Showing posts with label truth predicate. Show all posts
Showing posts with label truth predicate. Show all posts

Tuesday, 1 April 2014

Softening the Blow of Truth Fictionalism


In the last post I said that mathematical fictionalism has consequences that sound terrible, but really aren't worrisome at all, when you think about what they actually entail. Something similar could be said about alethic fictionalism, or fictionalism about truth. Consider the truth predicate.  It’s a widely held view that the purpose of having a truth predicate is to allow people to undertake commitments to certain claims without having to explicitly state those claims.  So, if a theory $\Gamma$ entails infinitely many claims that you want to endorse, you can say ‘Everything entailed by $\Gamma$ is true', rather than explicitly state every claim entailed by $\Gamma$, which would be impossible.  So the job of the truth predicate isn’t to ascribe a special property, TRUTH, to things, but to allow us to undertake commitments without having to articulate those commitments explicitly.
Nevertheless, you could consistently hold that, even though what explains why we have a truth predicate has nothing to do with ascribing the property TRUTH to things, the meaning of a predicate is always to ascribe a property to something.  And if, in addition, you held that there is no such property as TRUTH, then you would end up being a fictionalist about truth discourse.  Any claim of the form ' $\phi$ is true’ would be false, since nothing has the property of truth.  But this wouldn’t really matter, since the truth predicate would still allow us to do what it was designed to do.  (It would, however, sound like a really bad result.)

Friday, 30 August 2013

The Inverse Indispensability Argument


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.