Truthmakers are roughly the things that make true certain truth bearers. That definition is purposefully ambiguous as the exact definition of a truthmaker is dependent upon one’s notion of truth and what exactly the truth bearers are. Nonetheless, that’s enough detail to understand the idea.
The following is called truthmaker maximalism: for every truth, there is something in the world that makes it true. However, consider the following objection that has been raised against truthmaker maximalism in the literature:
(1) This sentence has no truthmaker.
Suppose (1) is true. Then, by the truth of (1) it is the case that (1) has no truthmaker. However, that contradicts truthmaker maximalism. If we suppose (1) is false, then (1) has a truthmaker even though it’s false. However, that’s a contradiction in terms and so that cannot be viable either. Thus, (1) shows that truthmaker maximalism is false.
Now, some have tried to argue against this example, but none of the responses seem very satisfying to me and so we shall go on by assuming (1) successfully shows that truthmaker maximalism is false.
The person who used to hold to truthmaker maximalism might regroup by saying, “sure, (1) shows that truthmaker maximalism is false, but then we can just stipulate that truthmaker maximalism excepting (1) is true.” Supposing this is an acceptable move, there is a problem. For we can now construct an infinite number of sentences that don’t have truthmakers.
Take any sentence that is true and thus has a truthmaker. Now, conjoin that sentence with (1). This new sentence does not have a truthmaker either. Thus, there are an infinite number of exceptions to truthmaker maximalism. The best route for the truthmaker proponent seems to regroup and exclude from the truthmaker maximalism definition any sentence that is (1) or contains (1) or rule out self-referential statements.