display all the ideas for this combination of philosophers
4 ideas
18281 | In mathematics everything is algorithm and nothing is meaning [Wittgenstein] |
Full Idea: In mathematics everything is algorithm and nothing is meaning; even when it doesn't look like that because we seem to be using words to talk about mathematical things. | |
From: Ludwig Wittgenstein (Philosophical Grammar [1932], p.468), quoted by J. Alberto Coffa - The Semantic Tradition from Kant to Carnap 13 'Constr' | |
A reaction: I would have thought that an algorithm needs some raw material to work with. This leads to the idea that meaning arises from rules of usage. |
18738 | We don't get 'nearer' to something by adding decimals to 1.1412... (root-2) [Wittgenstein] |
Full Idea: We say we get nearer to root-2 by adding further figures after the decimal point: 1.1412.... This suggests there is something we can get nearer to, but the analogy is a false one. | |
From: Ludwig Wittgenstein (Lectures 1930-32 (student notes) [1931], Notes) |
15364 | English expressions are denumerably infinite, but reals are nondenumerable, so many are unnameable [Horsten] |
Full Idea: The number of English expressions is denumerably infinite. But Cantor's theorem can be used to show that there are nondenumerably many real numbers. So not every real number has a (simple or complex name in English). | |
From: Leon Horsten (The Tarskian Turn [2011], 06.3) | |
A reaction: This really bothers me. Are we supposed to be committed to the existence of entities which are beyond our powers of naming? How precise must naming be? If I say 'pick a random real number', might that potentially name all of them? |
18708 | Infinity is not a number, so doesn't say how many; it is the property of a law [Wittgenstein] |
Full Idea: 'Infinite' is not an answer to the question 'How many?', since the infinite is not a number. ...Infinity is the property of a law, not of an extension. | |
From: Ludwig Wittgenstein (Lectures 1930-32 (student notes) [1931], A VII.2) |