18 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] |
| 16014 | It is controversial whether only 'numerical identity' allows two things to be counted as one [Noonan] |
| 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] |
| 16024 | I could have died at five, but the summation of my adult stages could not [Noonan] |
| 16023 | Stage theorists accept four-dimensionalism, but call each stage a whole object [Noonan] |
| 16015 | Problems about identity can't even be formulated without the concept of identity [Noonan] |
| 16017 | Identity is usually defined as the equivalence relation satisfying Leibniz's Law [Noonan] |
| 16016 | Identity definitions (such as self-identity, or the smallest equivalence relation) are usually circular [Noonan] |
| 16020 | Identity can only be characterised in a second-order language [Noonan] |
| 16018 | Indiscernibility is basic to our understanding of identity and distinctness [Noonan] |
| 16019 | Leibniz's Law must be kept separate from the substitutivity principle [Noonan] |
| 3061 | Anaxarchus said that he was not even sure that he knew nothing [Anaxarchus, by Diog. Laertius] |