One of the basic theories of “truth,” where the goal of enquiry stands in contrast to “falsity” and not in contrast to “opinion.” The correspondence theory is the most commonly used theory of the nature of truth because it says quite simply that a statement is true if it corresponds with reality, with the facts of how things are. For example the statement: “The cat is on the mat” is true only if indeed the cat is on the mat and untrue if the cat is not on the mat. Thus a statement is true if it corresponds with the situation or state of affairs that verifies it.
Correspondence theories appear in other disciplines. In mathematics the one-to-one (1:1) correspondence is an important principle. At its simplest it is a 1:1 correspondence between two series. Thus addition in the first series corresponds to multiplication in the second. In secret codes, the production and deciphering of which is a concern of mathematicians, there is a 1:1 correspondence between a cipher and what¬ ever letter or number or thing it represents. In sophisticated mathematics the test of whether there is a 1:1 correspondence between A and B is very important.