22 ideas
17082 | Paradox: why do you analyse if you know it, and how do you analyse if you don't? [Ruben] |
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] |
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] |
19540 | Don't confuse justified belief with justified believers [Dougherty/Rysiew] |
19539 | If knowledge is unanalysable, that makes justification more important [Dougherty/Rysiew] |
17087 | The 'symmetry thesis' says explanation and prediction only differ pragmatically [Ruben] |
17081 | Usually explanations just involve giving information, with no reference to the act of explanation [Ruben] |
17092 | An explanation needs the world to have an appropriate structure [Ruben] |
17090 | Most explanations are just sentences, not arguments [Ruben] |
17094 | The causal theory of explanation neglects determinations which are not causal [Ruben] |
17088 | Reducing one science to another is often said to be the perfect explanation [Ruben] |
17089 | Facts explain facts, but only if they are conceptualised or named appropriately [Ruben] |
19538 | Entailment is modelled in formal semantics as set inclusion (where 'mammals' contains 'cats') [Dougherty/Rysiew] |