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] |
| 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] |
| 22868 | The value and truth of knowledge are measured by success in activity [Dewey] |
| 13165 | Geometrical proofs do not show causes, as when we prove a triangle contains two right angles [Proclus] |
| 22865 | Habits constitute the self [Dewey] |
| 9569 | The origin of geometry started in sensation, then moved to calculation, and then to reason [Proclus] |
| 22871 | The good people are those who improve; the bad are those who deteriorate [Dewey] |
| 22876 | Democracy is the development of human nature when it shares in the running of communal activities [Dewey] |
| 22875 | Democracy is not just a form of government; it is a mode of shared living [Dewey] |
| 22874 | Individuality is only developed within groups [Dewey] |