21 ideas
13838 | A decent modern definition should always imply a semantics [Hacking] |
13834 | Gentzen's Cut Rule (or transitivity of deduction) is 'If A |- B and B |- C, then A |- C' [Hacking] |
13835 | Only Cut reduces complexity, so logic is constructive without it, and it can be dispensed with [Hacking] |
13833 | 'Thinning' ('dilution') is the key difference between deduction (which allows it) and induction [Hacking] |
13845 | The various logics are abstractions made from terms like 'if...then' in English [Hacking] |
13840 | First-order logic is the strongest complete compact theory with Löwenheim-Skolem [Hacking] |
13844 | A limitation of first-order logic is that it cannot handle branching quantifiers [Hacking] |
13842 | Second-order completeness seems to need intensional entities and possible worlds [Hacking] |
13837 | With a pure notion of truth and consequence, the meanings of connectives are fixed syntactically [Hacking] |
13839 | Perhaps variables could be dispensed with, by arrows joining places in the scope of quantifiers [Hacking] |
13733 | Frege considered definite descriptions to be genuine singular terms [Frege, by Fitting/Mendelsohn] |
9874 | Contradiction arises from Frege's substitutional account of second-order quantification [Dummett on Frege] |
13843 | If it is a logic, the Löwenheim-Skolem theorem holds for it [Hacking] |
18252 | Real numbers are ratios of quantities, such as lengths or masses [Frege] |
18271 | We can't prove everything, but we can spell out the unproved, so that foundations are clear [Frege] |
10623 | Frege defined number in terms of extensions of concepts, but needed Basic Law V to explain extensions [Frege, by Hale/Wright] |
9975 | Frege ignored Cantor's warning that a cardinal set is not just a concept-extension [Tait on Frege] |
18165 | My Basic Law V is a law of pure logic [Frege] |
9190 | A concept is a function mapping objects onto truth-values, if they fall under the concept [Frege, by Dummett] |
13665 | Frege took the study of concepts to be part of logic [Frege, by Shapiro] |
1590 | The just man does not harm his enemies, but benefits everyone [Plato] |