35 ideas
| 1489 | Modern philosophy tends to be a theory-constructing extension of science, but there is also problem-solving [Nagel] |
| 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] |
| 5791 | Reduction is either by elimination, or by explanation [Searle] |
| 5799 | Eliminative reduction needs a gap between appearance and reality, as in sunsets [Searle] |
| 5790 | A property is 'emergent' if it is caused by elements of a system, when the elements lack the property [Searle] |
| 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] |
| 5792 | Explanation of how we unify our mental stimuli into a single experience is the 'binding problem' [Searle] |
| 5786 | A system is either conscious or it isn't, though the intensity varies a lot [Searle] |
| 5794 | Consciousness has a first-person ontology, which only exists from a subjective viewpoint [Searle] |
| 5795 | There isn't one consciousness (information-processing) which can be investigated, and another (phenomenal) which can't [Searle] |
| 5788 | The use of 'qualia' seems to imply that consciousness and qualia are separate [Searle] |
| 17937 | Mathematical generalisation is by extending a system, or by abstracting away from it [Colyvan] |
| 5789 | I now think syntax is not in the physics, but in the eye of the beholder [Searle] |
| 5798 | Consciousness has a first-person ontology, so it cannot be reduced without omitting something [Searle] |
| 5787 | There is non-event causation between mind and brain, as between a table and its solidity [Searle] |
| 5797 | The pattern of molecules in the sea is much more complex than the complexity of brain neurons [Searle] |
| 5796 | If tree rings contain information about age, then age contains information about rings [Searle] |