ABSTRACT
R.E. JENNINGS Laboratory for Logic and Experimental Philosophy, Simon Fraser University, Burnaby, BC, Canada j enningsQsfu.ca
D. SARENAC Laboratory for Logic and Experimental Philosophy, Simon Fraser University, Burnaby, BC, Canada sarenacQstanford.edu
1 PRELIMINARIES At first blush the idea seems plausible enough. An argument is invalid if and only if the truth of its premisses does not force the truth of its conclusion. Therefore if the inference from P A ->P to Q is invalid, there must be a model in which P A ->P is true and Q false. If the truth-conditions of conjunction and negation do not permit such a model, then one or the other of the truth-conditions must be altered. It is not therefore that the inference from P A -iP to Q is invalid, but that the inference from P A' -/P to Q is invalid, so that one or the other of conjunction or negation is not (or perhaps only not') what we thought it was. It is natural to suppose that the only guide available to us for the devising of truth-conditions for these connectives is our conversational understanding of the English words and and not, and their correspondents in other natural languages. But if that is so, then it will surprise the classicalist that, of all the places where our understanding might have been misguided or insufficient, it should have been there that it has let us down rather than elsewhere. To put the matter another way, if earlier classical logicians had
been told that controversy would eventually arise about truth-conditions of some connectives, it seems unlikely that they would have been able to predict conjunction or negation as the locus of debate. Even if our conversational understanding of their natural counterparts could let us down, one might have supposed that their standard truth-conditions could be agreed by convention as the most useful that could be devised. To be sure, we should not ever take for granted the theoretical adequacy of conversational understanding. Consider only our improverished understanding of, say, truth and inference. But one might have thought that we could rely on our ordinary understanding of conjunction and negation.
