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Philosophical significance of the paradox of the heap


To: Mary J.
From: Geoffrey Klempner
Subject: Philosophical significance of the paradox of the heap
Date: 31 July 2002 10:18

Dear Mary,

Here is my response to your first essay for the Philosophy of Language program which you e-mailed to me on 7 July. Please accept my sincere apologies for this long delay.

'How would you explain to a non-philosopher the philosophical significance of the paradox of the Heap?'

I liked this essay a lot. It is worth making the point that the question of whether you call something a 'heap' or a 'pile' can be seen as a problem in addition to, or at least not he same as, the problem of vagueness. However, the indeterminacy in the question which is the best of two terms to use in a particular case is a phenomenon which the later Wittgenstein was just as interested in as the problem of vagueness.

The concept of a 'heap' is different from the concept of a 'pile' and the difference can be explained with some degree of precision. In a pile, things are balanced on top of one another, whereas in a heap, things are dropped on the top and allowed to tumble down. Some objects can be put in piles only with great difficulty, but easily form heaps. A very inexpertly arranged pile might be mistaken for a heap.

I am saying this in order to narrow our focus on the specific problem of vagueness, where we are concerned with a given term and its range of application, rather than with the choice between two different, overlapping terms.

The point about philosophers is not simply that they like precision. The response to the demand that every statement should be precise is to point out that there are many cases where we cannot give a precise description. We cannot count the grains of sand in a heap. So vague predicates are a genuine enrichment of the language which allow us to communicate information which we could not express in any other way.

What philosophers hate is having to accept a logical contradiction. However, you don't have to be a philosopher to wish to avoid logical contradictions. If it was OK to say things which were self-contradictory, there would be no complaints when, e.g. politicians contradicted themselves.

So what is the difference? Why are most non-philosophers simply not bothered by the fact that we are happy to allow that at a certain indeterminate point, a non-heap mysteriously turns into a heap? Why is this not perceived by non-philosophers as a form of self-contradiction?

A reasonable strategy when confronted with a paradox is to look for an assumption behind the paradox. The appearance of paradox can then be seen as showing that the assumption is in fact mistaken. The interesting thing in the case of vagueness is that most people, when asked, would agree with the assumption that lies behind the vagueness paradox: namely, that when we make a statement, we intend to state a fact. The statement is true if the facts are as the statement states them to be and false otherwise. But it seems that can't be right. If there were a 'fact' of the matter whether a given amount of stand made heap or not, then it would not be true that by adding one grain it is impossible to convert a non-heap into a heap.

The later Wittgenstein's view which you describe, 'language does not have "the truth" wrapped up inside it, but, hey, it works!' involves a radical rejection of the idea that a statement states facts. A statement is nothing of the sort. It is a counter which we use to make moves in a game, or a tool which we manipulate for a particular purpose. These are radical, unnerving ideas which seem to involve the total rejection of the ideas which the non-philosopher accepts implicitly.

(As I will argue later in the program, it is possible to redefine the concept of 'truth' in the light of Wittgenstein's arguments - but at a price.)

That's what makes this issue so gripping. It is not that the philosopher is a fusspot who sees problems where ordinary folk are quite happy to get by. On the contrary, it is the beliefs and ideas of ordinary folk which contain the seeds of the problem. The only reason we are able to 'get by' is because we fail to think things through.

Two things which appear in your essay which I haven't mentioned are solipsism, and the idea of saving the 'fact-stating' or 'truth conditions' view by defining vagueness in terms of the probability of a given response from the average speaker.

Solipsism gets a look in here because it is only when we move away from the point of view subject to see the individual as involved in a practice, that it becomes possible to formulate Wittgenstein's notion of a 'language game', as an alternative to the fact stating view.

My objection to the 'probability' view is that, if we are talking about truth here, then we cannot let this rest on what the 'average' speaker would say. Some individuals have better, more refined judgement about particular questions than others. We cannot allow the merely average response to determine truth. But there is no precise way to measure degrees of expertise.

All the best,