Correspondence

Truth understood as a relation between what is said and how things are - the theory almost everyone assumes and nobody can state.

Theme: Knowledge, truth and reason
Tradition: Western
Term fixed: c. 1270

In plain terms

A statement is true when it matches how things are. That is the default view, held by nearly everyone who has never thought about it and by many who have.

The trouble is saying what the matching consists in. It is clearly not resemblance - the sentence the cat is on the mat looks nothing like a cat on a mat, and nothing about the sounds resembles fur.

And the other side of the relation is elusive. What is a statement supposed to correspond to? A fact - but the only way anyone can specify the fact is by using the statement, which makes the theory look like it is saying that a statement is true when things are as it says. Which is true, and is not obviously a theory.

As a philosopher would put it

Aristotle's formulation gives the intuition; the scholastic adaequatio rei et intellectus names it. Russell and the early Wittgenstein give it its most literal development: the picture theory has propositions share a logical form with the states of affairs they represent, and the structure of the sentence mirrors the structure of the fact.

The difficulty is the correspondents. Facts have been called shadowy entities individuated only by the sentences that state them, and the slingshot argument - versions in Church, Davidson and Gödel - purports to show that if true sentences correspond to facts at all, they all correspond to the same one.

Tarski's semantic conception is often read as a rehabilitation: the recursive definition of satisfaction gives a formal account of how the truth of a sentence depends on what its parts refer to. Whether that is a correspondence theory or a technical device compatible with any of them is itself disputed, and Tarski said the definition was neutral. Deflationists take the T-schema to exhaust the content and conclude there is no relation to describe.

Where you meet it

Every flat map of the earth is wrong, and each is wrong in a way its maker chose.

Mercator preserves angles, which is why it was used for navigation for four centuries: a straight line on the chart is a constant compass bearing. It does this by stretching area toward the poles, so Greenland appears about the size of Africa when it is around a fourteenth of it. Gall-Peters preserves area and distorts shape instead. Equal-area, conformal and equidistant projections cannot be combined, and this is a theorem rather than an engineering limitation.

So a map corresponds to the territory, and it does so by not resembling it. What makes a Mercator chart true is a systematic relation between marks and coastlines under a stated transformation - and the transformation is chosen for a purpose. Nobody thinks Greenland is enormous, and nobody thinks the chart is lying. That is correspondence without picturing, which is what the theory needed and never quite specified.

What is actually disputed

Whether the correspondence relation can be specified.

Inflationists hold that truth consists in a real relation to the world, and that giving an account of it remains genuine unfinished business. Deflationists reply that the search has produced nothing in two thousand years, that the T-schema captures everything the notion does, and that facts are a shadow cast by grammar.

The slingshot argument is the sharpest technical objection and its force is contested - it depends on assumptions about substitution that a defender of facts can reject, at some cost. Meanwhile coherentists and pragmatists press the epistemic point: even granting that correspondence is what truth is, we have no access to the world unmediated by belief, so the theory tells us what truth would be while giving us no way to use it. Correspondence theorists regard that as a change of subject, and they are probably right, which does not make the difficulty go away.

Defined against

Coherence The two rival accounts of what truth consists in, and the choice between them decides whether a consistent fiction could be true

Philosophers

Aristotle The formulation everything else elaborates
Thomas Aquinas Adequation of intellect and thing
Bertrand Russell Facts and propositions as structurally matched
Ludwig Wittgenstein The picture theory, and its later abandonment
Willard Van Orman Quine Scepticism about facts as entities

Works

Metaphysics The classical statement
Summa Theologiae The scholastic formula
Tractatus Logico-Philosophicus Correspondence as picturing, at its most literal
Philosophical Investigations Where the same author dismantles it
Principia Mathematica The logical apparatus behind the structural version

Schools

Peripatetic school (Aristotelianism) Where the intuition originates
Thomism Where the formula is fixed
Logical Atomism Where facts become the furniture of the world
Vienna Circle Where correspondence meets verification
Ordinary Language Philosophy Where the picture theory is dissolved

Related concepts

Truth c. 330 BC · Coherence 1807 · Reference 1905 · Objectivity 1781 · Knowledge c. 369 BC

The formula adaequatio rei et intellectus is scholastic and traces to Isaac Israeli; Aristotle supplies the intuition and Russell and Wittgenstein give it its most literal twentieth-century form.