BEGIN:VCALENDAR PRODID:-//Grails iCalendar plugin//NONSGML Grails iCalendar plugin//EN VERSION:2.0 CALSCALE:GREGORIAN METHOD:PUBLISH BEGIN:VEVENT DTSTAMP:20260928T225735Z DTSTART;TZID=Australia/Melbourne:20130315T110000 DTEND;TZID=Australia/Melbourne:20130315T123000 SUMMARY:Aristotle-Fine Logic UID:20260929T195101Z-iCalPlugin-Grails@fe80:0:0:0:c469:93ff:feda:b6b0%3 TZID:Australia/Melbourne LOCATION:University of Melbourne\, Parkville\, Australia\, 3010 DESCRIPTION:

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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