33 ideas
| 19086 | Does the pragmatic theory of meaning support objective truth, or make it impossible? [Macbeth] |
| 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] |
| 19093 | Greek mathematics is wholly sensory, where ours is wholly inferential [Macbeth] |
| 17742 | Scotus based modality on semantic consistency, instead of on what the future could allow [Walicki] |
| 5806 | Belief is the power of metarepresentation [Dretske] |
| 5801 | A mouse hearing a piano played does not believe it, because it lacks concepts and understanding [Dretske] |
| 19091 | Seeing reality mathematically makes it an object of thought, not of experience [Macbeth] |
| 5802 | Representations are in the head, but their content is not, as stories don't exist in their books [Dretske] |
| 5809 | Some activities are performed better without consciousness of them [Dretske] |
| 5808 | Qualia are just the properties objects are represented as having [Dretske] |
| 5807 | Introspection is the same as the experience one is introspecting [Dretske] |
| 5803 | In a representational theory of mind, introspection is displaced perception [Dretske] |
| 5805 | Introspection does not involve looking inwards [Dretske] |
| 5804 | A representational theory of the mind is an externalist theory of the mind [Dretske] |
| 5800 | All mental facts are representation, which consists of informational functions [Dretske] |
| 19088 | For pragmatists a concept means its consequences [Macbeth] |