3 ideas
| 10190 | From the axiomatic point of view, mathematics is a storehouse of abstract structures [Bourbaki] |
| Full Idea: From the axiomatic point of view, mathematics appears as a storehouse of abstract forms - the mathematical structures. | |
| From: Nicholas Bourbaki (The Architecture of Mathematics [1950], 221-32), quoted by Fraser MacBride - Review of Chihara's 'Structural Acc of Maths' p.79 | |
| A reaction: This seems to be the culmination of the structuralist view that developed from Dedekind and Hilbert, and was further developed by philosophers in the 1990s. |
| 16463 | Adams says actual things have haecceities, but not things that only might exist [Adams,RM, by Stalnaker] |
| Full Idea: Adams favours haecceitism about actual things but no haecceities for things that might exist but don't. | |
| From: report of Robert Merrihew Adams (Actualism and Thisness [1981]) by Robert C. Stalnaker - Mere Possibilities 4.2 | |
| A reaction: This contrasts with Plantinga, who proposes necessary essences for everything, even for what might exist. Plantinga sounds crazy to me, Adams merely interesting but not too plausible. |
| 13166 | Essences are no use in mathematics, if all mathematical truths are necessary [Mancosu] |
| Full Idea: Essences and essential properties do not seem to be useful in mathematical contexts, since all mathematical truths are regarded as necessary (though Kit Fine distinguishes between essential and necessary properties). | |
| From: Paolo Mancosu (Explanation in Mathematics [2008], §6.1) | |
| A reaction: I take the proviso in brackets to be crucial. This represents a distortion of notion of an essence. There is a world of difference between the central facts about the nature of a square and the peripheral inferences derivable from it. |