Myths in the History of Induction John P. McCaskey Stanford University

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

Prior Analytics B 23 Induction then is—or the from-induction deduction— deducing one extreme [to belong] to the middle through the other extreme. Induction then is—or 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. Late 13 th century Byzantine manuscript. Princeton MS ” “ ” “

Conventional Reading of “a deduction from induction ” (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.

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 [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. “

Mentions of epagoge in Aristotle’s Works All professions... “ ” All wise men... All irresponsible custodians... All professions... All wise men... All irresponsible custodians... “ ” All causal interactions... All instances of contrariety... All causal interactions... All instances of contrariety... “ ” All instances of goodness... “ ” CategoriesCategories On Interpretation Prior Analytics Posterior Analytics TopicsTopics Sophistical Refutations RhetoricRhetoric PhysicsPhysics MetaphysicsMetaphysics Eudemian Ethics Nicomachean Ethics...

A Non-Mention of epagoge in Aristotle’s Works Scalene triangles... Isosceles triangles... Equilateral triangles... Therefore all triangles. Scalene triangles... Isosceles triangles... Equilateral triangles... Therefore all triangles. “ ” CategoriesCategories On Interpretation Prior Analytics Posterior Analytics TopicsTopics Sophistical Refutations RhetoricRhetoric PhysicsPhysics MetaphysicsMetaphysics Eudemian Ethics Nicomachean Ethics...

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

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. “ ”

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

Guidelines for Identifying Characteristics Distinguishing by Nature CategoriesCategories On Interpretation Prior Analytics Posterior Analytics TopicsTopics Sophistical Refutations RhetoricRhetoric PhysicsPhysics MetaphysicsMetaphysics Eudemian Ethics Nicomachean Ethics... 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 Book V Use observations and comparisons to...

Two Conceptions of Induction 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 23 misunderstood A kind of inference inferior to deduction. Positive instances determine reliability. Particulars and universals are primarily propositions 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. Topics Posterior Analytics Socrates Not an inference and not inferior to deduction. Breadth and depth of comparisons determine reliability. Particulars and universals are primarily things, concepts, or terms.

Transmission Aristotle Socrates

Cicero Aristotle Socrates 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. “ ” TopicsTopics On Invention

Epagōgē & Inductio in Antiquity Aristotle Socrates Cicero GalenStoicsEpicureansQuintilian

The Neo-Platonic Reinterpretation Aristotle Socrates Cicero GalenStoicsEpicureansQuintilian First to suggest that induction gains its force by a complete enumeration of particulars. 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 posterioriNeo-Platonists Clement Alexander of Aphrodisias Simplicius Philoponus

Arabic Transmission Aristotle Socrates Cicero GalenStoicsEpicureansQuintilian Neo-Platonists Clement Alexander of Aphrodisias Simplicius Philoponus al-Farabi Averroes Avicenna IsagogeIsagoge CategoriesCategories On Interpretation Prior Analytics Posterior Analytics TopicsTopics Syriac & then Arabic study of the Organon 6 th c. → 12 th c

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

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

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

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

Aristotle Socrates Boethius Scholastic Philosophers Neo-Platonists Clement Alexander of Aphrodisias Simplicius Philoponus al-Farabi Averroes Avicenna Wilson Zabarella Peter of Spain AlbertAquinasScotusOckham Cicero [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. “ ” 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 Formal vs. material reduction to syllogism Formally valid vs. materially valid Formally valid vs. materially valid Regular induction vs. abstraction Regular induction vs. abstraction Regular induction vs. demonstrative induction Regular induction vs. demonstrative induction Use of “et cetera” 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. 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. 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. “ ”

Aristotle Socrates Boethius John Buridan: The First Challenge Neo-Platonists Clement Alexander of Aphrodisias Simplicius Philoponus al-Farabi Averroes Avicenna Wilson Zabarella Peter of Spain AlbertAquinasScotusOckham Cicero Buridan

Aristotle Socrates Boethius The Humanist Revolt Neo-Platonists Clement Alexander of Aphrodisias Simplicius Philoponus al-Farabi Averroes Avicenna Wilson Zabarella Peter of Spain AlbertAquinasScotusOckham Cicero Buridan RenaissanceHumanists 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 VallaAgricola 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. “ ” Cicero defines induction as follows.... Boethius, who followed a different school, disagrees... “ ”

Aristotle Socrates Cicero Baconian Induction Neo-Platonists Clement Alexander of Aphrodisias Simplicius Philoponus al-Farabi Averroes Avicenna Wilson Zabarella Peter of Spain AlbertAquinasScotusOckham Buridan Boethius Idols Idols 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 RenaissanceHumanists VallaAgricola Bacon

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

Mill Aristotle Socrates Cicero “ As Archbishop Whately remarks... ” Neo-Platonists Clement Alexander of Aphrodisias Simplicius Philoponus al-Farabi Averroes Avicenna Wilson Zabarella Peter of Spain AlbertAquinasScotusOckham Buridan Boethius Whewell RenaissanceHumanists VallaAgricola Bacon Whately 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. ” “ 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. ”

Two Conceptions of Induction Aristotle Socrates Cicero Bacon Whewell MillWhately al-Farabi Averroes Avicenna Peter of Spain Boethius Neo-Platonists Clement Alexander of Aphrodisias Simplicius Philoponus GalenStoicsEpicureansQuintilian Wilson Zabarella Buridan RenaissanceHumanists AlbertAquinasScotusOckham VallaAgricola

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

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

Two Conceptions of Induction Aristotle Socrates Cicero Bacon Whewell MillWhately al-Farabi Averroes Avicenna Peter of Spain Boethius Neo-Platonists Clement Alexander of Aphrodisias Simplicius Philoponus GalenStoicsEpicureansQuintilian Wilson Zabarella Buridan RenaissanceHumanists AlbertAquinasScotusOckham VallaAgricola