33 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] |
| 21554 | Sets always exceed terms, so all the sets must exceed all the sets [Lackey] |
| 21553 | It seems that the ordinal number of all the ordinals must be bigger than itself [Lackey] |
| 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] |
| 5901 | Is 'productive of happiness' the definition of 'right', or the cause of it? [Ross on Bentham] |
| 5934 | Of Bentham's 'dimensions' of pleasure, only intensity and duration matter [Ross on Bentham] |
| 5271 | Prejudice apart, push-pin has equal value with music and poetry [Bentham] |
| 3777 | Pleasure and pain control all human desires and duties [Bentham] |
| 3554 | Bentham thinks happiness is feeling good, but why use morality to achieve that? [Annas on Bentham] |
| 3781 | The value of pleasures and pains is their force [Bentham] |
| 20977 | Natural rights are nonsense, and unspecified natural rights is nonsense on stilts [Bentham] |
| 3778 | The community's interest is a sum of individual interests [Bentham] |
| 21003 | Only laws can produce real rights; rights from 'law of nature' are imaginary [Bentham] |
| 20280 | Large mature animals are more rational than babies. But all that really matters is - can they suffer? [Bentham] |
| 3779 | Unnatural, when it means anything, means infrequent [Bentham] |
| 3780 | We must judge a thing morally to know if it conforms to God's will [Bentham] |