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Whately’s Revolution John P. McCaskey Stanford University.

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1 Whately’s Revolution John P. McCaskey Stanford University

2 Whately’s Revolutionary Footnote [Induction is] a Syllogism in Barbara with the major* Premiss suppressed. “ * Not the minor, as Aldrich represents it. ” As Archbishop Whately remarks... Every induction may be thrown into the form of a syllogism by supplying a major premise.... As Archbishop Whately remarks... Every induction may be thrown into the form of a syllogism by supplying a major premise.... ” “ {

3 “Why can’t a woman be more like a man?

4 “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.” “Induction and example are subsumed under syllogistic justification. Thus what we have said about them is enough.” “Induction takes its force from the syllogism. So it suffices to discuss the syllogism which is, as it were, principal.” “Why can’t induction be more like deduction? “An inductive inference can always be looked upon as an aspiring but failed deductive inference.” “... like social workers, providing under- privileged inductive inferences with the necessities enjoyed by valid deductions.” “This view takes inductions to be defective deductions—deductions that do not quite make the grade.”

5 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

6 Correct History of Induction SocraticSocraticScholasticScholasticHumanistHumanistWhatelianWhatelian

7 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. “ ”

8 Mentions of epagoge in Aristotle’s Works CategoriesCategories On Interpretation Prior Analytics Posterior Analytics TopicsTopics Sophistical Refutations RhetoricRhetoric PhysicsPhysics MetaphysicsMetaphysics Eudemian Ethics Nicomachean Ethics... We need to distinguish how many kinds of dialectical reasoning there are. One kind is induction, another is deduction. 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. “”

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

10 Guidelines for Identifying Primitively Universal Properties CategoriesCategories On Interpretation Prior Analytics Posterior Analytics TopicsTopics Sophistical Refutations RhetoricRhetoric PhysicsPhysics MetaphysicsMetaphysics Eudemian Ethics Nicomachean Ethics... Book V Ensure property applies in individual cases. Ensure property applies in individual cases. Test kinds broader and narrower. Test kinds broader and narrower. Identify linked contraries. Identify linked contraries. Ensure the predicate can be applied broadly. Ensure the predicate can be applied broadly. Use terms that are unambiguous. Use terms that are unambiguous. Identify temporal qualifications. Identify temporal qualifications. Identify dependencies. Identify dependencies. Use language that makes clear in what way exceptions are allowed. Use language that makes clear in what way exceptions are allowed. Check relationship of whole to parts. Check relationship of whole to parts. Be clear whether relationship is absolute or relative. Be clear whether relationship is absolute or relative Use observations and comparisons to...

11 Epagōgē & Inductio in Antiquity 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. “ ” TopicsTopics On Invention Socrates Aristotle Cicero GalenStoicsEpicureansQuintilian

12 Socrates Aristotle Cicero GalenStoicsEpicureansQuintilian The Neo-Platonic Reinterpretation 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. “ ” [Definition is the] summation resulting from Division. “ ” Socrates Aristotle Cicero GalenStoicsEpicureansQuintilian Neo-Platonists Clement Alexander of Aphrodisias Simplicius Philoponus

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

14 “ a deduction from induction is deducing... ” (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 are long-lived. By (1) and (3): (1)C 1, C 2, C 3 are A. (2)C 1, C 2, C 3 are B. (3)B is C 1, C 2, C 3. (4)All B is A.

15 Socrates Aristotle Cicero GalenStoicsEpicureansQuintilian The Neo-Platonic Reinterpretation 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 better known by nature vs. better known to us prior vs. posterior prior vs. posterior knowing the fact vs. knowing the reasoned fact knowing the fact vs. knowing the reasoned fact deduction vs. induction deduction vs. induction deduction as a priori vs. induction as a posteriori deduction as a priori vs. induction as a posteriori [Definition is the] summation resulting from Division. “ ” Neo-Platonists Clement Alexander of Aphrodisias Simplicius Philoponus

16 Socrates Aristotle Cicero GalenStoicsEpicureansQuintilian al-Farabi Averroes Avicenna Peter of Spain Boethius Neo-Platonists Clement Alexander of Aphrodisias Simplicius Philoponus WilsonAldrich Zabarella AlbertAquinasScotusOckham Scholastic Transmission IsagogeIsagoge CategoriesCategories On Interpretation Prior Analytics Posterior Analytics TopicsTopics Survived in Boethius’s translations and commentaries Largely replaced by B’s On Categorical Syllogisms Largely replaced by B’s On Categorical Syllogisms Fell out of use, then lost Replaced by B’s De Topicis Differentiis Replaced by B’s De Topicis Differentiis Peter of Spain’s Tractatus Tractatus B’s Topics [In induction it] is required to suppose that he has listed all the things. “ ” 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. 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. “ ” Induction: an Enthymeme in Barbara with the minor premise suppressed.

17 Scholastic Transmission SocraticSocraticScholasticScholastic Induction: an Enthymeme in Barbara with the minor premise suppressed.

18 al-Farabi Averroes Avicenna Peter of Spain Boethius Neo-Platonists Clement Alexander of Aphrodisias Simplicius Philoponus WilsonAldrich Zabarella Buridan AlbertAquinasScotusOckham The Humanist Revolt Cicero defines induction as follows.... Boethius, who followed a different school, disagrees... “ ” Boethius acts like one who has stolen a horse and tries to hide the theft by cutting and dyeing the horse’s hair. Increase in scope Increase in scope Attention to the Topics Attention to the Topics Interest in Cicero Interest in Cicero Access to Platonic dialogues Access to Platonic dialogues Socrates Aristotle Cicero GalenStoicsEpicureansQuintilian RenaissanceHumanists VallaAgricola

19 Socrates Aristotle Cicero GalenStoicsEpicureansQuintilian al-Farabi Averroes Avicenna Peter of Spain Boethius Neo-Platonists Clement Alexander of Aphrodisias Simplicius Philoponus WilsonAldrich Zabarella Buridan AlbertAquinasScotusOckham Baconian Induction Idols: Poorly defined notiones Idols: Poorly defined notiones Concepts, not propositions Concepts, not propositions Comparisons, not enumerations Comparisons, not enumerations The predicate, not the subject The predicate, not the subject Ignited French gunpowder is hot. Ignited French gunpowder is hot. Ignited German gunpowder is hot. Ignited German gunpowder is hot. Ignited English gunpowder is hot. Ignited English gunpowder is hot. Whewell Final Cause Final Cause Material Cause Material Cause Efficient Cause Efficient Cause Formal Cause Formal Cause Harvey Regula Socratis “” Bacon RenaissanceHumanists VallaAgricola

20 HumanistHumanist Humanist Induction SocraticSocraticScholasticScholastic Induction: “Regula Socratis”

21 Scholastic Induction SocraticSocraticScholasticScholastic Induction: an Enthymeme in Barbara with the minor premise suppressed.

22 Bacon Whewell Socrates al-Farabi Averroes Avicenna Peter of Spain Boethius Neo-Platonists Clement Alexander of Aphrodisias Simplicius Philoponus WilsonAldrich Zabarella Buridan RenaissanceHumanists AlbertAquinasScotusOckham VallaAgricola Aristotle Cicero GalenStoicsEpicureansQuintilian Whately’s Revolution 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. 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. * Not the minor, as Aldrich represents it. ” [Induction is] a Syllogism in Barbara with the major* Premiss suppressed. “ [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. [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: an Enthymeme in Barbara with the major premise suppressed. Whately

23 “As Bishop Whately remarks…” Whately Mill Hamilton Hamilton Mill 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. ” “ DeMorgan DeMorgan

24 Induction as Inference Whately Mill Hamilton DeMorgan Jevons Bain ReasoningReasoning JudgmentJudgment SimpleApprehensionSimpleApprehension InferencesInferences PropositionsPropositions Notions, Terms Bacon To be purged Correct bad notions Whately Better sense Original and strict sense Mill Induction: Inferring general propositions Description is not induction DeMorgan The original and logical sense The original and logical sense The sense nowadays Bain Yes!Yes! No!No! Induction is a proceeding from particulars to a universal. Induction is a proceeding from particulars to a universal. “ ” Jevons Derivative of deduction Every induction ends with a concept Whewell ?? ??  

25 Keynes Cassirer Venn HumeHume Where’s Hume? David Hume & the “Problem of Induction” Whately Mill Hamilton DeMorgan Jevons Bain Whewell Why is a single instance, in some cases, sufficient for a complete induction, while in others myriads of concurring instances, without a single exception known or presumed, go such a very little way towards establishing an universal proposition? Whoever can answer this question... has solved the problem of Induction. Why is a single instance, in some cases, sufficient for a complete induction, while in others myriads of concurring instances, without a single exception known or presumed, go such a very little way towards establishing an universal proposition? Whoever can answer this question... has solved the problem of Induction. “ ” Fowler Note 2.—Since the time of Hume, the nature of our conception of Cause has formed one of the principal topics of philosophical controversy.... (a controversy, however, which possesses a historical rather than a practical or scientific interest). Note 2.—Since the time of Hume, the nature of our conception of Cause has formed one of the principal topics of philosophical controversy.... (a controversy, however, which possesses a historical rather than a practical or scientific interest). “ ” Presumptions in any inference: Sense perception Memory Uniformity of nature In inductive inference: Belief in uniformity of nature Various defenses: Mill’s Reid’s Hume’s Venn’s own Presumptions in any inference: Sense perception Memory Uniformity of nature In inductive inference: Belief in uniformity of nature Various defenses: Mill’s Reid’s Hume’s Venn’s own The very concept of an experimental inference involves a great petitio principii. Induction owes all its force to the premise that the future will be like the past, which is just what the induction itself seeks to infer. Hume’s sceptical criticisms are usually associated with causality; but argument by induct- ion... was the real object of his attack.... Hume’s statement of the case against induction has never been improved upon. “ ” — as Hume relentlessly insisted — “”

26 Whately’s Legacy WhatelianWhatelian Induction is about universal propositions, not universal concepts. 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. It’s a risky kind of inference to be understood with reference to the better kind, deduction. Uniformity principle is a presumed major premise. Uniformity principle is a presumed major premise. Logicians and mathematicians displace philosophers of mind. Logicians and mathematicians displace philosophers of mind. It’s about propositional inference not abstraction. It’s about propositional inference not abstraction.

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28 Correct History of Induction SocraticSocraticScholasticScholasticHumanistHumanistWhatelianWhatelian

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