The Verification Principle: another puncture

Abstract

In Wright 1986 Crispin Wright proposed a formulation of the Verification Principle which he claimed to be free from the shortcomings that plague previous statements. Wright handled the problem posed by superfluous content using the notion of compact entailment. An entailment is compact, in Wright's sense, when it is liable to disruption by uniform replacement of any non-logical constituent in its premisses, but not in its conclusion. An entailment, A1, ..., An, SI} = B, is S-compact when it is liable to disruption by uniform replacement of any non-logical constituent in S. Thus, the entailment of 'Mary is a wife' by 'Mary is a woman and Mary is married' is compact, since it does not survive the replacement of 'married' by, for instance, 'mad' in its premiss. In contrast, the entailment of 'Maria Teresa is a horse' by 'Maria Teresa is a mare' and 'All mares are female horses' is non-compact, since it is indifferent to uniform substitutions for 'mare' in its premisses. Finally, let us say that two statements are compactly equivalent when their mutual entailment is compact. Wright's proposal, as amended in Wright 19891 to overcome an objection due to David Lewis (1988), was