Paradigms and self-reference: what is the point of asserting paradoxical sentences?

In Shyam Wuppuluri & Newton da Costa (eds.), Wittgensteinian (adj.): Looking at the World from the Viewpoint of Wittgenstein's Philosophy. Cham, Švýcarsko: pp. 123-134 (2020)
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Abstract
A paradox, according to Wittgenstein, is something surprising that is taken out of its context. Thus, one way of dealing with paradoxical sentences is to imagine the missing context of use. Wittgenstein formulates what I call the paradigm paradox: ‘one sentence can never describe the paradigm in another, unless it ceases to be a paradigm.’ (PG, p.346) There are several instances of this paradox scattered throughout Wittgenstein’s writings. I argue that this paradox is structurally equivalent to Russell’s paradox. The above quotation is Wittgenstein’s version of the vicious circle principle which counteracts the paradox. The prohibition Wittgenstein describes is, however, limited to a certain language-game. Finally, I argue that there is a structural analogy between a noun being employed as a self-membered set and a paradigmatic sample being included in or excluded from the set it generates. Paradoxical sentences are not prohibited forever; they can indicate a change in our praxis with a given paradigm.
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Archival date: 2020-02-11
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