The correspondence theory in its simplest form says that truth is a connection to reality. To be true is to accurately describe – in other words, match, picture, depict, express, conform to, agree with or correspond to – the real world or parts of it. For example, the proposition that a cat is on a mat is true if a real cat is on a real mat. Otherwise, that proposition fails to be true. In general, the truth of a proposition is sensitive to how real things are. In short, truth connects to reality.
There are different ways to articulate the connection between true things and the reality they describe. Some theories, for example, treat the connection as a structural relation that ties constituents of a true thing to constituents of the world. Other theories treat the connection as a nonstructural correlation between true things and the world. This difference between structural and correlation theories depends on one’s theories of three components: true things, real things described by the true things, and the correspondence between true things and real things. All versions of the correspondence theory arise from theories of these components.
A principle advantage of a correspondence theory is that it accounts for the apparent correlation between the aspects of reality and the truth-value of a proposition. When the cat is on the mat, the proposition that the cat is on the mat is true. If the cat gets off the mat, that proposition is not true. Therefore, a change in the cat correlates with a change in the proposition. Why? The correspondence theory predicts this correlation by analysing truth as a connection to reality.
A principle challenge, on the other hand, is to understand the nature of the connection. There are metaphysical and epistemological worries. On the metaphysical side, there is the worry that a correspondence relation is intolerably mysterious. Correspondence is not analysable in terms of familiar physical relations, like distance or force. So what is correspondence? Some philosophers worry that by analysing truth as correspondence you exchange the mystery of truth for a greater mystery. On the epistemology side, there is the worry that you could never know whether a proposition corresponds with things beyond your head, since you can’t get outside your head to see things as they are. The worry here is that you cannot know whether any proposition is true if truth requires correspondence.
Another challenge arises from alleged counterexamples. It is true that there are no hobbits. Yet, it is unclear how a true proposition about what is not real could correspond to something that is real.
A common response to the challenges involves developing theories of the components involved. For example, there are structural accounts of correspondence designed to remove the metaphysical and epistemological mysteries. Moreover, there are accounts of negative facts, which serve as correspondents for negative truths.
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