15 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] |
| 12312 | The real essence of a thing is its powers, or 'dispositional properties' [Copi] |
| 10937 | Essential properties are the 'deepest' ones which explain the others [Copi, by Rami] |
| 12308 | In modern science, nominal essence is intended to be real essence [Copi] |
| 12303 | Within the four types of change, essential attributes are those whose loss means destruction [Copi] |
| 21650 | No language is semantically referential; it all occurs at the level of thought or utterance [Pietroski, by Hofweber] |
| 12307 | Modern science seeks essences, and is getting closer to them [Copi] |
| 12310 | Real essences are scientifically knowable, but so are non-essential properties [Copi] |