The Slipperiness of Logic

Wittgenstein, Philosophical Investigations:

107. The more narrowly we examine actual language, the sharper becomes the conflict between it and our requirement. (For the crystalline purity of logic was, of course, not a result of investigation: it was a requirement.) The conflict becomes intolerable; the requirement is now in danger of becoming empty. — We have got on to slippery ice where there is no friction and so in a certain sense the conditions are ideal, but also, just because of that, we are unable to walk. We want to walk: so we need friction. Back to the rough ground!

Wittgenstein, Culture and Value, p. 30:

In the course of our conversations Russell would often exclaim: "Logic's hell!" — And this perfectly expresses the feeling we had when we were thinking about the problems of logic; that is to say, their immense difficulty, their hard and slippery texture.

I believe our main reason for feeling like this was the following fact: that every time some new linguistic phenomenon occurred to us, it could retrospectively show that our previous explanation was unworkable. (We felt that language could always make new, and impossible, demands; and that this made all explanation futile.)

But that is the difficulty Socrates gets into trying to give the definition of a concept. Again and again a use of the word emerges that seems not to be compatible with the concept that other uses have led us to form. We say: but that isn't how it is! — it is like that though! and all we can do is keep repeating these antitheses.

Wilson, Wandering Significance, p. 17:

Within the more developed and example-free presentations of philosophy, all visible surfaces have often become so highly polished that the underlying processes of ur-philosophical manufacture are no longer apparent and the grain that sometimes bewilders us becomes entirely hidden. There is not enough friction available to make forward traction possible.