32 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] |
12790 | Generalisations must be invariant to explain anything [Leuridan] |
12789 | Biological functions are explained by disposition, or by causal role [Leuridan] |
14388 | Mechanisms must produce macro-level regularities, but that needs micro-level regularities [Leuridan] |
12787 | Mechanisms can't explain on their own, as their models rest on pragmatic regularities [Leuridan] |
14384 | We can show that regularities and pragmatic laws are more basic than mechanisms [Leuridan] |
14386 | Mechanisms are ontologically dependent on regularities [Leuridan] |
14389 | There is nothing wrong with an infinite regress of mechanisms and regularities [Leuridan] |
1868 | The world was made as much for animals as for man [Celsus] |
14387 | Rather than dispositions, functions may be the element that brought a thing into existence [Leuridan] |
14382 | Pragmatic laws allow prediction and explanation, to the extent that reality is stable [Leuridan] |
14385 | Strict regularities are rarely discovered in life sciences [Leuridan] |
14383 | A 'law of nature' is just a regularity, not some entity that causes the regularity [Leuridan] |
1867 | Christians presented Jesus as a new kind of logos to oppose that of the philosophers [Celsus] |