7 ideas
| 17807 | To study formal systems, look at the whole thing, and not just how it is constructed in steps [Curry] |
| Full Idea: In the study of formal systems we do not confine ourselves to the derivation of elementary propositions step by step. Rather we take the system, defined by its primitive frame, as datum, and then study it by any means at our command. | |
| From: Haskell B. Curry (Remarks on the definition and nature of mathematics [1954], 'The formalist') | |
| A reaction: This is what may potentially lead to an essentialist view of such things. Focusing on bricks gives formalism, focusing on buildings gives essentialism. |
| 17806 | It is untenable that mathematics is general physical truths, because it needs infinity [Curry] |
| Full Idea: According to realism, mathematical propositions express the most general properties of our physical environment. This is the primitive view of mathematics, yet on account of the essential role played by infinity in mathematics, it is untenable today. | |
| From: Haskell B. Curry (Remarks on the definition and nature of mathematics [1954], 'The problem') | |
| A reaction: I resist this view, because Curry's view seems to imply a mad metaphysics. Hilbert resisted the role of the infinite in essential mathematics. If the physical world includes its possibilities, that might do the job. Hellman on structuralism? |
| 17808 | Saying mathematics is logic is merely replacing one undefined term by another [Curry] |
| Full Idea: To say that mathematics is logic is merely to replace one undefined term by another. | |
| From: Haskell B. Curry (Remarks on the definition and nature of mathematics [1954], 'Mathematics') |
| 8526 | We might treat both tropes and substances as fundamental, so we can't presume it is just tropes [Daly] |
| Full Idea: Since C.B. Martin accepts both tropes and substances as fundamental, the claim that tropes are the only fundamental constituents is a further, independent claim. | |
| From: Chris Daly (Tropes [1995], §4) | |
| A reaction: A dubious mode of argument. Martin may only make the claim because he is ignorant, of facts or of language. Why are some tropes perfectly similar? Is it the result of something more fundamental? |
| 8527 | More than one trope (even identical ones!) can occupy the same location [Daly] |
| Full Idea: More than one trope can occupy the same spatio-temporal location, and it even seems possible for a pair of exactly resembling tropes to occupy the same spatio-temporal location. | |
| From: Chris Daly (Tropes [1995], §6) | |
| A reaction: This may be the strongest objection to tropes. Being disc-shaped and red would occupy the same location. Aristotle's example of mixing white with white (Idea 557) would be the second case. Individuation of these 'particulars' is the problem. |
| 8528 | If tropes are linked by the existence of concurrence, a special relation is needed to link them all [Daly] |
| Full Idea: To explain how tropes form bundles, concurrence relations are invoked. But tropes F and G and a concurrence relation C don't ensure that F stands in C to G. So trope theory needs 'instantiation' relations (special relational tropes) after all. | |
| From: Chris Daly (Tropes [1995], §7) | |
| A reaction: Campbell presents relations as 'second-order' items dependent on tropes (Idea 8525), but that seems unclear. Daly's argument resembles Russell's (which he likes), that some sort of universal is inescapable. It also resembles Bradley's regress (7966). |
| 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? |