In chapter 4 Williamson argues against the understanding-truth link. He argues that for the understanding-truth link to hold it would have to be the case that Black and Rutherford either did not understand their own theory or that the theory is true. Since it has been proven that the phlogiston theory is false, it would seem that the only way to save the understanding-truth link we would have to say that Black and Rutherford did not understand their own theory. Clearly it is false that Black and Rutherford did not understand their own theory. The argument goes as follows:
1. If the understanding-truth links hold for phlogiston sentences, then either
Black and Rutherford did not understand their own theory or the theory
2. ~ (Black and Rutherford did not understand phlogiston theory & phlogiston
theory is true.)
3. ~ Understanding-truth links hold for phlogiston theory.
However, one may argue that premise 2. is false. One may argue that one of the disjuncts are true, namely, phlogiston is true. This disjunct maybe true if we replace the core of phlogiston theory with the conditional ‘If phlogiston exists then the core of phlogiston theory is true. Williamson dismisses this argument stating “Arguably, however, since ‘phlogiston’ fails to refer, that conditional too fails to express a proposition, so even this more cautions sentence is not true, although it is also not false.” (P. 11 chap 4)
I believe there are two things wrong with this. First, he states “Arguably, however, since ‘phlogiston’ fails to refer” that the conditional fails to have a truth value. This statement is arguable. There are theories that hold that abstract objects have truth values.
Second, even if we concede that it does not have a truth value just because this conditional fails to have a truth value does not mean that the conditional is false, which is what Williamson needs to make his claim that understanding-truth links do not hold. Since Williamson is the one who wants to argue that nothing is epistemically available simply on the basis of linguistic and conceptual competence then the onus of proof is on him if he wishes to accomplish this.