Showing incoherence ...

The statement 'It is not possible to talk' can't mean exactly what it says and still be true. However, the following seem reasonable (at least superficially):

(1) We know what it means, because otherwise we couldn't decide that it was false.

(2) There is some sense in which we can think that it's impossible to talk:

- there is behaviour that would be consistent with this (although it would also be consistent with other things which were inconsistent with it).

- it seems possible to imagine finding out (as in some nightmare) that we have never been able to talk, and that whenever we thought we were talking we were always making some kind of mistake.

- in order to understand the falsehood of the statement, we need to have some conception of what it would be for it to be true.

(3) When I say 'It is not possible to talk', you might think 'well - can this be true?'. If you thought it was true, you would (a) not answer me (or not answer me honestly) and (b) realise that I hadn't really spoken to you. You might think 'these sounded like words that meant something, and because I was taken in by their apparent meaning they made me think - and come to a remarkable conclusion - but in fact they didn't mean anything at all'.

All this clearly has a kind of fairytale quality to it, and, I think (for reasons that are peripheral for the present, but related to the private language argument), may also be incoherent.

However - it suggests something useful:

We can show things without saying them (obviously), but we may also be able to show things by saying something, and even by seeming to say what it is that we mean to show - even though what we seem to be saying can't be true.

Imagine you have a rare kind of colour blindness, so that under indoor lighting you see red as green & green as red, but in daylight you don't. You are coming to me for evening classes in road safety, and I need to show you which colour of light means stop and which means go. What do I show you?

And what if we don't know which one of us is making the mistake? What do the words 'red' and 'green' mean here? All we know is that we don't agree about which indoor light looks like the outdoor light. We can talk, though, because we can predict what each other will say when asked.

If I wanted to show you what to look for in an outdoor red light, I would show you an indoor light that looked green to me. I might even say 'look - this is a red light'.

When I say 'it is possible to talk' must be true in any language game in which its equivalent (under interpretation) can be constructed, I may be simultaneously introducing you to the possibility of its contrary.

And: maybe if you can't imagine the contrary you can't understand the statement.

The construction of the theoretical certainty depends upon an appreciation of the phenomenological uncertainty. If you can't think the unsayable - if you can't live with Cartesian anxiety - then you will never have theoretical certainty.

My thesis depends upon showing you a possibility that cannot be articulably entertained, and showing you by pretending to entertain it - the argument is a reductio from the presumption of its own unintelligibility.

Instead of an axiomatic contradiction, we have a contradiction with the possibility of axiomatisation.