25 ideas
15557 | Verisimilitude has proved hard to analyse, and seems to have several components [Lewis] |
6299 | Axioms are often affirmed simply because they produce results which have been accepted [Resnik] |
11022 | Gentzen introduced a natural deduction calculus (NK) in 1934 [Gentzen, by Read] |
11065 | The inferential role of a logical constant constitutes its meaning [Gentzen, by Hanna] |
11023 | The logical connectives are 'defined' by their introduction rules [Gentzen] |
11213 | Each logical symbol has an 'introduction' rule to define it, and hence an 'elimination' rule [Gentzen] |
6304 | Mathematical realism says that maths exists, is largely true, and is independent of proofs [Resnik] |
10067 | Gentzen proved the consistency of arithmetic from assumptions beyond arithmetic [Gentzen, by Musgrave] |
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] |
15554 | A disposition needs a causal basis, a property in a certain causal role. Could the disposition be the property? [Lewis] |
15560 | We can explain a chance event, but can never show why some other outcome did not occur [Lewis] |
15559 | Does a good explanation produce understanding? That claim is just empty [Lewis] |
15556 | Science may well pursue generalised explanation, rather than laws [Lewis] |
15558 | A good explanation is supposed to show that the event had to happen [Lewis] |
4809 | Lewis endorses the thesis that all explanation of singular events is causal explanation [Lewis, by Psillos] |
14321 | To explain an event is to provide some information about its causal history [Lewis] |
15555 | Explaining match lighting in general is like explaining one lighting of a match [Lewis] |
15551 | Ways of carving causes may be natural, but never 'right' [Lewis] |
15552 | We only pick 'the' cause for the purposes of some particular enquiry. [Lewis] |
15553 | Causal dependence is counterfactual dependence between events [Lewis] |