56 ideas
22270 | Frege changed philosophy by extending logic's ability to check the grounds of thinking [Potter on Frege] |
8939 | We should not describe human laws of thought, but how to correctly track truth [Frege, by Fisher] |
4971 | I don't use 'subject' and 'predicate' in my way of representing a judgement [Frege] |
17745 | For Frege, 'All A's are B's' means that the concept A implies the concept B [Frege, by Walicki] |
9570 | In Field's Platonist view, set theory is false because it asserts existence for non-existent things [Field,H, by Chihara] |
7728 | Frege has a judgement stroke (vertical, asserting or judging) and a content stroke (horizontal, expressing) [Frege, by Weiner] |
16881 | The laws of logic are boundless, so we want the few whose power contains the others [Frege] |
7622 | In 1879 Frege developed second order logic [Frege, by Putnam] |
10260 | Logical consequence is defined by the impossibility of P and ¬q [Field,H, by Shapiro] |
7729 | Frege replaced Aristotle's subject/predicate form with function/argument form [Frege, by Weiner] |
9950 | A quantifier is a second-level predicate (which explains how it contributes to truth-conditions) [Frege, by George/Velleman] |
9991 | For Frege the variable ranges over all objects [Frege, by Tait] |
10536 | Frege's domain for variables is all objects, but modern interpretations first fix the domain [Dummett on Frege] |
7730 | Frege introduced quantifiers for generality [Frege, by Weiner] |
7742 | Frege reduced most quantifiers to 'everything' combined with 'not' [Frege, by McCullogh] |
13824 | Proof theory began with Frege's definition of derivability [Frege, by Prawitz] |
13609 | Frege produced axioms for logic, though that does not now seem the natural basis for logic [Frege, by Kaplan] |
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] |
17855 | It may be possible to define induction in terms of the ancestral relation [Frege, by Wright,C] |
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] |
10607 | Frege's logic has a hierarchy of object, property, property-of-property etc. [Frege, by Smith,P] |
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] |
11008 | Existence is not a first-order property, but the instantiation of a property [Frege, by Read] |
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] |
22280 | Frege's account was top-down and decompositional, not bottom-up and compositional [Frege, by Potter] |
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] |
7741 | The predicate 'exists' is actually a natural language expression for a quantifier [Frege, by Weiner] |