80 ideas
11006 | Russell started a whole movement in philosophy by providing an analysis of descriptions [Read on Russell] |
9641 | Definitions should be replaceable by primitives, and should not be creative [Brown,JR] |
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] |
18944 | Russell's theories aim to preserve excluded middle (saying all sentences are T or F) [Sawyer on Russell] |
9605 | If a proposition is false, then its negation is true [Brown,JR] |
7758 | 'Elizabeth = Queen of England' is really a predication, not an identity-statement [Russell, by Lycan] |
5772 | The idea of a variable is fundamental [Russell] |
18941 | Names don't have a sense, but are disguised definite descriptions [Russell, by Sawyer] |
4945 | Russell says names are not denotations, but definite descriptions in disguise [Russell, by Kripke] |
18942 | Russell says a name contributes a complex of properties, rather than an object [Russell, by Sawyer] |
7745 | Are names descriptions, if the description is unknown, false, not special, or contains names? [McCullogh on Russell] |
10449 | Logically proper names introduce objects; definite descriptions introduce quantifications [Russell, by Bach] |
15159 | The meaning of a logically proper name is its referent, but most names are not logically proper [Russell, by Soames] |
2612 | Russell rewrote singular term names as predicates [Russell, by Ayer] |
7757 | "Nobody" is not a singular term, but a quantifier [Russell, by Lycan] |
18943 | Russell implies that all sentences containing empty names are false [Sawyer on Russell] |
6411 | Critics say definite descriptions can refer, and may not embody both uniqueness and existence claims [Grayling on Russell] |
10433 | Definite descriptions fail to refer in three situations, so they aren't essentially referring [Russell, by Sainsbury] |
1608 | The theory of descriptions eliminates the name of the entity whose existence was presupposed [Russell, by Quine] |
7754 | Russell's theory explains non-existents, negative existentials, identity problems, and substitutivity [Russell, by Lycan] |
21529 | Russell showed how to define 'the', and thereby reduce the ontology of logic [Russell, by Lackey] |
6333 | The theory of definite descriptions reduces the definite article 'the' to the concepts of predicate logic [Russell, by Horwich] |
6412 | Russell implies that 'the baby is crying' is only true if the baby is unique [Grayling on Russell] |
7743 | Russell explained descriptions with quantifiers, where Frege treated them as names [Russell, by McCullogh] |
7310 | Russell avoids non-existent objects by denying that definite descriptions are proper names [Russell, by Miller,A] |
12006 | Denying definite description sentences are subject-predicate in form blocks two big problems [Russell, by Forbes,G] |
4569 | Russell says apparent referring expressions are really assertions about properties [Russell, by Cooper,DE] |
11009 | Russell's theory must be wrong if it says all statements about non-existents are false [Read on Russell] |
21549 | The theory of descriptions lacks conventions for the scope of quantifiers [Lackey on Russell] |
12796 | Non-count descriptions don't threaten Russell's theory, which is only about singulars [Laycock on Russell] |
7532 | Denoting is crucial in Russell's account of mathematics, for identifying classes [Russell, by Monk] |
11988 | Russell's analysis means molecular sentences are ambiguous over the scope of the description [Kaplan on Russell] |
6061 | Existence is entirely expressed by the existential quantifier [Russell, by McGinn] |
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] |
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] |
9619 | David's 'Napoleon' is about something concrete and something abstract [Brown,JR] |
18775 | Russell showed that descriptions may not have ontological commitment [Russell, by Linsky,B] |
7533 | The Theory of Description dropped classes and numbers, leaving propositions, individuals and universals [Russell, by Monk] |
6063 | Russell can't attribute existence to properties [McGinn on Russell] |
18777 | If the King of France is not bald, and not not-bald, this violates excluded middle [Linsky,B on 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] |
4567 | Russell argued with great plausibility that we rarely, if ever, refer with our words [Russell, by Cooper,DE] |
5810 | Referring is not denoting, and Russell ignores the referential use of definite descriptions [Donnellan on Russell] |
16385 | A definite description 'denotes' an entity if it fits the description uniquely [Russell, by Recanati] |
5774 | Denoting phrases are meaningless, but guarantee meaning for propositions [Russell] |
5775 | In 'Scott is the author of Waverley', denotation is identical, but meaning is different [Russell] |
16987 | By eliminating descriptions from primitive notation, Russell seems to reject 'sense' [Russell, by Kripke] |
4570 | Russell assumes that expressions refer, but actually speakers refer by using expressions [Cooper,DE on Russell] |
16349 | Russell rejected sense/reference, because it made direct acquaintance with things impossible [Russell, by Recanati] |
7313 | 'Sense' is superfluous (rather than incoherent) [Russell, by Miller,A] |
7767 | The theory of definite descriptions aims at finding correct truth conditions [Russell, by Lycan] |
21726 | In graspable propositions the constituents are real entities of acquaintance [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] |
5773 | The ontological argument begins with an unproven claim that 'there exists an x..' [Russell] |