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Private language argument and Zeno's paradox


To: Chris H.
From: Geoffrey Klempner
Subject: Private language argument and Zeno's paradox
Date: 18 February 2004 13:27

Dear Chris,

Thank you for your e-mail of 9 February, with your essay for units 4-6 of the Philosophy of Language program, 'Discuss the implications of the private language argument.'

It was imaginative of you to compare the private language argument - or Kripke's version of it - with Zeno's paradox.

Let's start with Zeno's paradox, because this will be instructive.

I would not accept that the 'fallacy' in Zeno's logical argument lies in the assumption that an infinite series cannot have a finite sum. It is possible to have the correct view of the mathematics of infinite series and still be gripped by the paradox.

In fact, there seems general (though not universal) agreement amongst commentators that the false assumption is that if a process can be broken down into infinitely many parts, this means that an infinite number of separate *acts* are required to accomplish the process. The example of Achilles and the tortoise shows that this is not the case.

The general moral one might draw from this is that we made a false assumption in describing the case (the race between Achilles and the tortoise) as we did. When the case is redescribed, the paradox disappears.

Can we do the same with the rule-following argument?

Something is assumed, and this leads to a paradox. The paradox is proof that a false assumption has been made. The challenge is to see whether we can identify the false assumption, and, having removed it, redescribe the case (the coffee table and the balloon) so that the paradox disappears.

I claim that the paradox results from either one of two false assumptions:

A1. When I learn a linguistic rule R, my mind makes epistemic contact with an external reality containing every instance - infinitely many - of R (Platonism).

A2. When I learn a linguistic rule R, my mind constructs a mental model containing every instance - infinitely many - of R (Psychologism).

Of course, in everyday conversation no-one is ever tempted to talk like this. But this was precisely what is implied by the sceptical thought that I cannot be sure that I know my own rule. When tomorrow I call the coffee table a 'balloon' this shows that my rule was different from what I thought it was.

However, there is another way to describe this: There is something we call 'following a rule' or 'going against a rule' in actual cases. It is in reference to the practice of rule-speak that the concept of 'rule' has application, and *only* in reference to that practice.

In relation to this empirically constrained concept of a rule, the assertion, 'I have a rule, but I don't know for sure what my rule is' might have a marginal role for some obscure cases (think of some examples) but it does not have the meaning that it has in A1 or A2.

Admittedly, this begs the question why we are *tempted* to think of linguistic rules platonistically or psychologistically. In the Investigations, Wittgenstein comes at this from different angles.

The upshot is that I disagree with Kripke. There is no 'sceptical solution'. Wittgenstein does not say anything that implies that to apply rule R correctly *is* (by definition) to agree with the majority in applying R. The problem with this interpretation is that this takes us right back to the problem of infinity. Which 'majority' are we talking about? The majority of my friends? All speakers of English? Every human being (or alien) who will ever use the English language now or forever more?

If we are making historical allusions, Kant is arguably closer than Hume. Agreement in judgements - agreement in 'forms of life' - is the a priori condition for the possibility of language. Forms of life are the bedrock for Wittgenstein, in the way that space and time, causality and substance are in Kant's metaphysic of experience. Kant's response to Hume's scepticism is that experience is only *possible* in the context of experience of a world of causally related objects located in space. Similarly, following a rule is only possible in the context of a speaker of a language sharing a form of life with other speakers of that language.

Thinking about this makes one's head spin. There's no denying it. The sense of paradox does not easily go away. How do I know what I mean by any word? Wittgenstein says I just know. This is the standard case. I am confident, after having the meaning of the word explained to me, that I know how to go on. Sometimes, this confidence is misplaced. I find I have got the wrong end of the stick. But such cases are necessarily the exception.

Reading Kripke, one is struck by the thought, 'I know what I mean by plus!' And of course this is true. You and I do know what we mean. What we don't know - what we don't realize, prior to doing philosophy - is what 'knowing what X means' really means.

All the best,