34 ideas
| 6420 | Only by analysing is progress possible in philosophy [Russell] |
| 6432 | Analysis gives new knowledge, without destroying what we already have [Russell] |
| 6437 | The theory of types makes 'Socrates and killing are two' illegitimate [Russell] |
| 6442 | Truth belongs to beliefs, not to propositions and sentences [Russell] |
| 6436 | I gradually replaced classes with properties, and they ended as a symbolic convenience [Russell] |
| 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] |
| 7528 | Leibniz bases everything on subject/predicate and substance/property propositions [Russell] |
| 10754 | In proof-theory, logical form is shown by the logical constants [Rossberg] |
| 6439 | Names are meaningless unless there is an object which they designate [Russell] |
| 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] |
| 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] |
| 6423 | We tried to define all of pure maths using logical premisses and concepts [Russell] |
| 6424 | Formalists say maths is merely conventional marks on paper, like the arbitrary rules of chess [Russell] |
| 6425 | Formalism can't apply numbers to reality, so it is an evasion [Russell] |
| 6426 | Intuitionism says propositions are only true or false if there is a method of showing it [Russell] |
| 6419 | In 1899-1900 I adopted the philosophy of logical atomism [Russell] |
| 6438 | Complex things can be known, but not simple things [Russell] |
| 6434 | Facts are everything, except simples; they are either relations or qualities [Russell] |
| 6440 | Universals can't just be words, because words themselves are universals [Russell] |
| 6430 | In epistemology we should emphasis the continuity between animal and human minds [Russell] |
| 6441 | Pragmatism judges by effects, but I judge truth by causes [Russell] |
| 6431 | Empiricists seem unclear what they mean by 'experience' [Russell] |
| 6444 | True belief about the time is not knowledge if I luckily observe a stopped clock at the right moment [Russell] |
| 7413 | Without confidence in our beliefs, how should we actually live? [Tuck] |
| 6433 | Behaviourists struggle to explain memory and imagination, because they won't admit images [Russell] |
| 6443 | Surprise is a criterion of error [Russell] |
| 6427 | Unverifiable propositions about the remote past are still either true or false [Russell] |
| 6435 | You can believe the meaning of a sentence without thinking of the words [Russell] |