Online research in philosophy

: The traditional "doctrinal" approach to interpreting Plato's dialogues has been criticized in recent literature on grounds that it can neither account for the structural complexities of the dialogues nor resolve conflicts within or between dialogues. Accordingly, a non-doctrinal, dramatic approach has been offered in its place. In response to this literature, I argue that, though the doctrinal approach is flawed, the non-doctrinal, dramatic approach does not provide a viable alternative. Instead, I offer a revised doctrinal approach based upon Socrates' (...) discussion of "summoners" in Republic 522e–525a and supported by the Meno. (shrink)

In their book Entailment, Anderson and Belnap investigate the consequences of defining Lp (it is necessary that p) in system E as (pp)p. Since not all theorems are equivalent in E, this raises the question of whether there are reasonable alternative definitions of necessity in E. In this paper, it is shown that a definition of necessity in E satisfies the conditions { E Lpp, EL(pq)(LpLq), E pLp} if and only if its has the form C 1.C2 .... Cnp, where (...) each C iis equivalent in E to either pp or ((pp)p)p. (shrink)