What Is the Correspondence Theory of Truth?

What is truth? This is a perennial philosophical question because its answer lies at the intersection of knowledge and reality. Knowledge requires truth, for we cannot know things that are false; and truth surely has to do with the way the world actually is. The correspondence theory of truth, which dates back to Plato and Aristotle and is a predominant theory in contemporary Anglophone philosophy, fills out this picture. In this article we’ll examine what this theory says, and some challenges associated with formulating it.  

Echoing Plato’s discussion of truth in Sophist (263b), Aristotle famously says in his Metaphysics that “To say of what is that it is not, or of what is not that it is, is false, while to say of what is that it is, and of what is not that it is not, is true” (1011b25). More simply, a statement is false when it does not correspond with reality; it is true when it does. This commonsense view is called the correspondence theory of truth, and in the twentieth century it was famously endorsed by Bertrand Russell and G.E. Moore, among many others.  

The correspondence theory has three elements: truth is a (1) two-part (or ‘dyadic’) relation of correspondence between (2) a proposition and (3) a fact (or ‘state of affairs’) in the world. The conjunction of these three elements makes the correspondence theory a realist account of truth. This means that truth is an objective fact about the connection between propositions and facts. This contrasts with anti-realist accounts of truth, which say that truth depends in an essential way on someone’s perspective or what he believes. 

Let’s look at these three elements in some more detail. 

Propositions Are Claims About Facts

Propositions are perhaps the least controversial element in the correspondence theory of truth. These are declarative statements that can be true or false, like ‘India has over 1 billion inhabitants’ and ‘Australia’s warmest months are December and January.’ Imperatives, like ‘Turn right at the next corner,’ and questions, like ‘Do you like summer more than winter?’ are not propositions because they do not purport to state facts. 

The facts or states of affairs to which true propositions should correspond are a bit fuzzier. Analyzing these is a task for metaphysics, since this area of philosophy is concerned with understanding reality, and reality is comprised of the totality of facts. But it suffices to say that facts or states of affairs are ways the world actually is. 

Correspondence theorists should be careful when pushing this analysis further. For example, analyzing facts in terms of ‘things to which true statements correspond’ is circular, since we are trying to understand correspondence in the first place. But this need to push further is arguably not a problem for correspondence theorists, since it is not the task of every philosophical theory to assume the burdens of other branches of philosophy. 

So, propositions seem clear enough, and the facts to which they are thought to correspond are a bit fuzzier, but perhaps not alarmingly so. What about the relation of correspondence? This is much more difficult to spell out. Let’s take things one step at a time. 

Correspondence is an objective relation between propositions and facts. So on this theory there is no such thing as ‘my truth’ or ‘your truth.’ Truth is a relation between a proposition and the world. But relations are extremely diverse things: I’m related to my brothers, water is related to hydrogen and oxygen, and the numbers two and four are related in virtue of both being even. So what kind of relation obtains between propositions and facts in the correspondence theory of truth?  

The Correspondence Relation Involves Correlation and Isomorphism

Two features help us distinguish this relation. One feature says propositions correspond with facts when they are correlated with facts. This means that every true proposition is true in virtue of one fact, no more or less. This ensures a proposition like ‘Ottawa is the capital of Canada’ is not true in virtue of multiple, divergent facts about Canada, which would be clearly problematic for any theory of truth. 

Another, more informative, feature says propositions correspond with facts when the two are isomorphic, that is, when they exhibit the same structure. This is very difficult to make precise, but the general idea is reasonably straightforward. 

Roughly, the proposition ‘Ottawa is the capital of Canada’ will be isomorphic with the fact <Ottawa is the capital of Canada> when there is a one-to-one relation between the elements of each. So there must be a country called Canada, a city called Ottawa, a property of cities that makes them capital cities, this property must inhere in the city of Ottawa.  

Working out this isomorphism in more detail puts us squarely into a variety of technical areas of philosophy: philosophy of language, metaphysics and ontology. For now, it suffices to say that the correspondence theory of truth is a realist account of truth that says a proposition is true only when it corresponds with the fact in the world that makes it true.