22 ideas
10301 | The axiom of choice is controversial, but it could be replaced [Shapiro] |
7548 | Classes, grouped by a convenient property, are logical constructions [Russell] |
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] |
7545 | Visible things are physical and external, but only exist when viewed [Russell] |
10591 | Logicians use 'property' and 'set' interchangeably, with little hanging on it [Shapiro] |
7549 | If my body literally lost its mind, the object seen when I see a flash would still exist [Russell] |
7553 | Sense-data are purely physical [Russell] |
19398 | Minds are best explained by their ends, and bodies by efficient causes [Leibniz] |
7546 | A man is a succession of momentary men, bound by continuity and causation [Russell] |
7550 | We could probably, in principle, infer minds from brains, and brains from minds [Russell] |
7551 | Matter is a logical construction [Russell] |
7547 | Matter requires a division into time-corpuscles as well as space-corpuscles [Russell] |
7552 | Six dimensions are needed for a particular, three within its own space, and three to locate that space [Russell] |