18 ideas
6299 | Axioms are often affirmed simply because they produce results which have been accepted [Resnik] |
9358 | There are several logics, none of which will ever derive falsehoods from truth [Lewis,CI] |
9357 | Excluded middle is just our preference for a simplified dichotomy in experience [Lewis,CI] |
9364 | Names represent a uniformity in experience, or they name nothing [Lewis,CI] |
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] |
6302 | Structuralism must explain why a triangle is a whole, and not a random set of points [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] |
9362 | Necessary truths are those we will maintain no matter what [Lewis,CI] |
9365 | We can maintain a priori principles come what may, but we can also change them [Lewis,CI] |
14802 | Physical and psychical laws of mind are either independent, or derived in one or other direction [Peirce] |
9361 | We have to separate the mathematical from physical phenomena by abstraction [Lewis,CI] |
14800 | The world is full of variety, but laws seem to produce uniformity [Peirce] |
9363 | Science seeks classification which will discover laws, essences, and predictions [Lewis,CI] |
14801 | Darwinian evolution is chance, with the destruction of bad results [Peirce] |