16 ideas
| 8964 | Entities can be multiplied either by excessive categories, or excessive entities within a category [Hoffman/Rosenkrantz] |
| 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] |
| 16659 | Relations do not add anything to reality, though they are real aspects of the world [Olivi] |
| 8962 | 'There are shapes which are never exemplified' is the toughest example for nominalists [Hoffman/Rosenkrantz] |
| 8961 | Nominalists are motivated by Ockham's Razor and a distrust of unobservables [Hoffman/Rosenkrantz] |
| 16672 | Quantity is the quantified parts of a thing, plus location and coordination [Olivi] |
| 16673 | Quantity just adds union and location to the extension of parts [Olivi] |
| 8963 | Four theories of possible worlds: conceptualist, combinatorial, abstract, or concrete [Hoffman/Rosenkrantz] |
| 16663 | Things are limited by the species to certain modes of being [Olivi] |