49 ideas
6095 | The business of metaphysics is to describe the world [Russell] |
6106 | Reducing entities and premisses makes error less likely [Russell] |
6090 | Facts make propositions true or false, and are expressed by whole sentences [Russell] |
18348 | Not only atomic truths, but also general and negative truths, have truth-makers [Russell, by Rami] |
6103 | Normally a class with only one member is a problem, because the class and the member are identical [Russell] |
13011 | New axioms are being sought, to determine the size of the continuum [Maddy] |
8679 | We perceive the objects of set theory, just as we perceive with our senses [Gödel] |
13013 | The Axiom of Extensionality seems to be analytic [Maddy] |
13014 | Extensional sets are clearer, simpler, unique and expressive [Maddy] |
13021 | The Axiom of Infinity states Cantor's breakthrough that launched modern mathematics [Maddy] |
13022 | Infinite sets are essential for giving an account of the real numbers [Maddy] |
13023 | The Power Set Axiom is needed for, and supported by, accounts of the continuum [Maddy] |
13024 | Efforts to prove the Axiom of Choice have failed [Maddy] |
13025 | Modern views say the Choice set exists, even if it can't be constructed [Maddy] |
13026 | A large array of theorems depend on the Axiom of Choice [Maddy] |
9942 | Gödel proved the classical relative consistency of the axiom V = L [Gödel, by Putnam] |
13019 | The Iterative Conception says everything appears at a stage, derived from the preceding appearances [Maddy] |
13018 | Limitation of Size is a vague intuition that over-large sets may generate paradoxes [Maddy] |
6092 | In a logically perfect language, there will be just one word for every simple object [Russell] |
6101 | Romulus does not occur in the proposition 'Romulus did not exist' [Russell] |
6102 | You can understand 'author of Waverley', but to understand 'Scott' you must know who it applies to [Russell] |
10423 | There are a set of criteria for pinning down a logically proper name [Russell, by Sainsbury] |
7744 | Treat description using quantifiers, and treat proper names as descriptions [Russell, by McCullogh] |
10426 | A name has got to name something or it is not a name [Russell] |
18062 | Set-theory paradoxes are no worse than sense deception in physics [Gödel] |
10868 | The Continuum Hypothesis is not inconsistent with the axioms of set theory [Gödel, by Clegg] |
13517 | If set theory is consistent, we cannot refute or prove the Continuum Hypothesis [Gödel, by Hart,WD] |
10271 | Basic mathematics is related to abstract elements of our empirical ideas [Gödel] |
6104 | Numbers are classes of classes, and hence fictions of fictions [Russell] |
21708 | Russell's new logical atomist was of particulars, universals and facts (not platonic propositions) [Russell, by Linsky,B] |
19051 | Russell's atomic facts are actually compounds, and his true logical atoms are sense data [Russell, by Quine] |
6089 | Logical atomism aims at logical atoms as the last residue of analysis [Russell] |
6100 | Once you have enumerated all the atomic facts, there is a further fact that those are all the facts [Russell] |
6105 | Logical atoms aims to get down to ultimate simples, with their own unique reality [Russell] |
21709 | You can't name all the facts, so they are not real, but are what propositions assert [Russell] |
18376 | Russell asserts atomic, existential, negative and general facts [Russell, by Armstrong] |
5465 | Modern trope theory tries, like logical atomism, to reduce things to elementary states [Russell, by Ellis] |
6060 | 'Existence' means that a propositional function is sometimes true [Russell] |
6099 | Modal terms are properties of propositional functions, not of propositions [Russell] |
6098 | Perception goes straight to the fact, and not through the proposition [Russell] |
6097 | The theory of error seems to need the existence of the non-existent [Russell] |
9022 | Russell uses 'propositional function' to refer to both predicates and to attributes [Quine on Russell] |
6091 | Propositions don't name facts, because each fact corresponds to a proposition and its negation [Russell] |
21702 | In 1918 still believes in nonlinguistic analogues of sentences, but he now calls them 'facts' [Russell, by Quine] |
6094 | An inventory of the world does not need to include propositions [Russell] |
6096 | I no longer believe in propositions, especially concerning falsehoods [Russell] |
21712 | I know longer believe in shadowy things like 'that today is Wednesday' when it is actually Tuesday [Russell] |
6093 | The names in a logically perfect language would be private, and could not be shared [Russell] |
6119 | You can discuss 'God exists', so 'God' is a description, not a name [Russell] |