39 ideas
8092 | Logic was merely a branch of rhetoric until the scientific 17th century [Devlin] |
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] |
8081 | 'No councillors are bankers' and 'All bankers are athletes' implies 'Some athletes are not councillors' [Devlin] |
8085 | Modern propositional inference replaces Aristotle's 19 syllogisms with modus ponens [Devlin] |
8086 | Predicate logic retains the axioms of propositional logic [Devlin] |
9013 | We can eliminate 'or' from our basic theory, by paraphrasing 'p or q' as 'not(not-p and not-q)' [Quine] |
9020 | My logical grammar has sentences by predication, then negation, conjunction, and existential quantification [Quine] |
8091 | Situation theory is logic that takes account of context [Devlin] |
8087 | Golden ages: 1900-1960 for pure logic, and 1950-1985 for applied logic [Devlin] |
8089 | Montague's intensional logic incorporated the notion of meaning [Devlin] |
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] |
8082 | Where a conditional is purely formal, an implication implies a link between premise and conclusion [Devlin] |
9024 | Excluded middle has three different definitions [Quine] |
10012 | Quantification theory can still be proved complete if we add identity [Quine] |
8072 | Sentences of apparent identical form can have different contextual meanings [Devlin] |
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] |
8075 | Space and time are atomic in the arrow, and divisible in the tortoise [Devlin] |
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] |
8088 | People still say the Hopi have no time concepts, despite Whorf's later denial [Devlin] |
9009 | Single words are strongly synonymous if their interchange preserves truth [Quine] |
8073 | How do we parse 'time flies like an arrow' and 'fruit flies like an apple'? [Devlin] |
8076 | The distinction between sentences and abstract propositions is crucial in logic [Devlin] |
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] |
468 | Musical performance can reveal a range of virtues [Damon of Ath.] |