32 ideas
| 19695 | The devil was wise as an angel, and lost no knowledge when he rebelled [Whitcomb] |
| 5182 | Claims about 'the Absolute' are not even verifiable in principle [Ayer on Bradley] |
| 6864 | Metaphysics is finding bad reasons for instinctive beliefs [Bradley] |
| 17925 | Showing a disproof is impossible is not a proof, so don't eliminate double negation [Colyvan] |
| 17926 | Rejecting double negation elimination undermines reductio proofs [Colyvan] |
| 17924 | Excluded middle says P or not-P; bivalence says P is either true or false [Colyvan] |
| 10999 | Names need a means of reidentifying their referents [Bradley, by Read] |
| 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] |
| 6422 | Internal relations are said to be intrinsic properties of two terms, and of the whole they compose [Bradley, by Russell] |
| 7966 | Relations must be linked to their qualities, but that implies an infinite regress of relations [Bradley] |
| 6404 | British Idealists said reality is a single Mind which experiences itself [Bradley, by Grayling] |
| 22299 | Bradley's objective idealism accepts reality (the Absolute), but says we can't fully describe it [Bradley, by Potter] |
| 21343 | Qualities and relations are mere appearance; the Absolute is a single undifferentiated substance [Bradley, by Heil] |
| 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] |
| 17937 | Mathematical generalisation is by extending a system, or by abstracting away from it [Colyvan] |
| 5655 | Happiness is not satisfaction of desires, but fulfilment of values [Bradley, by Scruton] |
| 6406 | Reality is one, because plurality implies relations, and they assert a superior unity [Bradley] |