23 ideas
6299 | Axioms are often affirmed simply because they produce results which have been accepted [Resnik] |
13134 | We negate predicates but do not negate names [Westerhoff] |
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] |
13124 | Categories can be ordered by both containment and generality [Westerhoff] |
13117 | How far down before we are too specialised to have a category? [Westerhoff] |
13116 | Maybe objects in the same category have the same criteria of identity [Westerhoff] |
13118 | Categories are base-sets which are used to construct states of affairs [Westerhoff] |
13125 | Categories are held to explain why some substitutions give falsehood, and others meaninglessness [Westerhoff] |
13126 | Categories systematize our intuitions about generality, substitutability, and identity [Westerhoff] |
13130 | Categories as generalities don't give a criterion for a low-level cut-off point [Westerhoff] |
13131 | The aim is that everything should belong in some ontological category or other [Westerhoff] |
13123 | All systems have properties and relations, and most have individuals, abstracta, sets and events [Westerhoff] |
13115 | Ontological categories are like formal axioms, not unique and with necessary membership [Westerhoff] |
13119 | Categories merely systematise, and are not intrinsic to objects [Westerhoff] |
13135 | A thing's ontological category depends on what else exists, so it is contingent [Westerhoff] |
13129 | Essential kinds may be too specific to provide ontological categories [Westerhoff] |
1513 | The Egyptians were the first to say the soul is immortal and reincarnated [Herodotus] |