33 ideas
| 5893 | A wise man has integrity, firmness of will, nobility, consistency, sobriety, patience [Cicero] |
| 5891 | Philosophy is the collection of rational arguments [Cicero] |
| 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] |
| 17763 | Axiomatic systems are purely syntactic, and do not presuppose any interpretation [Walicki] |
| 17761 | A compact axiomatisation makes it possible to understand a field as a whole [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] |
| 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] |
| 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] |
| 15538 | Semantic indecision explains vagueness (if we have precisifications to be undecided about) [Lewis] |
| 15537 | If cats are vague, we deny that the many cats are one, or deny that the one cat is many [Lewis] |
| 15536 | We have one cloud, but many possible boundaries and aggregates for it [Lewis] |
| 17742 | Scotus based modality on semantic consistency, instead of on what the future could allow [Walicki] |
| 5879 | The soul is the heart, or blood in the heart, or part of the brain, of something living in heart or brain, or breath [Cicero] |
| 5884 | How can one mind perceive so many dissimilar sensations? [Cicero] |
| 5887 | The soul has a single nature, so it cannot be divided, and hence it cannot perish [Cicero] |
| 5886 | Like the eye, the soul has no power to see itself, but sees other things [Cicero] |
| 5885 | Souls contain no properties of elements, and elements contain no properties of souls [Cicero] |
| 15539 | Basic to pragmatics is taking a message in a way that makes sense of it [Lewis] |
| 5890 | We should not share the distress of others, but simply try to relieve it [Cicero] |
| 5894 | All men except philosophers fear poverty [Cicero] |
| 5895 | If one despises illiterate mechanics individually, they are not worth more collectively [Cicero] |