Doukas Kapantais

The present paper aims to show that the reconstruction of the formal framework of the proofs in Pr. An. 1.15, as proposed by Malink and Rosen 2013 (‘Proof by Assumption of the Possible in Prior Analytics 1.15’, Mind, 122, 953-85) is due to affront a double impasse. Malink and Rosen argue convincingly that Aristotle operates with two different modal frameworks, one as found in the system of modal logic presented in Prior Analytics 1.3 and 8-22, and one occurring in many of Aristotle’s works, such as the Physics, De Caelo and the Metaphysics. However, they misconstrue the latter framework. More precisely, they misconstrue the domain of significance of what they call the ‘Principle of Necessitation’. As a consequence, bringing the two frameworks into one results into a contradictory modal logic. On the other hand, if the Principle of Necessitation is rectified, the proofs put forward by Malink and Rosen in the same paper are no longer available.

Since the publication of The verb “be” in Ancient Greek by Charles Kahn, people have put a lot of emphasis and invested too much labor in all kinds of historico-philological analyses in order to resolve philosophical questions regarding the concept of existence in Greek thought. Useful as these analyses might be, they cannot provide us with conclusive answers to the specific philosophical questions under scrutiny, and, perhaps, it is time for us to abandon the overwhelming optimist motivating the pioneers behind these attempts. I use the Sophist as a case study. I conclude that whether the Form of Being represents existence or predication cannot be settled on speculation regarding the syntax of the verb εἶναι; absolute εἶναι need not be existential in meaning, and complemented εἶναι may be existential in meaning.

I argue that if one applies the standard intuitionistic criterion for truth to Kp in (p) (p&Kp), one avoids Fitch’s paradox, but with disastrous consequences having to do with the expressive resources of one’s semantics. On the other hand, if one conceives of Kp as a function recording what happens in the actual world, one gets a double benefit. First, the semantics become tolerably expressive. Second, and because of the same move, the paradox can be blocked. (The solution I provide bares resemblances with the ones proposed by Edgington 1985, 2009 and Kvanvig 1995, 2006, and especially with this latter as it has been reformulated by Brogaard and Salerno 2007). Finally, I shown that in some models for temporal intuitionistic logic (Kapantaïs 2009), and which are extensions of Beth models, (i) the knowability principle can be assumed to be valid, (ii) the paradox is blocked in the above mentioned way, and also (iii) a sentence saying that we will come to know something we now ignore becomes true and known in some worlds.