46 ideas
| 17926 | Rejecting double negation elimination undermines reductio proofs [Colyvan] |
| 17925 | Showing a disproof is impossible is not a proof, so don't eliminate double negation [Colyvan] |
| 6548 | Physicalism requires the naturalisation or rejection of set theory [Lycan] |
| 17924 | Excluded middle says P or not-P; bivalence says P is either true or false [Colyvan] |
| 17929 | Löwenheim proved his result for a first-order sentence, and Skolem generalised it [Colyvan] |
| 17930 | Axioms are 'categorical' if all of their models are isomorphic [Colyvan] |
| 17928 | Ordinal numbers represent order relations [Colyvan] |
| 17923 | Intuitionists only accept a few safe infinities [Colyvan] |
| 17941 | Infinitesimals were sometimes zero, and sometimes close to zero [Colyvan] |
| 17922 | Reducing real numbers to rationals suggested arithmetic as the foundation of maths [Colyvan] |
| 17936 | Transfinite induction moves from all cases, up to the limit ordinal [Colyvan] |
| 17940 | Most mathematical proofs are using set theory, but without saying so [Colyvan] |
| 17931 | Structuralism say only 'up to isomorphism' matters because that is all there is to it [Colyvan] |
| 17932 | If 'in re' structures relies on the world, does the world contain rich enough structures? [Colyvan] |
| 6531 | Institutions are not reducible as types, but they are as tokens [Lycan] |
| 6532 | Types cannot be reduced, but levels of reduction are varied groupings of the same tokens [Lycan] |
| 6534 | One location may contain molecules, a metal strip, a key, an opener of doors, and a human tragedy [Lycan] |
| 6529 | I see the 'role'/'occupant' distinction as fundamental to metaphysics [Lycan] |
| 6549 | I think greenness is a complex microphysical property of green objects [Lycan] |
| 17943 | Probability supports Bayesianism better as degrees of belief than as ratios of frequencies [Colyvan] |
| 17939 | Mathematics can reveal structural similarities in diverse systems [Colyvan] |
| 17938 | Mathematics can show why some surprising events have to occur [Colyvan] |
| 17934 | Proof by cases (by 'exhaustion') is said to be unexplanatory [Colyvan] |
| 17933 | Reductio proofs do not seem to be very explanatory [Colyvan] |
| 17935 | If inductive proofs hold because of the structure of natural numbers, they may explain theorems [Colyvan] |
| 17942 | Can a proof that no one understands (of the four-colour theorem) really be a proof? [Colyvan] |
| 6543 | Intentionality comes in degrees [Lycan] |
| 6537 | Teleological views allow for false intentional content, unlike causal and nomological theories [Lycan] |
| 6546 | Pain is composed of urges, desires, impulses etc, at different levels of abstraction [Lycan] |
| 6547 | The right 'level' for qualia is uncertain, though top (behaviourism) and bottom (particles) are false [Lycan] |
| 17937 | Mathematical generalisation is by extending a system, or by abstracting away from it [Colyvan] |
| 6527 | If energy in the brain disappears into thin air, this breaches physical conservation laws [Lycan] |
| 6528 | In lower animals, psychology is continuous with chemistry, and humans are continuous with animals [Lycan] |
| 6554 | Two behaviourists meet. The first says,"You're fine; how am I?" [Lycan] |
| 6545 | If functionalism focuses on folk psychology, it ignores lower levels of function [Lycan] |
| 6541 | Functionalism must not be too abstract to allow inverted spectrum, or so structural that it becomes chauvinistic [Lycan] |
| 6539 | The distinction between software and hardware is not clear in computing [Lycan] |
| 6533 | Mental types are a subclass of teleological types at a high level of functional abstraction [Lycan] |
| 6535 | Teleological characterisations shade off smoothly into brutely physical ones [Lycan] |
| 6544 | Identity theory is functionalism, but located at the lowest level of abstraction [Lycan] |
| 6530 | We reduce the mind through homuncular groups, described abstractly by purpose [Lycan] |
| 6536 | Teleological functionalism helps us to understand psycho-biological laws [Lycan] |
| 6542 | A Martian may exhibit human-like behaviour while having very different sensations [Lycan] |
| 23420 | In a pluralist society we can't expect a community united around one conception of the good [Rawls] |
| 6538 | We need a notion of teleology that comes in degrees [Lycan] |
| 6551 | 'Physical' means either figuring in physics descriptions, or just located in space-time [Lycan] |