15 ideas
6299 | Axioms are often affirmed simply because they produce results which have been accepted [Resnik] |
16489 | Is it possible to state every possible truth about the whole course of nature without using 'not'? [Russell] |
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] |
16490 | Some facts about experience feel like logical necessities [Russell] |
16488 | It is hard to explain how a sentence like 'it is not raining' can be found true by observation [Russell] |
16491 | If we define 'this is not blue' as disbelief in 'this is blue', we eliminate 'not' as an ingredient of facts [Russell] |
13304 | Learned men gain more in one day than others do in a lifetime [Posidonius] |
4786 | Russell's 'at-at' theory says motion is to be at the intervening points at the intervening instants [Russell, by Psillos] |
20820 | Time is an interval of motion, or the measure of speed [Posidonius, by Stobaeus] |