Semidisquotation and the infinitary function of truth

Erkenntnis:1-16 (forthcoming)
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The infinitary function of the truth predicate consists in its ability to express infinite conjunctions and disjunctions. A transparency principle for truth states the equivalence between a sentence and its truth predication; it requires an introduction principle---which allows the inference from "snow is white" to "the sentence 'snow is white' is true"---and an elimination principle---which allows the inference from "the sentence 'snow is white' is true" to "snow is white". It is commonly assumed that a theory of truth needs to satisfy a transparency principle to fulfil the infinitary function. Picollo and Schindler (Erkenntnis 83:899--928, 2017) argue against this idea. They prove that, given certain assumptions, an elimination principle is sufficient for the purpose. Then, they pose a challenge: to show why we should incorporate introduction principles to our theory of truth. In this essay I take on the challenge. I show that, given the authors' assumptions, an introduction principle is also sufficient to perform the infinitary function.
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First archival date: 2021-02-22
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