display all the ideas for this combination of texts
7 ideas
| 21493 | Pure mathematics deals only with hypotheses, of which the reality does not matter [Peirce] |
| Full Idea: The pure mathematician deals exclusively with hypotheses. Whether or not there is any corresponding real thing, he does not care. | |
| From: Charles Sanders Peirce (works [1892], CP5.567), quoted by Albert Atkin - Peirce 3 'separation' | |
| A reaction: [Dated 1902] Maybe we should identify a huge branch of human learning as Hyptheticals. Professor of Hypotheticals at Cambridge University. The trouble is it would have to include computer games. So why does maths matter more than games? |
| 17620 | Critics of if-thenism say that not all starting points, even consistent ones, are worth studying [Maddy] |
| Full Idea: If-thenism denies that mathematics is in the business of discovering truths about abstracta. ...[their opponents] obviously don't regard any starting point, even a consistent one, as equally worthy of investigation. | |
| From: Penelope Maddy (Defending the Axioms [2011], 3.3) | |
| A reaction: I have some sympathy with if-thenism, in that you can obviously study the implications of any 'if' you like, but deep down I agree with the critics. |
| 19102 | Bivalence is a regulative assumption of enquiry - not a law of logic [Peirce, by Misak] |
| Full Idea: Peirce takes bivalence not to be a law of logic, but a regulative assumption of enquiry. | |
| From: report of Charles Sanders Peirce (works [1892]) by Cheryl Misak - Pragmatism and Deflationism 2 n10 | |
| A reaction: I like this. For most enquiries it's either true or not true, it's either there or it's not there. When you aren't faced with these simple dichotomies (in history, or quantum mechanics) you can relax, and allow truth value gaps etc. |
| 12876 | Philosophy is stuck on the Fregean view that an individual is anything with a proper name [Simons] |
| Full Idea: Modern philosophy is still under the spell of Frege's view that an individual is anything that has a proper name. (Note: But not only are empty names now recognised, but some are aware of the existence of plural reference). | |
| From: Peter Simons (Parts [1987], 8.1) | |
| A reaction: Presumably every electron in the universe is an individual, and every (finite) number which has never been named has a pretty clear identity. Presumably Pegasus, John Doe, and 'the person in the kitchen' have to be accommodated. |
| 12845 | Some natural languages don't distinguish between singular and plural [Simons] |
| Full Idea: The syntactic distinction between singular and plural is not a universal feature of natural languages. Chinese manages nicely without it, and Sanskrit makes a tripartite distinction between singular, dual, and plural (more than two). | |
| From: Peter Simons (Parts [1987], 4.3) | |
| A reaction: Simons is mounting an attack on the way in which modern philosophy and logic has been mesmerised by singular terms and individuated objects. Most people seem now to agree with Simons. There is stuff, as well as plurals. |
| 17605 | Hilbert's geometry and Dedekind's real numbers were role models for axiomatization [Maddy] |
| Full Idea: At the end of the nineteenth century there was a renewed emphasis on rigor, the central tool of which was axiomatization, along the lines of Hilbert's axioms for geometry and Dedekind's axioms for real numbers. | |
| From: Penelope Maddy (Defending the Axioms [2011], 1.3) |
| 17625 | If two mathematical themes coincide, that suggest a single deep truth [Maddy] |
| Full Idea: The fact that two apparently fruitful mathematical themes turn out to coincide makes it all the more likely that they're tracking a genuine strain of mathematical depth. | |
| From: Penelope Maddy (Defending the Axioms [2011], 5.3ii) |