A Topological Approach to Yablo's Paradox

Notre Dame Journal of Formal Logic 50 (3):331-338 (2009)
Abstract
Some years ago, Yablo gave a paradox concerning an infinite sequence of sentences: if each sentence of the sequence is 'every subsequent sentence in the sequence is false', a contradiction easily follows. In this paper we suggest a formalization of Yablo's paradox in algebraic and topological terms. Our main theorem states that, under a suitable condition, any continuous function from 2N to 2N has a fixed point. This can be translated in the original framework as follows. Consider an infinite sequence of sentences, where any sentence refers to the truth values of the subsequent sentences: if the corresponding function is continuous, no paradox arises
Keywords fixed point of a continuous function   ungrounded sentence
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DOI 10.1215/00294527-2009-014
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