Perceived necessity explains the dissociation between logic and meaning: the case of "only if"

The purpose of this article was to investigate why sentences of the form "p only if q" often appear to have a different meaning than sentences of the form "if p, then q," despite their logical equivalence. The results of 3 experiments indicate that when "if ... then" statements were equated with respect to necessity and temporal relations, different pragmatic relations (such as permission, causation, etc.) elicited similar "only if" judgments. However, different necessity relations elicited different "only if" judgments, regardless of the type of pragmatic relation expressed in the "if then" statement. These data suggest that "only if" judgements are primarily mediated by necessity and temporal relations and that pragmatic contexts may play a more indirect role, such as in the interpretation of necessity and temporal relations. Suggestions for how these findings might be incorporated into pragmatic schema theory (P. W. Cheng & K. J. Holyoak, 1985; P. W. Cheng, K. J. Holyoak, R. E. Nisbett, & L. M. Oliver, 1986) and mental models theory (P. N. Johnson-Laird & R. M. J. Byrne, 1991) are discussed.