37 ideas
3972 | Truth and objectivity depend on a community of speakers to interpret what they mean [Davidson] |
3969 | There are no ultimate standards of rationality, since we only assess others by our own standard [Davidson] |
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] |
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] |
3960 | There are no such things as minds, but people have mental properties [Davidson] |
17937 | Mathematical generalisation is by extending a system, or by abstracting away from it [Colyvan] |
3964 | If the mind is an anomaly, this makes reduction of the mental to the physical impossible [Davidson] |
3961 | Obviously all mental events are causally related to physical events [Davidson] |
3963 | There are no strict psychophysical laws connecting mental and physical events [Davidson] |
3965 | Mental entities do not add to the physical furniture of the world [Davidson] |
3966 | The correct conclusion is ontological monism combined with conceptual dualism [Davidson] |
3967 | Absence of all rationality would be absence of thought [Davidson] |
3974 | Our meanings are partly fixed by events of which we may be ignorant [Davidson] |
3968 | Propositions explain nothing without an explanation of how sentences manage to name them [Davidson] |
3970 | Thought is only fully developed if we communicate with others [Davidson] |
3971 | There is simply no alternative to the 'principle of charity' in interpreting what others do [Davidson] |
7903 | The six perfections are giving, morality, patience, vigour, meditation, and wisdom [Nagarjuna] |
3973 | Without a teacher, the concept of 'getting things right or wrong' is meaningless [Davidson] |
3962 | Cause and effect relations between events must follow strict laws [Davidson] |