This tightly-written and self-contained four-page paper must be studied and not just skimmed. It meticulously analyses quotations from Aristotle and Lukasiewicz to establish that Aristotle was using indirect deductions—as required by the natural-deduction interpretation—and not indirect proofs—as required by the axiomatic interpretation. Lukasiewicz was explicit and clear about the subtle fact that Aristotle’s practice could not be construed as correctly performed indirect proof. Lukasiewicz evidence is presented fully; it is irrefutable. But, instead of considering the possibility that Aristotle’s discourses were not intended to express indirect proofs of universalized conditions presupposing axiomatic premises, Lukasiewicz came to the amazing conclusion that Aristotle did not understand indirect proof.
This paper builds on the admirable Lukasiewicz scholarship to establish a conclusion diametrically opposed to the one Lukasiewicz asserted.
Article Aristotelian Syllogisms: Valid Arguments or True Universaliz...
Well, there is a paper from 1972 by the same author, this Corcoran-something-or-other, who also published (if memory serves) several other papers on ancient logic and who had a hand in the publication of e.g., a 2008 paper from the journal History and Philosophy of Logic (Andrade, E. J., & Becerra, E. S. (2008). Establishing connections between Aristotle's natural deduction and first-order logic. History and Philosophy of Logic, 29(4), 309-325.). I would suggest, Dr. Corcoran, that you try reading some of Corcoran's work. It's rather brilliant.
Other than Martin, I didn't know many other works that refer directly to your own in terms of critiquing Łukasiewicz here, but am curious why you don't here, as (mostly) elsewhere, you don't use Łukasiewicz' own motivation for his work as well as the only place in Aristotle where we find anything on defining a universal protasis, i.e., De Interpretatione (you relegate to a parenthetical "but cf." statement Aristotle's work here in e.g., "Aristotle's natural deductive system" in the volume you edited Ancient Logic and its Modern Interpretations, where you refer to chap. 1 of De Intpretatione while Łukasiewicz' 1957 (2nd Ed.) classic points out that chap. 1 is a contradiction of Aristotle's clear usage in chapter 7; he also supports his interpretation by citing Alexander's commentary, esp. "κατὰ γὰρ αἰσθητοῦ καὶ ἑνὸς κατ’ ἀριθμὸν οὐκέθ’ ἁρμόζει τὸ κατὰ παντὸς οὐδὲὁ διορισμὸς ὅλως"; I'm assuming you can read ancient Greek but if not I will provide my translation of the above).
Interestingly, in Aristotle's Theory of Syllogism by Patzig Lukasiewicz is criticized for his interpretation of the relevant section from De Interpretatione because of Aristotle's contradiction, despite the fact that Lukasiewicz notes this feature: "No doubt, the traditional interpretation which Lukasiewicz attacks is compatible with the letter of our passage. But our review of the other relevant texts has shown that this reading makes Aristotle not only err, but actually contradict himself. In such circumstances (by Uberweg's maxim, cf. p. 122) we must always prefer the interpretation which both squares with the text and frees Aristotle from the charge of inconsistency.
What logical laws does Aristotle use in this reduction? Again, as in the case of conversion, he presupposes certain logical principles, some of which belong to predicate and some to propositional logic. He twice uses the fact that AaB and AoB are contradictories. Here he cannot refer back to introductory remarks in the Analytics itself as he did in the case of conversion. He tacitly assumes that the reader knows the relevant passages in De Interpretatione (chapters 7 sqq.)."
Thus it seems important to address (as Haack does in Deviant Logics) the basis for Lukasiewicz's many-valued logic including his treatment of syllogisms as it rests on the interpretation of (ironically) De Interpretatione. Haack is of course critical here, not that Lukasiewicz is wrong in his interpretation of Aristotle but of Aristotle and any many-valued logic based upon Aristotle's treatment of "universals" or many-valued logic rooted in the relevant sections of in De Int. It is in this section that Lukasiewicz uses Aristotle most for his argument that Aristotle failed and for his many-valued (modal or proto-modal) logic.
- Badges
- Science topic
- Similar topics
- Philosophy
- Esthetics
- Interpretation