15 ideas
| 18261 | A simplification which is complete constitutes a definition [Kant] |
| 6299 | Axioms are often affirmed simply because they produce results which have been accepted [Resnik] |
| 22275 | Logic gives us the necessary rules which show us how we ought to think [Kant] |
| 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] |
| 18260 | If we knew what we know, we would be astonished [Kant] |
| 17402 | Mendeleev saw three principles in nature: matter, force and spirit (where the latter seems to be essence) [Mendeleev, by Scerri] |
| 17399 | Elements don't survive in compounds, but the 'substance' of the element does [Mendeleev] |
| 17400 | Mendeleev focused on abstract elements, not simple substances, so he got to their essence [Mendeleev, by Scerri] |
| 17401 | Mendeleev had a view of elements which allowed him to overlook some conflicting observations [Mendeleev] |