30 ideas
| 6396 | A sentence is held true because of a combination of meaning and belief [Davidson] |
| 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] |
| 17742 | Scotus based modality on semantic consistency, instead of on what the future could allow [Walicki] |
| 11145 | Having a belief involves the possibility of being mistaken [Davidson] |
| 6397 | The concept of belief can only derive from relationship to a speech community [Davidson] |
| 14802 | Physical and psychical laws of mind are either independent, or derived in one or other direction [Peirce] |
| 6392 | Thought depends on speech [Davidson] |
| 6393 | A creature doesn't think unless it interprets another's speech [Davidson] |
| 11144 | Concepts are only possible in a language community [Davidson] |
| 6395 | An understood sentence can be used for almost anything; it isn't language if it has only one use [Davidson] |
| 6394 | The pattern of sentences held true gives sentences their meaning [Davidson] |
| 14800 | The world is full of variety, but laws seem to produce uniformity [Peirce] |
| 14801 | Darwinian evolution is chance, with the destruction of bad results [Peirce] |