31 ideas
9593 | Progress in philosophy is incremental, not an immature seeking after drama [Williamson] |
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] |
16664 | Everything that exists is either a substance or an accident [Albert of Saxony] |
9601 | The realist/anti-realist debate is notoriously obscure and fruitless [Williamson] |
9599 | There cannot be vague objects, so there may be no such thing as a mountain [Williamson] |
9602 | Common sense and classical logic are often simultaneously abandoned in debates on vagueness [Williamson] |
16703 | God could make a successive thing so that previous parts cease to exist [Albert of Saxony] |
16699 | Successive entities just need parts to succeed one another, without their existence [Albert of Saxony] |
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] |
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] |