31 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] |
15127 | A categorical basis could hardly explain a disposition if it had no powers of its own [Hawthorne] |
15123 | Is the causal profile of a property its essence? [Hawthorne] |
15122 | Could two different properties have the same causal profile? [Hawthorne] |
15124 | If properties are more than their powers, we could have two properties with the same power [Hawthorne] |
14590 | If we accept scattered objects such as archipelagos, why not think of cars that way? [Hawthorne] |
15128 | We can treat the structure/form of the world differently from the nodes/matter of the world [Hawthorne] |
15121 | An individual essence is a necessary and sufficient profile for a thing [Hawthorne] |
14591 | Four-dimensionalists say instantaneous objects are more fundamental than long-lived ones [Hawthorne] |
8970 | Our notion of identical sets involves identical members, which needs absolute identity [Hawthorne] |
14589 | A modal can reverse meaning if the context is seen differently, so maybe context is all? [Hawthorne] |
19542 | It is nonsense that understanding does not involve knowledge; to understand, you must know [Dougherty/Rysiew] |
19543 | To grasp understanding, we should be more explicit about what needs to be known [Dougherty/Rysiew] |
19541 | Rather than knowledge, our epistemic aim may be mere true belief, or else understanding and wisdom [Dougherty/Rysiew] |
19553 | Commitment to 'I have a hand' only makes sense in a context where it has been doubted [Hawthorne] |
19540 | Don't confuse justified belief with justified believers [Dougherty/Rysiew] |
19539 | If knowledge is unanalysable, that makes justification more important [Dougherty/Rysiew] |
19551 | How can we know the heavyweight implications of normal knowledge? Must we distort 'knowledge'? [Hawthorne] |
19552 | We wouldn't know the logical implications of our knowledge if small risks added up to big risks [Hawthorne] |
19554 | Denying closure is denying we know P when we know P and Q, which is absurd in simple cases [Hawthorne] |
19538 | Entailment is modelled in formal semantics as set inclusion (where 'mammals' contains 'cats') [Dougherty/Rysiew] |
15126 | Maybe scientific causation is just generalisation about the patterns [Hawthorne] |
15125 | We only know the mathematical laws, but not much else [Hawthorne] |
14588 | Modern metaphysicians tend to think space-time points are more fundamental than space-time regions [Hawthorne] |