Tuesday, June 28, 2011

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

To: Max T.
From: Geoffrey Klempner
Subject: 'Snow is white' is true if and only if snow is white
Date: 12 June 2003

Dear Max,

Thank you for your e-mail of 2 June, 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.

The first thing one has to ask is why we are considering this question. In the program, the equivalence statement arises as a way of approaching the concept of truth. This is why we are interested in it. The predicate '...is true' is the only predicate which, when attached to the name of any sentence, gives a true statement if, and only if that sentence is itself true. This identifies, but does not provide any further information about, the concept of truth.

In para 1 you say, 'To the left of "if, and only if" is a compound proposition and to the right is a simple proposition.' Is that true? A compound proposition would be one like, 'snow is white and grass is green', or 'either snow is red or grass is green'. In these two cases, we have simple subject-predicate statements of the form, 'a is F' (Fa) joined by a truth functional connective ('and', 'or').

On the other hand, the statement, "Snow is white" is true has the logical form, a is F. This is because "Snow is white" is treated as a name referring to an object, in this case a string of words which makes a sentence.

[For simplicity I have represented 'snow is white' as a subject predicate proposition, the subject, snow, being treated as an individual entity. An alternative way to represent this would be, 'For all x, if x is snow then x is white' or, (x)(x is snow -> x is white). In this version, 'snow' appears in the quantified proposition as a predicate.]

In para 2, you say that it would not be true that '"Snow is white" is true' could be substituted for 'snow is white' in a world where snow is pink. I disagree. In a world where snow is pink, the proposition 'snow is white' is false, and so is the proposition '"snow is white" is true'. HOWEVER, if we are considering the meanings of words, not as fixed in the actual world, but as relativized to the world being described, then in a world slightly different from the actual world, where the English language word 'white' refers to the colour pink, and 'pink' refers to white, then it would be true to say, in our language, that snow is white in that alternative world - because their snow is just like our snow - but false to say that 'snow is white' is true in that world, because the English speaking inhabitants of that world do not use 'white' to mean what we mean by 'white'. I have a feeling that this is what you might have meant.

Does '"Snow is white" is true' mean the same as 'snow is white'? someone might argue the meanings are not the same, because the first proposition explicitly refers to a concept (truth) which the second proposition does not refer to. However, there is a more basic sense in which the two propositions do mean the same, in that the truth conditions for 'snow is white' are the same as for ""snow is white" is true'.

Does 'It is true that the King is dead' suggests that the speaker has evidence, whereas 'The King is dead' does not carry this suggestion? I would be inclined to say that any assertion carries the suggestion that the speaker has grounds for that assertion. To assert that P implies that you believe that P. If you do not believe that P then you are telling a lie. If you do believe that P, then there must be something that counts for you as grounds for that belief. However, there does seem to be an implication of increased support for a belief when someone says, 'It is true that...'. I would explain this as simply a function of the fact that two heads are better than one. If someone believes the same thing as you, then each of you can cite the other's support as increasing the probability that the belief is true.

Why say, 'It is true that the King is dead', and not simply, 'The King is dead'? There are lots of things one can say: 'I agree', 'Yes', 'Yes indeed', 'that's true' and so on. All these replies have the same function, namely, to take whatever the first speaker said and signal agreement. Someone can make a five minute speech and you can say, 'That's true', or 'That's all true'. In other words, you don't have to repeat the speech.

That still doesn't prove that the 'redundancy' theorists are right, that *all* there is to the concept of truth is a useful device for indicating agreement.

This leads on to the substance of your essay:

If '"Snow is white" is true if and only if snow is white' merely serves to identify the concept of truth, then we may indeed be tempted to try to say *what it is* that makes 'snow is white' true. And you give various suggested alternatives. Let's look at these:

(a) "Snow is white" is true if and only if there is evidence supporting snow is white.

The objection here is that sometimes evidence can support a proposition, which subsequently turns out to be false. There was once evidence in support of the phlogiston theory.

(b) "Snow is white" is true if and only if the belief that snow is white is consistent with our other beliefs.

The objection here is a society where so many beliefs are false (say, a society ruled by paranoia and superstition) that the test of consistency merely yields more false propositions.

(c) "Snow is white" is true if and only if we can pair up the terms 'snow' and 'white' with real things in the world and those things are related in a way that corresponds to the way the words referring to them are related in that proposition.

The difficulty in explaining the guiding idea here - the idea of correspondence - is that the explanation easily collapses into a version of the original equivalence. All there is to 'correspondence' is the fact that 'snow' refers to snow and 'is white' refers to the property of being white. As Frege argued, the attempt to get a stronger notion of 'correspondence' leads to an infinite regress. If one said that the sentence 'snow is white' stands in relation R to the world, then one can still ask whether all sentences which stand in relation R to the world are true.

However, we *can* raise the question of correspondence in an interesting way by recasting the question of truth in terms of the debate between realism and anti-realism. But that is another story!

All the best,

Geoffrey