A Topological Approach to Yablo's Paradox

Bernardi, Claudio

Notre Dame J. Formal Logic, Tome 50 (2009) no. 1, p. 331-338 / Harvested from Project Euclid

Résumé

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 2^N to 2^N 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.

Publié le : 2009-07-15
Classification: fixed point of a continuous function, ungrounded sentence, 03A05, 03F45, 54D30

@article{1257862041,
     author = {Bernardi, Claudio},
     title = {A Topological Approach to Yablo's Paradox},
     journal = {Notre Dame J. Formal Logic},
     volume = {50},
     number = {1},
     year = {2009},
     pages = { 331-338},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1257862041}
}

Bernardi, Claudio. A Topological Approach to Yablo's Paradox. Notre Dame J. Formal Logic, Tome 50 (2009) no. 1, pp.  331-338. http://gdmltest.u-ga.fr/item/1257862041/