18 ideas
| 9978 | Analytic philosophy focuses too much on forms of expression, instead of what is actually said [Tait] |
| 9986 | The null set was doubted, because numbering seemed to require 'units' [Tait] |
| 9984 | We can have a series with identical members [Tait] |
| 18755 | Validity is explained as truth in all models, because that relies on the logical terms [McGee] |
| 18751 | Natural language includes connectives like 'because' which are not truth-functional [McGee] |
| 18761 | Second-order variables need to range over more than collections of first-order objects [McGee] |
| 18753 | An ontologically secure semantics for predicate calculus relies on sets [McGee] |
| 18754 | Logically valid sentences are analytic truths which are just true because of their logical words [McGee] |
| 13416 | Mathematics must be based on axioms, which are true because they are axioms, not vice versa [Tait, by Parsons,C] |
| 18757 | Soundness theorems are uninformative, because they rely on soundness in their proofs [McGee] |
| 18760 | The culmination of Euclidean geometry was axioms that made all models isomorphic [McGee] |
| 9981 | Abstraction is 'logical' if the sense and truth of the abstraction depend on the concrete [Tait] |
| 9982 | Cantor and Dedekind use abstraction to fix grammar and objects, not to carry out proofs [Tait] |
| 9985 | Abstraction may concern the individuation of the set itself, not its elements [Tait] |
| 9972 | Why should abstraction from two equipollent sets lead to the same set of 'pure units'? [Tait] |
| 9980 | If abstraction produces power sets, their identity should imply identity of the originals [Tait] |
| 18762 | A maxim claims that if we are allowed to assert a sentence, that means it must be true [McGee] |
| 3031 | The greatest good is not the achievement of desire, but to desire what is proper [Menedemus, by Diog. Laertius] |