36 ideas
| 4262 | If the only aim was consistent beliefs then new evidence and experiments would be irrelevant [Goldman] |
| 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] |
| 18946 | Unreflectively, we all assume there are nonexistents, and we can refer to them [Reimer] |
| 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] |
| 4045 | Children may have three innate principles which enable them to learn to count [Goldman] |
| 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] |
| 4044 | Rat behaviour reveals a considerable ability to count [Goldman] |
| 4048 | Infant brains appear to have inbuilt ontological categories [Goldman] |
| 17742 | Scotus based modality on semantic consistency, instead of on what the future could allow [Walicki] |
| 4043 | Elephants can be correctly identified from as few as three primitive shapes [Goldman] |
| 4049 | The way in which colour experiences are evoked is physically odd and unpredictable [Goldman] |
| 4047 | Gestalt psychology proposes inbuilt proximity, similarity, smoothness and closure principles [Goldman] |
| 8830 | A belief can be justified when the person has forgotten the evidence for it [Goldman] |
| 6871 | We can't only believe things if we are currently conscious of their justification - there are too many [Goldman] |
| 6872 | Internalism must cover Forgotten Evidence, which is no longer retrievable from memory [Goldman] |
| 6874 | Internal justification needs both mental stability and time to compute coherence [Goldman] |
| 8832 | If justified beliefs are well-formed beliefs, then animals and young children have them [Goldman] |
| 6873 | Coherent justification seems to require retrieving all our beliefs simultaneously [Goldman] |
| 8829 | Justification depends on the reliability of its cause, where reliable processes tend to produce truth [Goldman] |
| 6875 | Reliability involves truth, and truth is external [Goldman] |
| 8831 | Introspection is really retrospection; my pain is justified by a brief causal history [Goldman] |