105 ideas
9593 | Progress in philosophy is incremental, not an immature seeking after drama [Williamson] |
9184 | We can't presume that all interesting concepts can be analysed [Williamson] |
6859 | Analytic philosophy has much higher standards of thinking than continental philosophy [Williamson] |
21616 | Truth and falsity apply to suppositions as well as to assertions [Williamson] |
21623 | True and false are not symmetrical; false is more complex, involving negation [Williamson] |
15134 | The truthmaker principle requires some specific named thing to make the difference [Williamson] |
15141 | Truthmaker is incompatible with modal semantics of varying domains [Williamson] |
15140 | The converse Barcan formula will not allow contingent truths to have truthmakers [Williamson] |
9594 | Correspondence to the facts is a bad account of analytic truth [Williamson] |
13913 | The four 'perfect syllogisms' are called Barbara, Celarent, Darii and Ferio [Engelbretsen/Sayward] |
13914 | Syllogistic logic has one rule: what is affirmed/denied of wholes is affirmed/denied of their parts [Engelbretsen/Sayward] |
13915 | Syllogistic can't handle sentences with singular terms, or relational terms, or compound sentences [Engelbretsen/Sayward] |
13916 | Term logic uses expression letters and brackets, and '-' for negative terms, and '+' for compound terms [Engelbretsen/Sayward] |
15131 | If metaphysical possibility is not a contingent matter, then S5 seems to suit it best [Williamson] |
14626 | In S5 matters of possibility and necessity are non-contingent [Williamson] |
15135 | If the domain of propositional quantification is constant, the Barcan formulas hold [Williamson] |
15130 | If a property is possible, there is something which can have it [Williamson] |
15139 | Converse Barcan: could something fail to meet a condition, if everything meets that condition? [Williamson] |
21602 | Many-valued logics don't solve vagueness; its presence at the meta-level is ignored [Williamson] |
6862 | Fuzzy logic uses a continuum of truth, but it implies contradictions [Williamson] |
6858 | Formal logic struck me as exactly the language I wanted to think in [Williamson] |
13850 | In modern logic all formal validity can be characterised syntactically [Engelbretsen/Sayward] |
13849 | Classical logic rests on truth and models, where constructivist logic rests on defence and refutation [Engelbretsen/Sayward] |
21611 | Formal semantics defines validity as truth preserved in every model [Williamson] |
21606 | 'Bivalence' is the meta-linguistic principle that 'A' in the object language is true or false [Williamson] |
21605 | Excluded Middle is 'A or not A' in the object language [Williamson] |
13851 | Unlike most other signs, = cannot be eliminated [Engelbretsen/Sayward] |
18492 | Not all quantification is either objectual or substitutional [Williamson] |
15136 | Substitutional quantification is metaphysical neutral, and equivalent to a disjunction of instances [Williamson] |
15138 | Not all quantification is objectual or substitutional [Williamson] |
21612 | Or-elimination is 'Argument by Cases'; it shows how to derive C from 'A or B' [Williamson] |
13852 | Axioms are ω-incomplete if the instances are all derivable, but the universal quantification isn't [Engelbretsen/Sayward] |
21599 | A sorites stops when it collides with an opposite sorites [Williamson] |
9183 | Platonism claims that some true assertions have singular terms denoting abstractions, so abstractions exist [Williamson] |
9601 | The realist/anti-realist debate is notoriously obscure and fruitless [Williamson] |
15137 | If 'fact' is a noun, can we name the fact that dogs bark 'Mary'? [Williamson] |
21589 | When bivalence is rejected because of vagueness, we lose classical logic [Williamson] |
21596 | Vagueness undermines the stable references needed by logic [Williamson] |
21601 | A vague term can refer to very precise elements [Williamson] |
21629 | Equally fuzzy objects can be identical, so fuzziness doesn't entail vagueness [Williamson] |
9599 | There cannot be vague objects, so there may be no such thing as a mountain [Williamson] |
21591 | Vagueness is epistemic. Statements are true or false, but we often don't know which [Williamson] |
21619 | If a heap has a real boundary, omniscient speakers would agree where it is [Williamson] |
21620 | The epistemic view says that the essence of vagueness is ignorance [Williamson] |
21622 | If there is a true borderline of which we are ignorant, this drives a wedge between meaning and use [Williamson] |
9120 | Vagueness in a concept is its indiscriminability from other possible concepts [Williamson] |
6863 | Close to conceptual boundaries judgement is too unreliable to give knowledge [Williamson] |
21625 | The vagueness of 'heap' can remain even when the context is fixed [Williamson] |
21614 | The 'nihilist' view of vagueness says that 'heap' is not a legitimate concept [Williamson] |
21617 | We can say propositions are bivalent, but vague utterances don't express a proposition [Williamson] |
21618 | If the vague 'TW is thin' says nothing, what does 'TW is thin if his perfect twin is thin' say? [Williamson] |
21590 | Asking when someone is 'clearly' old is higher-order vagueness [Williamson] |
21592 | Supervaluation keeps classical logic, but changes the truth in classical semantics [Williamson] |
21603 | You can't give a precise description of a language which is intrinsically vague [Williamson] |
21604 | Supervaluation assigns truth when all the facts are respected [Williamson] |
21607 | Supervaluation has excluded middle but not bivalence; 'A or not-A' is true, even when A is undecided [Williamson] |
21608 | Truth-functionality for compound statements fails in supervaluation [Williamson] |
21609 | Supervaluationism defines 'supertruth', but neglects it when defining 'valid' [Williamson] |
21610 | Supervaluation adds a 'definitely' operator to classical logic [Williamson] |
21613 | Supervaluationism cannot eliminate higher-order vagueness [Williamson] |
21633 | Nominalists suspect that properties etc are our projections, and could have been different [Williamson] |
6861 | What sort of logic is needed for vague concepts, and what sort of concept of truth? [Williamson] |
9602 | Common sense and classical logic are often simultaneously abandoned in debates on vagueness [Williamson] |
21630 | If fuzzy edges are fine, then why not fuzzy temporal, modal or mereological boundaries? [Williamson] |
21632 | A river is not just event; it needs actual and counterfactual boundaries [Williamson] |
14625 | Necessity is counterfactually implied by its negation; possibility does not counterfactually imply its negation [Williamson] |
14623 | Strict conditionals imply counterfactual conditionals: □(A⊃B)⊃(A□→B) [Williamson] |
14624 | Counterfactual conditionals transmit possibility: (A□→B)⊃(◊A⊃◊B) [Williamson] |
14531 | Rather than define counterfactuals using necessity, maybe necessity is a special case of counterfactuals [Williamson, by Hale/Hoffmann,A] |
21621 | We can't infer metaphysical necessities to be a priori knowable - or indeed knowable in any way [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] |
15142 | Our ability to count objects across possibilities favours the Barcan formulas [Williamson] |
18925 | If talking donkeys are possible, something exists which could be a talking donkey [Williamson, by Cameron] |
21627 | We have inexact knowledge when we include margins of error [Williamson] |
4760 | Belief aims at knowledge (rather than truth), and mere believing is a kind of botched knowing [Williamson] |
19527 | We don't acquire evidence and then derive some knowledge, because evidence IS knowledge [Williamson] |
19512 | Don't analyse knowledge; use knowledge to analyse other concepts in epistemology [Williamson, by DeRose] |
19528 | Knowledge is prior to believing, just as doing is prior to trying to do [Williamson] |
19529 | Belief explains justification, and knowledge explains belief, so knowledge explains justification [Williamson] |
19530 | A neutral state of experience, between error and knowledge, is not basic; the successful state is basic [Williamson] |
19531 | Internalism about mind is an obsolete view, and knowledge-first epistemology develops externalism [Williamson] |
19536 | Knowledge-first says your total evidence IS your knowledge [Williamson] |
19526 | Surely I am acquainted with physical objects, not with appearances? [Williamson] |
9597 | There are 'armchair' truths which are not a priori, because experience was involved [Williamson] |
6860 | How can one discriminate yellow from red, but not the colours in between? [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] |
21626 | Knowing you know (KK) is usually denied if the knowledge concept is missing, or not considered [Williamson] |
3061 | Anaxarchus said that he was not even sure that he knew nothing [Anaxarchus, by Diog. Laertius] |
14628 | Imagination is important, in evaluating possibility and necessity, via counterfactuals [Williamson] |
21631 | To know, believe, hope or fear, one must grasp the thought, but not when you fail to do them [Williamson] |
21600 | 'Blue' is not a family resemblance, because all the blues resemble in some respect [Williamson] |
9595 | You might know that the word 'gob' meant 'mouth', but not be competent to use it [Williamson] |
21615 | References to the 'greatest prime number' have no reference, but are meaningful [Williamson] |
18038 | The 't' and 'f' of formal semantics has no philosophical interest, and may not refer to true and false [Williamson] |
19534 | How does inferentialism distinguish the patterns of inference that are essential to meaning? [Williamson] |
19535 | Internalist inferentialism has trouble explaining how meaning and reference relate [Williamson] |
19533 | Inferentialist semantics relies on internal inference relations, not on external references [Williamson] |
19532 | Truth-conditional referential semantics is externalist, referring to worldly items [Williamson] |
21624 | It is known that there is a cognitive loss in identifying propositions with possible worlds [Williamson] |
19216 | Propositions (such as 'that dog is barking') only exist if their items exist [Williamson] |
9600 | If languages are intertranslatable, and cognition is innate, then cultures are all similar [Williamson] |
15133 | A thing can't be the only necessary existent, because its singleton set would be as well [Williamson] |