ABSTRACT
This chapter analyses the problem of defining significance, having seen the failures of complete verifiability and complete falsifiability as bases for appropriate definitions. It considers definitions which do not require either complete verifiability or complete falsifiability, but only some looser logical tie to observation. The chapter looks, first, at a definition such as Alfred Jules Ayer's original proposal in Language, Truth, and Logic, which confers empirical significance on S if, and only if, in conjunction with additional premises, S logically implies some observation statement not implied by these additional premises alone. Ayer proposed to require that the additional premises be either analytic, or else independently shown to be empirically significant in accord with the definition itself. In a review of Ayer's second edition, Alonzo Church shows that the definition rules every statement or its negation empirically significant, provided only that there are three observation-statements such that none implies any other.
