45 ideas
| 3656 | The greatest good for a state is true philosophers [Descartes] |
| 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] |
| 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] |
| 16744 | All powers can be explained by obvious features like size, shape and motion of matter [Descartes] |
| 5016 | Five universals: genus, species, difference, property, accident [Descartes] |
| 5015 | A universal is a single idea applied to individual things that are similar to one another [Descartes] |
| 16630 | If we perceive an attribute, we infer the existence of some substance [Descartes] |
| 5013 | A substance needs nothing else in order to exist [Descartes] |
| 16633 | A substance has one principal property which is its nature and essence [Descartes] |
| 3658 | Total doubt can't include your existence while doubting [Descartes] |
| 5005 | I think, therefore I am, because for a thinking thing to not exist is a contradiction [Descartes] |
| 5006 | 'Thought' is all our conscious awareness, including feeling as well as understanding [Descartes] |
| 5012 | 'Nothing comes from nothing' is an eternal truth found within the mind [Descartes] |
| 5004 | We can know basic Principles without further knowledge, but not the other way round [Descartes] |
| 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] |
| 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] |
| 17934 | Proof by cases (by 'exhaustion') is said to be unexplanatory [Colyvan] |
| 5014 | We can understand thinking occuring without imagination or sensation [Descartes] |
| 17937 | Mathematical generalisation is by extending a system, or by abstracting away from it [Colyvan] |
| 20618 | Persons must be conscious, reasoning, motivated, communicative, self-aware [Warren, by Tuckness/Wolf] |
| 5017 | In thinking we shut ourselves off from other substances, showing our identity and separateness [Descartes] |
| 5010 | Our free will is so self-evident to us that it must be a basic innate idea [Descartes] |
| 5011 | There are two ultimate classes of existence: thinking substance and extended substance [Descartes] |
| 5018 | Even if tightly united, mind and body are different, as God could separate them [Descartes] |
| 5007 | Most errors of judgement result from an inaccurate perception of the facts [Descartes] |
| 5009 | We do not praise the acts of an efficient automaton, as their acts are necessary [Descartes] |
| 5008 | The greatest perfection of man is to act by free will, and thus merit praise or blame [Descartes] |
| 15987 | Physics only needs geometry or abstract mathematics, which can explain and demonstrate everything [Descartes] |
| 12730 | We will not try to understand natural or divine ends, or final causes [Descartes] |
| 16601 | Matter is not hard, heavy or coloured, but merely extended in space [Descartes] |