40 ideas
8755 | Maddy replaces pure sets with just objects and perceived sets of objects [Maddy, by Shapiro] |
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] |
17518 | Counting 'coin in this box' may have coin as the unit, with 'in this box' merely as the scope [Ayers] |
17516 | If counting needs a sortal, what of things which fall under two sortals? [Ayers] |
18221 | 'Metric' axioms uses functions, points and numbers; 'synthetic' axioms give facts about space [Field,H] |
10718 | A natural number is a property of sets [Maddy, by Oliver] |
8757 | The Indispensability Argument is the only serious ground for the existence of mathematical entities [Field,H] |
8756 | Intuition doesn't support much mathematics, and we should question its reliability [Maddy, by Shapiro] |
18212 | Nominalists try to only refer to physical objects, or language, or mental constructions [Field,H] |
17733 | We know mind-independent mathematical truths through sets, which rest on experience [Maddy, by Jenkins] |
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] |
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] |
17520 | Events do not have natural boundaries, and we have to set them [Ayers] |
18211 | You can reduce ontological commitment by expanding the logic [Field,H] |
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] |
17519 | To express borderline cases of objects, you need the concept of an 'object' [Ayers] |
17511 | Recognising continuity is separate from sortals, and must precede their use [Ayers] |
17510 | Speakers need the very general category of a thing, if they are to think about it [Ayers] |
17522 | We use sortals to classify physical objects by the nature and origin of their unity [Ayers] |
17515 | Seeing caterpillar and moth as the same needs continuity, not identity of sortal concepts [Ayers] |
17517 | Could the same matter have more than one form or principle of unity? [Ayers] |
17513 | If there are two objects, then 'that marble, man-shaped object' is ambiguous [Ayers] |
17523 | Sortals basically apply to individuals [Ayers] |
17521 | You can't have the concept of a 'stage' if you lack the concept of an object [Ayers] |
17514 | Temporal 'parts' cannot be separated or rearranged [Ayers] |
17509 | Some say a 'covering concept' completes identity; others place the concept in the reference [Ayers] |
17512 | If diachronic identities need covering concepts, why not synchronic identities too? [Ayers] |
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] |
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] |