I’ve posted a new draft paper 'Necessary truth, truthmaking and triviality'. The main motivation of the paper is to defend the view that the necessary truths are all and only the trivial truths. A secondary motivation is to argue that, given truthmaker theory, this entails that the necessary truths are exactly the truths that lack a truthmaker.
A sentence is trivially true if and only if its truth makes no demand on the world. That is to say, its truth-conditions are trivially met. Nothing is required of the world for the truth conditions of a trivial truth to be met. Crucially, this is not the same as saying that the world meets the demands that the truth of the sentence imposes on it as a matter of necessity. It is conceptually consistent that the truth of a sentence makes demands on the world that the world necessarily meets. The substantial claim defended in this paper is that there are no such truths: all substantial truths (ones whose truth makes a demand on the world) are contingent.
To make sense of the idea of a truth with trivial truth-conditions, we must have a non-modal understanding of ‘demands’. The demands the truth of a sentence makes on the world can’t simply be what must be the case if the sentence is true. That is independently plausible: even if there are necessary existents such as numbers, or God, we should want an understanding of ‘demands’ such that the truth of ‘Socrates is a philosopher’ demands that Socrates exist and be a philosopher, but not that God or the number 2 exists. Indeed, I argue in the paper that if you only have a modal understanding of ‘demands’ there are a bunch of apparent conceptual possibilities that you simply can’t make sense of. Now if it makes sense that the truth of a sentence not demand that p be the case, even when p is necessary, we can make sense of the idea that the truth of the sentence makes no demands at all.
I argue that such trivial truths must be necessary, lest we violate a very weak version of the principle that truth is grounded in reality (one far weaker than the truthmaker principle). In that case we have an explanation for the necessity of at least some necessary truths: they are necessary because trivial. I further argue that if this is true we should hold that all necessary truths are trivial, lest we admit unexplained necessitites.
This has real consequences for certain debates in metaphysics. It settles the debate over whether there could have been no concrete objects, since ‘there are concrete objects’ is a substantial truth (it demands that there be concreta), hence a contingent one. It motivates, I argue, in favour of states of affairs as opposed to tropes as the truthmakers for contingent intrinsic predications. That is because ‘If the state of affairs of A being F exists, A is F’ is trivially true if true whereas ‘If the particular redness of A exists, A is red’ is substantially true if true (since more is required for A’s existence than that one of A’s properties exist, whereas since A is a constituent of the state of affairs of A being F, the conditions for A’s existence are already met in meeting the conditions for the existence of the state of affairs), and so only the former can be necessary – and given truthmaker necessitarianism, whichever is true is necessarily true.
(I want to give a shout out to Agustin Rayo. I've been much inspired and influenced by his recent work on truth-conditions, ontological commitment, etc. Go to his webpage and read 'On Specifying Truth-Conditions', 'Ontological Commitment' and 'Towards a Trivialist Account of Mathematics'. It's all really excellent stuff, and will give you an idea of the background I'm operating with in this paper.)