Correspondence Theory of Truth

The basic picture

The correspondence theory is the philosophical version of common sense about truth. The proposition that snow is white is true because snow is, in fact, white. The proposition that the moon is made of cheese is false because the moon, in fact, is not. Truth is a relation: between something propositional (a sentence, a belief, a thought) and something worldly (a fact, a state of affairs, an arrangement of objects and properties).

The cleanest ancient statement is Aristotle's. Metaphysics IV.7: "To say of what is that it is, and of what is not that it is not, is true; to say of what is that it is not, or of what is not that it is, is false." That sentence stares at you across 2,400 years and looks unimprovable.

Aquinas reformulates it as a slogan: veritas est adaequatio rei et intellectus — truth is the adequation of thing and intellect (Summa Theologiae I.16.1). The intellect, in forming a proposition, mirrors a way the thing is. When the mirroring succeeds, the proposition is true.

So far so simple. The trouble starts the moment we try to make the relation precise. What is the proposition, really? What is a fact? And what does corresponding amount to?

The Russell–Moore version (early 20th century)

Bertrand Russell and G.E. Moore developed the modern correspondence theory in articles between 1899 and 1912. On their view, the world is built from particulars (this cat) and universals (the property of being on the mat, the relation being on). A fact is a complex entity composed of these: the cat's being on the mat is a fact when the cat stands in the "on" relation to the mat.

A proposition has a parallel structure: a mental or linguistic complex composed of concepts of the same particulars and universals. Truth is a structural mirroring: the proposition is true when its constituents are arranged in a way that matches the constituents of the corresponding fact. The early Wittgenstein took this picture to its sharpest expression in the Tractatus (1921): a proposition is a logical picture of a fact.

Tarski's schema (1933)

Alfred Tarski's "The Concept of Truth in Formalised Languages" (1933) offered the most influential modern technical treatment. Tarski set down the "Convention T": an adequate definition of truth, for a language L, must entail every instance of the schema

(T)  S is true iff p

where S is a name for a sentence and p is its translation into the metalanguage. The canonical example: "Snow is white" is true if and only if snow is white. Tarski then showed how to construct, recursively, a truth-predicate for formal languages that satisfies Convention T. The trick is to define truth in terms of satisfaction by sequences of objects.

Whether Tarski's theory is a correspondence theory is debated. Karl Popper called it the rehabilitation of correspondence; Hartry Field (1972) argued it gives correspondence real bite; deflationists (Horwich, Quine) read it as showing truth is not substantive. The schema itself is neutral; the metaphysics depends on what you build around it.

Five theories of truth compared

Theory	What truth is	Truthbearer	Champion(s)	Strength	Weakness
Correspondence	Match between proposition and fact	Proposition	Aristotle; Aquinas; Russell; Moore; Tarski; Armstrong	Matches everyday usage	Hard to specify "fact" without circularity
Coherence	Membership in a maximally coherent set of beliefs	Belief / proposition	Spinoza; Bradley; Blanshard; Neurath	Handles webs of belief well	Multiple coherent sets; isolation objection
Pragmatist	What works / would be agreed at end of inquiry	Belief / hypothesis	Peirce; James; Dewey; Putnam (later)	Connects truth to action and inquiry	Conflates truth with utility
Deflationary / disquotational	Nothing — "is true" just disquotes	Sentence	Ramsey; Quine; Horwich; Field	Avoids metaphysical baggage	Can't explain truth's explanatory role
Identity theory	True propositions are identical to facts	Proposition	Bradley (mature); Hornsby; McDowell	Closes the gap correspondence opens	Strange ontology of fact-propositions
Truthmaker (semi-correspondence)	Truth grounded in worldly truthmakers	Proposition	Armstrong; Bigelow; Fine	Avoids facts as ad-hoc	Negative truths still problematic

A worked example: the cat on the mat

Take the proposition that the cat is on the mat. The cat (Felix) is in fact on the mat. The correspondence theorist's diagnosis:

1. The proposition has constituents: the concept of Felix, the concept of the mat, and the concept of the relation being on.
2. The world contains a corresponding fact: Felix, the mat, and Felix's actually standing in the on relation to the mat.
3. The proposition is true because its constituents match the constituents of the fact, and they are arranged in the same structure (Felix on mat, not mat on Felix).

Now run the false case. That the cat is on the table when Felix is on the mat. The proposition has the same kind of structure, but no fact in the world has Felix in the on relation to the table. There is nothing to correspond to. Falsity is the absence of a corresponding fact.

This account already raises questions. Are there negative facts (that Felix is not on the table)? Russell, in his 1918 lectures, reluctantly accepted them. The Tractatus denies them; the world consists only of positive facts. The literature on this question alone runs to thousands of pages.

Counterarguments

• The slingshot argument. If true sentences refer to facts, and logically equivalent sentences refer to the same fact, then by chained substitutions every true sentence refers to the same fact. Davidson's 1969 version is the sharpest. Defenders escape by restricting which substitutions count.
• Frege's circularity charge. "The proposition that snow is white is true iff it corresponds to the fact that snow is white" threatens to mean nothing more than "true iff snow is white." The right-hand side just rephrases the proposition. So "corresponds to a fact" reduces to "is true."
• Negative existentials. "There are no unicorns" is true. What fact does it correspond to? Russell's answer (1918): a totality fact about everything that exists. Critics find totality facts metaphysically extravagant.
• Mathematical and modal truths. "7 is prime"; "water could have been H₃O." If facts are concrete, no concrete fact makes these true. Either we accept abstract facts (a Platonist commitment) or we treat these truths differently.
• The view from nowhere worry. Pragmatists (James, later Putnam) argue we never compare a proposition to bare reality — we only ever compare propositions to other propositions or to perceptions, which are themselves propositional. Correspondence requires a comparison no agent can ever make.
• Coherence challenge. Bradley argued that any judgment about correspondence is itself just another belief, evaluable only by its coherence with other beliefs. Correspondence collapses into coherence at the level of evaluation.

Variants

• Logical-atomism correspondence (Russell, early Wittgenstein). Facts are structured complexes of particulars and universals; propositions mirror them.
• Truthmaker theory (Armstrong 1997, Bigelow 1988). Truths require truthmakers — entities whose existence necessitates the truth of the proposition. Avoids commitment to facts as a basic category.
• Tarskian semantic theory. Truth defined recursively via satisfaction; whether this is "real" correspondence depends on metaphysical add-ons.
• Tropes-and-bundles correspondence (Mulligan, Simons, Smith 1984). Facts replaced by tropes — particularised properties — to avoid commitment to universals.
• Causal correspondence (Field 1972). Reference is fixed by causal connections; correspondence is built compositionally from these.

Common confusions

• Correspondence means each word matches a thing. No. The relation is between whole propositions and whole facts. Words refer; propositions correspond.
• Tarski settled the matter. Tarski gave a formal definition for formal languages. Whether his theory captures the metaphysical correspondence intuition is contested.
• It says we can verify truths by inspecting facts. No — correspondence is a theory of what truth is, not of how we know truths. Epistemology and metaphysics are separate.
• Correspondence requires naive realism. No. Anti-realists like Wright and Putnam have defended forms of correspondence; realism is one motivation but not a requirement.
• It can't handle abstract truths. Truthmaker theorists argue abstract truthmakers (numbers, sets) suffice; the question is whether we accept them.
• Coherence and correspondence are mutually exclusive. Some philosophers (Walker 1989; later Putnam) argue truth involves both — coherent best theory is correspondence with reality, suitably understood.