Katz’s good angel versus Kripke’s evil demon: the privilege argument, algorithms, and semantic platonism

Kripke’s skeptical arguments about the meaning of linguistic expressions are usually seen as the starting point of a discussion around the rule-following problem. Kripke believed that no one (including God) is able to produce a fact that allows one to establish whether one really meant by “+” the addition function in the simple arithmetic calculation “57 + 68 = 125”. Many of Kripke’s critics, however, believe that semantic dispositionalism can offer effective ways to avoid his skeptical arguments. A number of proponents of semantic dispositionalism (Simon Blackburn, Carl Ginet, Tomoji Shogenji, Adam Podlaskowski, Jared Warren, and others) propose that we expand the number of our dispositions and diversify their character in significant ways. The proposal is that we work not only with simple dispositions concerning the computation of particular pairs of small numbers, but also with special composite dispositions containing algorithms for applying the results of such computations to any pairs of really huge numbers. This article provides a critique of semantic dispositionalism and its proposed responses to the skeptical challenge from the rule-following problem. The proposal of semantic dispositionalism runs into a new skeptical objection, the so-called privilege argument. It shows that, in concrete examples of computations with “+” for pairs of really huge numbers, proponents of semantic dispositionalism cannot establish a distinction for two fundamentally different cases: (i) cases where we incorrectly follow the addition rule, and (ii) cases where we correctly follow some other rule. An alternative option of answering this new skeptical challenge is Jerrold Katz’s semantic Platonism, in which semantic structures are based on syntax, the formal aspect of grammar responsible for the correctness of the construction of linguistic expressions. According to Katz, rule-following occurs not because one by “+” means the addition function that one derives from his previous experience with ordered triples of numbers, but because of the existence of a syntactic relation between two abstract objects -the sense of the expression “57+68” and the number “125”. For proponents of semantic Platonism, the problem of rule-following is not the existence of infinitely large extensions of linguistic expressions (like in the examples of our calculations with “+”), but the explanation of how exactly abstract meanings are “grasped”. This process is based on the principle of decomposition. The “graspable” abstract meanings of a certain type of expressions “e”, forming autonomous structures of some language L, are not infinite objects, but quite finite syntactic combinations of this type of expressions “e” in the language L. In the course of one’s language learning one becomes familiar with such combinations, so that later, if necessary, when encountering a type of expression “e” in practice, one has an idea of what one should, can, or has reason to do in all such cases (in particular, so that one can notice and correct one’s own and others’ mistakes in the use of expressions of type “e”). Proponents of semantic Platonism believe that it should be enough to successfully avoid the skeptical challenge of the rule-following problem. The author declares no conflicts of interests.

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