Tag Archives: Ludwig Wittgenstein

"Typically 2 the integer is used for counting, whereas 2 the real number is used for measuring. But in higher mathematics there's a technical sense in which integers aren't real numbers -- we say instead that they can be identified with real numbers." -- Timothy Gowers 1.0 Introduction Numbers, in some sense, are only defined in mathematics up to isomorphisms. This post runs quickly through some math to explain what this means. I begin by assuming knowledge of the natural numbers,...

"One must be able to say at all times - instead of points, straight lines, and planes -- tables, chairs, and beer mugs." -- David Hilbert (as quoted by Constance Reid, Hilbert, Springer-Verlag, 1970: p. 57) Consider the Fibonacci sequence: 1, 2, 3, 5, 8, 13, ... The first two terms in this sequence are 1 and 2. After this, each term is the arithmetic sum of the previous two terms. Let A be the set of elements in this series. Let s be the function mapping an element in A onto another...

I present four claims about Marx's Capital. I strive for topics more general than, for example, squabbles about the transformation problem. I suggest that some of these claims present a useful focus for reading Marx's book, even if part of your focus is arguing why the claim is wrong. If this were more than a blog post, I would need to cite various Marxists and scholars that inspired me. Thesis I: Capital is organized around a model of a pure, two-class capitalist economy. I think the...

Fun if you are interested in Joan Robinson, Ludwig Wittgenstein, Cambridge of the Twenties, and enjoy personal anecdotes. Incidentally, I am surprised and not surprised that Joan Robinson confessed to not understand the first propositions of Wittgenstein's Tractatus Logico-Philosophicus. I am not surprised in that they sound like metaphysical statements and many if not most readers are at least initially confused by this appearance.  I am surprised, however, than Robinson did not...