Logical Equivalence

Abstract

AbstractChs. 8 and 9 convert the two basic forms of slingshot (collapsing) argument—one used by Alonzo Church, W. V. Quine, and Donald Davidson, the other by Kurt Gödel—into knock‐down deductive proofs that Donald Davidson's and Richard Rorty's cases against facts and the representation of facts are unfounded, and their slingshot arguments for discrediting the existence of facts unsatisfactory. The proofs are agnostic on key semantic issues; in particular, they assume no particular account of reference and do not even assume that sentences have references. Using this procedure, Ch. 8 shows that cleaned‐up versions of the slingshot arguments used by Davidson, Church, and Quine demonstrate theses weaker than those their authors were seeking—the impossibility of facts and non‐truth‐functional (e.g. modal and causal) connectives. This is primarily because the arguments depend upon (a) logical equivalences and (b) theories of definite descriptions (or class abstracts) that must satisfy certain semantic conditions if the aforementioned logical equivalences are to obtain. The four sections of the chapter are: Introductory Remarks; The Quinean Strategy; An Incomplete Connective Proof; and A Complete Connective Proof.