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This number of newly comissioned essays via foreign members bargains a consultant evaluate of an important advancements in modern philosophical logic.

•Presents controversies in philosophical implications and purposes of formal symbolic common sense.

•Surveys significant traits and provides unique insights.

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The medieval theories as to the truth of propositional combinations of terms – categorical predications – vary. According to one theory, the (extensional) identity theory, the proposition [S is P] is true when the supposition of both terms is the same, that is, when both terms stand for the same entity. Thus, for instance, the predication [Sortes is a man] is true when [Sortes] and [man] both supposit for the same entity, namely Socrates. The main rival of the identity theory of truth is the (intensional) inherence theory.

If I point to Dion and say ‘He is alive,’ then I utter a proposition the subject of which is fixed by a demonstrative (in modern terms, an indexical). However, if Dion dies, then I can no longer point to Dion at all, since he does not exist; therefore, the proposition that was formerly expressed by ‘He is alive’ also ceases to exist rather than becoming false. Now, Chrysippus offers for consideration the proposition ‘If Dion has died, then this one has died’ (pointing to a living Dion, obviously).

If the first then the second; not the first; therefore not the second. Not both the first and the second; the first; therefore not the second. Either the first or the second; the first; therefore not the second. Either the first or the second; not the first; therefore the second. The Stoics then demonstrated the validity of other valid arguments by means of these indemonstrables (unfortunately, our knowledge of their views is very fragmentary: see Kneale and Kneale 1978; Mates 1953; Mueller 1978 for reconstructions).

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