1. See generally THE OLDER SOPHISTS (Rosamund Kent Sprague ed. lst ed. 1972).
2. See generally MORRIS R. COHEN & ERNEST NAGEL, AN INTRODUCTION TO LOGIC AND SCIENTIFIC METHOD (1st ed. 1934).
3. See generally BENSON MATES, STOIC LOGIC (1961).
4. For example, syllogistic inference was originally criticized because it was not a logic of discovery as the logic of experimentation and the logic behind formalized algebraic reasoning was understood to be; today, it is understood to be a limited logic restricted to the subject-predicate relation. The logic of experimental science is now regarded as "applied logic," a peculiar reinterpretation of the scholastic distinction between formal and material logic, which may itself have been a reinterpretation of the proper distinction between the Prior and Posterior Analytics of Aristotle.
5. In order for us to claim that we understand a technical writing of past times, the minimum criterion ought to be that we can give a reason why the writer chose the terminology that he did. By this standard, the logical writings of Aristotle are among the least well understood of all. Take as an example one of the terms he employs to characterize both the conclusion of a syllogism as well as the inferential process itself—namely, the noun sumperasmos and the verb sumperainesthai. If we attend only to the roots of this word, it could mean one of four things: 1) the joint delimitation of the conclusion by the premises; 2) the joint completion or perfection of the conclusion by the premises; 3) the absolute delimitation of the conclusion by the premises; or 4) the absolute completion of the conclusion by the premises. In order to really understand Aristotle's inferential procedure, to look over his shoulder and see it as he saw it, we would have to explicate clearly how one of these four possibilities applies. The Latin word conclusio, from which we get our word `conclusion', represents a judgment as to one of these four meanings. It concretely means `shutting or closing in', and effectively corresponds to meaning 1) cited above. Now, I am fairly convinced that this is the incorrect meaning, though it at least has the virtue of making a clear decision. For us, the word `conclusion' has no longer such a concrete meaning, and we only understand it in a general way as the result of an inferential procedure. There are numerous other examples of such puzzling language throughout the works collectively known as the Organon, the most notable of which is the word analutikos, or `analytic'. In fact, Aristotle himself often refers to the works known to us as the Prior and Posterior Analytics as "The Analytics" (ta analutika). In my opinion, no one has ever satisfactorily explained why ta analutika is a suitable title for the works in question, and thus one might reasonably conclude that we do not really know what the books are about. Several of these technical logical terms will be explicated in the course of this paper. A word of caution for those attempting to read Aristotle's logical writings in English translation: In general, these are among the worst translations of any ancient writings, primarily because modern logical terminology is anachronistically projected back on them.
6. See Jacob Klein's GREEK MATHEMATICAL THOUGHT AND THE ORIGIN OF ALEGEBRA (Eva Brann trans., M.I.T. Press 1968) for a discussion of the fundamental shift in the intentionality belonging to mathematical and scientific concepts that took place in the late Renaissance, in particular, the development of symbol generating abstraction. See id. at 117-25.
7. An enthymeme is so called presumably because it appeals to thumos, the seat of the emotions, not because it is a defective syllogism as some definitions purport.
8. Porphyry in his commentary on this work defends Aristotle against the criticism that he is using a non-standard Greek word to explicate a "simple" idea like predication. This is itself an indication that Aristotle must have chosen this word very deliberately, and that we should pay considerable attention to its root meaning. Unfortunately, Porphyry does not go on to show how Aristotle's unprecedented characterization of the conclusion to a syllogism gives us any more concrete insight into the inferential process.
9. I should mention that in numerous writings Heidegger tries to attribute the term apophainesthai to the phenomena being spoken about rather than the opinion expressed by a speaker, citing this very passage. According to his view, language lets the phenomena show themselves forth, and this is why Aristotle characterizes it as apophantic. Although I think that Heidegger's view of the disclosive power of language is profound, it is not clear that he can project it back on Aristotle with the authority of this passage.
10. See ARISTOTLE, METAPHYSICS 1017a 23-34 (Oxford Classical Edition, Oxford Univ. Press).
11. See ARISTOTLE, POSTERIOR ANALYTICS 72a 8-14 (Oxford Classical Edition, Oxford Univ. Press).
12. See ARISTOTLE, PRIOR ANALYTICS 24b16-17 (Oxford Classical Edition, Oxford Univ. Press).
13. The prefix apo in the Greek work apodeixis means 'from'.
14. This procedure was lampooned by a later comic playwright who has Plato defining man as 'a featherless biped with flat nails.'
15. Francis Bacon, The Great Instauration in THE NEW ORGANON AND RELATED WRITINGS 25 (F.H. Anderson ed., Bobbs-Merill 1960).
16. Francis Bacon, Aphorism I, in THE NEW ORGANON AND RELATED WRITINGS 273 (F.H. Anderson ed., Bobbs-Merill 1960).
17. Francis Bacon, Aphorism V, in THE NEW ORGANON AND RELATED WRITINGS 277-78 (F.H. Anderson ed., Bobbs-Merill 1960).
18. Francis Bacon, Preparative toward a Natural and Experimental History in THE NEW ORGANON AND RELATED WRITINGS 284 (F.H. Anderson ed., Bobbs-Merill 1960).
19. The connection between proof and torture is also well established in Greek legal terminology with the word basanos, which originally means the touchstone or procedure for determining the genuineness of gold, but comes to be applied to legal inquiries conducted by torture. Cf. ARISTOTLE, RHETORIC 1355b 37-38; 1375a 22-24 (Oxford Classical Edition, Oxford Univ. Press).
20. Francois Viète, Introduction to the Analytic Art (J. Winfree Smith trans.), in JACOB KLEIN, GREEK MATHEMATICAL THOUGHT AND THE ORIGIN OF ALGEBRA 328 (Eva Brann trans. M.I.T. Press 1968).
21. JOHN WALLIS, A TREATISE OF ALGEBRA 66 (London, Oxford Univ. Press 1685).
22. See Viète, supra note 20, at 322-24.
23. There are other historical instances of the legal paradigm being invoked to clarify fundamental logical questions. For example, at a crucial moment in the articulation of his transcendental logic, when he needs to validate the use or "objective validity" of the pure concepts of the understanding in human knowledge, Kant adverts to a legal metaphor:
| Jurists, when speaking of rights and claims, distinguish in a legal action the question of right (quid juris) from the question of fact (quid facti); and they demand that both be proved. Proof of the former, which has to state the right or the legal claim, they entitle the deduction. Many empirical concepts are employed without question from anyone. Since experience is always available for the proof of their objective reality, we believe ourselves, even without a deduction, to be justified in appropriating to them a meaning, an ascribed significance. But there are also usurpatory concepts, such as fortune, fate, which, though allowed to circulate by almost universal indulgence, are yet from time to time challenged by the question: quid juris. This demand for a deduction involves us in considerable perplexity, no clear legal title, sufficient to justify their employment, being obtainable either from experience or from reason.
Now among the manifold concepts which form the highly complicated web of human knowledge, there are some which are marked out for pure a priori employment, in complete independence of all experience; and their right to be so employed always demands a deduction. For since empirical proofs do not suffice to justify this kind of employment, we are faced by the problem how these concepts can relate to objects which they yet do not obtain from any experience. The explanation of the manner in which concepts can thus relate a priori to objects I entitle their transcendental deduction; and from it I distinguish empirical deduction, which shows the manner in which a concept is acquired through experience and through reflection upon experience, and which therefore concerns, not its legitimacy, but only its de facto mode of origination. |
24. To complete the symmetry here, we might add that astrology and divinatory practices in general may be understood to deal with events as inherently future. When dealing with events of the past or present, astrologers treat them as if they could have been predicted.
25. Most of the following treatment of historical science is derived from an essay by Jacob Klein called "History and the Liberal Arts. " See Jacob Klein, History and the Liberal Arts, in LECTURES AND ESSAYS 127-38 (Robert B. Williamson & Elliott Zuckerman eds., St. John's College Press 1985).
26. Arch
, usually translated as "principle" was often rendered by Jacob Klein as "ruling beginning" or "commanding origin" to bring out a sense which we no longer notice in the Latin derived word. 27. See ARISTOTLE, supra note 19, at 1365b 30-38.
28. See ARISTOTLE, supra note 11, at 43a 25-44.
29. Cf. BENEDICTUS DE SPINOZA, THE PRINCIPLES OF DESCARTES' PHILOSOPHY 14 (Halbert Hains Britan trans., Open Ct. Pub. Co. 1961).
30. The overall context of Descartes' Meditations and the hypothetical character of the Cogito argument raise the interesting question whether the logic for removing doubt is the same as the demonstrative logic of persuasion.
31. Another example might be Kant's claim in the CRITIQUE OF PURE REASON that the pure concepts of the understanding (that is, the categories) have objective validity, or a necessary relation to objects; for otherwise, any knowledge whatsoever would be impossible. And in fact, if one is on the way toward (rather than away from) first principles, which is how Plato characterized philosophical inquiry, one must reason hypothetically, since the more general or higher ranking entities that could insure a regular syllogism have not yet been secured.
32. Unfortunately, this type of syllogism has played too great a role in logical discussions, with the ubiquitous "All men are mortal; Socrates is a man: therefore Socrates is mortal." This syllogism is atypical and does not appear in Aristotle. As I said earlier, Aristotle exemplifies his syllogisms in the PRIOR ANALYTICS by drawing from the intermediate level of predication, not the lowest or highest levels. Anyone who takes the trouble to read Aristotle's works, particularly in Greek, will get a quite different impression about his real concerns.
33. See ARISTOTLE, supra not 11, 70a 3-6.
34. For example, Aristotle treats Plato's method of dichotomous division for the purpose of arriving at definitions as a kind of weak syllogism.
35. To put this a little more accurately, Aristotle says that hypothetical syllogisms cannot be analyzed.
36. Laplace, one of the founders of the mathematical theory of probability, is famous for the statement that probability is nothing but common sense reduced to calculation.
37. This kind of inquiry into concept formation was first pioneered by Jacob Klein in his Greek Mathematical Thought and the Origin of Algebra. That work concerns the transformation of the number concept that took place in the late Renaissance. Klein explains how modern concept formation is the result of a self-conscious opposition to the concepts of an existing science (namely, that of the Scholastics), whereas concept formation in Greek thought was the result of an opposition to the concepts of everyday life. See KLEIN, supra note 6, at 117-25. In both cases, the new concepts retain a kind of "ruptured" relationship to the original concepts to which they are set in opposition. Klein considers the transformation of the number concept to be the most representative instance, although in other writings he also follows out analogous transformations in the concepts of physics. For the most part Klein simply diagnoses these concept shifts. However, I believe that the study of concept formation in the history of logic actually gives us insight into the historical process of the history of ideas itself, as I will indicate in the upcoming conclusion.