Most philosophers take it that the truth term plays the role of a predicate. Since predicates denote properties this provides prima facie reason to think that truth is a property; many claims that we take to be correct appear to be ascriptions of a truth property to sentences or propositions. However, as Quine famously pointed out, we would require the truth predicate for certain expressive functions—viz. undertaking commitments without the need to express them explicitly—whether or not there is a property of truth, and this fact constitutes an undercutting defeater for the prima facie reason to think that truth is a property. In other words, the indispensability of a truth predicate (for purposes other than attributing a property of truth to sentences) undercuts the reason to think that ‘is true’ denotes a property.
Mathematical talk refers to quantifies over abstract mathematical objects. Since referring terms denotes objects, mathematical talk provides prima facie reason to think that mathematical objects exist.; many claims that we take to be correct appear to be descriptions of an abstract realm of mathematical objects. However, we would require reference (or apparent reference) to mathematical objects in order to describe concrete systems (in order to model physical phenomena mathematically) whether or not there are mathematical objects, and this fact constitutes an undercutting defeater for the prima facie reason to think that there are mathematical objects. In other words, the indispensability of mathematics (for purposes other than describing a realm of abstract mathematical objects) undercuts the reason to think that mathematical terms denote extant abstract mathematical objects.
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