55 ideas
2056 | Philosophers are always switching direction to something more interesting [Plato] |
2086 | Understanding mainly involves knowing the elements, not their combinations [Plato] |
2083 | Either a syllable is its letters (making parts as knowable as whole) or it isn't (meaning it has no parts) [Plato] |
2082 | A rational account is essentially a weaving together of things with names [Plato] |
2052 | Eristic discussion is aggressive, but dialectic aims to help one's companions in discussion [Plato] |
15854 | A primary element has only a name, and no logos, but complexes have an account, by weaving the names [Plato] |
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] |
10216 | We master arithmetic by knowing all the numbers in our soul [Plato] |
2060 | There seem to be two sorts of change: alteration and motion [Plato] |
2084 | If a word has no parts and has a single identity, it turns out to be the same kind of thing as a letter [Plato] |
15844 | A sum is that from which nothing is lacking, which is a whole [Plato] |
15843 | The whole can't be the parts, because it would be all of the parts, which is the whole [Plato] |
2080 | Things are only knowable if a rational account (logos) is possible [Plato] |
16126 | Expertise is knowledge of the whole by means of the parts [Plato] |
2050 | It is impossible to believe something which is held to be false [Plato] |
2076 | How can a belief exist if its object doesn't exist? [Plato] |
2045 | Perception is infallible, suggesting that it is knowledge [Plato] |
2067 | Our senses could have been separate, but they converge on one mind [Plato] |
7628 | Broad rejects the inferential component of the representative theory [Broad, by Maund] |
2068 | With what physical faculty do we perceive pairs of opposed abstract qualities? [Plato] |
2078 | You might mistake eleven for twelve in your senses, but not in your mind [Plato] |
2069 | Thought must grasp being itself before truth becomes possible [Plato] |
2089 | An inadequate rational account would still not justify knowledge [Plato] |
2085 | Parts and wholes are either equally knowable or equally unknowable [Plato] |
2091 | Without distinguishing marks, how do I know what my beliefs are about? [Plato] |
2087 | A rational account might be seeing an image of one's belief, like a reflection in a mirror [Plato] |
2090 | A rational account involves giving an image, or analysis, or giving a differentiating mark [Plato] |
2081 | Maybe primary elements can be named, but not receive a rational account [Plato] |
2088 | A rational account of a wagon would mean knowledge of its hundred parts [Plato] |
2047 | What evidence can be brought to show whether we are dreaming or not? [Plato] |
2053 | If you claim that all beliefs are true, that includes beliefs opposed to your own [Plato] |
2059 | How can a relativist form opinions about what will happen in the future? [Plato] |
2054 | Clearly some people are superior to others when it comes to medicine [Plato] |
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] |
2058 | God must be the epitome of goodness, and we can only approach a divine state by being as good as possible [Plato] |
2057 | There must always be some force of evil ranged against good [Plato] |