properties “Primitively Universal,” aka “Distinguishing by Nature” In Greek: proton katholou; idionkatahauto Three sides Three angles Angles sum to 2R Lack bile Long-lived Contrariety Maximum difference Complete difference Goodness Fitness for function Property that causes change Property with respect to which change takes place Computer image by Anil Sabharwal

11. Guidelines for Identifying Characteristics Distinguishing by Nature Use observations and comparisons to . . . Categories • 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. • . . . On Interpretation Prior Analytics Posterior Analytics Book V Topics Sophistical Refutations Rhetoric Physics Metaphysics Eudemian Ethics Nicomachean Ethics . . .

12. Two Conceptions of Induction Prior Analytics B 23 misunderstood A kind of inference that gains force the more it is like a complete enumeration, an argument that can be rendered as a syllogism. A kind of inference inferior to deduction. Positive instances determine reliability. Particulars and universals are primarily propositions Topics Posterior Analytics Socrates 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. Not an inference and not inferior to deduction. Breadth and depth of comparisons determine reliability. Particulars and universals are primarily things, concepts, or terms.

13. Transmission Aristotle Socrates

14. 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 ” Cicero Aristotle Socrates

15. Epagōgē&Inductio in Antiquity Galen Stoics Epicureans Quintilian Cicero Aristotle Socrates

16. The Neo-Platonic Reinterpretation • 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 Philoponus Simplicius Neo- Platonists 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. Alexander of Aphrodisias “ Clement Galen Stoics Epicureans Quintilian ” Cicero First to suggest that induction gains its force by a complete enumeration of particulars. Aristotle Socrates

17. Arabic Transmission Avicenna Averroes al-Farabi Syriac & then Arabic study of the Organon Philoponus Simplicius Neo- Platonists Alexander of Aphrodisias 0 Isagoge Clement Categories 1 0 On Interpretation Galen Stoics Epicureans Quintilian 2 Prior Analytics 10 Posterior Analytics 13 27 Topics Cicero 6th c. → 12th c. Aristotle Socrates

18. Latin Transmission Through Boethius Avicenna Averroes al-Farabi 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. “ Philoponus Simplicius Neo- Platonists Alexander of Aphrodisias Boethius Clement Cicero ” Aristotle Socrates

19. Latin Transmission Through Boethius Avicenna Averroes al-Farabi Philoponus Simplicius Neo- Platonists Alexander of Aphrodisias 0 Boethius Clement 1 Isagoge Survived in Boethius’s translations and commentaries 0 2 Categories 10 On Interpretation 13 Largely replaced by B’s On Categorical Syllogisms Prior Analytics 27 Cicero Posterior Analytics Fell out of use, then lost Replaced by B’s De TopicisDifferentiis Topics Aristotle Socrates

20. Scholastic Textbooks Avicenna Wilson Averroes al-Farabi Philoponus Simplicius Neo- Platonists Alexander of Aphrodisias Peter of Spain 0 Zabarella Boethius Clement 1 Isagoge Survived in Boethius’s translations and commentaries Peter of Spain’s Tractatus 0 2 Categories 10 On Interpretation 13 Largely replaced by B’s On Categorical Syllogisms Prior Analytics 27 Cicero Posterior Analytics Fell out of use, then lost Replaced by B’s De TopicisDifferentiis Topics B’s Topics Aristotle Socrates

21. Scholastic Textbooks Avicenna Wilson Averroes al-Farabi Philoponus Simplicius Neo- Platonists Alexander of Aphrodisias Peter of Spain Zabarella Boethius Clement “ “ 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. Cicero ” ” Aristotle Socrates

22. Scholastic Philosophers “ 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. Avicenna Wilson Averroes al-Farabi ” Philoponus Albert Aquinas Scotus Ockham Simplicius Neo- Platonists “ [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. Alexander of Aphrodisias Peter of Spain Zabarella Boethius Clement ” • 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. Cicero Aristotle Socrates

23. John Buridan: The First Challenge Avicenna Wilson Averroes al-Farabi Philoponus Albert Aquinas Scotus Ockham Simplicius Neo- Platonists Alexander of Aphrodisias Peter of Spain Buridan Zabarella Boethius Clement Cicero Aristotle Socrates

24. The Humanist Revolt • Increase in scope • Attention to the Topics • Interest in Cicero • Access to Platonic dialogues Avicenna Wilson Averroes al-Farabi Philoponus Albert Aquinas Scotus Ockham “ 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. Simplicius Neo- Platonists Alexander of Aphrodisias Peter of Spain Buridan Zabarella Boethius Clement Renaissance Humanists Cicero Valla Agricola ” Cicero defines induction as follows . . . . Boethius, who followed a different school, disagrees . . . “ Aristotle ” Socrates

25. Baconian Induction • Idols • Concepts, not propositions • Comparisons, not enumerations • The predicate, not the subject Avicenna Wilson Averroes al-Farabi Philoponus Albert Aquinas Scotus Ockham Simplicius Neo- Platonists Alexander of Aphrodisias Peter of Spain Buridan Zabarella Boethius Clement • Ignited French gunpowder is hot. • Ignited German gunpowder is hot. • Ignited English gunpowder is hot. Renaissance Humanists Cicero Whewell Bacon Valla Agricola Aristotle Socrates

26. Whately’s Revival “ [Induction is] a Syllogism in Barbara with the major* Premiss suppressed. Avicenna Wilson Averroes al-Farabi Philoponus Albert Aquinas Scotus Ockham Simplicius * Not the minor, as Aldrich represents it. ” Neo- Platonists Alexander of Aphrodisias Peter of Spain Buridan Whately Zabarella Boethius 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. Clement [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. Renaissance Humanists Cicero Whewell Bacon Valla Agricola Aristotle Socrates

27. “ As Archbishop Whately remarks . . . ” “ Every induction may be thrown into the form of a syllogism by supplying a major premise. . . . Avicenna Wilson Averroes al-Farabi Philoponus Albert Aquinas Scotus Ockham Simplicius The uniformity of nature will appear as the ultimate major premise of all inductions. Neo- Platonists ” Alexander of Aphrodisias Peter of Spain Buridan Whately Mill Zabarella Boethius Clement 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. Renaissance Humanists ” Cicero Whewell Bacon Valla Agricola Aristotle Socrates

28. Two Conceptions of Induction Avicenna Wilson Averroes al-Farabi Philoponus Albert Aquinas Scotus Ockham Simplicius Neo- Platonists Alexander of Aphrodisias Peter of Spain Buridan Whately Mill Zabarella Boethius Clement Galen Stoics Epicureans Quintilian Renaissance Humanists Cicero Whewell Bacon Valla Agricola Aristotle Socrates

29. 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

30. Two Conceptions of Induction Treats concept-formation as a normative process. Does not depend on a principle whose own justification relies on induction. Prior Analytics B 23 misunderstood A kind of inference that gains force the more it is like a complete enumeration, an argument that can be rendered as a syllogism. A kind of inference inferior to deduction. Positive instances determine reliability. Particulars and universals are primarily propositions Helps explain the remarkable scientific progress between Bacon and Whewell . . . Says ampliation occurs at the conceptual, not the propositional, level. Topics Posterior Analytics Socrates 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. Not an inference and not inferior to deduction. Breadth and depth of comparisons determine reliability. Particulars and universals are primarily things, concepts, or terms. and the poor regard practicing scientists have had for philosophers of science ever since.

31. Two Conceptions of Induction Avicenna Wilson Averroes al-Farabi Philoponus Albert Aquinas Scotus Ockham Simplicius Neo- Platonists Alexander of Aphrodisias Peter of Spain Buridan Whately Mill Zabarella Boethius Clement Galen Stoics Epicureans Quintilian Renaissance Humanists Cicero Whewell Bacon Valla Agricola Aristotle Socrates