3 ideas
| 10247 | We have no adequate logic at the moment, so mathematicians must create one [Veblen] |
| Full Idea: Formal logic has to be taken over by mathematicians. The fact is that there does not exist an adequate logic at the present time, and unless the mathematicians create one, no one else is likely to do so. | |
| From: Oswald Veblen (Presidential Address of Am. Math. Soc [1924], 141), quoted by Stewart Shapiro - Philosophy of Mathematics | |
| A reaction: This remark was made well after Frege, but before the advent of Gödel and Tarski. That implies that he was really thinking of meta-logic. |
| 20653 | Six reduction levels: groups, lives, cells, molecules, atoms, particles [Putnam/Oppenheim, by Watson] |
| Full Idea: There are six 'reductive levels' in science: social groups, (multicellular) living things, cells, molecules, atoms, and elementary particles. | |
| From: report of H.Putnam/P.Oppenheim (Unity of Science as a Working Hypothesis [1958]) by Peter Watson - Convergence 10 'Intro' | |
| A reaction: I have the impression that fields are seen as more fundamental that elementary particles. What is the status of the 'laws' that are supposed to govern these things? What is the status of space and time within this picture? |
| 14014 | Space alone, and time alone, will fade away, and only their union has an independent reality [Minkowski] |
| Full Idea: Henceforth, space by itself, and time by itself, are doomed to fade away into mere shadows, and only a kind of union of the two will preserve an independent reality. | |
| From: Hermann Minkowski (Space and Time [1908], Intro) | |
| A reaction: Notice the qualification that it is a 'kind of' union. Deep confusion arises from exaggerating the analogy between space and time. Craig Bourne remarks (2006:157) that this shows independence of measurement, not of reality |