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Aristotelian syllogistic logic incorporates proofs by contradiction.
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Scholarly literature and reference sources covering Aristotle's Prior Analytics and syllogistic logic discuss methods of indirect proof and reduction akin to proofs by contradiction.

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The Place of Reduction in Aristotle's Prior Analytics: History and Philosophy of Logic: Vol 46, No 1 ## Abstract Studies of Aristotle’s syllogistic system, since Corcoran’s deductionist interpretation supplanted Łukasiewicz’ axiomaticist interpretation, misrepresent Aristotle’s logic in two important respects. Following Corcoran, they take indirect deduction to occur only once in a deduction discourse; they then obviate the system having a reductio rule. Second, they represent reduction as a deductive process for deriving ‘imperfect’ syllogisms from ‘perfect’ syllogisms to impose an axiomatic interpretation on the logic. Denying that Aristotle's logic admits of a reductio rule results from this misrepresentation of reduction. This discussion shows that the defects imputed to Aristotle's logic, and systems devised to resolve them, result from misunderstanding reduction, which itself results from misapprehending Prior Analytics expressly to identify in a metadiscourse deduction rules and not deductions per se. KEYWORDS: ## Disclosure statement No potential conflict of interest was reported by the author(s). ## Notes 1 An underlying logic (Church Citation1956) falls within the
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Nested Indirect Proofs in Aristotle’s Deductive Logic | Studia Logica | Springer Nature Link ## Your privacy, your choice We use essential cookies to make sure the site can function. We also use optional cookies for advertising, personalisation of content, usage analysis, and social media, as well as to allow video information to be shared for both marketing, analytics and editorial purposes. By accepting optional cookies, you consent to the processing of your personal data - including transfers to third parties. Some third parties are outside of the European Economic Area, with varying standards of data protection. See our privacy policy for more information on the use of your personal data. Manage preferences for further information and to change your choices. Accept all cookies Reject optional cookies # Nested Indirect Proofs in Aristotle’s Deductive Logic - Open access - Published: 18 February 2026 - (2026) - Cite this article You have full access to this open access article Download PDF Save article View saved research Studia Logica Aims and scope ## Abstract Aristotle’s Analytica Priora contains three systems of syllogistic proof, what are known as ‘figures’
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  1. The Place of Reduction in Aristotle's Prior Analytics: History and Philosophy of Logic: Vol 46, No 1referenceno side taken
  2. Nested Indirect Proofs in Aristotle’s Deductive Logic | Studia Logica | Springer Nature Linkreferenceno side taken
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