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4 ideas
14775 | Numbers are just names devised for counting [Peirce] |
Full Idea: Numbers are merely a system of names devised by men for the purpose of counting. | |
From: Charles Sanders Peirce (Scientific Attitude and Fallibilism [1899], II) | |
A reaction: This seems a perfectly plausible view prior to the advent of Cantor, set theory and modern mathematical logic. I suppose the modern reply to this is that Peirce may be right about origin, but that men thereby stumbled on an Aladdin's Cave of riches. |
10808 | Mathematics is generalisations about singleton functions [Lewis] |
Full Idea: We can take the theory of singleton functions, and hence set theory, and hence mathematics, to consist of generalisations about all singleton functions. | |
From: David Lewis (Mathematics is Megethology [1993], p.03) | |
A reaction: At first glance this sounds like a fancy version of the somewhat discredited Greek idea that mathematics is built on the concept of a 'unit'. |
10815 | We don't need 'abstract structures' to have structural truths about successor functions [Lewis] |
Full Idea: We needn't believe in 'abstract structures' to have general structural truths about all successor functions. | |
From: David Lewis (Mathematics is Megethology [1993], p.16) |
14776 | That two two-eyed people must have four eyes is a statement about numbers, not a fact [Peirce] |
Full Idea: To say that 'if' there are two persons and each person has two eyes there 'will be' four eyes is not a statement of fact, but a statement about the system of numbers which is our own creation. | |
From: Charles Sanders Peirce (Scientific Attitude and Fallibilism [1899], II) | |
A reaction: One eye for each arm of the people is certainly a fact. Frege uses this equivalence to build numbers. I think Peirce is wrong. If it is not a fact that these people have four eyes, I don't know what 'four' means. It's being two pairs is also a fact. |