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] |
| 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] |
| 4608 | Minds are hard-wired, or trial-and-error, or experimental, or full self-aware [Dennett, by Heil] |
| 4880 | Sentience comes in grades from robotic to super-human; we only draw a line for moral reasons [Dennett] |
| 4873 | What is it like to notice an uncomfortable position when you are asleep? [Dennett] |
| 4881 | Being a person must involve having second-order beliefs and desires (about beliefs and desires) [Dennett] |
| 4875 | We descend from robots, and our intentionality is composed of billions of crude intentional systems [Dennett] |
| 4879 | There is no more anger in adrenaline than silliness in a bottle of whiskey [Dennett] |
| 4876 | Maybe there is a minimum brain speed for supporting a mind [Dennett] |
| 4878 | The materials for a mind only matter because of speed, and a need for transducers and effectors [Dennett] |
| 4874 | The predecessor and rival of the language of thought hypothesis is the picture theory of ideas [Dennett] |
| 4882 | Concepts are things we (unlike dogs) can think about, because we have language [Dennett] |
| 4872 | Most people see an abortion differently if the foetus lacks a brain [Dennett] |
| 1748 | Archelaus was the first person to say that the universe is boundless [Archelaus, by Diog. Laertius] |
| 4877 | Maybe plants are very slow (and sentient) animals, overlooked because we are faster? [Dennett] |
| 5989 | Archelaus said life began in a primeval slime [Archelaus, by Schofield] |