Fabrice Pataut, Centre National de la Recherche Scientifique, Sorbonne Université

— In order to either prove or disprove the validity of a logical law, more than a definition of the logical constants occurring in the expression of the law must be given. One needs an argument in favor of the semantics that gives the constants their meaning. How neutral may that semantics be so that no petitio principii is involved in the argument to the effect that some meanings must be ruled out and that, as a result, some logical laws turn out to be invalid? Michael Dummett urges that a full-blooded semantics that gives a non-circular explanation of the concepts expressed by the most primitive terms is what we should be looking for. Unfortunately, as far as intuitionistic logic is concerned, Beth trees fail to provide the required result because there is no way to make sure that all closed formulas are verified at any given node of a Beth tree. Dummett’s conclusion is that, as far a neutrality is concerned, the explanation of the meaning of the constants in terms of Beth trees is as circular as the classical one in terms of, say, introduction and elimination rules. Although John McDowell’s rejoinder is only indirectly concerned with the intuitionistic case, his plea for a modest semantics in which meaning or content may only be grasped “from the inside,” so that the meaning of the most primitive concepts is taken for granted, clearly applies to the case of the constants, in particular to the cases of disjunction and negation.

I shall argue against Dummett that, in the classical case, some fairly minimum presupposition may be achieved concerning the conceptual resources required to grasp the classical meaning of disjunction and negation, so that full-bloodedness isn’t entirely beyond our ken and the defense of excluded middle no longer appears arbitrary. Against McDowell, I shall argue that neither the Dummettian antirealist’s stance nor its realist’s rejoinder in terms of full-bloodedness need be worked out within the framework of an objectified conception of deductive practices. McDowell’s complaint that Dummett’s manifestability argument is a “typical piece of Enlightenment objectification,” akin to Condillac’s views on verbal propensities, is misguided. The defense of excluded middle by way of a grasp of the relevant contents “from the outside” need not be objectified in this sense. Quite the opposite: thoughts will have to play an essential role.