29 ideas
291 | Don't assume that wisdom is the automatic consequence of old age [Plato] |
17749 | Post proved the consistency of propositional logic in 1921 [Walicki] |
17765 | Propositional language can only relate statements as the same or as different [Walicki] |
17764 | Boolean connectives are interpreted as functions on the set {1,0} [Walicki] |
17752 | The empty set is useful for defining sets by properties, when the members are not yet known [Walicki] |
17753 | The empty set avoids having to take special precautions in case members vanish [Walicki] |
17759 | Ordinals play the central role in set theory, providing the model of well-ordering [Walicki] |
10397 | Abelard's mereology involves privileged and natural divisions, and principal parts [Abelard, by King,P] |
17741 | To determine the patterns in logic, one must identify its 'building blocks' [Walicki] |
17747 | A 'model' of a theory specifies interpreting a language in a domain to make all theorems true [Walicki] |
17748 | The L-S Theorem says no theory (even of reals) says more than a natural number theory [Walicki] |
17761 | A compact axiomatisation makes it possible to understand a field as a whole [Walicki] |
17763 | Axiomatic systems are purely syntactic, and do not presuppose any interpretation [Walicki] |
17758 | Ordinals are transitive sets of transitive sets; or transitive sets totally ordered by inclusion [Walicki] |
17755 | Ordinals are the empty set, union with the singleton, and any arbitrary union of ordinals [Walicki] |
17756 | The union of finite ordinals is the first 'limit ordinal'; 2ω is the second... [Walicki] |
17760 | Two infinite ordinals can represent a single infinite cardinal [Walicki] |
17757 | Members of ordinals are ordinals, and also subsets of ordinals [Walicki] |
17762 | In non-Euclidean geometry, all Euclidean theorems are valid that avoid the fifth postulate [Walicki] |
17754 | Inductive proof depends on the choice of the ordering [Walicki] |
10396 | If 'animal' is wholly present in Socrates and an ass, then 'animal' is rational and irrational [Abelard, by King,P] |
10395 | Abelard was an irrealist about virtually everything apart from concrete individuals [Abelard, by King,P] |
15384 | Only words can be 'predicated of many'; the universality is just in its mode of signifying [Abelard, by Panaccio] |
17742 | Scotus based modality on semantic consistency, instead of on what the future could allow [Walicki] |
8481 | The de dicto-de re modality distinction dates back to Abelard [Abelard, by Orenstein] |
15385 | Abelard's problem is the purely singular aspects of things won't account for abstraction [Panaccio on Abelard] |
15383 | Nothing external can truly be predicated of an object [Abelard, by Panaccio] |
293 | Being unafraid (perhaps through ignorance) and being brave are two different things [Plato] |
10398 | Natural kinds are not special; they are just well-defined resemblance collections [Abelard, by King,P] |