Linguistic platonism and Kripke’s problem

In his article “Katz’s Good Angel vs. Kripke’s Evil Demon: The Priviledge Argument, Algorithms, and Semantic Platonism” in this issue of the journal, Andrei Nekhaev examines the ability of Katz’s linguistic Platonism to provide a solution to the famous problem of rule-following stated by Kripke. He claims that Katz’s theory does provide a solution, at least to some cases of rule-following, and argues that this solution is immune to the Privilege Argument put forward by Guardo. (Originally, the argument was formulated as an objection to dispositionalist theory of meaning but it can be made applicable to Platonism as well.) Nekhaev illustrates his claim showing how linguistic Platonism can be applied to the problem of continuation of a given sequence of symbols. He considers two solutions to the problem and argues that one of them is correct while the other is not. This claim is based on a syntactic analysis of the given sequence, and he maintains that the (in)correctness of solutions is determined by the syntactic structure of the sequence. If this view would be true, there exists a unique rule for continuation of the sequence, and this rule is determined objectively by the sequence itself, which would provide a solution to Kripke’s problem. The aim of my paper is to show that this view is untrue. I examine Nekhaev’s example and show that there is infinity of rules for continuation of the given sequence, and that none of them has any advantage over others. In this respect, the problem is analogous to the situation with addition and “quaddition” described by Kripke: the given sequence of symbols is analogous to the intersection of addition and “quaddition” (both operations conceived as sets of ordered triples of natural numbers), and its continuations are analogous to the operations themselves. In my view, this shows that Katz’s treatment of senses/rules as abstract objects is irrelevant to the problem of rule-following because, no matter what the nature of senses is, the given sequence of symbols is compatible with many of senses, and it does not provide any privilege to any of them. The author declares no conflicts of interests.

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