21 ideas
2546 | Philosophy is a magnificent failure in its attempt to overstep the limits of our knowledge [McGinn] |
17962 | The truth-maker principle is that every truth has a sufficient truth-maker [Forrest] |
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] |
2544 | Thoughts have a dual aspect: as they seem to introspection, and their underlying logical reality [McGinn] |
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] |
2539 | Mental modules for language, social, action, theory, space, emotion [McGinn] |
2545 | Free will is mental causation in action [McGinn] |
2543 | Brains aren't made of anything special, suggesting panpsychism [McGinn] |
2540 | Examining mind sees no brain; examining brain sees no mind [McGinn] |
2547 | There is information if there are symbols which refer, and which can combine into a truth or falsehood [McGinn] |
2542 | Causation in the material world is energy-transfer, of motion, electricity or gravity [McGinn] |