18 ideas
| 9978 | Analytic philosophy focuses too much on forms of expression, instead of what is actually said [Tait] |
| 9470 | Modal logic is not an extensional language [Parsons,C] |
| 9986 | The null set was doubted, because numbering seemed to require 'units' [Tait] |
| 13418 | The old problems with the axiom of choice are probably better ascribed to the law of excluded middle [Parsons,C] |
| 9984 | We can have a series with identical members [Tait] |
| 9469 | Substitutional existential quantifier may explain the existence of linguistic entities [Parsons,C] |
| 9468 | On the substitutional interpretation, '(∃x) Fx' is true iff a closed term 't' makes Ft true [Parsons,C] |
| 13416 | Mathematics must be based on axioms, which are true because they are axioms, not vice versa [Tait, by Parsons,C] |
| 17447 | Parsons says counting is tagging as first, second, third..., and converting the last to a cardinal [Parsons,C, by Heck] |
| 18201 | General principles can be obvious in mathematics, but bold speculations in empirical science [Parsons,C] |
| 13419 | If functions are transfinite objects, finitists can have no conception of them [Parsons,C] |
| 13417 | If a mathematical structure is rejected from a physical theory, it retains its mathematical status [Parsons,C] |
| 8249 | Class membership is not transitive, unlike being part of a part of the whole [Lesniewski, by George/Van Evra] |
| 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] |