16 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] |
5662 | Maybe induction could never prove the existence of something unobservable [Ayer] |
5664 | Consciousness must involve a subject, and only bodies identify subjects [Ayer] |
5668 | People own conscious states because they are causally related to the identifying body [Ayer] |
5661 | We identify experiences by their owners, so we can't define owners by their experiences [Ayer] |
5665 | Memory is the best proposal as what unites bundles of experiences [Ayer] |
5666 | Not all exerience can be remembered, as this would produce an infinite regress [Ayer] |
5669 | Personal identity can't just be relations of experiences, because the body is needed to identify them [Ayer] |
5845 | Niceratus learnt the whole of Homer by heart, as a guide to goodness [Xenophon] |