EntretenidaDiscusiónSobreLaContradicción

WITTGENSTEIN: ...Think of the case of the Liar. It is very queer in a way that this should have puzzled anyone - much more extraordinary than you might think... Because the thing works like this: if a man says 'I am lying' we say that it follows that he is not lying, from which it follows that he is lying and so on. Well, so what? You can go on like that until you are black in the face. Why not? It doesn't matter... it is just a useless language-game, and why should anybody be excited?TURING: What puzzles one is that one usually uses a contradiction as a criterion for having done something wrong. But in this case one cannot find anything done wrong.WITTGENSTEIN: Yes - and more: nothing has been done wrong... where will the harm come?TURING: The real harm will not come in unless there is an application, in which a bridge may fall down or something of that sort.WITTGENSTEIN: ... The question is: Why are people afraid of contradictions? It is easy to understand why they should be afraid of contradictions in orders, descriptions, etc., outside mathematics. The question is: Why should they be afraid of contradictions inside mathematics? Turing says, 'Because something may go wrong with the application'. But nothing need go wrong. And if something does go wrong - if the bridge breaks down - then your mistake was of the kind of using a wrong natural law...TURING: You cannot be confident about applying your calculus until you know that there is no hidden contradiction in it.WITTGENSTEIN: There seems to me to be an enormous mistake there. ... Suppose I convince Rhees of the paradox of the Liar, and he says, 'I lie, therefore I do not lie, therefore I lie and I do not lie, therefore we have a contradiction, therefore 2*2=369.' Well, we should not call this 'multiplication', that is all...TURING: Although you do not know that the bridge will fall if there are no contradictions, yet it is almost certain that if there are contradictions it will go wrong somewhere.WITTGENSTEIN: But nothing has ever gone wrong that way yet...
De las "Wittgenstein's Lectures on the Foundations of Mathematics, Cambridge, 1939", editadas por Cora Diamond (Harvester Press, 1976).",1]