The Research Centre for Greek Philosophy at the Academy of Athens

Invites you in the course of the Monthly Philosophy Seminar

to the lecture which will take place on

**Wednesday 6 December 2023,** **16:00-18:00 (ATH, GR timezone).**

Speaker: **Marko Malink**, Professor of Philosophy at New York University,

Topic: **Aristotle on ***reductio ad impossibile*: from dialectic to syllogistic logic

Those interested may attend via Zoom.

**ABSTRACT**

**Aristotle on ***reductio ad impossibile*: from dialectic to syllogistic logic

Marko Malink (New York University)

The method of *reductio ad impossibile *plays an important role in Aristotle's logical writings. I argue that Aristotle countenances two different conceptions of the method. One is a dialectical conception which is found, e.g., in *Topics *8.2 and *Prior Analytics *2.11-13. The other is a formal conception which is found, e.g., in *Prior Analytics *1.5-7 and 2.14. I will explore how the two conceptions of *reductio *differ from one another, and why Aristotle prefers to employ the one or the other in a given context. I argue that transitioning from the dialectical to the formal conception is key to his argument in *Prior Analytics *2.14 that everything derivable by *reductio *can be derived by means of a direct deduction.

The Research Centre for Greek Philosophy at the Academy of Athens

Invites you in the course of the Monthly Philosophy Seminar

to the lecture which will take place on

**Wednesday 15 November 2023,** **16:00-18:00 (ATH, GR timezone) at the Elli Lambridis Philosophical Library (9 Hypsilantou str., Athens)**.

Speaker: **Michel Crubellier**, Emeritus Professor of Philosophy at the University of Lille,

Topic: **How is it possible to claim that every ****συλλογισμός ****is a syllogism?**

Those interested may attend either in person or via Zoom.

**ABSTRACT**

I intend to examine and – to some extent – vindicate two important claims made by Aristotle at the outcome of the two main theoretical elaborations of Prior Analytics Book 1, namely the ‘Syllogistic’ (1.1-7) and the Pons Asinorum (1.27-30):

‘Every deduction (συλλογισμός) must necessarily come about through the three figures described above’ (1.23, 41b1-3)

‘It is evident (…), not only that it is possible for all deductions (συλλογισμοί) to come about through this route [= the machine of the Pons Asinorum], but also that this is impossible through any other’. (1.29, 45b36-38)

These claims are often criticized as being exceedingly confident; the more so if – as I think we should – one does not take συλλογισμός in the sense of the specific forms of argument (figures and ‘moods’) discussed in chapters 1.4-7, but in its broader dialectical sense, meaning any compelling argument based on explicitly assumed premises. For it seems that there are many kinds of arguments which cannot fit in with the models introduced in the Syllogistic or in the Pons Asinorum section: suffice it to mention proofs by reduction to impossibility and most mathematical, especially geometrical, proofs.

However, Aristotle himself explicitly mentions some such cases in the very chapters in which he argues for those two claims: he declares that he has, or at least aims at and discerns, a solution for the case of proofs by reduction, and he uses mathematical examples in order to illustrate his views. The notion that he could have considered that such cases were but unimoprtant exceptions seems very hard to swallow.

So, the aim of this presentation, centered mainly on the first claim and on chapter 1.23, is to look more closely at the passages in which he mentions these cases in order to grasp better how he could have apprehended them (using part of that time for the discussion of mathematical examples).

I will reach the conclusion that both claims are much more defensible than it is commonly said, if we can reconsider and flesh out our understanding of some of the basic terms in which he addresses the problem and of its inscription in a dialectical perspective. Notably, I suggest understanding some concepts (for instance ὑπάρχει τῷ Α, or ὅρος) in a sense broader than that in which they are usually taken, but in my view they must not become vague or confused.

However, the effectivity of that solution remains uncertain in the case of ‘deductions fom assumption’.

As a side-lesson of that first conclusion, I will end with a reflection on the heuristic value of the Pons Asinorum machine and its limits, and on the epistemological meaning of the second claim.

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The Research Centre for Greek Philosophy at the Academy of Athens

Invites you to the first meeting

of the Monthly Philosophy Seminar for the academic year 2023-2024

which will take place on

**Wednesday 25 October 2023,** **16:00-18:00 (ATH, GR timezone) at the Elli Lambridis Philosophical Library (9 Hypsilantou str., Athens)**.

Speaker: **Doukas Kapantais**, Research Director at the RCGPh,

Topic: **Prior Analytics 1.23; an elimination theorem to avail the scientist and the dialectician alike**.

** **** **

** ****ABSTRACT**

I apprehend the *Prior Analytics *not as a treatise about a single “formal” theory but as a treatise on the deductive interplay between two such theories: (i) what Corcoran, Smiley and others have identified as the Syllogistic, and (ii) the fourteen syllogisms of the scholastics. The metatheory exploring their properties and deductive interaction is a contentual theory containing (primarily) the *dicta*, a pretheoretical *reductio ad impossibile *rule, and the square of opposition.* *The above interplay–I claim–culminates in the construction of the algorithmic *apparatus* in 1.28 aimed at availing both scientists and dialecticians. I take stock of some puzzling claims by Aristotle according to which whatever can be proved by *reductio ad impossibile *can also be proved ostensively. I argue that apprehending the content of the *Prior Analytics *that way vindicates these claims.

**FULL SCHEDULE**

**October 25, Doukas Kapantaïs**

Prior Analytics 1.23; an elimination theorem to avail the scientist and the dialectician alike

**November 15, Michel Crubellier**

How is it possible to claim that every συλλογισμός is a syllogism?

**December 6, Marko Malink**

Aristotle on reductio ad impossibile: from dialectic to syllogistic logic

**January 17, Christof Rapp**

Reasonableness of Argument and strategic maneuvering in Topics VIII

**February 28, Mathieu Marion**

Semantics of Interaction: A New Perspective on the relation between Topics and Prior Analytics

**March 20, Paolo Fait**

How can the investigation of demonstration and demonstrative science (Prior Analytics 1.1 24a10–11) accommodate dialectical syllogisms?

**April 3, Gisela Striker**

The place of dialectic in Aristotle's Prior Analytics

**May 15, Laura Castelli**

Universal premises in the Topics

**May 29, Colin G. King**

Language formalization in the Topics and the Prior Analytics

**June 12, Zoe McConaughey**

Syllogistic and dialogues

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**Επετηρίς του Κέντρου Ερεύνης της Ελληνικής Φιλοσοφίας**
**Περιοδικό "Διοτίμα"**
**THALIS PROJECT**

- Dr. Maria Protopapa-Marneli
- Dr. Doukas Kapantaϊs
- Apostolos N. Stavelas