19 ideas
23367 | Even pointing a finger should only be done for a reason [Epictetus] |
12204 | The logic of metaphysical necessity is S5 [Rumfitt] |
14249 | Boolos reinterprets second-order logic as plural logic [Boolos, by Oliver/Smiley] |
10830 | Second-order logic metatheory is set-theoretic, and second-order validity has set-theoretic problems [Boolos] |
12199 | There is a modal element in consequence, in assessing reasoning from suppositions [Rumfitt] |
12195 | Soundness in argument varies with context, and may be achieved very informally indeed [Rumfitt] |
12201 | We reject deductions by bad consequence, so logical consequence can't be deduction [Rumfitt] |
10829 | A sentence can't be a truth of logic if it asserts the existence of certain sets [Boolos] |
12194 | Contradictions include 'This is red and not coloured', as well as the formal 'B and not-B' [Rumfitt] |
10832 | '∀x x=x' only means 'everything is identical to itself' if the range of 'everything' is fixed [Boolos] |
12198 | Geometrical axioms in logic are nowadays replaced by inference rules (which imply the logical truths) [Rumfitt] |
10834 | Weak completeness: if it is valid, it is provable. Strong: it is provable from a set of sentences [Boolos] |
13841 | Why should compactness be definitive of logic? [Boolos, by Hacking] |
10833 | Many concepts can only be expressed by second-order logic [Boolos] |
14532 | A distinctive type of necessity is found in logical consequence [Rumfitt, by Hale/Hoffmann,A] |
12193 | Logical necessity is when 'necessarily A' implies 'not-A is contradictory' [Rumfitt] |
12200 | A logically necessary statement need not be a priori, as it could be unknowable [Rumfitt] |
12202 | Narrow non-modal logical necessity may be metaphysical, but real logical necessity is not [Rumfitt] |
12203 | If a world is a fully determinate way things could have been, can anyone consider such a thing? [Rumfitt] |