"Mathematical logic" has completely deformed the thinking of mathematicians and of philosophers, by setting up a superficial interpretation of the forms of our everyday language as an analysis of the structures of facts. Of course in this it has only continued to build on the Aristotelian logic.It's what he says about Aristotelian logic which is the interesting one. There's a school of thought in the medievalist world according to which Aristotelian (scholastic) logic is somehow more faithful to ordinary language than modern mathematical logic. Wittgenstein would clearly have disagreed. I have also been looking at the donkey sophism in Worcester 13 again. The problem is that 'every man's donkey is running' has the form 'every A is B', where A = man's-donkey and B = running. According to Aristotelian logic 'every A is B' and 'every A is non-B' are contraries, they can't both be true at once. But clearly the ordinary language sentences 'every man's donkey is running' and 'every man's donkey is not running' can both be true at the same time, namely in the case where every man has two donkeys, one of which is running and the other of which isn't. It's not a problem for ordinary language at all. But it is a problem for the Aristotelian formalism of the sentence. In that formalism every sentence has two terms, joined by a copula and a quantifier attached to the subject term. It is a procrustean bed which fits our actual thinking very badly, in some cases.
I also noticed this other comment by Wittgenstein in the same place:
The curse of the invasion of mathematics by mathematical logic is that now any proposition can be represented in a mathematical symbolism, and this makes us feel obliged to understand it. Although of course this method of writing is nothing but the translation of vague ordinary prose.What on earth does he mean by that?