32 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] |
| 21554 | Sets always exceed terms, so all the sets must exceed all the sets [Lackey] |
| 21553 | It seems that the ordinal number of all the ordinals must be bigger than itself [Lackey] |
| 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] |
| 6230 | If the soul were a tabula rasa, with no innate ideas, there could be no moral goodness or justice [Cudworth] |
| 6228 | Senses cannot judge one another, so what judges senses cannot be a sense, but must be superior [Cudworth] |
| 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] |
| 6229 | Sense is fixed in the material form, and so can't grasp abstract universals [Cudworth] |
| 6227 | Keeping promises and contracts is an obligation of natural justice [Cudworth] |
| 6231 | There is a self-determing power in each person, which makes them what they are [Cudworth] |
| 6225 | Obligation to obey all positive laws is older than all laws [Cudworth] |
| 6224 | An omnipotent will cannot make two things equal or alike if they aren't [Cudworth] |
| 6223 | If the will and pleasure of God controls justice, then anything wicked or unjust would become good if God commanded it [Cudworth] |
| 6226 | The requirement that God must be obeyed must precede any authority of God's commands [Cudworth] |