Aristotle-Fine Logic
Tomasz Kowalski (La Trobe University)

March 15, 2013, 3:00pm - 4:30pm
School of Historical and Philosophical Studies, University of Melbourne

Common Room, Old Quad
University of Melbourne
Parkville 3010
Australia

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In "Aristotle's Megarian Maneuvers" (forthcoming in Mind),
Kit Fine argues that Aristotle's propositional modal logic should be
identified with the logic he calls KP2D, where K and D are what you
expect, and P2 is (p & -q) (p & -q). He shows, among many
other things, that KP2D is (1) reductive (any nested occurrence of a
modality is equivalent to a non-nested one), and (2) strongly
anti-Megarean (any consistent non-modal formula constitutes a genuine
possibility). In an earlier draft of the article, Fine stated that
there were precisely two normal logics having the properties above,
namely, S5 and his Aristotelian system. I pointed out in an email
conversation that because of a subtlety involving D in fact there were
four. (To my grateful surprise, Fine gives me credit for this little
observation.) So, we have:

Theorem. There are precisely 4 reductive and strongly anti-Megarean
normal modal logics: S5, S5 x Ver, KP2D, KP2 (= KP2D x Ver).   

I will sketch a proof and, time permitting, say something more on the
similarities between S5 (S5 x Ver) and KP2D (KP2).

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