In his new book Modal Logic as Metaphysics Timothy Williamson briefly discusses the following argument:
- Being is necessary (premise).
- Truth supervenes on being (premise).
- Truth is necessary (from 1 and 2).
Premise (A) is Williamson’s position, which he calls necessitism. Necessitism is the view that necessarily, everything is necessarily something, i.e.
◻∀x ◻(∃y x=y)
This is to say, in effect, that all being/existence is necessary being/existence.
Premise (B) is associated with the so-called ‘truthmaker principle’, according to which every truth is made true by something. In other words, every truth is strictly implied by the being of something.
Since all being is necessary being given (A), and every truth is strictly implied by the being of something given (B), it follows that all truth is necessary truth (C) (2013: 393).
The moral for Williamson is that we ought to give up the truthmaker principle in order to preserve the compatibility between necessitism and contingent truth, i.e. in order to prevent the collapse of the former into necessitarianism, the view that all truths are necessary. The consequence of following Williamson here is the prima facie implausible result that no contingent truths have truthmakers (p. 397).
As Williamson notes, the strategy of contingentists (i.e. those who reject necessitism) has typically been to argue that necessitism has wildly unacceptable consequences (p. 384). Necessitarianism is one putative consequence (denied by Williamson), allowing contingent truth to hinge free of being is another (accepted by Williamson). Williamson presents the latter as a sort of anti-reductionism: since being is necessary and some truths are contingent, the latter cannot be reduced to the former. However, for a Spinozist there is little difference between saying that either there is no contingent truth or else contingent truth hinges free from being (since the latter seems to violate the PSR). Thus for a Spinozist (and probably anyone who defends the PSR in similarly strong form) arguments for necessitism are automatically arguments for necessitarianism. From this angle the truthmaker principle and the PSR are similar in nature. To get contingency on the table at all, then, one would have to reject necessitism. This amounts to saying that there is ultimately no difference between Williamson’s sort of anti-reductionism, and eliminativism about contingency.
Finally, if the resultant contingency of being is interpreted as the contingency of all beings taken together (rather than the contingency of any particular being taken in isolation), then it follows that the contingency of truth requires that there could have been nothing. For me establishing this requirement is a sort of unholy grail.
- Timothy Williamson, Modal Logic as Metaphysics, (OUP: 2013).