17 ideas
| 6299 | Axioms are often affirmed simply because they produce results which have been accepted [Resnik] |
| 21642 | If quantification is all substitutional, there is no ontology [Quine] |
| 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] |
| 1633 | Absolute ontological questions are meaningless, because the answers are circular definitions [Quine] |
| 18964 | Ontology is relative to both a background theory and a translation manual [Quine] |
| 18965 | We know what things are by distinguishing them, so identity is part of ontology [Quine] |
| 1634 | Two things are relative - the background theory, and translating the object theory into the background theory [Quine] |
| 8470 | Reference is inscrutable, because we cannot choose between theories of numbers [Quine, by Orenstein] |
| 18963 | Indeterminacy translating 'rabbit' depends on translating individuation terms [Quine] |
| 1748 | Archelaus was the first person to say that the universe is boundless [Archelaus, by Diog. Laertius] |
| 5989 | Archelaus said life began in a primeval slime [Archelaus, by Schofield] |