43 ideas
| 3750 | "It is true that x" means no more than x [Ramsey] |
| 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] |
| 13430 | Infinity: there is an infinity of distinguishable individuals [Ramsey] |
| 13428 | Reducibility: to every non-elementary function there is an equivalent elementary function [Ramsey] |
| 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] |
| 13427 | Either 'a = b' vacuously names the same thing, or absurdly names different things [Ramsey] |
| 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] |
| 13334 | Contradictions are either purely logical or mathematical, or they involved thought and language [Ramsey] |
| 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] |
| 6409 | The 'simple theory of types' distinguishes levels among properties [Ramsey, by Grayling] |
| 13426 | Formalists neglect content, but the logicists have focused on generalizations, and neglected form [Ramsey] |
| 13425 | Formalism is hopeless, because it focuses on propositions and ignores concepts [Ramsey] |
| 8495 | The distinction between particulars and universals is a mistake made because of language [Ramsey] |
| 8493 | We could make universals collections of particulars, or particulars collections of their qualities [Ramsey] |
| 8494 | Obviously 'Socrates is wise' and 'Socrates has wisdom' express the same fact [Ramsey] |
| 17742 | Scotus based modality on semantic consistency, instead of on what the future could allow [Walicki] |
| 13766 | 'If' is the same as 'given that', so the degrees of belief should conform to probability theory [Ramsey, by Ramsey] |
| 10993 | Ramsey's Test: believe the consequent if you believe the antecedent [Ramsey, by Read] |
| 14279 | Asking 'If p, will q?' when p is uncertain, then first add p hypothetically to your knowledge [Ramsey] |
| 3212 | Beliefs are maps by which we steer [Ramsey] |
| 22328 | I just confront the evidence, and let it act on me [Ramsey] |
| 22325 | A belief is knowledge if it is true, certain and obtained by a reliable process [Ramsey] |
| 19724 | Belief is knowledge if it is true, certain, and obtained by a reliable process [Ramsey] |
| 6894 | Mental terms can be replaced in a sentence by a variable and an existential quantifier [Ramsey] |
| 19143 | Ramsey gave axioms for an uncertain agent to decide their preferences [Ramsey, by Davidson] |
| 20653 | Six reduction levels: groups, lives, cells, molecules, atoms, particles [Putnam/Oppenheim, by Watson] |
| 18818 | Sentence meaning is given by the actions to which it would lead [Ramsey] |
| 9418 | All knowledge needs systematizing, and the axioms would be the laws of nature [Ramsey] |
| 9420 | Causal laws result from the simplest axioms of a complete deductive system [Ramsey] |