Amit Pinsker

How should we respond to semantic paradoxes? I argue that the answer to this question depends on what we take the relation between logic and natural language to be. Focusing on the Liar paradox as a study case, I distinguish two approaches solving it: one approach (henceforth ‘NL’) takes logic to be a model of Natural Language, while the other (henceforth ‘CC’) suggests that a solution should be guided by Conceptual Considerations pertaining to truth. As it turns out, different solutions can be understood as taking one approach or the other. Furthermore, even solutions within the same ‘family’ take different approaches, and are motivated by NL and CC to different extents, which suggests that the distinction is not a binary one – NL and CC are two extremes of a spectrum.

Acknowledging this has two significant upshots. First, some allegedly competing solutions are in fact not competing, since they apply logic for different purposes. Thus, various objections and evaluations of solutions in the literature are in fact misplaced: they object to NL-solutions based on considerations that are relevant only to CC or vice versa. Second, the plausible explanation of this discrepancy is that NL and CC are two ways of cashing out what Priest calls “the canonical application of logic”: deductive ordinary reasoning. These two ways are based on two different assumptions about the fundamental relation between logic and natural language. The overall conclusion is thus that a better understanding of the relation between logic and natural language could give us a better understanding of what a good solution to semantic paradoxes should look like.

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