31 ideas
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] |
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] |
17742 | Scotus based modality on semantic consistency, instead of on what the future could allow [Walicki] |
16422 | The necessity of a proposition concerns reality, not our words or concepts [Stalnaker] |
16423 | Conceptual possibilities are metaphysical possibilities we can conceive of [Stalnaker] |
16421 | Critics say there are just an a priori necessary part, and an a posteriori contingent part [Stalnaker] |
16429 | A 'centred' world is an ordered triple of world, individual and time [Stalnaker] |
18969 | How do you distinguish three beliefs from four beliefs or two beliefs? [Quine] |
16428 | Meanings aren't in the head, but that is because they are abstract [Stalnaker] |
16432 | One view says the causal story is built into the description that is the name's content [Stalnaker] |
16430 | Two-D says that a posteriori is primary and contingent, and the necessity is the secondary intension [Stalnaker] |
16431 | In one view, the secondary intension is metasemantic, about how the thinker relates to the content [Stalnaker] |
18967 | A 'proposition' is said to be the timeless cognitive part of the meaning of a sentence [Quine] |
18968 | The problem with propositions is their individuation. When do two sentences express one proposition? [Quine] |
18970 | The concept of a 'point' makes no sense without the idea of absolute position [Quine] |