28 ideas
15545 | Armstrong's analysis seeks truthmakers rather than definitions [Lewis] |
13838 | A decent modern definition should always imply a semantics [Hacking] |
15546 | Predications aren't true because of what exists, but of how it exists [Lewis] |
15548 | Say 'truth is supervenient on being', but construe 'being' broadly [Lewis] |
14399 | Presentism says only the present exists, so there is nothing for tensed truths to supervene on [Lewis] |
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] |
10301 | The axiom of choice is controversial, but it could be replaced [Shapiro] |
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] |
10588 | First-order logic is Complete, and Compact, with the Löwenheim-Skolem Theorems [Shapiro] |
13842 | Second-order completeness seems to need intensional entities and possible worlds [Hacking] |
10298 | Some say that second-order logic is mathematics, not logic [Shapiro] |
10299 | If the aim of logic is to codify inferences, second-order logic is useless [Shapiro] |
10300 | Logical consequence can be defined in terms of the logical terminology [Shapiro] |
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] |
10290 | Second-order variables also range over properties, sets, relations or functions [Shapiro] |
10590 | Up Löwenheim-Skolem: if natural numbers satisfy wffs, then an infinite domain satisfies them [Shapiro] |
10296 | The Löwenheim-Skolem Theorems fail for second-order languages with standard semantics [Shapiro] |
10297 | The Löwenheim-Skolem theorem seems to be a defect of first-order logic [Shapiro] |
13843 | If it is a logic, the Löwenheim-Skolem theorem holds for it [Hacking] |
10292 | Downward Löwenheim-Skolem: if there's an infinite model, there is a countable model [Shapiro] |
10294 | Second-order logic has the expressive power for mathematics, but an unworkable model theory [Shapiro] |
15543 | How do things combine to make states of affairs? Constituents can repeat, and fail to combine [Lewis] |
10591 | Logicians use 'property' and 'set' interchangeably, with little hanging on it [Shapiro] |