20 ideas
13838 | A decent modern definition should always imply a semantics [Hacking] |
11178 | The essence or definition of an essence involves either a class of properties or a class of propositions [Fine,K] |
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] |
11175 | Logical concepts rest on certain inferences, not on facts about implications [Fine,K] |
13839 | Perhaps variables could be dispensed with, by arrows joining places in the scope of quantifiers [Hacking] |
11176 | The property of Property Abstraction says any suitable condition must imply a property [Fine,K] |
11174 | A logical truth is true in virtue of the nature of the logical concepts [Fine,K] |
13843 | If it is a logic, the Löwenheim-Skolem theorem holds for it [Hacking] |
11177 | Can the essence of an object circularly involve itself, or involve another object? [Fine,K] |
11173 | Being a man is a consequence of his essence, not constitutive of it [Fine,K] |
11179 | If there are alternative definitions, then we have three possibilities for essence [Fine,K] |
13304 | Learned men gain more in one day than others do in a lifetime [Posidonius] |
20820 | Time is an interval of motion, or the measure of speed [Posidonius, by Stobaeus] |