Turing differed fundamentally on the question of inconsistency from Wittgenstein when he attended Wittgensteinâ€™s seminar on the Foundations of Mathematic:ssee Historical development of Incompleteness and Inconsistency]:

Wittgenstein: *Think of the case of the Liar: It is very queer in a way that this should have puzzled anyone â€” 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 anyone 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 â€” 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 sortâ€¦. You cannot be confident about applying your calculus until you know that there are no hidden contradictions in it.*

Wittgenstein: *There seems to me an enormous mistake there. ... Suppose I convince [someone] 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 2x2 = 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...*

**Because contemporary large software systems are pervasively inconsistent, it is not safe to reason about them using classical logic.** [see Common sense for inconsistency robust information integration].

## Recent comments

1 day 8 hours ago

2 days 7 hours ago

3 days 10 hours ago

5 days 7 hours ago

1 week 2 hours ago

1 week 3 hours ago

1 week 4 hours ago

1 week 12 hours ago

2 weeks 3 days ago

2 weeks 6 days ago