The Law of Excluded Middle

Abstract

“QC(w)” is according to TP71 equivalent to “MX(w),” this, in turn, according to DP25, is equivalent to “all x(xPw or neg(x)Pw),” this, in turn, according to DP31, to “all x[O(x) or O(neg(x))],” and this, in turn, according to DP32 and DP33, equivalent to “all x(V(x) or F(x))” — “every state of affairs is true or false.” All the mentioned equivalences hold true analytically with respect to states of affairs on the basis of the posited definitions, given that AP1 — AP6 are analytically true for states of affairs (“tPt′” being synonymous with “t is analytically implied by t′”). Consequently, we have in particular the analytical truth of “QC(w) iff all x[O(x) or O(neg(x))].”