41 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] |
| 14239 | The empty set is usually derived from Separation, but it also seems to need Infinity [Oliver/Smiley] |
| 14240 | The empty set is something, not nothing! [Oliver/Smiley] |
| 14241 | We don't need the empty set to express non-existence, as there are other ways to do that [Oliver/Smiley] |
| 17752 | The empty set is useful for defining sets by properties, when the members are not yet known [Walicki] |
| 14242 | Maybe we can treat the empty set symbol as just meaning an empty term [Oliver/Smiley] |
| 17753 | The empty set avoids having to take special precautions in case members vanish [Walicki] |
| 14243 | The unit set may be needed to express intersections that leave a single member [Oliver/Smiley] |
| 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] |
| 14234 | If you only refer to objects one at a time, you need sets in order to refer to a plurality [Oliver/Smiley] |
| 14237 | We can use plural language to refer to the set theory domain, to avoid calling it a 'set' [Oliver/Smiley] |
| 14245 | Logical truths are true no matter what exists - but predicate calculus insists that something exists [Oliver/Smiley] |
| 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] |
| 14246 | If mathematics purely concerned mathematical objects, there would be no applied mathematics [Oliver/Smiley] |
| 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] |
| 14247 | Sets might either represent the numbers, or be the numbers, or replace the numbers [Oliver/Smiley] |
| 17742 | Scotus based modality on semantic consistency, instead of on what the future could allow [Walicki] |
| 7352 | Jesus said learning was unnecessary, and only the spirit of the Law was needed [Jesus, by Johnson,P] |
| 6289 | Love your enemies [Jesus] |
| 6292 | Love thy neighbour as thyself [Jesus] |
| 5356 | Treat others as you would have them treat you [Jesus] |
| 6286 | Blessed are the merciful: for they shall obtain mercy [Jesus] |
| 6290 | Except ye become as little children, ye shall not enter heaven [Jesus] |
| 6287 | If you lust after a woman, you have committed adultery [Jesus] |
| 6285 | Blessed are the meek; for they shall inherit the earth [Jesus] |
| 6288 | Don't resist evil, but turn the other cheek [Jesus] |
| 6293 | It is almost impossible for the rich to go to heaven [Jesus] |
| 6291 | No one is good except God [Jesus] |
| 7351 | Jesus turned the ideas of Hillel into a theology reduced to its moral elements [Jesus, by Johnson,P] |