46 ideas
9023 | If you say that a contradiction is true, you change the meaning of 'not', and so change the subject [Quine] |
21752 | Prior to Gödel we thought truth in mathematics consisted in provability [Gödel, by Quine] |
9012 | Talk of 'truth' when sentences are mentioned; it reminds us that reality is the point of sentences [Quine] |
9011 | Truth is redundant for single sentences; we do better to simply speak the sentence [Quine] |
12129 | 'Truth' may only apply within a theory [Kuhn] |
9013 | We can eliminate 'or' from our basic theory, by paraphrasing 'p or q' as 'not(not-p and not-q)' [Quine] |
17835 | Gödel show that the incompleteness of set theory was a necessity [Gödel, by Hallett,M] |
9020 | My logical grammar has sentences by predication, then negation, conjunction, and existential quantification [Quine] |
9028 | Maybe logical truth reflects reality, but in different ways in different languages [Quine] |
10014 | Quine rejects second-order logic, saying that predicates refer to multiple objects [Quine, by Hodes] |
10828 | Quantifying over predicates is treating them as names of entities [Quine] |
9024 | Excluded middle has three different definitions [Quine] |
10012 | Quantification theory can still be proved complete if we add identity [Quine] |
9016 | Names are not essential, because naming can be turned into predication [Quine] |
9015 | Universal quantification is widespread, but it is definable in terms of existential quantification [Quine] |
9025 | You can't base quantification on substituting names for variables, if the irrationals cannot all be named [Quine] |
9026 | Some quantifications could be false substitutionally and true objectually, because of nameless objects [Quine] |
10705 | Putting a predicate letter in a quantifier is to make it the name of an entity [Quine] |
9027 | A sentence is logically true if all sentences with that grammatical structure are true [Quine] |
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] |
17888 | The undecidable sentence can be decided at a 'higher' level in the system [Gödel] |
10621 | Gödel's First Theorem sabotages logicism, and the Second sabotages Hilbert's Programme [Smith,P on Gödel] |
10132 | There can be no single consistent theory from which all mathematical truths can be derived [Gödel, by George/Velleman] |
10072 | First Incompleteness: arithmetic must always be incomplete [Gödel, by Smith,P] |
3198 | Gödel showed that arithmetic is either incomplete or inconsistent [Gödel, by Rey] |
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] |
9017 | Predicates are not names; predicates are the other parties to predication [Quine] |
9018 | A physical object is the four-dimensional material content of a portion of space-time [Quine] |
9019 | Four-d objects helps predication of what no longer exists, and quantification over items from different times [Quine] |
9014 | Some conditionals can be explained just by negation and conjunction: not(p and not-q) [Quine] |
6809 | Kuhn came to accept that all scientists agree on a particular set of values [Kuhn, by Bird] |
12128 | In theory change, words shift their natural reference, so the theories are incommensurable [Kuhn] |
3192 | Basic logic can be done by syntax, with no semantics [Gödel, by Rey] |
9009 | Single words are strongly synonymous if their interchange preserves truth [Quine] |
9007 | It makes no sense to say that two sentences express the same proposition [Quine] |
9008 | There is no rule for separating the information from other features of sentences [Quine] |
9010 | We can abandon propositions, and just talk of sentences and equivalence [Quine] |
9021 | A good way of explaining an expression is saying what conditions make its contexts true [Quine] |