36 ideas
12585 | Most people can't even define a chair [Peacocke] |
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] |
12581 | Perceptual concepts causally influence the content of our experiences [Peacocke] |
12579 | Perception has proto-propositions, between immediate experience and concepts [Peacocke] |
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] |
12586 | Consciousness of a belief isn't a belief that one has it [Peacocke] |
17937 | Mathematical generalisation is by extending a system, or by abstracting away from it [Colyvan] |
18568 | Philosophy should merely give necessary and sufficient conditions for concept possession [Peacocke, by Machery] |
18571 | Peacocke's account of possession of a concept depends on one view of counterfactuals [Peacocke, by Machery] |
18572 | Peacocke's account separates psychology from philosophy, and is very sketchy [Machery on Peacocke] |
12577 | Possessing a concept is being able to make judgements which use it [Peacocke] |
12578 | A concept is just what it is to possess that concept [Peacocke] |
12587 | Employing a concept isn't decided by introspection, but by making judgements using it [Peacocke] |
12584 | An analysis of concepts must link them to something unconceptualized [Peacocke] |
9335 | Concepts are constituted by their role in a group of propositions to which we are committed [Peacocke, by Greco] |
9336 | A concept's reference is what makes true the beliefs of its possession conditions [Peacocke, by Horwich] |
541 | Virtue comes more from habit than character [Critias] |
542 | Fear of the gods was invented to discourage secret sin [Critias] |