philosophy is for everyone
and not just philosophers

philosophers should know lots
of things besides philosophy

Philosophical Connections

Electronic Philosopher

Feature Articles

University of London BA

Philosophy Lovers Gallery

PhiloSophos Home

International Society for Philosophers

Notes on vagueness, and essay on private language


To: Susie P.
From: Geoffrey Klempner
Subject: Notes on vagueness, and essay on private language

Dear Susie,

Thank you for your email of 4 April, with your notes on unit 3 of the Philosophy of Language program, and your first essay on the topic, 'S'. I apologize for taking longer to respond than I would normally do.

Unit 3

We are in agreement about the necessity for vague concepts, which makes a good starting point. One question to ask (which you address to some point) is what is the utility of vague concepts, why do we need them?

One answer, which you give, is because of the limitations of human knowledge. 'How tall is he?' 'Not very tall.' It's not often you get the chance to measure a person's height precisely, but 'not very tall' is useful information, for example, if we are considering candidates for a job which is difficult to perform if you are short.

However, 'not very tall' is less useful to the human resources manager, say, than, '5 feet 7 inches'. So in this case, the vague statement was second best.

It is tempting to generalize from this case to the assertion that the use of a vague term 'implies a precise condition that either I can't get information about or that there no way of measuring, though measurements would be possible if wanted.' 'It also tells you that there is a precise condition which could be known.' - I don't, in fact, think this is true about a heap.

Consider the following exchanges:

'He's quite tall.'
'How tall?'

'There's a heap of sand on my front drive.'
'How much of a heap?'

You can ask, 'how much of a heap' but unlike the case of a person's height there can never be a precise answer. Any given heap of sand must have a specific number of grains, but this does not tell us how much of a heap it is. The paradox of the heap could be run just as effectively if we patted the heap down by tiny degrees until the point came where we had sand spread on the floor which was definitely not in a heap.

One way in which one might be tempted to put this - which brings in the question of subjective and objective - is to say that height exists even in a world where we are completely indifferent to a person's height and have no way to measure it, whereas heaps only exist because we are interested in them. In fact, this is not strictly true. I remember my father (who made a career as a mining engineer after emigrating from Austria to South Africa) telling me that the was a formula for calculating the height of a heap made from different materials (sand, smooth pebbles, rocks) as well as the angle at the top (e.g 30 degrees). Heaps are a 'natural kind' studied by mechanics. The mechanics of heaps explains why there are, in fact, such things heaps. That much is objective. But there is no measurable state of affairs which the use of 'heap' implies which would be the answer to the question, 'How much of a heap?'

So here is a word (it might not be the best example, given that there is a 'theory of heaps' in mechanics) which we get along with even though there is no precise underlying condition. Heaps are just one of those things which are useful to recognize or know about. 'It's not a neat pile, it's a heap.' Or, 'It's not spread around, it's a heap.'

The paradox of the heap has a solution. But the solution is purchased at a high price. That is why I have to disagree with you and insist that it is an important paradox (whereas the paradox of the Barber is a mere puzzle with an easy solution - 'There is a barber in Sheffield who shaves all and only those men who do not shave themselves. Does he shave himself?' - the answer is not 'yes' or 'no' but, 'You lied, there cannot as a matter of logic be such a barber.').

The high price (to express this vaguely for the moment) is giving up the notion of 'truth' which implies the law of excluded middle. Of course, you can say, 'I knew this all along,' but this is a very significant result.


On my 'Wood Paths' web site is an article, 'Truth and subjective knowledge' which is relevant to this topic:

I want to agree with the thought that there is something 'given' to us which is inexpressible, beyond language. There is no way, in principle, to know how the world presents itself to a given subject other than by being that subject. This can be formulated in a purely materialistic way. 'In the amazing complexity of a human brain, information is encoded, encrypted in a way that is, in principle, accessible only to the person whose brain it is.'

What is S?

The crucial point here is the qualification which Wittgenstein gives, 'A definition of the sign cannot be formulated.' Anyone can have a weird sensation which they have never experienced before, then notice that the sensation occurs again. You go to the doctor, 'I am having these weird sensations, I can't describe them.' 'Well, where are they?' 'Kind of, all over.' The doctor gives you an exam and tells you nothing's wrong. But you know there is.

Here's a different kind of case. You are a painter, working in the general style of abstract expressionism. There is a feeling you get, when you know when you are in 'the zone', when you are onto something, the splashes and drips cease to be splashes and drips, when the composition seems to be guided by an invisible hand.

These are both examples where the coinage of a new word would be possible. 'I'm having the S-feeling again.' But this is NOT the use of 'S' that Wittgenstein is considering. In both cases, there is an assumption that there is something objective corresponding to the feeling (just what you said about vague concepts!). You go to the doctor because you are worried about your physical condition. The painter believes that the S-feeling is a sign that something of quality is being produced, which anyone with aesthetic judgement could recognize.

This is not how the philosopher - the 'private language theorist' - who is attracted to the idea of 'S' thinks. The scenario of the notebook looks attractive, but it gains its plausibility from cases like the above. But what the philosopher thinks is that, 'I would know I had S even if there was nothing in the objective world which corresponded to occurrences of S.'

The worried patient seeks a second opinion and is told that she has a problem with her thyroid gland. Now S acquires a 'definition' in Wittgenstein's sense. (Wittgenstein gives the example of a manometer showing that one's blood pressure has risen.)

I'm not sure what to say about the painter, but it's along similar lines. What would you say?

Neither of these correspond to what the private language theorist has in mind. The plausibility of a private language is that it seems that 'I would just know whether I had THE SAME or not.' But now Wittgenstein's argument kicks in. There is no right or wrong here, because your judgement is not aiming at anything, you are shooting an arrow which is attached to its target. 'Always get rid of the idea of the private object in this way: assume that it constantly changes, but that you do not notice the change because your memory constantly deceives you' (Philosophical Investigations p. 207).

The worry here isn't that, 'My memory might be deceiving me, how can I be sure.' There are lots of things we cannot be sure about because we can't rely on our memories, nor is there any other way of seeking corroboration. Wittgenstein is saying that there is nothing to remember because there is no meaningful content to the thought that you might be 'right' or you might be 'wrong'.

All the best,