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By Pascal Massie

Properly deciding on and faithfully following his historical and sleek assets, Pascal Massie proves himself to be a skilled and loyal consultant for uncovering the ontological foundations of contingency within the worlds of Aristotle and John Duns Scotus.

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Extra info for Contingency, Time, and Possibility: An Essay on Aristotle and Duns Scotus

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It ignores the probability function that assigns values to those outcomes. p/ (I is less than zero: If any Pi = 0, then C. = 0: 1 e" = (Epj-IIIII)-IIIII-l = [Ep)'1. ]w. 1 1. 1 j J 1 If Pi '" 0, then IIp}'" I is finite. If Pi = 0, then the limit of 1lp/ al becomes infinite as Pi approaches zero and thus the limit of C. equals zero as Pi approaches zero (since one infInite factor overwhelms all finite factors). This result means then that the following different kinds of rules all have C. = 0 when (I < 0: (1) any deterministic rule, J ~ 2; (2) any biased rule with at least one non-occurring outcome; (3) any rule whose distribution is at least partially continuous.

First of all, a(2-a)j(a-1)2 > -1, which implies that [a(2-a)j(a-1)2]p+/, > -P+/'. Secondly, we have LjP +/' JPH ~ LjP +/' ~ P +/'. JP+j") IP i .. > -P+j +" P+j (u-l) j = 0, so that a 2(f, .. japi/ > 0 for all (i,j). Thus the critical value is a minimum. The same results hold for u = 1. Taking the logarithm of Ch we have lnC1(S) = E E Pi+Pjli lnPjli = E E Pij(lnPij -lnPiJ i j i j (where we ignore any Pij = 0). Given ~l = lnC1(S) - ~ AI+(~>ij-PI+) - ~ A+j(~Plj-P++ we obtain a(f,ljapij = In (Pt/PH) + 1- AH - A+i .

S' such that each system in the derivation is immediately derived from its immediate predecessor. When S' is immediately derived from S (by splitting up the rule Rm into {R ml ,Rm2 , ... ,Rmk , ... 8 The Effect on Certainty of Splitting up a Rule WE now show that if a system S' is immediately derived from a system S, then C.. (S') :?! C.. (S), with equality holding only when Pmkj = Pmk+ 'Pmj for all (k,j). The proof of this relationship is virtually identical to the proof that C .. (S) :?! C..

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