33 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] |
| 10017 | Truth in a model is more tractable than the general notion of truth [Hodes] |
| 10018 | Truth is quite different in interpreted set theory and in the skeleton of its language [Hodes] |
| 14239 | The empty set is usually derived from Separation, but it also seems to need Infinity [Oliver/Smiley] |
| 14240 | The empty set is something, not nothing! [Oliver/Smiley] |
| 14241 | We don't need the empty set to express non-existence, as there are other ways to do that [Oliver/Smiley] |
| 14242 | Maybe we can treat the empty set symbol as just meaning an empty term [Oliver/Smiley] |
| 14243 | The unit set may be needed to express intersections that leave a single member [Oliver/Smiley] |
| 10015 | Higher-order logic may be unintelligible, but it isn't set theory [Hodes] |
| 10011 | Identity is a level one relation with a second-order definition [Hodes] |
| 14234 | If you only refer to objects one at a time, you need sets in order to refer to a plurality [Oliver/Smiley] |
| 14237 | We can use plural language to refer to the set theory domain, to avoid calling it a 'set' [Oliver/Smiley] |
| 10016 | When an 'interpretation' creates a model based on truth, this doesn't include Fregean 'sense' [Hodes] |
| 14245 | Logical truths are true no matter what exists - but predicate calculus insists that something exists [Oliver/Smiley] |
| 10027 | Mathematics is higher-order modal logic [Hodes] |
| 10026 | Arithmetic must allow for the possibility of only a finite total of objects [Hodes] |
| 14246 | If mathematics purely concerned mathematical objects, there would be no applied mathematics [Oliver/Smiley] |
| 14247 | Sets might either represent the numbers, or be the numbers, or replace the numbers [Oliver/Smiley] |
| 10021 | It is claimed that numbers are objects which essentially represent cardinality quantifiers [Hodes] |
| 10022 | Numerical terms can't really stand for quantifiers, because that would make them first-level [Hodes] |
| 9601 | The realist/anti-realist debate is notoriously obscure and fruitless [Williamson] |
| 10023 | Talk of mirror images is 'encoded fictions' about real facts [Hodes] |
| 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] |
| 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] |
| 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] |