35 ideas
16477 | Asserting not-p is saying p is false [Russell] |
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] |
16484 | There are four experiences that lead us to talk of 'some' things [Russell] |
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] |
16486 | The physical world doesn't need logic, but the mental world does [Russell] |
2947 | Questions wouldn't lead anywhere without the law of excluded middle [Russell] |
16480 | A disjunction expresses indecision [Russell] |
16479 | 'Or' expresses hesitation, in a dog at a crossroads, or birds risking grabbing crumbs [Russell] |
16481 | 'Or' expresses a mental state, not something about the world [Russell] |
16487 | Maybe the 'or' used to describe mental states is not the 'or' of logic [Russell] |
16483 | Disjunction may also arise in practice if there is imperfect memory. [Russell] |
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] |
16475 | A 'heterological' predicate can't be predicated of itself; so is 'heterological' heterological? Yes=no! [Russell] |
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] |
17757 | Members of ordinals are ordinals, and also subsets of ordinals [Walicki] |
17758 | Ordinals are transitive sets of transitive sets; or transitive sets totally ordered by inclusion [Walicki] |
17760 | Two infinite ordinals can represent a single infinite cardinal [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] |
16482 | All our knowledge (if verbal) is general, because all sentences contain general words [Russell] |
4758 | Naïve realism leads to physics, but physics then shows that naïve realism is false [Russell] |
16476 | For simple words, a single experience can show that they are true [Russell] |
16485 | Perception can't prove universal generalisations, so abandon them, or abandon empiricism? [Russell] |
16478 | A mother cat is paralysed if equidistant between two needy kittens [Russell] |
7903 | The six perfections are giving, morality, patience, vigour, meditation, and wisdom [Nagarjuna] |