36 ideas
11103 | We aren't stuck with our native conceptual scheme; we can gradually change it [Quine] |
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] |
11092 | A river is a process, with stages; if we consider it as one thing, we are considering a process [Quine] |
11093 | We don't say 'red' is abstract, unlike a river, just because it has discontinuous shape [Quine] |
11101 | General terms don't commit us ontologically, but singular terms with substitution do [Quine] |
11096 | Discourse generally departmentalizes itself to some degree [Quine] |
11099 | Understanding 'is square' is knowing when to apply it, not knowing some object [Quine] |
11094 | 'Red' is a single concrete object in space-time; 'red' and 'drop' are parts of a red drop [Quine] |
11097 | Red is the largest red thing in the universe [Quine] |
17595 | To unite a sequence of ostensions to make one object, a prior concept of identity is needed [Quine] |
11095 | We should just identify any items which are indiscernible within a given discourse [Quine] |
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] |
7906 | When the Buddha reached the highest level of insight, he could detect no self in the world [Ashvaghosha] |
11104 | Concepts are language [Quine] |
11102 | Apply '-ness' or 'class of' to abstract general terms, to get second-level abstract singular terms [Quine] |
7904 | The first stage of trance is calm amidst applied and discursive thinking [Ashvaghosha] |
7905 | The Buddha sought ultimate reality and the final goal of existence in his meditations [Ashvaghosha] |