63 ideas
9593 | Progress in philosophy is incremental, not an immature seeking after drama [Williamson] |
17663 | If you know what it is, investigation is pointless. If you don't, investigation is impossible [Armstrong] |
9594 | Correspondence to the facts is a bad account of analytic truth [Williamson] |
8729 | Intuitionists deny excluded middle, because it is committed to transcendent truth or objects [Shapiro] |
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] |
9601 | The realist/anti-realist debate is notoriously obscure and fruitless [Williamson] |
17688 | Negative facts are supervenient on positive facts, suggesting they are positive facts [Armstrong] |
9599 | There cannot be vague objects, so there may be no such thing as a mountain [Williamson] |
17691 | Nothing is genuinely related to itself [Armstrong] |
17679 | All instances of some property are strictly identical [Armstrong] |
12677 | Armstrong holds that all basic properties are categorical [Armstrong, by Ellis] |
17666 | Actualism means that ontology cannot contain what is merely physically possible [Armstrong] |
17667 | Dispositions exist, but their truth-makers are actual or categorical properties [Armstrong] |
17687 | If everything is powers there is a vicious regress, as powers are defined by more powers [Armstrong] |
17678 | Universals are just the repeatable features of a world [Armstrong] |
17669 | Realist regularity theories of laws need universals, to pick out the same phenomena [Armstrong] |
17677 | Past, present and future must be equally real if universals are instantiated [Armstrong] |
15442 | Universals are abstractions from their particular instances [Armstrong, by Lewis] |
17686 | Universals are abstractions from states of affairs [Armstrong] |
17668 | It is likely that particulars can be individuated by unique conjunctions of properties [Armstrong] |
9602 | Common sense and classical logic are often simultaneously abandoned in debates on vagueness [Williamson] |
17680 | The identity of a thing with itself can be ruled out as a pseudo-property [Armstrong] |
17693 | The necessary/contingent distinction may need to recognise possibilities as real [Armstrong] |
9598 | Modal thinking isn't a special intuition; it is part of ordinary counterfactual thinking [Williamson] |
16536 | Williamson can't base metaphysical necessity on the psychology of causal counterfactuals [Lowe on Williamson] |
9596 | We scorn imagination as a test of possibility, forgetting its role in counterfactuals [Williamson] |
9597 | There are 'armchair' truths which are not a priori, because experience was involved [Williamson] |
8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |
9592 | Intuition is neither powerful nor vacuous, but reveals linguistic or conceptual competence [Williamson] |
20181 | When analytic philosophers run out of arguments, they present intuitions as their evidence [Williamson] |
17685 | Induction aims at 'all Fs', but abduction aims at hidden or theoretical entities [Armstrong] |
17683 | Science suggests that the predicate 'grue' is not a genuine single universal [Armstrong] |
17675 | Unlike 'green', the 'grue' predicate involves a time and a change [Armstrong] |
17674 | The raven paradox has three disjuncts, confirmed by confirming any one of them [Armstrong] |
17672 | A good reason for something (the smoke) is not an explanation of it (the fire) [Armstrong] |
17684 | To explain observations by a regular law is to explain the observations by the observations [Armstrong] |
17676 | Best explanations explain the most by means of the least [Armstrong] |
17664 | Each subject has an appropriate level of abstraction [Armstrong] |
9595 | You might know that the word 'gob' meant 'mouth', but not be competent to use it [Williamson] |
9600 | If languages are intertranslatable, and cognition is innate, then cultures are all similar [Williamson] |
17692 | We can't deduce the phenomena from the One [Armstrong] |
17689 | Absences might be effects, but surely not causes? [Armstrong] |
17682 | A universe couldn't consist of mere laws [Armstrong] |
17662 | Science depends on laws of nature to study unobserved times and spaces [Armstrong] |
17690 | Oaken conditional laws, Iron universal laws, and Steel necessary laws [Armstrong, by PG] |
17670 | Newton's First Law refers to bodies not acted upon by a force, but there may be no such body [Armstrong] |
8582 | Regularities are lawful if a second-order universal unites two first-order universals [Armstrong, by Lewis] |
17671 | A naive regularity view says if it never occurs then it is impossible [Armstrong] |
17681 | The laws of nature link properties with properties [Armstrong] |
16246 | Rather than take necessitation between universals as primitive, just make laws primitive [Maudlin on Armstrong] |
9480 | Armstrong has an unclear notion of contingent necessitation, which can't necessitate anything [Bird on Armstrong] |