Disquotation and Infinite Conjunctions
Picollo, Lavinia, LP
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Schindler, T., & Picollo, L. L. (2017). Disquotation and Infinite Conjunctions. Erkenntnis https://doi.org/10.1007/s10670-017-9919-x
One of the main logical functions of the truth predicate is to enable us to express so-called `infi nite conjunctions'. Several authors claim that the truth predicate can serve this function only if it is fully disquotational (transparent), which leads to triviality in classical logic. As a consequence, many have concluded that classical logic should be rejected. The purpose of this paper is threefold. First, we consider two accounts available in the literature of what it means to express infi nite conjunctions with a truth predicate and argue that they fail to support the necessity of trans- parency for that purpose. Second, we show that, with the aid of some regimentation, many expressive functions of the truth predicate can actually be performed using truth principles that are consistent in classical logic. Finally, we suggest a reconceptualisation of deflationism, according to which the principles that govern the use of the truth predicate in natural language are largely irrelevant for the question of what formal theory of truth we should adopt. Many philosophers think that the paradoxes pose a special problem for deflationists; we will argue, on the contrary, that deflationists are in a much better position to deal with the paradoxes than their opponents.
This work was supported by the Alexander von Humboldt Foundation and the German Research Foundation (DFG, “Reference patterns of paradox”).
External DOI: https://doi.org/10.1007/s10670-017-9919-x
This record's URL: https://www.repository.cam.ac.uk/handle/1810/269727
Attribution 4.0 International
Licence URL: http://creativecommons.org/licenses/by/4.0/