Intuitionism, Entailment, Negation

Publisher Summary

This chapter discusses intuitionism, entailment, and negation. The extensional analysis of the conditional has been in favor of late. In the first place it is clearer, at least superficially. Efficient logical techniques have been developed with its aid. But the intensional analysis is gaining ground. There has, of course, existed a hard core of mathematical intuitionists and others who reject classic logic on philosophical grounds. Their ranks have been swelled, ironically, by the very success of classic semantical analysis in explicating intensionally motivated logics. Contextual elimination of sentential constants stood behind the use of these constants to characterize intuitionistic and material implication and intuitionistic and elliptical negation. But logic has come a long way from the days when every successful elimination in context brought automatic cheers that another putative entity had bit the dust.