38 ideas
13838 | A decent modern definition should always imply a semantics [Hacking] |
15557 | Verisimilitude has proved hard to analyse, and seems to have several components [Lewis] |
13833 | 'Thinning' ('dilution') is the key difference between deduction (which allows it) and induction [Hacking] |
13834 | Gentzen's Cut Rule (or transitivity of deduction) is 'If A |- B and B |- C, then A |- C' [Hacking] |
13835 | Only Cut reduces complexity, so logic is constructive without it, and it can be dispensed with [Hacking] |
13845 | The various logics are abstractions made from terms like 'if...then' in English [Hacking] |
13840 | First-order logic is the strongest complete compact theory with Löwenheim-Skolem [Hacking] |
13844 | A limitation of first-order logic is that it cannot handle branching quantifiers [Hacking] |
13842 | Second-order completeness seems to need intensional entities and possible worlds [Hacking] |
8729 | Intuitionists deny excluded middle, because it is committed to transcendent truth or objects [Shapiro] |
13837 | With a pure notion of truth and consequence, the meanings of connectives are fixed syntactically [Hacking] |
13839 | Perhaps variables could be dispensed with, by arrows joining places in the scope of quantifiers [Hacking] |
13843 | If it is a logic, the Löwenheim-Skolem theorem holds for it [Hacking] |
8763 | The number 3 is presumably identical as a natural, an integer, a rational, a real, and complex [Shapiro] |
18249 | Cauchy gave a formal definition of a converging sequence. [Shapiro] |
8764 | Categories are the best foundation for mathematics [Shapiro] |
8762 | Two definitions of 3 in terms of sets disagree over whether 1 is a member of 3 [Shapiro] |
8760 | Numbers do not exist independently; the essence of a number is its relations to other numbers [Shapiro] |
8761 | A 'system' is related objects; a 'pattern' or 'structure' abstracts the pure relations from them [Shapiro] |
8744 | Logicism seems to be a non-starter if (as is widely held) logic has no ontology of its own [Shapiro] |
8749 | Term Formalism says mathematics is just about symbols - but real numbers have no names [Shapiro] |
8750 | Game Formalism is just a matter of rules, like chess - but then why is it useful in science? [Shapiro] |
8752 | Deductivism says mathematics is logical consequences of uninterpreted axioms [Shapiro] |
8753 | Critics resent the way intuitionism cripples mathematics, but it allows new important distinctions [Shapiro] |
8731 | Conceptualist are just realists or idealist or nominalists, depending on their view of concepts [Shapiro] |
8730 | 'Impredicative' definitions refer to the thing being described [Shapiro] |
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] |
8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |
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] |