Truthmaker theory is "the branch of metaphysics that explores the relationships between what is true and what exists."
A truthmaker for a truthbearer is that entity in virtue of which the truthbearer is true. Philosophers have speculated on the question whether every truthbearer requires a truthmaker. Parmenides' classic claim that what does not exist cannot be thought about has been read as a claim that every truthbearer must have a truthmaker, since otherwise the truthbearer is not about anything. A falsemaker for a proposition is that existent reality in virtue of which that proposition is false, assuming it is false.
In "Truth-Makers" (1984), Mulligan, Simons and Smith introduced the truth-maker idea as a contribution to the correspondence theory of truth. Logically atomic empirical sentences such as "John kissed Mary" have truthmakers, typically events or tropes corresponding to the main verbs of the sentences in question. Mulligan et al. explore extensions of this idea to sentences of other sorts, but they do not embrace any position of truthmaker maximalism, according to which every truthbearer has a truthmaker.
This maximalist position leads to philosophical difficulties, such as the question of what the truthmaker for an ethical, modal or mathematical truthbearer could be. Of course someone who is deeply enough committed to truthmakers and who simultaneously doubts that a truthmaker could be found for a certain kind of truthbearer will simply deny that that truthbearer could be true. Those who find the Parmenidean insight sufficiently compelling often take it to be a particularly enlightening metaphysical pursuit to search for truthmakers of these kinds of propositions.
Another difficulty for the claim that every truthbearer has a truthmaker is with negations of existential propositions (or, equivalently, universal propositions). What entity makes it true that unicorns do not exist? Proposals include the totality of all things, or some worldly state of affairs such as x1's not being a unicorn, x2's not being a unicorn, ..., and everything's being x1, or x2, or ... (the latter suggestion is due to Richard M. Gale).
David Lewis has proposed a more moderate version of the truthmaker theory on which truthmakers are only required for positive propositions (e.g., there must be a truthmaker for the proposition that there are horses, but not for the equally true proposition that there are no unicorns). What makes a negative proposition p true is the lack of a falsemaker for it, i.e., the lack of a truthmaker for the negation of p. Thus what makes it true that there are no unicorns is the lack of a truthmaker for the proposition that there are unicorns, i.e., the lack of unicorns. This may be what Protagoras was getting at when he said that to speak truly is to say of what is that it is and of what is not that it is not.
Truthmaker theorists differ as to what entities are the truthmakers of various truthbearers. Some say that the truthmaker of the proposition that Socrates is sitting (assuming he is!) is Socrates' being seated (whatever exactly that might turn out to be on the correct ontology) and in general the truthmaker of the truthbearer expressed by a sentence s can be denoted by the participial nominalization of s. Others will say that the truthmaker of the proposition that Socrates is sitting is just Socrates himself. In any case, the truthmaker is supposed to be something concrete, and on the first view is that whose existence is reported by the truthbearer and on the second view is that which the truthbearer is about.
While the existence of truthmakers may seem an abstruse question, concrete instances are at the heart of a number of philosophical issues. Thus, J. L. Mackie has argued that the truthmakers of moral claims would be "queer entities", too strange to exist, and hence all moral claims are false. Alternatively, a divine command metaethicist may insist that the only possible candidate for a truthmaker of a moral claim is a command from a perfect God, and hence if moral claims are true and a truthmaker theory holds, then God exists. Thus the disagreement between various metaethical schools is in part a disagreement over what kinds of truthmakers moral claims would have if these claims were true and over whether such truthmakers exist.