51 ideas
| 9023 | If you say that a contradiction is true, you change the meaning of 'not', and so change the subject [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] |
| 9013 | We can eliminate 'or' from our basic theory, by paraphrasing 'p or q' as 'not(not-p and not-q)' [Quine] |
| 10859 | A set is 'well-ordered' if every subset has a first element [Clegg] |
| 10857 | Set theory made a closer study of infinity possible [Clegg] |
| 10864 | Any set can always generate a larger set - its powerset, of subsets [Clegg] |
| 10872 | Extensionality: Two sets are equal if and only if they have the same elements [Clegg] |
| 10875 | Pairing: For any two sets there exists a set to which they both belong [Clegg] |
| 10876 | Unions: There is a set of all the elements which belong to at least one set in a collection [Clegg] |
| 10878 | Infinity: There exists a set of the empty set and the successor of each element [Clegg] |
| 10877 | Powers: All the subsets of a given set form their own new powerset [Clegg] |
| 10879 | Choice: For every set a mechanism will choose one member of any non-empty subset [Clegg] |
| 10871 | Axiom of Existence: there exists at least one set [Clegg] |
| 10874 | Specification: a condition applied to a set will always produce a new set [Clegg] |
| 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] |
| 10880 | Mathematics can be 'pure' (unapplied), 'real' (physically grounded); or 'applied' (just applicable) [Clegg] |
| 10860 | An ordinal number is defined by the set that comes before it [Clegg] |
| 10861 | Beyond infinity cardinals and ordinals can come apart [Clegg] |
| 10854 | Transcendental numbers can't be fitted to finite equations [Clegg] |
| 10858 | By adding an axis of imaginary numbers, we get the useful 'number plane' instead of number line [Clegg] |
| 10853 | Either lack of zero made early mathematics geometrical, or the geometrical approach made zero meaningless [Clegg] |
| 10866 | Cantor's account of infinities has the shaky foundation of irrational numbers [Clegg] |
| 10869 | The Continuum Hypothesis is independent of the axioms of set theory [Clegg] |
| 10862 | The 'continuum hypothesis' says aleph-one is the cardinality of the reals [Clegg] |
| 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] |
| 21515 | Incoherence may be more important for enquiry than coherence [Olsson] |
| 21514 | Coherence is the capacity to answer objections [Olsson] |
| 21496 | Mere agreement of testimonies is not enough to make truth very likely [Olsson] |
| 21499 | Coherence is only needed if the information sources are not fully reliable [Olsson] |
| 21502 | A purely coherent theory cannot be true of the world without some contact with the world [Olsson] |
| 21512 | Extending a system makes it less probable, so extending coherence can't make it more probable [Olsson] |
| 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] |