By Ludwig Wittgenstein
For numerous phrases at Cambridge in 1939, Ludwig Wittgenstein lectured at the philosophical foundations of arithmetic. A lecture classification taught through Wittgenstein, in spite of the fact that, rarely resembled a lecture.He sat on a chair in the course of the room, with the various classification sitting in chairs, a few at the flooring. He by no means used notes. He paused often, occasionally for numerous mins, whereas he wondered out an issue. He frequently requested his listeners questions and reacted to their replies. Many conferences have been mostly conversation.These lectures have been attended by means of, between others, D. A. T. Gasking, J. N. Findlay, Stephen Toulmin, Alan Turing, G. H. von Wright, R. G. Bosanquet, Norman Malcolm, Rush Rhees, and Yorick Smythies. Notes taken by means of those final 4 are the root for the thirty-one lectures during this book.The lectures coated such subject matters because the nature of arithmetic, the differences among mathematical and daily languages, the reality of mathematical propositions, consistency and contradiction in formal platforms, the logicism of Frege and Russell, Platonism, identification, negation, and worthwhile fact. The mathematical examples used are almost always straightforward.
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Additional resources for Wittgenstein's Lectures on the Foundations of Mathematics, Cambridge, 1939
Sample text
Suppose 1 said that it changes his idea of constructing an n-gon by this method. What does that mean? Well, if someone asked him what he was trying to do, he would now give an entirely different sort of explanation. Before, he would have said, "Oh, I d o this sort of thing" and begin to draw a few 90 1 LECTURE IX 1 91 LECTURE IX He saw my construction, and it no longer interested him to construct the 100-gon. He might have gone on trying to find approximate constructions. If h e gave up, he gave up because he acknowledged this to be the method of construction he had always wanted to follow, but had thought of in a vague way.
If one calls something the result of the calculation, is that same thing the result of the experiment? IVatson: Not necessarily. Mttgenstein: No, not necessarily-but is it even possibly? Turing has called the calculation an experiment. But what would it mean to say that the result of the experiment is the result of the calculation?
Turing might say this is drawing something in a different projection. Is this the case of the man who invented the construction of the heptacaidecagon? Does he follow a rule for projecting it (like drawing on a different scale)? Wasn't he introducing a new mode of projection? H e znuented a new mode of projection, which there is reason to call so-and-so. H e discovered a new kind of analogy. H e had learnt one mode of projection in the one case, but not in the other. H e was given a picture. And the point was to invent a mode of projection.