26 ideas
10301 | The axiom of choice is controversial, but it could be replaced [Shapiro] |
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] |
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] |
10292 | Downward Löwenheim-Skolem: if there's an infinite model, there is a countable model [Shapiro] |
10631 | If 'x is heterological' iff it does not apply to itself, then 'heterological' is heterological if it isn't heterological [Hale/Wright] |
10294 | Second-order logic has the expressive power for mathematics, but an unworkable model theory [Shapiro] |
10624 | The incompletability of formal arithmetic reveals that logic also cannot be completely characterized [Hale/Wright] |
10629 | If structures are relative, this undermines truth-value and objectivity [Hale/Wright] |
10628 | The structural view of numbers doesn't fit their usage outside arithmetical contexts [Hale/Wright] |
10622 | The neo-Fregean is more optimistic than Frege about contextual definitions of numbers [Hale/Wright] |
10591 | Logicians use 'property' and 'set' interchangeably, with little hanging on it [Shapiro] |
10626 | Objects just are what singular terms refer to [Hale/Wright] |
12066 | Aristotelian and Kripkean essentialism are very different theories [Witt] |
12067 | An Aristotelian essence is a nonlinguistic correlate of the definition [Witt] |
12082 | If unity is a matter of degree, then essence may also be a matter of degree [Witt] |
12089 | Essences mainly explain the existence of unified substance [Witt] |
12102 | Essential properties of origin are too radically individual for an Aristotelian essence [Witt] |
10630 | Abstracted objects are not mental creations, but depend on equivalence between given entities [Hale/Wright] |
10627 | Many conceptual truths ('yellow is extended') are not analytic, as derived from logic and definitions [Hale/Wright] |
12085 | Reality is directional [Witt] |