23 ideas
12124 | Metaphysics is the best knowledge, because it is the simplest [Bacon] |
12123 | Natural history supports physical knowledge, which supports metaphysical knowledge [Bacon] |
12119 | Physics studies transitory matter; metaphysics what is abstracted and necessary [Bacon] |
12120 | Physics is of material and efficient causes, metaphysics of formal and final causes [Bacon] |
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] |
10297 | The Löwenheim-Skolem theorem seems to be a defect of first-order logic [Shapiro] |
10590 | Up Löwenheim-Skolem: if natural numbers satisfy wffs, then an infinite domain satisfies them [Shapiro] |
10292 | Downward Löwenheim-Skolem: if there's an infinite model, there is a countable model [Shapiro] |
10296 | The Löwenheim-Skolem Theorems fail for second-order languages with standard semantics [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] |
12121 | We don't assume there is no land, because we can only see sea [Bacon] |
12117 | Science moves up and down between inventions of causes, and experiments [Bacon] |
12127 | Many different theories will fit the observed facts [Bacon] |
12126 | People love (unfortunately) extreme generality, rather than particular knowledge [Bacon] |
19216 | Propositions (such as 'that dog is barking') only exist if their items exist [Williamson] |
12125 | Teleological accounts are fine in metaphysics, but they stop us from searching for the causes [Bacon] |
12118 | Essences are part of first philosophy, but as part of nature, not part of logic [Bacon] |