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How to Name a Real Number

Summary/Abstract: The article deals with Cantor’s diagonal argument and its alleged philosophical consequences such as that (1) there are more reals than integers and, hence, (2) that some of the reals must be independent of language because the totality of words and sentences is always countable. My claim is that the main flaw of the argument for the existence of non-nameable (hence unrecognizable) objects or truths lies in a very superficial understanding of what a name or representation actually is. The article concludes by offering solutions to some famous semantic paradoxes based on the diagonal construction as corroboration for this claim.

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