Wittgenstein/Foundations of Mathematics

Quotes taken from Wittgenstein's Lectures on the Foundations of Mathematics, Cambridge, 1939

Cornell University Press

Lecture 1

What kind of misunderstandings am I talking about? They arise from a tendency to assimilate to each other expressions which have very different functions in the language. We use the word "number" in all sorts of different cases, guided by a certain analogy. We try to talk of very different things by means of the same schema. This is partly a matter of economy; and, like primitive peoples, we are much more inclined to say, "All these things, though looking different, are really the same" than we are to say, "All these things, though looking the same, are really different." Hence, I will have to stress the differences between things, where ordinarily the similarities are stressed, though this, too, can lead to misunderstandings.

- p. 15

Suppose Smith tells the municipal authorities, "I have provided all Cambridge with telephones - but some are invisible." He uses the phrase "Turing has an invisible telephone" instead of "Turing has no phone."

There is a difference of degree. In each case he has done something but not the whole. As he does less and less, in the end what he has done is to cahnge his phraseology and nothing else at all.

To think this difference is irrelevant because it is a difference of degree is stupid.

Lecture 2

Should you... say, "I believe that I intend to play chess, but I don't know. Let's just see" - ? Just as Russel once suggested that we don't know what we wish, don't know whether we want an apple or not.

Suppose we said, "What he said was just a description of his state of mind." But why should we call the state of mind he is in at present "intending to play chess"? For playing chess is an activity...

One might say, "Intending to play chess is a state of mind which experience has shown generally to precede playing chess." But this will not do at all. Do you have a peculiar feeling and say, "This is the queer feeling I have before playing chess. I wonder whether I'm going to play"? - this queer feeling which precedes playing chess one would never call "intending to play chess."

...I have been considering the word "intend" because it throws light on the words "understand" and "mean". The grammar of the three words is very similar; for in all three cases, the words seem to apply both to what happens at one moment and to what happens in the future.