For a very long time truth-value gaps were under a cloud of suspicion because they were considered logically unmanageable. So Frege declared that:“as regards concepts we have a requirement of sharp delimitation; if this were not satisfied it would be impossible to set forth logical laws about them”.Three-valued logic promised to dispel the cloud but in the eyes of many it had promised more than it could deliver. So in response to Reichenbach's plea for a three-valued quantum logic Russell replied:“This (...) is one of a number of questions as to which I am prevented from accepting a certain view by difficulties in carrying it out, but am prepared to alter my opinion if technical skill supplies an answer to my difficulties”.‘By now technical skill has supplied many alternative systems of three-valued logic, but few answers and numerous additional difficulties.’. (shrink)

It seems generally agreed that a theory of sensory episodes that mentions sensory objects and a sensing relation — the ‘act-object’ theory — is unacceptable and should be replaced by some other account. A chief competitor is the Adverbial Theory, and one of its chief advocates is Wilfrid Sellars. While it is clear that there are serious difficulties for the act-object theory not facing the adverbial theory, I will argue that the latter has difficulties of its own.

This paper contains an axiomatic theory of first order modal logic with operations, identity, and descriptions together with a formal semantics which interprets the theory in such a manner that empty universes of discourse and denotationless terms are allowed for at each possible world. The intuitive basis of the theory is discussed in preliminary sections, the syntax and semantics of theory are then characterized, its semantical adequacy is demonstrated, and certain important axioms and theorems are discussed in detail in later (...) sections. (shrink)