32 ideas
19081 | Coherence with a set of propositions suggests we can know the proposition corresponds [Davidson, by Donnellan] |
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] |
10580 | Mathematics is both necessary and a priori because it really consists of logical truths [Yablo] |
10579 | Putting numbers in quantifiable position (rather than many quantifiers) makes expression easier [Yablo] |
10577 | Concrete objects have few essential properties, but properties of abstractions are mostly essential [Yablo] |
10578 | We are thought to know concreta a posteriori, and many abstracta a priori [Yablo] |
17742 | Scotus based modality on semantic consistency, instead of on what the future could allow [Walicki] |
8806 | The concepts of belief and truth are linked, since beliefs are meant to fit reality [Davidson] |
8252 | Davidson believes experience is non-conceptual, and outside the space of reasons [Davidson, by McDowell] |
8255 | Davidson says the world influences us causally; I say it influences us rationally [McDowell on Davidson] |
8804 | Reasons for beliefs are not the same as evidence [Davidson] |
8802 | Sensations lack the content to be logical; they cause beliefs, but they cannot justify them [Davidson] |
8801 | Coherent justification says only beliefs can be reasons for holding other beliefs [Davidson] |
8805 | Skepticism is false because our utterances agree, because they are caused by the same objects [Davidson] |
18703 | Davidson's Cogito: 'I think, therefore I am generally right' [Davidson, by Button] |