Rule-following and Reihenornamente: a reply to my opponents

The article contains answers to the critical remarks made in the course of the discussion about the possibilities of applying a modernized version of Katz’s semantic Platonism in solutions to the problem of rule-following. Ladov points out that my interpretation of Katz’s semantic Platonism is not quite correct in relation to Katz’s original works. He specifically emphasizes that my interpretation of Katz’s semantic platonism places an undue focus on the syntactic treatment of the decomposition principle. In the reply, I take apart the most significant differences between Katz’s original position and my interpretation, pointing to the line of drift of his views from Fregean views of sense to more or less radical token-type views of language structures. Andrushkevich makes a remark of a historical-philosophical character, drawing attention to the fact that I unjustifiably qualify the problem of rule-following exclusively as a metaphysical one, ignoring its important epistemological aspects. In the reply, I establish a distinction between so-called R-facts, which provide knowledge about the rule R itself, and C-facts, which give us only knowledge about whether someone correctly follows the rule R in cases where one intends to follow it. I then show that before we can decide what kind of knowledge we need to follow the rule, we must figure out what kinds of facts there are in our world, since all knowledge of this kind will ultimately be supervenient on them. In parallel, I take apart another important plot in the discussions of the rule-following problem. In particular, drawing on Lane’s work, I argue that the problem of rule-following arises already at the level of the notion of repetition of a sign, and that the solution to this problem can only be metaphysical, since it involves the investigation of identity criteria for special objects of arbitrary nature such as words. Finally, I examine the critical comments made by Borisov and Sulaev regarding my Reihenornamente example. In the opinion of my critics, the “-••-••-” sampling I have given can be continued in many ways other than the way I suggested in my article. In my reply, I establish and explain the distinction between two types of tasks that could be formulated with respect to the entire set of Reihenornamente examples: (1) to continue the sampling using the series of “•” and “-” symbols it contains without breaking the pattern already given in the sampling, and (2) to continue the sampling using the series of “•” and “-” symbols it contains, but in such a way that the sampling together with its continuation forms some pattern out of the infinite set of possible patterns. In the reply, I emphasize that in my example Reihenornamente task (2) was not assigned, but only task (1). I separately explain that the conditions of task (1) can be translated into the language of metaphysics as follows: the “-••-••-” sampling contains C-facts about the pattern and these are all the C-facts you should use to construct a continuation for the sampling using the symbols “•” and “-” without breaking the pattern already given in it. Based on these additional clarifications, I make the assertion that for the “-••-••-” sampling there is only one correct sequence that continues the sampling in a way that does not break the pattern given in it. The author declares no conflicts of interests.

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