53 ideas
5893 | A wise man has integrity, firmness of will, nobility, consistency, sobriety, patience [Cicero] |
5891 | Philosophy is the collection of rational arguments [Cicero] |
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] |
10170 | While true-in-a-model seems relative, true-in-all-models seems not to be [Reck/Price] |
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] |
10166 | ZFC set theory has only 'pure' sets, without 'urelements' [Reck/Price] |
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] |
10175 | Three types of variable in second-order logic, for objects, functions, and predicates/sets [Reck/Price] |
9027 | A sentence is logically true if all sentences with that grammatical structure are true [Quine] |
10165 | 'Analysis' is the theory of the real numbers [Reck/Price] |
10174 | Mereological arithmetic needs infinite objects, and function definitions [Reck/Price] |
10164 | Peano Arithmetic can have three second-order axioms, plus '1' and 'successor' [Reck/Price] |
10172 | Set-theory gives a unified and an explicit basis for mathematics [Reck/Price] |
10167 | Structuralism emerged from abstract algebra, axioms, and set theory and its structures [Reck/Price] |
10169 | Relativist Structuralism just stipulates one successful model as its arithmetic [Reck/Price] |
10179 | There are 'particular' structures, and 'universal' structures (what the former have in common) [Reck/Price] |
10181 | Pattern Structuralism studies what isomorphic arithmetic models have in common [Reck/Price] |
10182 | There are Formalist, Relativist, Universalist and Pattern structuralism [Reck/Price] |
10168 | Formalist Structuralism says the ontology is vacuous, or formal, or inference relations [Reck/Price] |
10178 | Maybe we should talk of an infinity of 'possible' objects, to avoid arithmetic being vacuous [Reck/Price] |
10176 | Universalist Structuralism is based on generalised if-then claims, not one particular model [Reck/Price] |
10177 | Universalist Structuralism eliminates the base element, as a variable, which is then quantified out [Reck/Price] |
10171 | The existence of an infinite set is assumed by Relativist Structuralism [Reck/Price] |
9017 | Predicates are not names; predicates are the other parties to predication [Quine] |
10173 | A nominalist might avoid abstract objects by just appealing to mereological sums [Reck/Price] |
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] |
5879 | The soul is the heart, or blood in the heart, or part of the brain, of something living in heart or brain, or breath [Cicero] |
5884 | How can one mind perceive so many dissimilar sensations? [Cicero] |
5887 | The soul has a single nature, so it cannot be divided, and hence it cannot perish [Cicero] |
5886 | Like the eye, the soul has no power to see itself, but sees other things [Cicero] |
5885 | Souls contain no properties of elements, and elements contain no properties of souls [Cicero] |
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] |
5890 | We should not share the distress of others, but simply try to relieve it [Cicero] |
5894 | All men except philosophers fear poverty [Cicero] |
5895 | If one despises illiterate mechanics individually, they are not worth more collectively [Cicero] |