Truthmaker theory
Truthmaker theory is "the branch of metaphysics that explores the relationships between what is true and what exists".[1] The basic intuition behind truthmaker theory is that truth depends on being. For example, a perceptual experience of a green tree may be said to be true because there actually is a green tree. But if there were no tree there, it would be false. So the experience by itself does not ensure its truth or falsehood, it depends on something else. Expressed more generally, truthmaker theory is the thesis that "the truth of truthbearers depends on the existence of truthmakers". A perceptual experience is the truthbearer in the example above. Various representational entities, like beliefs, thoughts or assertions can act as truthbearers. Truthmaker theorists are divided about what type of entity plays the role of truthmaker; popular candidates include states of affairs and tropes.
Truthmaker maximalism is the thesis that every truth has a truthmaker. An alternative view is truthmaker atomism, the thesis that only atomic sentences have truthmakers. Truthmaker atomism remains true to the basic intuition that truth depends on being by holding that the truth of molecular sentences depends on the truth of atomic sentences, whose truth in turn depends on being. All non-maximalist positions accept that there are truthmaker gaps: truths without truthmakers. Opponents have tried to disprove truthmaker theory by showing that there are so-called deep truthmaker gaps: truthbearers that not only lack a truthmaker but whose truths do not even depend on being. Various principles governing the truthmaking relation have been proposed in order to make the intuitions about the role and nature of truthmaking explicit. Truthmaker theory is closely related to the correspondence theory of truth, but not identical to it. Truthmaker theory has been applied to various fields in metaphysics, often with the goal of exposing ontological cheaters: theorists who are committed to certain beliefs but do not or cannot account for the existence of a truthmaker for these beliefs.
Truthmaker gaps[edit]
A truthmaker gap is a truth that lacks a truthmaker. Truthmaker maximalists hold that there are no truthmaker gaps: every truth has a truthmaker.[6] Truthmaker non-maximalists, on the other hand, allow that some truths lack a truthmaker. Truthmaker non-maximalists still count as truthmaker theorists in the sense that they hold onto the core intuition of truthmaker theory that truth depends on being.[1]
Atomic truthmaker theories, which have their root in logical atomism, are examples of such a position. According to them, only atomic sentences have truthmakers.[7] A sentence is atomic or simple if it does not have other sentences as proper parts.[8] For example, "The sun is shining" is an atomic sentence while "The sun is shining and the wind is blowing" is a non-atomic or molecular sentence since it is made up of two sentences linked by the conjunction "and". In propositional calculus molecular sentences are composed through truth-functional logical connectives.[9] Molecular sentences lack truthmakers according to atomic truthmaker theories and therefore constitute truthmaker gaps. But the fact that the truth values of molecular sentences depends on the truth values of its constituents (if only truth-functional connectives are allowed) ensures that truth still depends on being.[7]
This type of truthmaker gap has been called a "shallow" truthmaker gap. Shallow truthmaker gaps are contrasted with "deep" truthmaker gaps. Deep truthmaker gaps are truths that do not depend on being.[1] They therefore pose a challenge to any type of truthmaker theory. In terms of possible worlds, a deep truthmaker gap is a proposition that is true in one possible world and false in another where there is no difference between these two worlds beside the truth value of this proposition. Critics of truthmaker theory have tried to find deep truthmaker gaps in order to refute truthmaker theory in general.[10][11]
Truthmaking principles[edit]
Various principles governing the truthmaking relation have been proposed.[1][6] They aim to make our intuitions about the role and nature of truthmaking explicit.
The entailment principle states that if entity e is a truthmaker for proposition p and p entails proposition q then e is also a truthmaker for q.
The conjunction principle states that if entity e is a truthmaker for the conjunction of proposition p and proposition q then e is also a truthmaker for p.
The disjunction principle states that if entity e is a truthmaker for the disjunction of proposition p and proposition q then e is either a truthmaker of p or a truthmaker of q.
These principles seem intuitively to be true but it has been shown that they lead to implausible conclusions when combined with other plausible principles.[12][13]
The correspondence theory of truth states that truth consists in correspondence with reality.[7] Or in the words of Thomas Aquinas: "A judgment is said to be true when it conforms to the external reality".[14] Truthmaker theory is closely related to correspondence theory; some authors see it as a modern version of correspondence theory.[15] The similarity between the two can be seen in the following example definitions:
But despite the obvious similarities there are a few important differences between truthmaker theory and correspondence theory. For one, correspondence theory aims to give a substantive account or a definition of what truth is. Truthmaker theory, on the other hand, has the goal of determining how truth depends on being.[16] So it presupposes the notion of truth instead of defining it. While it seems natural to combine truthmaker theory with a correspondence-conception of truth, this is not necessary.[1] Another difference between the two theories is that correspondence is a symmetric relation while the truthmaking relation is asymmetric.[17]