38 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] |
| 16665 | There are entities, and then positive 'modes', modifying aspects outside the thing's essence [Suárez] |
| 16666 | A mode determines the state and character of a quantity, without adding to it [Suárez] |
| 16667 | Substances are incomplete unless they have modes [Suárez, by Pasnau] |
| 17007 | Forms must rule over faculties and accidents, and are the source of action and unity [Suárez] |
| 16780 | Partial forms of leaf and fruit are united in the whole form of the tree [Suárez] |
| 16758 | The best support for substantial forms is the co-ordinated unity of a natural being [Suárez] |
| 16743 | We can get at the essential nature of 'quantity' by knowing bulk and extension [Suárez] |
| 13074 | Only natural kinds and their members have real essences [Suárez, by Cover/O'Leary-Hawthorne] |
| 16742 | We only know essences through non-essential features, esp. those closest to the essence [Suárez] |
| 22143 | Identity does not exclude possible or imagined difference [Suárez, by Boulter] |
| 22144 | Real Essential distinction: A and B are of different natural kinds [Suárez, by Boulter] |
| 22146 | Minor Real distinction: B needs A, but A doesn't need B [Suárez, by Boulter] |
| 22145 | Major Real distinction: A and B have independent existences [Suárez, by Boulter] |
| 22147 | Conceptual/Mental distinction: one thing can be conceived of in two different ways [Suárez, by Boulter] |
| 22148 | Modal distinction: A isn't B or its property, but still needs B [Suárez, by Boulter] |
| 17742 | Scotus based modality on semantic consistency, instead of on what the future could allow [Walicki] |
| 22149 | Scholastics assess possibility by what has actually happened in reality [Suárez, by Boulter] |
| 9381 | If some inferences are needed to fix meaning, but we don't know which, they are all relevant [Fodor/Lepore, by Boghossian] |
| 7563 | The old 'influx' view of causation says it is a flow of accidental properties from A to B [Suárez, by Jolley] |
| 16682 | Other things could occupy the same location as an angel [Suárez] |