27 ideas
13838 | A decent modern definition should always imply a semantics [Hacking] |
13833 | 'Thinning' ('dilution') is the key difference between deduction (which allows it) and induction [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] |
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] |
8525 | Relations need terms, so they must be second-order entities based on first-order tropes [Campbell,K] |
13843 | If it is a logic, the Löwenheim-Skolem theorem holds for it [Hacking] |
8518 | Events are trope-sequences, in which tropes replace one another [Campbell,K] |
8513 | Two red cloths are separate instances of redness, because you can dye one of them blue [Campbell,K] |
8514 | Red could only recur in a variety of objects if it was many, which makes them particulars [Campbell,K] |
8522 | Tropes solve the Companionship Difficulty, since the resemblance is only between abstract particulars [Campbell,K] |
8523 | Tropes solve the Imperfect Community problem, as they can only resemble in one respect [Campbell,K] |
8524 | Trope theory makes space central to reality, as tropes must have a shape and size [Campbell,K] |
8521 | Nominalism has the problem that without humans nothing would resemble anything else [Campbell,K] |
8515 | Tropes are basic particulars, so concrete particulars are collections of co-located tropes [Campbell,K] |
8519 | Bundles must be unique, so the Identity of Indiscernibles is a necessity - which it isn't! [Campbell,K] |
4033 | Two pure spheres in non-absolute space are identical but indiscernible [Campbell,K] |
8512 | Abstractions come before the mind by concentrating on a part of what is presented [Campbell,K] |
19813 | All legislators invoke God in support of extraordinary laws, because their justification is not obvious [Machiavelli] |
7126 | Rulers should preserve the foundations of religion, to ensure good behaviour and unity [Machiavelli] |
8517 | Causal conditions are particular abstract instances of properties, which makes them tropes [Campbell,K] |
8516 | Davidson can't explain causation entirely by events, because conditions are also involved [Campbell,K] |