To: Lisa H.
From: Geoffrey Klempner
Subject: 'Snow is white' is true if and only if snow is white
Date: 11 May 2006 10:18

Dear Lisa,

Thank you for your email of 25 April, 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.

We are understanding this as a 'question of metaphysics'. So it looks as though we first need to know what metaphysics is. If the question had appeared a course on meteorology then one might well ask why meteorology should be interested in the whiteness of snow. The simple answer (and it is really not at all simple, it only looks that way) is that the question mentions the concept of 'truth'. In a meteorology course, the question might have been, 'Snow is white.' - Discuss. And then the answer might have taken the form of a discussion about how different kinds of snow appear different shades of white, and what you can learn from measuring the precise whiteness index of a given sample of snow.

Truth is the concept in question. What does the above quote tell us about truth? A lot, in fact.

'True' is the only predicate which you can apply to any given sentence in quotes, which has the effect of removing the quotes. Assume you didn't know the colour of snow. It is not the case that:

'Snow is white' is poetic if and only if snow is white.

'Snow is white' is funny if and only if snow is white.

'Snow is white' is believed by lots of people if and only if snow is white.

If 'snow is white' is poetic, or funny, or believed by lots of people, that still doesn't tell you whether snow is, in fact white. But if you know that 'snow is white' is true, then you know that snow is white. End of discussion. That's what truth is.

But how can 'snow is white' be true?

You raise two very legitimate questions about this. First, the statement 'snow is white' describes a fact about the world. But all we have to go on is our experience. How can anything that we discover about our experience be sufficient to establish a 'truth' about the world apart from our experience?

The second question concerns the pervasive phenomenon of vagueness. The most potent way to raise the problem is using the ancient paradox of 'the heap'. A grain of sand is not a heap. If you add one grain of sand to something that is not a heap you cannot turn it into a heap. Therefore (by mathematical induction) it logically follows that no amount of sand can be a heap.

The paradox works by exploiting the vagueness of the concept of 'heap'. There is no precise point where a non-heap turns into a heap. A similar paradox can be run for a colour word like 'white' (you can try this as an exercise).

Let's look at the first question. 'Snow is white' is maybe not the best example because it is a statement about our experience. There are issues about the 'objectivity' of colour words. Are there colours in reality or is colour merely subjective? One response is to say that colour is defined in terms of normal perceivers in normal conditions. But let's not get into that. Consider instead the statement, 'Snow is H20'. This is something we learn from experience. The molecular structure of water was a scientific discovery.

'Snow is H20' is true if and only if snow is H20.

When we state that it is true that snow is H20 we are talking about the world itself. Our experiences, all that we learn from investigating the world, provide the basis or justification for stating that snow is H20. But justification is not the same as truth. It looks as though when we are stating something as true, we are making a claim which goes beyond anything we can ever know. We can only know how things appear to us, never how things are 'in reality'.

Kant distinguished between the 'phenomenal world' of appearances in space and time and the 'noumenal world' of non-temporal, non-spatial things in themselves. He did not regard the world of appearances as illusory. He describes himself as an 'empirical realist' about such things as snow, or H20, or physical things in general. Truth, for him, is not particularly problematic. Statements are judged 'true' or 'false' in relation to the world of appearances.

There is another issue with truth, which relates to the discussion of realism and anti-realism. As you will discover, the simple formula, 'P' is true if and only if P while serving to identify the truth concept, is not sufficient to distinguish the realist view of truth from the anti-realist view. That is why I would argue that the simple formula cannot be the last word on truth.,

And what about vagueness? Arguably, one would say the same thing. To the extent that I am justified in saying that snow is white, or that Fred is bald, or that this is a heap of sand, I am justified in saying that it is true that snow is white, or that Fred is bald or that this is a heap of sand. Not all philosophers are agreed on this. Some logicians have tried to understand the problem of vagueness by developing multi-valued logic, so that in addition to saying that 'Fred is bald' is true, or saying that 'Fred is bald' is false, we have the option of saying that 'Fred is bald' is a tiny bit true, or slightly true, or fairly true, or very true. The problem with that is however many truth 'values' you invent, the heap paradox breaks out again whenever you are looking at borderline cases between two adjacent 'values'. E.g. at what point, in pulling hairs one by one from Fred's head, does it cease to be 'slightly true' that Fred is bald and become 'fairly true'?

All the best,

Geoffrey