Can there be a satisfactory account of the notion of correspondence employed in the claim that
'a proposition or statement is true if it corresponds to the facts'?

J.L. Austin summarized it thus: "To assert that a proposition p is true is to maintain that 'p' corresponds to the facts", which he says is "a piece of standard English" and therefore "can hardly be wrong".(1)

Consider "a proposition or statement is true if it corresponds to the facts".   So "True" means "corresponds with the facts."   The Correspondence Theory of Truth, referred to in the essay title, maintains that the truth or falsity of a proposition is determined only by how it relates to the world, and whether it accurately describes (corresponds with) that world.  

The essay title raises the most commonly cited challenge for the correspondence theory - Can there be a satisfactory account of the notion of correspondence?   When and how does a proposition "correspond" with the facts?   What does it mean for a proposition (which is an abstract conceptual entity) to correspond with "The facts" (which is presumably a material concrete entity)?   How do we tell (and I don't mean judge, I mean sense) whether it corresponds?  

The proper account of correspondence is a sort of mapping relation.   If a mapping can be proposed that maps the relationship between concepts expressed by the proposition with the relationship between the facts that the concepts denote in reality, then that is what it means for the proposition to correspond to that fact.   And that mapping would constitute a satisfactory account of correspondence.   The main criticism of this account of correspondence is the claim that the precise nature of any such proposed mapping is in fact undefined and undefinable.   In the case of a map, we have a straightforward spatial isomorphism between the marks on the paper and the geography being mapped.   But what of the proposition "The cat is on the mat"?   Clearly the proposition does not resemble and hence cannot possibly be congruent in any way with either the cat, the mat, or the relationship between the cat and the mat.   So precisely what does the correspondence mapping consist in?   Obviously it cannot be correspondence in any geometric sense.

The traditional answer is that it consists of a complicated mapping function that comprises the conventions that govern our use of language.   Consider a function "F" that maps the set of propositions ("P") expressible in a language like English onto the set of facts "A" - F(P)=>A.   Or proceed in the reverse direction.   Consider a function "M" that maps the relationship between existents in reality "R" onto a set of propositions "P".   Thus: M(R)=>P.   Therein lies the correspondence between propositions and the facts that they represent or describe.   In general, if "p" is some proposition, then p is true if and only if the fact F(p) obtains in reality.   Or alternatively, in the reverse direction, p is true if and only if there is a relationship between a set of existents in reality "r" that is mapped by the function M into that proposition p:   M(r)=>p.   Admittedly, the functions F and M are massively complex, and will incorporate a lot of information about the language, human culture, and about the world.   Nevertheless, they are well-defined functions.   They are of the same kind of thing as the spatial isomorphism between a street plan and the streets of Toronto.   And they are "Simple" functions to learn how to use - everyone who learns to use a language knows how to use those functions.

A detailed description of nature of the correspondence mapping - of functions F and M - is in fact a theory of how a sentence or proposition has a particular meaning - just how linguistic entities refer to (talk about) non-linguistic entities.   A satisfactory account of the notion of correspondence employed in the claim that "a proposition or statement is true if it corresponds to the facts" is then just that theory of meaning which demonstrates what saying "le neige est blanc" actually means, and how the employment of linguistic terms (such as "True" or "Snow" or "white") relate to what those terms refer to in reality.   The apparently "Simple" process of disquotation employed in Tarski's equivalence schema is just the process of bi-directional translation between the proposition "le neige est blanc" and the fact in reality that snow is white.

In any case, in order for this account of the correspondence mapping to work, there must be some fact to which a proposition can correspond.   So a fact (a relationship between entities in reality) has to exist in order to be mapped to a proposition (an entertained relationship between concepts).   We've already determined which fact that a proposition has to correspond with: the proposition that P has to correspond with the fact that P.   Therefore, we can say that that P is true if and only if there exists a fact that P.   This provides another account of "correspondence."   We can say that "a proposition or statement is true if there exists a fact that the proposition describes".   So an account of correspondence is - if there exists a fact that P, then that fact corresponds with the proposition that P.

But what are facts, and what does it mean to say that facts exist, or that there is some alleged fact?   Our problematic title sentence claims that "True proposition" means "factual proposition".   Aren't we just letting this other word, fact, do all the work of the word we're trying to explain - "correspondence"?

In order to provide a satisfactory account of "correspondence", we therefore have to offer a theory of what facts are.   Facts are combinations of entities in reality together with their properties and/or relations.   So, given some particular context, the fact that the cat is on the mat is the combination of two differentiable entities in reality (ie. a cat, and a mat) together with one of the discernable relationships between them (ie. that the cat is on the mat).   Notice that I did not suggest that these entities and relationships has to be observed.   All that is necessary for the concept of a fact is that they be observable in principle.

But of course the cat being on the mat is only one fact; there might also be other facts, about all cats; or about the relation between cat hairs and cats; and so on.   But the idea is that it is possible, using a Searlean description-cluster-theory of meaning, and limiting the discourse to minimal propositions, to specify and categorise all those different kinds of facts that are relevant to the propositions that we entertain.   An analogy perhaps might help.   Imagine that Reality is the chessboard with its chessmen.   Facts are all the possible configurations of chessmen on any part of the chessboard.   So there is nothing that ontologically exists in addition to the board and the men.   There is one board of 64 squares, and 32 chessmen.   But there is an almost infinite number of facts that can be considered with that limited ontology.

Facts are abstract entities - ways in which the world can be considered.   Although I myself am a realist about reality, the abstract conception of facts would apply equally well to an idealist metaphysical approach to reality.   As Berkeley might suggest, the necessary differentiable entities and discernable relationships might exist only as ideas in the mind of God.

In 1918 Gottlob Frege (1848 - 1925) wrote a relatively short paper entitled "The Thought: A Logical Inquiry".   It is sometimes claimed that in this paper Frege presented a "decisive refutation" of the relational view of truth that is central to the account provided above of "correspondence.

The key passage seems to be rather short, and appears quite early in a paper seemingly more focussed on a different topic.   With a little help from materials found on the internet, I interpret Frege's reasoning as -

(1)     Assume that truth is a relation of correspondence with the world.   Then...

(2)     In order to judge whether "p" is true, we would need to judge whether " 'p' corresponds to the world" is true.

(3)     In order to judge whether " 'p' corresponds to the world" is true, we would need to judge whether " " 'p' corresponds to the world" is true" is true... and so forth.

(4)     Hence, if we assume that truth is a relation of correspondence with the world, we can never judge whether a given thought is true.

(5)     We do in fact judge whether a given proposition is true.

(6)     Therefore, truth must not be a relation of correspondence.

Frege is here talking about whether we can judge whether a thought is true or not.   He is not discussing whether the thought is true or not independently of whether we can judge it so.   Therefore, at best, Frege's argument (if valid) demonstrates that our judgement of truth cannot involve a judgement that " 'p' corresponds to the world" is true.   What Frege's argument clearly does not do is demonstrate that what makes a thought true (judgement transcendently) cannot be a relation of correspondence.   Even if the process of judgement leads to an infinite regress, as Frege suggests, it still may be possible that the judgement-transcendent truth of the thought might never-the-less be definable as a relation of correspondence.

The second error is the assumption in (2) above that to judge whether "p" is true, it is necessary to judge whether " 'p' corresponds to the world" is true.   However, as Frege maintains later in his paper, it is not necessary that a thought be entertained for a thought to be true.   I would argue that instead to judge whether "p" is true it is merely necessary to judge whether " 'p' corresponds with the world", without having to judge whether " 'p' corresponds with the world" is true.   Elsewhere, Frege demonstrates the equivalence of the two thoughts - to entertain the thought that " 'p' corresponds with the world" is to entertain the thought that " 'p' corresponds with the world" is true.   But to entertain the thought is not to judge that the thought is true.

I do not suggest that the one-step resolution is the judgement that "p" is true, or even that " 'p' corresponds with the world" is true.   For if I were to do so, as Frege does, the infinite regress is indeed vicious.   But if instead one focuses on the relationship between the words that express "p" and the world that "p" supposedly refers to and/or describes, then it is the process of linguistic comprehension that establishes whether " 'p' corresponds with the world".   The base of the regress is resolved at once, and the regress collapses.

In 1950 J.L. Austin (John Langshaw Austin 1911 - 1960) and P.F. Strawson (Sir Peter Frederick Strawson 1919 - 2006) exchanged articles in the philosophical periodical Proceedings of the Aristotelian Society in a debate over the Correspondence Theory of Truth.   Austin defended the notion of truth as correspondence, while Strawson attempted to demolish the notion.   Amongst critics of the Correspondence Theory of Truth, Strawson's attack on Austin's position is repeatedly considered to have been sufficiently definitive to have changed the whole nature of the debate over Correspondence theories.

The most curious passage from Strawson's article would seem to me to be -

"In using . . . sentences to make statements, we refer to a thing or person (object) in order to go on to characterize it: (we demonstrate in order to describe).   A reference can be correct or incorrect.   A description can fit or fail to fit, the thing or person to which it is applied.   When we refer correctly, there certainly is a conventionally established relation between the words, so used, and the thing to which we refer.   When we describe correctly, there certainly is a conventionally established relation between the words we use in describing and the type of thing or person we describe."
                                                                                              (Truth: Oxford Readings in Philosophy(2), Pg 165)

It seems to me that in this passage, Strawson is actually agreeing with Austin that truth is a relation of correspondence between the words we use to frame a thought, statement, or proposition and the world that those words are about.   As Austin asks at the end of his article, if "Truth" is not our label for a correct reference or a description that fits, then what else is?   Truth just is the very correctness of reference, and/or fitness of description.   This constitutes another account of "correspondence".

Later on in his critique of Austin's article, Strawson says -

"If Mr. Austin is right   . . .   in declaring a statement to be true, we are either

(a)       talking about the meanings of the words used by the speaker whose making of the statement is the occasion for our use of 'true' . . . or

(b)     saying that the speaker has used correctly the words he did use.

It is patently false that we are doing either of these things."
                                                                                              (Truth: Oxford Readings in Philosophy, Pg 173)

But there are cases of the use of the word 'true' in common discourse where one of these is just exactly what we are in fact explicitly saying.   I would argue that this is in fact what we are always implicitly saying.   For Strawson here omits the more reasonable interpretation of Austin -

(c)       saying that, given the conventional meanings of the words used by the speaker, the reference of the statement is correct and the description of the statement fits what the statement is about.

This more appropriate interpretation of the notion of correspondence clearly includes the assumption of (a) and (b).   So in declaring a statement true because we are saying (c), we are also implicitly saying both (a) and (b).

'sentences of type x are true or false in virtue of: (1) their structure; (2) the referential relations between their parts and reality; (3) the objective and mind-independent nature of that reality."
                                                                                              (Devitt, Realism and Truth(3), Pg 27)

Once one adopts metaphysical Realism, then (following Devitt) one can also employ the method of abduction (inference to the best explanation) to argue that the notion of "Truth" is best considered as a relation of correspondence.   Drawing upon his arguments, and adding my own twist, I would argue that the Correspondence Theory of Truth is the best available explanation for the concept of "Truth" because:

(1)     The language of "Truth as Correspondence" is necessary to permit communications - even for philosophers.   One simply cannot talk about truth, facts, states of affairs, reality, beliefs, or judgements without employing the language of a Correspondence Theory of Truth.   The English language is configured to speak of truth as a relation of correspondence.   Any other conception of "Truth*" is simply the assigning of some philosopher's idiosyncratic notion to a common English word that usually means something else.  

(2)     A focus on linguistic analysis erroneously assigns to the word "Truth" a meaning (or lack thereof) derived from the common employment of "True" in English sentences.   This ignores the function of the concept of "Truth" as it applies to the aim of judgements and beliefs, and to the description of scenarios where our judgements or beliefs might be inconsistent with the objectively and mind-independently existing reality.

(3)     A focus on judgement and "Truth conditions" erroneously assigns to the word "Truth" an epistemologically derived meaning.   All forms of verificationism, like all forms of deflationism, ignore the metaphysical function of the concept of "Truth" as a relationship between the reference and descriptive function of words (and propositions, sentences, thoughts, et al) and the objective and mind-independent reality that they are about.

In the final analysis, I firmly believe that the mapping account of "correspondence" is the only notion that makes any coherent sense in world described by Metaphysical realism.   In the marketplace of philosophical ideas, there simply is no other notion of what "Truth" means that is competitive.

Notes

(1)

(2)

(3)

(4)     Auston, John L.; Sense and Sensibilia; Geoffrey J. Warnock (Editor); Oxford University Press, 1962. ISBN 0-19-500307-1

(5)     Austin, J.L.; "Truth" and Strawson, P.F.; "Truth"   in Truth:Oxford Readings in Philosophy, Simon Blackburn and Keith Simmons, Eds., Oxford University Press, Oxford, England, ISBN 0-19-875250-4

(6)     Devitt, Michael. Realism and Truth (Second Edition), Princeton University Press, Princeton, New Jersey. 1997. ISBN 0-691-01187-7

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