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] |
| 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] |
| 4986 | A weaker kind of reductionism than direct translation is the use of 'bridge laws' [Kirk,R] |
| 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] |
| 5001 | Maybe we should see intentionality and consciousness as a single problem, not two [Kirk,R] |
| 4993 | If a bird captures a worm, we could say its behaviour is 'about' the worm [Kirk,R] |
| 5000 | Behaviourism says intentionality is an external relation; language of thought says it's internal [Kirk,R] |
| 17937 | Mathematical generalisation is by extending a system, or by abstracting away from it [Colyvan] |
| 4982 | Dualism implies some brain events with no physical cause, and others with no physical effect [Kirk,R] |
| 4991 | Behaviourism seems a good theory for intentional states, but bad for phenomenal ones [Kirk,R] |
| 4994 | Behaviourism offers a good alternative to simplistic unitary accounts of mental relationships [Kirk,R] |
| 4992 | In 'holistic' behaviourism we say a mental state is a complex of many dispositions [Kirk,R] |
| 4990 | The inverted spectrum idea is often regarded as an objection to behaviourism [Kirk,R] |
| 4984 | All meaningful psychological statements can be translated into physics [Kirk,R] |
| 4998 | Instead of representation by sentences, it can be by a distribution of connectionist strengths [Kirk,R] |
| 4985 | If mental states are multiply realisable, they could not be translated into physical terms [Kirk,R] |
| 4997 | It seems unlikely that most concepts are innate, if a theory must be understood to grasp them [Kirk,R] |
| 4999 | For behaviourists language is just a special kind of behaviour [Kirk,R] |
| 4995 | Behaviourists doubt whether reference is a single type of relation [Kirk,R] |
| 2705 | How can intuitionists distinguish universal convictions from local cultural ones? [Hare] |
| 2712 | You can't use intuitions to decide which intuitions you should cultivate [Hare] |
| 2706 | Emotivists mistakenly think all disagreements are about facts, and so there are no moral reasons [Hare] |
| 2709 | Prescriptivism sees 'ought' statements as imperatives which are universalisable [Hare] |
| 2704 | If morality is just a natural or intuitive description, that leads to relativism [Hare] |
| 2703 | Descriptivism say ethical meaning is just truth-conditions; prescriptivism adds an evaluation [Hare] |
| 2707 | If there can be contradictory prescriptions, then reasoning must be involved [Hare] |
| 2708 | An 'ought' statement implies universal application [Hare] |
| 2711 | Prescriptivism implies a commitment, but descriptivism doesn't [Hare] |
| 2710 | Moral judgements must invoke some sort of principle [Hare] |