34 ideas
7990 | Serene wisdom is freedom from ties, and indifference to fortune [Anon (Bhag)] |
7989 | Seek salvation in the wisdom of reason [Anon (Bhag)] |
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] |
7996 | I am all the beauty and goodness of things, says Krishna [Anon (Bhag)] |
3061 | Anaxarchus said that he was not even sure that he knew nothing [Anaxarchus, by Diog. Laertius] |
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] |
7995 | In all living beings I am the light of consciousness, says Krishna [Anon (Bhag)] |
17937 | Mathematical generalisation is by extending a system, or by abstracting away from it [Colyvan] |
7999 | All actions come from: body, lower self, perception, means of action, or Fate [Anon (Bhag)] |
7991 | Hate and lust have their roots in man's lower nature [Anon (Bhag)] |
7988 | There is no greater good for a warrior than to fight in a just war [Anon (Bhag)] |
7992 | The visible forms of nature are earth, water, fire, air, ether; mind, reason, and the sense of 'I' [Anon (Bhag)] |
7994 | Everything, including the gods, comes from me, says Krishna [Anon (Bhag)] |
7993 | Brahman is supreme, Atman his spirit in man, and Karma is the force of creation [Anon (Bhag)] |
7997 | Only by love can men see me, know me, and come to me, says Krishna [Anon (Bhag)] |
7998 | The three gates of hell are lust, anger and greed [Anon (Bhag)] |