Abstract: According to a familiar, simple argument, numbers exist because sentences like ‘Two is an even number’ are true. Whereas realists accept the argument as sound, anti-realists either reject that number words function referentially in such sentences (non-referentialism) or else that such sentences are true (fictionalism). We argue that this dialectic, though familiar, drastically underestimates the extent to which natural language supports realism. Indeed, if dominant accounts of number and measurement-related expressions within linguistic semantics are correct, then far more than just our overt talk about numbers as objects would not be true if numbers do not exist. The purpose of this paper is to sketch this strengthened argument for realism and to survey its consequences for extant forms of anti-realism.
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