61 ideas
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] |
21752 | Prior to Gödel we thought truth in mathematics consisted in provability [Gödel, by Quine] |
21602 | Many-valued logics don't solve vagueness; its presence at the meta-level is ignored [Williamson] |
17835 | Gödel show that the incompleteness of set theory was a necessity [Gödel, by Hallett,M] |
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] |
21612 | Or-elimination is 'Argument by Cases'; it shows how to derive C from 'A or B' [Williamson] |
17886 | The limitations of axiomatisation were revealed by the incompleteness theorems [Gödel, by Koellner] |
10071 | Second Incompleteness: nice theories can't prove their own consistency [Gödel, by Smith,P] |
19123 | If soundness can't be proved internally, 'reflection principles' can be added to assert soundness [Gödel, by Halbach/Leigh] |
10621 | Gödel's First Theorem sabotages logicism, and the Second sabotages Hilbert's Programme [Smith,P on Gödel] |
17888 | The undecidable sentence can be decided at a 'higher' level in the system [Gödel] |
21599 | A sorites stops when it collides with an opposite sorites [Williamson] |
10132 | There can be no single consistent theory from which all mathematical truths can be derived [Gödel, by George/Velleman] |
3198 | Gödel showed that arithmetic is either incomplete or inconsistent [Gödel, by Rey] |
10072 | First Incompleteness: arithmetic must always be incomplete [Gödel, by Smith,P] |
9590 | Arithmetical truth cannot be fully and formally derived from axioms and inference rules [Gödel, by Nagel/Newman] |
11069 | Gödel's Second says that semantic consequence outruns provability [Gödel, by Hanna] |
10118 | First Incompleteness: a decent consistent system is syntactically incomplete [Gödel, by George/Velleman] |
10122 | Second Incompleteness: a decent consistent system can't prove its own consistency [Gödel, by George/Velleman] |
10611 | There is a sentence which a theory can show is true iff it is unprovable [Gödel, by Smith,P] |
10867 | 'This system can't prove this statement' makes it unprovable either way [Gödel, by Clegg] |
8747 | Realists are happy with impredicative definitions, which describe entities in terms of other existing entities [Gödel, by Shapiro] |
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] |
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] |
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] |
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] |
21621 | We can't infer metaphysical necessities to be a priori knowable - or indeed knowable in any way [Williamson] |
21627 | We have inexact knowledge when we include margins of error [Williamson] |
21626 | Knowing you know (KK) is usually denied if the knowledge concept is missing, or not considered [Williamson] |
3192 | Basic logic can be done by syntax, with no semantics [Gödel, by Rey] |
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] |
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] |
21624 | It is known that there is a cognitive loss in identifying propositions with possible worlds [Williamson] |
541 | Virtue comes more from habit than character [Critias] |
542 | Fear of the gods was invented to discourage secret sin [Critias] |