EXISTENTIALISM IN PHILOSOPHICAL LOGIC IS THE DOCTRINE THAT STATES OF AFFAIRS, PROPOSITIONS AND PROPERTIES INVOLVING OBJECTS INCLUDE THESE OBJECTS AS DIRECT CONSTITUENTS IN AT LEAST THE SENSE THAT THE NONEXISTENCE IN A WORLD w OF SOCRATES, SAY, IMPLIES THE NONEXISTENCE IN w OF SOCRATES' BEING SNUB-NOSED. JOHN POLLOCK HAS RECENTLY ARGUED (IN "THE FOUNDATIONS OF PHILOSOPHICAL SEMANTICS") THAT SUCH AN EXISTENTIALISM HARBOURS AN INCONSISTENCY. THE PRESENT PAPER REBUTS POLLOCK'S ARGUMENT BY ARGUING THAT IT DEPENDS ON A CHARACTERIZATION OF EXISTENTIALISM THAT (...) EXISTENTIALISTS HAVE NO REASON TO ACCEPT, AND, INDEED, GOOD REASON TO REJECT. (shrink)

Let g E(m, n)=o mean that n is the Gödel-number of the shortest derivation from E of an equation of the form (m)=k. Hao Wang suggests that the condition for general recursiveness mn(g E(m, n)=o) can be proved constructively if one can find a speedfunction s s, with s(m) bounding the number of steps for getting a value of (m), such that mn s(m) s.t. g E(m, n)=o. This idea, he thinks, yields a constructivist notion of an effectively computable function, (...) one that doesn't get us into a vicious circle since we intuitively know, to begin with, that certain proofs are constructive and certain functions effectively computable. This paper gives a broad possibility proof for the existence of such classes of effectively computable functions, with Wang's idea of effective computability generalized along a number of dimensions. (shrink)

This paper deals with a philosophical question that arises within the theory of computational complexity: how to understand the notion of INTRINSIC complexity or difficulty, as opposed to notions of difficulty that depend on the particular computational model used. The paper uses ideas from Blum's abstract approach to complexity theory to develop an extensional approach to this question. Among other things, it shows how such an approach gives detailed confirmation of the view that subrecursive hierarchies tend to rank functions in (...) terms of their intrinsic, and not just their model-dependent, difficulty, and it shows how the approach allows us to model the idea that intrinsic difficulty is a fuzzy concept. (shrink)