Thursday, June 7, 2012

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

To: John D.
From: Geoffrey Klempner
Subject: 'Snow is white' is true if and only if snow is white
Date: 25 October 2007 12:41

Dear John,

Thank you for your email of 14 October, with your essay for units 4-6 of the Metaphysics program in response to the question, '''Snow is white' is true, if and only if snow is white.' - Discuss.'

What is there worth discussing in this question? Apparently, there are philosophers who call themselves 'idealists', who have one view of the things we call 'snow', 'white', 'truth', and maybe also 'if and only if', and another group of philosophers who call themselves 'realists' who take a different view of these things. Or do they?

Interesting things can be said about the way a mass noun like 'snow' gets its meaning and also about the different way that a name for a perceptible quality like 'white' gets its meaning. This is not really relevant to the question: ANY true or false sentence could have been substituted for 'Snow is white', e.g. 'Snow is purple', 'Cows eat grass', 'Tony Blair is an alien', and so on. However, it is worth while looking at how a term which seemingly applies to each person's internal experience can have an accepted meaning.

A philosopher's definition of 'white' would start something like this: X is white if and only if normal perceivers in normal conditions would agree in calling it 'white'. There is a lot more that needs to be added to this 'biconditional' in order to make it an effective definition, but you get the general idea: the very possibility that a term like 'white' has a meaning already assumes a great deal about ourselves and the world.

What about the claims that you consider, e.g. 'The opposite of white is black'? Suppose someone put forward the following account: The opposite of white is black if and only if normal language users in normal circumstances would agree that the opposite of white is black. What is wrong with that?

In the first case, with the definition of 'white' were talking about the capacity of human beings to successfully identify things by colour, a capacity which gives rise to colour judgements, whereas in the latter case we are simply referring to a judgement that people happen to agree about, for no particular reason. That is why the first definition works and the second doesn't. I am fully in agreement with you here.

To get back to the original question: what is interesting about the claim that 'Snow is white' is true if and only if snow is white?

The formula is intended to tell us something about truth. But it also indirectly tells us what is the point of language.

First, about truth. The example is in fact taken from a famous paper by Alfred Tarski, 'On the definition of truth in formalised languages'. Tarski argued that whatever your philosophical or metaphysical views on truth, any acceptable definition of truth must logically entail that, for any sentence P, we can write:

'P' is T if and only if P.

He called this 'Convention T'.

In the Metaphysics program, a number of inadequate definitions of truth are considered, in order to illustrate this claim. For example, suppose someone put forward the theory that a proposition is true if and only if everyone agrees to it. Then we have:

'P' is T if and only if everyone agrees that P.

The problem with this is that there are some values of P where this biconditional is false. Therefore, truth cannot be the same as agreement.

Although Tarski was prepared, in principle, to consider that there might be more than one account of truth which satisfies Convention T, a 'minimalist' about truth would that Convention T tells the whole truth about truth. Truth is indefinable except in these logical terms.

What, then, does this show about the point of language? Consider your example, 'There is snow on that mountain.' I am looking out of the window, gazing with delight at the brilliant sun reflected off the upper snow-covered slopes of the jagged mountain looming in the distance above the green hills. So much information, all reduced to six words!

But in fact, there is only one truth that you and I both know which is in question, even though our knowledge is arrived at through different routes: mine through perception and yours through testimony: There is snow on that mountain.

Of course, I know lots of things that you don't know, because I have the mountain in view, while you are merely relying on my words, but that is irrelevant so far as the truth of 'There is snow on that mountain' is concerned. That is how language works.

All the best,