13 ideas
6299 | Axioms are often affirmed simply because they produce results which have been accepted [Resnik] |
6304 | Mathematical realism says that maths exists, is largely true, and is independent of proofs [Resnik] |
6300 | Mathematical constants and quantifiers only exist as locations within structures or patterns [Resnik] |
6303 | Sets are positions in patterns [Resnik] |
6295 | There are too many mathematical objects for them all to be mental or physical [Resnik] |
6296 | Maths is pattern recognition and representation, and its truth and proofs are based on these [Resnik] |
6301 | Congruence is the strongest relationship of patterns, equivalence comes next, and mutual occurrence is the weakest [Resnik] |
6302 | Structuralism must explain why a triangle is a whole, and not a random set of points [Resnik] |
15645 | Nominal essence are the observable properties of things [Eagle] |
15642 | If kinds depend only on what can be observed, many underlying essences might produce the same kind [Eagle] |
15643 | Nominal essence mistakenly gives equal weight to all underlying properties that produce appearances [Eagle] |
1799 | If we can't know minds, we can't know if Pyrrho was a sceptic [Theodosius, by Diog. Laertius] |
15641 | Kinds are fixed by the essential properties of things - the properties that make it that kind of thing [Eagle] |