20 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] |
16435 | Plantinga proposes necessary existent essences as surrogates for the nonexistent things [Plantinga, by Stalnaker] |
14655 | The 'identity criteria' of a name are a group of essential and established facts [Plantinga] |
14658 | 'Being Socrates' and 'being identical with Socrates' characterise Socrates, so they are among his properties [Plantinga] |
14656 | Does Socrates have essential properties, plus a unique essence (or 'haecceity') which entails them? [Plantinga] |
14654 | Properties are 'trivially essential' if they are instantiated by every object in every possible world [Plantinga] |
14653 | X is essentially P if it is P in every world, or in every X-world, or in the actual world (and not ¬P elsewhere) [Plantinga] |
14660 | If a property is ever essential, can it only ever be an essential property? [Plantinga] |
14661 | Essences are instantiated, and are what entails a thing's properties and lack of properties [Plantinga] |
14657 | Does 'being identical with Socrates' name a property? I can think of no objections to it [Plantinga] |
14652 | 'De re' modality is as clear as 'de dicto' modality, because they are logically equivalent [Plantinga] |
14659 | We can imagine being beetles or alligators, so it is possible we might have such bodies [Plantinga] |
20239 | Unlike us, the early Greeks thought envy was a good thing, and hope a bad thing [Hesiod, by Nietzsche] |