30 ideas
| 13479 | Given that thinking aims at truth, logic gives universal rules for how to do it [Burge] |
| 10751 | Second-order logic needs the sets, and its consequence has epistemological problems [Rossberg] |
| 10757 | Henkin semantics has a second domain of predicates and relations (in upper case) [Rossberg] |
| 10759 | There are at least seven possible systems of semantics for second-order logic [Rossberg] |
| 10753 | Logical consequence is intuitively semantic, and captured by model theory [Rossberg] |
| 10752 | Γ |- S says S can be deduced from Γ; Γ |= S says a good model for Γ makes S true [Rossberg] |
| 8132 | We now have a much more sophisticated understanding of logical form in language [Burge] |
| 10754 | In proof-theory, logical form is shown by the logical constants [Rossberg] |
| 10756 | A model is a domain, and an interpretation assigning objects, predicates, relations etc. [Rossberg] |
| 10758 | If models of a mathematical theory are all isomorphic, it is 'categorical', with essentially one model [Rossberg] |
| 17622 | We come to believe mathematical propositions via their grounding in the structure [Burge] |
| 10761 | Completeness can always be achieved by cunning model-design [Rossberg] |
| 10755 | A deductive system is only incomplete with respect to a formal semantics [Rossberg] |
| 16901 | The equivalent algebra model of geometry loses some essential spatial meaning [Burge] |
| 9159 | You can't simply convert geometry into algebra, as some spatial content is lost [Burge] |
| 16902 | Peano arithmetic requires grasping 0 as a primitive number [Burge] |
| 19542 | It is nonsense that understanding does not involve knowledge; to understand, you must know [Dougherty/Rysiew] |
| 19543 | To grasp understanding, we should be more explicit about what needs to be known [Dougherty/Rysiew] |
| 19541 | Rather than knowledge, our epistemic aim may be mere true belief, or else understanding and wisdom [Dougherty/Rysiew] |
| 16892 | Is apriority predicated mainly of truths and proofs, or of human cognition? [Burge] |
| 19540 | Don't confuse justified belief with justified believers [Dougherty/Rysiew] |
| 19539 | If knowledge is unanalysable, that makes justification more important [Dougherty/Rysiew] |
| 9382 | Subjects may be unaware of their epistemic 'entitlements', unlike their 'justifications' [Burge] |
| 8126 | Anti-individualism says the environment is involved in the individuation of some mental states [Burge] |
| 8127 | Broad concepts suggest an extension of the mind into the environment (less computer-like) [Burge] |
| 8129 | Anti-individualism may be incompatible with some sorts of self-knowledge [Burge] |
| 8131 | Some qualities of experience, like blurred vision, have no function at all [Burge] |
| 3115 | Are meaning and expressed concept the same thing? [Burge, by Segal] |
| 19538 | Entailment is modelled in formal semantics as set inclusion (where 'mammals' contains 'cats') [Dougherty/Rysiew] |
| 14349 | If there are no finks or antidotes at the fundamental level, the laws can't be ceteris paribus [Burge, by Corry] |