19 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] |
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] |
15148 | Powers give explanations, without being necessary for some class membership [Chakravartty] |
15145 | A kind essence is the necessary and sufficient properties for membership of a class [Chakravartty] |
15147 | Cluster kinds are explained simply by sharing some properties, not by an 'essence' [Chakravartty] |
15144 | Explanation of causal phenomena concerns essential kinds - but also lack of them [Chakravartty] |
22489 | 'Good' is an attributive adjective like 'large', not predicative like 'red' [Geach, by Foot] |
15146 | Some kinds, such as electrons, have essences, but 'cluster kinds' do not [Chakravartty] |
15151 | Many causal laws do not refer to kinds, but only to properties [Chakravartty] |