Three views on definite descriptions are summarized and discussed, including that of P. F. Strawson in which reference failure results in lack of truth value. When reference failure is allowed, a problem arises concerning Universal Instantiation. Van Fraassen solves the problem by the use of supervaluations, preserving as well such theorems as a=a, and Fa Fa, even when the term a fails to refer. In the present paper a form of relevant, quasi-analytic implication is set out which allows reference failure (...) to infect even a=a and Fa Fa with lack of truth-value. Reference failure causes lack of truth-value in a subwff to spread throughout any wff built up by the classical connectives. As a result none of the classical firstorder axiom schemes remain as axiom schemes in the system presented. (shrink)
<span class='Hi'></span> In <span class='Hi'></span>[2]<span class='Hi'></span> a semantics for implication is offered that makes use of stories <span class='Hi'></span>— sets of sentences assembled under various constraints.<span class='Hi'></span> Sentences are evaluated at an actual world and in each member of a set of stories.<span class='Hi'></span> A sentence B is true in a story s just when B s.<span class='Hi'></span> A implies B iff for all stories and the actual world,<span class='Hi'></span> whenever A is true,<span class='Hi'></span> B is true.<span class='Hi'></span> In this (...) article the first-order language of <span class='Hi'></span>[2]<span class='Hi'></span> is extended by the addition of the operator the story <span class='Hi'></span>..<span class='Hi'></span>. says that <span class='Hi'></span>..<span class='Hi'></span>.,<span class='Hi'></span> as in The story Flashman among the Redskins says that Flashman met Sitting Bull.<span class='Hi'></span> The resulting language is shown to be sound and complete. (shrink)
In this paper a system, RPF, of second-order relevance logic with S5 necessity is presented which contains a defined, notion of identity for propositions. A complete semantics is provided. It is shown that RPF allows for more than one necessary proposition. RPF contains primitive syntactic counterparts of the following semantic notions: (1) the reflexive, symmetrical, transitive binary alternativeness relation for S5 necessity, (2) the ternary Routley-Meyer alternativeness relation for implication, and (3) the Routley-Meyer notion of a prime intensional theory, as (...) well as defined syntactic counterparts, of the semantic notions of a possible world and the Routley-Meyer * operator. (shrink)
