Truth is important to us, it’s what we all strive for. But what is it, and how do we know when we’ve arrived at it?

Aristotle defined it as: ‘Saying of what is that it is or of what is not that it is not’.  Here’s a simple modern version of what is now called a correspondence theory of truth: ‘For any P, to say that P, where P, is true’. Simple, huh?

Hold on a minute… Philosophers tell us that we should always be suspicious of seemingly simple solutions, and there are two basic problems with the correspondence theory that any philosopher worthy of the name is obliged to point out.

Firstly we need to identify the items – propositions and facts – that are supposed to correspond where there is truth, and fail to correspond where there is falsehood. Secondly it’s necessary to know in what correspondence consists.

Specific failings of such theories are that one of the two items tends to collapse into the other, and that the relation called correspondence remains obscure. So, how do we distinguish consistently between propositions and facts, and what is correspondence?

The word proposition is a term that enables us to speak generally about what is said, what is belived, and so on. It is a statement about something that is or that we believe to be, and as such it has a truth value. It is, more often than not, contained within a sentence. But sentences in general do not have truth values; they may be uttered by different speakers at different times and in different places, and may therefore be sometimes true and sometimes false.

It’s only when we abstract the notion of what is said or expressed by the uttering of a certain kind of sentence – one in the indicative or declarative, which makes sense and doesn’t fail in its references – that we have a proposition. Accordingly, propositions are truth-bearers because they are the objects of thought and belief.

For Wittgenstein, propositions are verbal complexes compounded out of elementary or atomic propositions, which in turn are constituted by arrangements of “names”. The world consists of “simples”, logical atoms in various complexes, which are “facts”. In other words, propositions relate to facts and are essentially composite; the elementary propositions that are their constituents are correlated by consciousness to “states of affairs”, which are in turn correlated by human choice to objects in the world.

If this account strains belief and threatens total obscurity for the correspondence between propositions and facts, Bertrand Russell’s version puts the distinction between the two in grave danger of collapse.

In Russell, Wittgenstein’s simples become “directly perceived sense data”. The names become “simple objects of acquaintance”. What this means in effect is that propositions acquire their meaningfulness from the relation of their constituents to the atomic simples with which we are directly acquainted in perception. Descriptive knowledge is inferred from or referred back to “episodes of acquaintance”, and a simple proposition links directly to the state of affairs presented in that episode.

By both of the above accounts correspondence is a relation of “structural isomorphism“, the idea in each case being to show a consistency between linguistic structure and the structure of the world: the structure of propositions reveals the structure of the corresponding fact.

But the notion of correspondence is made no clearer by interpreting it as structural isomorpism, since neither the idea of structure in propositions nor the notion of a supposed isomorphism is palpable.

Isomorphism is a concept that can only be understood in terms of structure and correspondence, therefore any thesis inclusive of the three elements is circular.

Also, consider the proposition “the baby is on the rug”, which contains at least three constituents, the baby, the rug and the relation “on”. The physical fact to which this is supposed to correspond has only two, the baby and the rug. Since the relation “on” in the proposition has no truth value, the proposition might just as well be “the rug is under the baby” or “the rug is part of the baby”, and so on. Indeed, how, even if we could get over the problem of the negative truth value of relations, could we say how many elements a proposition has when it is quite possible that in some language other than English there is a proposition expressible in a single word, which says exactly the same thing as “the baby is on the rug”?

The notion of correspondence interpreted as structural isomorphism is intimately connected with the two distinguishing theses of logical atomism, a theory about the ultimate structure of the world, and the ideal of a perfectly coherent language. Therefore, a viable correspondence theory of truth must be free of atomist metaphysics, and must not rely on an ideal language.

Another philosopher, JL Austin, seeks to explain correspondence in terms of purely conventional relations between words and the world. He thinks that lexical choices and physicality are related in two ways:

1) by means of “descriptive conventions” correlating words (sentences) with types of situations in the world;

2) by means of “demonstrative conventions” correlating words (statements or actually issued sentences) with actual situations in the world, matters of “fact”.

The idea is that in a statement like “I am typing” issued by S at T, the descriptive conventions correlate the words with situations in which someone types, and the demonstrative conventions correlate the words with the state of S at T. The statement is true if the specific situation correlated with the words by 2) is of the type correlated with the words by 1).

In other words, what S says at T will be true if the actual situation, correlated with the words S speaks by the demonstrative conventions, is of the type correlated with those words by the descriptive conventions.

Austin stresses the conventional aspect of the correlations: any words may be correlated with any situation as long as the correlations are sufficiently consistent for the purpose of successful communication; the correlation is in no manner reliant on isomorphism between items of language and the world.

The obvious difficulty with this is that it only works for statements tied to a particular speaker at a particular time of speaking; it applies in a direct manner only to statements expressed in indexical sentences, statements which, because they are not explicitly referential, as are general or indefinite statements, cannot be used in different situations.

Austin’s account depends on both kinds of correlation but, in the case of general or indefinite statements, the demonstrative conventions would be redundant in the determination of their truth.

A further criticism is that Austin seems to confuse the semantic conditions that must be satisfied for the truth of a statement S1, which states of some other statement S2, that S2 is true, and what is being asserted when S2 is stated to be true.

If Austin is correct in his statement that to say a statement is true is to say that the relevant demonstrative and descriptive conventions are followed or satisfied, then it follows that in saying of some statement that it is true we are talking either about the meanings of the words used, or we are saying that the speaker used the words correctly.

It is patently false, however, that we are doing either of these things. It is not, in fact, the words at all that we are talking about; rather we are confirming or agreeing with what was said.

Be that as it may, Austin’s version improves hugely on Russell’s or Wittgenstein’s because it avoids the collapse of the distinction between fact and proposition, by locating the truth of the statement that P not in its correspondence to the fact that P, but rather in the facts being as P says.

What seems to be crucial and at the core of any correspondence theory of truth is the strength of the notion of correspondence itself. Some philosophers have distinguished between two competing interpretations: correspondence as correlation, what might be called a ”weak” relation; and correspondence as congruity, a stronger one.

We might also contrast “correspondence with” and “correspondence to”, the former being correspondence as congruity, the latter as correlation. A key may correspond with its keyhole, one half of a stamp may correspond with the other half; while an entry in a ledger may correspond to a sale, and one rank in the Army to another in the Navy.

Of the two interpretations of correspondence above, correspondence as congruity generally serves in traditional theories. However, as can be seen, there are still some holes in the generalisation that “For any P, to say that P, where P, is true”. 

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