Abstract
Truth-value gaps have received little attention from a foundational perspective, a fact which has rightfully opened up gap theories to charges of vacuousness. This paper develops an account of the foundations of gap-like behavior which has some hope of avoiding such charges. I begin by reviewing and sharpening a powerful argument of Dummett’s to constrain the options that gap theorists have to make sense of their views. I then show that within these strictures, we can give an account of gaps by drawing on elements of a broadly Stalnakerian framework for assertion and using gaps to track an amalgamation of assertoric effects. The discussion reveals that we may need special resources in our theories of assertion to posit gaps, that gaps may be unusable in characterizing the structure of mental states, and that gaps may have heterogeneous linguistic sources that result in equally heterogeneous projective and inferential behavior.
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Shaw, J.R. What is a truth-value gap?. Linguist and Philos 37, 503–534 (2014). https://doi.org/10.1007/s10988-014-9160-x
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DOI: https://doi.org/10.1007/s10988-014-9160-x