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] |
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] |
6299 | Axioms are often affirmed simply because they produce results which have been accepted [Resnik] |
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] |
10016 | When an 'interpretation' creates a model based on truth, this doesn't include Fregean 'sense' [Hodes] |
6304 | Mathematical realism says that maths exists, is largely true, and is independent of proofs [Resnik] |
10027 | Mathematics is higher-order modal logic [Hodes] |
10026 | Arithmetic must allow for the possibility of only a finite total of objects [Hodes] |
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] |
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] |