35 ideas
17651 | Without words or other symbols, we have no world [Goodman] |
17652 | Truth is irrelevant if no statements are involved [Goodman] |
9570 | In Field's Platonist view, set theory is false because it asserts existence for non-existent things [Field,H, by Chihara] |
10260 | Logical consequence is defined by the impossibility of P and ¬q [Field,H, by Shapiro] |
8958 | In Field's version of science, space-time points replace real numbers [Field,H, by Szabó] |
18221 | 'Metric' axioms uses functions, points and numbers; 'synthetic' axioms give facts about space [Field,H] |
8757 | The Indispensability Argument is the only serious ground for the existence of mathematical entities [Field,H] |
18212 | Nominalists try to only refer to physical objects, or language, or mental constructions [Field,H] |
10261 | The application of mathematics only needs its possibility, not its truth [Field,H, by Shapiro] |
18218 | Hilbert explains geometry, by non-numerical facts about space [Field,H] |
9623 | Field needs a semantical notion of second-order consequence, and that needs sets [Brown,JR on Field,H] |
8628 | I hold that algebra and number are developments of logic [Jevons] |
18215 | It seems impossible to explain the idea that the conclusion is contained in the premises [Field,H] |
18216 | Abstractions can form useful counterparts to concrete statements [Field,H] |
18214 | Mathematics is only empirical as regards which theory is useful [Field,H] |
18210 | Why regard standard mathematics as truths, rather than as interesting fictions? [Field,H] |
17656 | Being primitive or prior always depends on a constructional system [Goodman] |
17661 | We don't recognise patterns - we invent them [Goodman] |
17659 | Reality is largely a matter of habit [Goodman] |
17657 | We build our world, and ignore anything that won't fit [Goodman] |
18211 | You can reduce ontological commitment by expanding the logic [Field,H] |
17654 | A world can be full of variety or not, depending on how we sort it [Goodman] |
8959 | Field presumes properties can be eliminated from science [Field,H, by Szabó] |
18213 | Abstract objects are only applicable to the world if they are impure, and connect to the physical [Field,H] |
17653 | Things can only be judged the 'same' by citing some respect of sameness [Goodman] |
17660 | Discovery is often just finding a fit, like a jigsaw puzzle [Goodman] |
17658 | Users of digital thermometers recognise no temperatures in the gaps [Goodman] |
17650 | We lack frames of reference to transform physics, biology and psychology into one another [Goodman] |
17655 | Grue and green won't be in the same world, as that would block induction entirely [Goodman] |
18222 | Beneath every extrinsic explanation there is an intrinsic explanation [Field,H] |
9917 | 'Abstract' is unclear, but numbers, functions and sets are clearly abstract [Field,H] |
17649 | If the world is one it has many aspects, and if there are many worlds they will collect into one [Goodman] |
18223 | In theories of fields, space-time points or regions are causal agents [Field,H] |
18220 | Both philosophy and physics now make substantivalism more attractive [Field,H] |
18219 | Relational space is problematic if you take the idea of a field seriously [Field,H] |