23 ideas
19259 | If 2-D conceivability can a priori show possibilities, this is a defence of conceptual analysis [Vaidya] |
18261 | A simplification which is complete constitutes a definition [Kant] |
10301 | The axiom of choice is controversial, but it could be replaced [Shapiro] |
22275 | Logic gives us the necessary rules which show us how we ought to think [Kant] |
10588 | First-order logic is Complete, and Compact, with the Löwenheim-Skolem Theorems [Shapiro] |
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] |
10290 | Second-order variables also range over properties, sets, relations or functions [Shapiro] |
10292 | Downward Löwenheim-Skolem: if there's an infinite model, there is a countable model [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] |
10294 | Second-order logic has the expressive power for mathematics, but an unworkable model theory [Shapiro] |
10591 | Logicians use 'property' and 'set' interchangeably, with little hanging on it [Shapiro] |
19262 | Essential properties are necessary, but necessary properties may not be essential [Vaidya] |
19267 | Define conceivable; how reliable is it; does inconceivability help; and what type of possibility results? [Vaidya] |
19268 | Inconceivability (implying impossibility) may be failure to conceive, or incoherence [Vaidya] |
19265 | Can you possess objective understanding without realising it? [Vaidya] |
19260 | Gettier deductive justifications split the justification from the truthmaker [Vaidya] |
19266 | In a disjunctive case, the justification comes from one side, and the truth from the other [Vaidya] |
18260 | If we knew what we know, we would be astonished [Kant] |
19264 | Aboutness is always intended, and cannot be accidental [Vaidya] |