What Is Wrong with Interpretation Q?:

A Case of Concrete Skepticʼs Alternative Interpretation of Algebra

Abstract

    Previous discussion of skepticism about meaning as it appears in Kripke's Wittgenstein has not provided complete examples of an alternative interpretation of a language. Sakakibara recently gave an instance of a nonstandard interpretation of algebra called interpretation Q. The present paper compares interpretation Q and the standard interpretation C of algebra in three respects: complexity of meaning, engagement with reality, and convenience of use. Although both interpretations are equal in complexity and engage with reality properly, interpretation C is superior to interpretation Q because interpretation C alone allows digit-by-digit calculations, which justifies our asserting that interpretation C is the correct one. Since this way of reasoning does not make mention of the linguistic community we belong to, the present case study suggests that the link between language and community is not necessary.