66 ideas
| 6095 | The business of metaphysics is to describe the world [Russell] |
| 6106 | Reducing entities and premisses makes error less likely [Russell] |
| 9641 | Definitions should be replaceable by primitives, and should not be creative [Brown,JR] |
| 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] |
| 9634 | Set theory says that natural numbers are an actual infinity (to accommodate their powerset) [Brown,JR] |
| 9613 | Naïve set theory assumed that there is a set for every condition [Brown,JR] |
| 9615 | Nowadays conditions are only defined on existing sets [Brown,JR] |
| 9617 | The 'iterative' view says sets start with the empty set and build up [Brown,JR] |
| 9642 | A flock of birds is not a set, because a set cannot go anywhere [Brown,JR] |
| 9605 | If a proposition is false, then its negation is true [Brown,JR] |
| 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] |
| 9649 | Axioms are either self-evident, or stipulations, or fallible attempts [Brown,JR] |
| 9638 | Berry's Paradox finds a contradiction in the naming of huge numbers [Brown,JR] |
| 9604 | Mathematics is the only place where we are sure we are right [Brown,JR] |
| 9622 | 'There are two apples' can be expressed logically, with no mention of numbers [Brown,JR] |
| 9648 | π is a 'transcendental' number, because it is not the solution of an equation [Brown,JR] |
| 9621 | Mathematics represents the world through structurally similar models. [Brown,JR] |
| 9646 | There is no limit to how many ways something can be proved in mathematics [Brown,JR] |
| 9647 | Computers played an essential role in proving the four-colour theorem of maps [Brown,JR] |
| 9643 | Set theory may represent all of mathematics, without actually being mathematics [Brown,JR] |
| 9644 | When graphs are defined set-theoretically, that won't cover unlabelled graphs [Brown,JR] |
| 9625 | To see a structure in something, we must already have the idea of the structure [Brown,JR] |
| 9628 | Sets seem basic to mathematics, but they don't suit structuralism [Brown,JR] |
| 9606 | The irrationality of root-2 was achieved by intellect, not experience [Brown,JR] |
| 9612 | There is an infinity of mathematical objects, so they can't be physical [Brown,JR] |
| 9610 | Numbers are not abstracted from particulars, because each number is a particular [Brown,JR] |
| 9620 | Empiricists base numbers on objects, Platonists base them on properties [Brown,JR] |
| 9639 | Does some mathematics depend entirely on notation? [Brown,JR] |
| 9629 | For nomalists there are no numbers, only numerals [Brown,JR] |
| 9630 | The most brilliant formalist was Hilbert [Brown,JR] |
| 6104 | Numbers are classes of classes, and hence fictions of fictions [Russell] |
| 9608 | There are no constructions for many highly desirable results in mathematics [Brown,JR] |
| 9645 | Constructivists say p has no value, if the value depends on Goldbach's Conjecture [Brown,JR] |
| 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] |
| 9619 | David's 'Napoleon' is about something concrete and something abstract [Brown,JR] |
| 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] |
| 9611 | 'Abstract' nowadays means outside space and time, not concrete, not physical [Brown,JR] |
| 9609 | The older sense of 'abstract' is where 'redness' or 'group' is abstracted from particulars [Brown,JR] |
| 9640 | A term can have not only a sense and a reference, but also a 'computational role' [Brown,JR] |
| 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] |
| 468 | Musical performance can reveal a range of virtues [Damon of Ath.] |
| 9635 | Given atomism at one end, and a finite universe at the other, there are no physical infinities [Brown,JR] |
| 6119 | You can discuss 'God exists', so 'God' is a description, not a name [Russell] |