I defend the hypothesis that the semantic paradoxes, the paradoxes about collections, and the sorites paradoxes, are all paradoxes of reference fixing: they show that certain conventionally adopted and otherwise functional reference-fixing principles cannot provide consistent assignments of reference to certain relevant expressions in paradoxical cases. I note that the hypothesis has interesting implications concerning the idea of a unified account of the semantic, collection and sorites paradoxes, as well as about the explanation of their “recalcitrance”. I also note that (...) it does not necessarily imply that one should not expect the sometimes hoped for “unique” solution to a paradox of these kinds. (shrink)

This paper presents an analysis of the sorites paradox for collective nouns and gradable adjectives within the framework of classical logic. The paradox is explained by distinguishing between qualitative and quantitative representations. This distinction is formally represented by the use of a different mathematical model for each type of representation. Quantitative representations induce Archimedean models, but qualitative representations induce non-Archimedean models. By using a non-standard model of \ called \, which contains infinite and infinitesimal numbers, the two paradoxes are shown (...) to have distinct structures. The sorites paradox for collective nouns arises from the use of infinite numbers, whereas the sorites paradox for gradable adjectives arises from the use of infinitesimal numbers. Each paradox can be traced to a different source of vagueness. The sorites paradox for collective nouns is caused by \, and the sorites paradox for gradable adjectives is caused by \ \. If correct, this analysis implies that infinite and infinitesimal numbers are cognitively real, and that they play a role in the semantic interpretation of natural language. (shrink)

The tolerance principle, the idea that vague predicates are insensitive to sufficiently small changes, remains the main bone of contention between theories of vagueness. In this paper I examine three sources behind our ordinary belief in the tolerance principle, to establish whether any of them might give us a good reason to revise classical logic. First, I compare our understanding of tolerance in the case of precise predicates and in the case of vague predicates. While tolerance in the case of (...) precise predicates results from approximation, tolerance in the case of vague predicates appears to originate from two more specific sources: semantic indeterminacy on the one hand, and epistemic indiscriminability on the other. Both give us good and coherent grounds to revise classical logic. Epistemic indiscriminability, it is argued, may be more fundamental than semantic indeterminacy to justify the intuition that vague predicates are tolerant. (shrink)