Friday, July 29, 2011

'Snow is white' is true if and only if snow is white

To: Steve B.
From: Geoffrey Klempner
Subject: 'Snow is white' is true if and only if snow is white
Date: 3 February 2004 12:25

Dear Steve,

Thank you for your e-mail of 25 January, with your second essay for the Metaphysics program, in response to the question, ''Snow is white' is true, if, and only if, snow is white'. Discuss.

I don't know what it is about this question, but seems to have been an upsurge in its popularity recently. Yours is the third or fourth essay I've had on this topic in the last month!

Although this was not the intention of the question, you have found a way to use the formula to contrast the realist and anti-realist conceptions of truth, showing the danger of adopting 'extreme' versions of either theory.

Extreme anti-realism, on your account, makes 'the fact...so mind-dependent that fact and proposition come into existence as one - the two are really just two aspects of the same element of reality' the result being that the sentence 'becomes effectively empty'.

Extreme realism, by contrast, makes 'the fact...utterly independent of the proposition' in which case 'it is hard to see the basis for a relationship between fact and proposition' so 'the sentence as a whole becomes meaningless'.

I read your critique of extreme anti-realism as an application of the Reality principle. The extreme anti-realist makes facts so mind-dependent that there is no longer any room for the possibility of false judgement, and all objectivity is lost.

Your critique of extreme realism might be read as a refutation of a version of the correspondence theory of truth, according to which any proposition which we regard as 'true' might turn out to be false because it fails to correspond with the facts. In other words, what we have is an extreme scepticism, where human minds lose all prospect of making contact with the facts 'out there'.

In terms of the image of the arrow and its target, the extreme anti-realist attaches the arrow to the target, while the extreme realist puts the target so far away that we can never know whether the arrow has hit the target or not.

The strange thing is that the formula, 'Snow is white' is true if and only if snow is white appears to be neutral between these, or any other positions on the spectrum between realism and anti-realism.

What the formula does is identify the predicate, '...is true' as the ONLY predicate which removes the quotation marks from ANY indicative sentence which we might substitute for 'Snow is white'. That is indeed a remarkable property if you think about it.

There is indeed scope, as you want to say, for 'realist' and 'anti-realist' accounts of how concepts get their meaning. Take snow, for example. Does the concept snow refer to something out there (realist) or to an idea in our minds (anti-realist)? Although that is not the primary sense in which I am using these terms in the program, there is undoubtedly an issue here. Following a seminal paper by Saul Kripke 'Naming and Necessity' (later published in book form by Blackwell) attention has been drawn to the semantics of terms for natural kinds, like snow, or gold, or tiger. Kripke argued that gold could conceivable turn out to be white, not yellow (in fact, I seem to recall his remarking that this is in fact true, that the yellowness of gold is due to tiny amounts of impurities). Natural kind terms function like names, picking out aspects of the world: 'I call anything like that, gold.' As science progresses, we learn more and more about what it really means for X to be 'like' Y. Fool's gold may look more like our subjective idea of 'gold' than real gold, but fools gold is not gold because its chemical constitution is different from the thing which we originally named 'gold'.

Again, although the issue is well worth discussing, it was not what I had in mind when I set the question!

This is what I did have in mind:

We seem to be able to identify two 'positions', realism and anti-realism, which differ in striking ways. Is there any way of using the snow is white formula to argue for one theory and against another?

When the logician Alfred Tarski first proposed the formula as a condition for any acceptable definition of truth, he claimed that this vindicated the correspondence theory of truth. But is this so? Only if 'correspondence' is understood in so weak a sense as to fail to distinguish the realist from the anti-realist.

In fact, I would argue that what we have here is a definition of truth which succeeds in logically identifying the truth predicate, while leaving completely open the metaphysical issue of realism versus anti-realism. In other words, two very different books could be written on the question, 'What is truth?', one which gave the logical answer, and one which delved into the metaphysics.

All the best,

Geoffrey