73 ideas
| 11006 | Russell started a whole movement in philosophy by providing an analysis of descriptions [Read on Russell] |
| Full Idea: Russell started a whole movement in philosophy by providing an analysis of descriptions. | |
| From: comment on Bertrand Russell (On Denoting [1905]) by Stephen Read - Thinking About Logic Ch.5 |
| 9542 | The best known axiomatization of PL is Whitehead/Russell, with four axioms and two rules [Russell/Whitehead, by Hughes/Cresswell] |
| Full Idea: The best known axiomatization of PL is Whitehead/Russell. There are four axioms: (p∨p)→p, q→(p∨q), (p→q)→(q∨p), and (q→r)→((p∨q)→(p∨r)), plus Substitution and Modus Ponens rules. | |
| From: report of B Russell/AN Whitehead (Principia Mathematica [1913]) by GE Hughes/M Cresswell - An Introduction to Modal Logic Ch.1 |
| 21720 | Russell saw Reducibility as legitimate for reducing classes to logic [Linsky,B on Russell/Whitehead] |
| Full Idea: The axiom of Reducibility ...is crucial in the reduction of classes to logic, ...and seems to be a quite legitimate logical notion for Russell. | |
| From: comment on B Russell/AN Whitehead (Principia Mathematica [1913]) by Bernard Linsky - Russell's Metaphysical Logic 6.4 | |
| A reaction: This is an unusual defence of the axiom, which is usually presumed to have been kicked into the long grass by Quine. If one could reduce classes to logic, that would destroy the opposition to logicism in a single neat coup. |
| 10044 | Russell denies extensional sets, because the null can't be a collection, and the singleton is just its element [Russell/Whitehead, by Shapiro] |
| Full Idea: Russell adduces two reasons against the extensional view of classes, namely the existence of the null class (which cannot very well be a collection), and the unit classes (which would have to be identical with their single elements). | |
| From: report of B Russell/AN Whitehead (Principia Mathematica [1913]) by Stewart Shapiro - Structure and Ontology p.459 | |
| A reaction: Gödel believes in the reality of classes. I have great sympathy with Russell, when people start to claim that sets are not just conveniences to help us think about things, but actual abstract entities. Is the singleton of my pencil is on this table? |
| 18208 | We regard classes as mere symbolic or linguistic conveniences [Russell/Whitehead] |
| Full Idea: Classes, so far as we introduce them, are merely symbolic or linguistic conveniences, not genuine objects. | |
| From: B Russell/AN Whitehead (Principia Mathematica [1913], p.72), quoted by Penelope Maddy - Naturalism in Mathematics III.2 |
| 8204 | Lewis's 'strict implication' preserved Russell's confusion of 'if...then' with implication [Quine on Russell/Whitehead] |
| Full Idea: Russell call 'if...then' implication, when the material conditional is a much better account; C.I.Lewis (in founding modern modal logic) preserved Russell's confusion by creating 'strict implication', and called that implication. | |
| From: comment on B Russell/AN Whitehead (Principia Mathematica [1913]) by Willard Quine - Reply to Professor Marcus p.177 | |
| A reaction: [A compession of Quine's paragraph]. All of this assumes that logicians can give an accurate account of what if...then means, when ordinary usage is broad and vague. Strict implication seems to drain all the normal meaning out of 'if...then'. |
| 9359 | Russell's implication means that random sentences imply one another [Lewis,CI on Russell/Whitehead] |
| Full Idea: In Mr Russell's idea of implication, if twenty random sentences from a newspaper were put in a hat, and two of them drawn at random, one will certainly imply the other, and it is an even bet the implication will be mutual. | |
| From: comment on B Russell/AN Whitehead (Principia Mathematica [1913]) by C.I. Lewis - A Pragmatic Conception of the A Priori p.366 | |
| A reaction: This sort of lament leads modern logicians to suggest 'relevance' as an important criterion. It certainly seems odd that so-called 'classical logic' should contain a principle so at variance with everyday reasoning. |
| 21707 | Russell unusually saw logic as 'interpreted' (though very general, and neutral) [Russell/Whitehead, by Linsky,B] |
| Full Idea: Russell did not view logic as an uninterpreted calculus awaiting interpretations [the modern view]. Rather, logic is a single 'interpreted' body of a priori truths, of propositions rather than sentence forms - but maximally general and topic neutral. | |
| From: report of B Russell/AN Whitehead (Principia Mathematica [1913]) by Bernard Linsky - Russell's Metaphysical Logic 1 | |
| A reaction: This is the view which Wittgenstein challenged, saying logic is just conventional. Linsky claims that Russell's logicism is much more plausible, once you understand his view of logic. |
| 18944 | Russell's theories aim to preserve excluded middle (saying all sentences are T or F) [Sawyer on Russell] |
| Full Idea: Russell's account of names and definite descriptions was concerned to preserve the law of excluded middle, according to which every sentence is either true or false (but it is not obvious that the law ought to be preserved). | |
| From: comment on Bertrand Russell (On Denoting [1905]) by Sarah Sawyer - Empty Names 3 | |
| A reaction: That is the strongest form of excluded middle, but things work better if every sentence is either 'true' or 'not true', leaving it open whether 'not true' actually means 'false'. |
| 7758 | 'Elizabeth = Queen of England' is really a predication, not an identity-statement [Russell, by Lycan] |
| Full Idea: On Russell's view 'Elizabeth II = Queen of England' is only superficially an identity-statement; really it is a predication, and attributes a complex relational property to Elizabeth. | |
| From: report of Bertrand Russell (On Denoting [1905]) by William Lycan - Philosophy of Language Ch.1 | |
| A reaction: The original example is 'Scott = author of Waverley'. Why can't such statements be identities, in which the reference of one half of the identity is not yet known? 'The murderer is violent' and 'Smith is violent' suggests 'Smith is the murderer'. |
| 5772 | The idea of a variable is fundamental [Russell] |
| Full Idea: I take the notion of the variable as fundamental. | |
| From: Bertrand Russell (On Denoting [1905], p.42) | |
| A reaction: A key idea of twentieth century philosophy, derived from Frege and handed on to Quine. A universal term, such as 'horse', is a variable, for which any particular horse can be its value. You can calculate using x, and generalise about horses. |
| 10036 | In 'Principia' a new abstract theory of relations appeared, and was applied [Russell/Whitehead, by Gödel] |
| Full Idea: In 'Principia' a young science was enriched with a new abstract theory of relations, ..and not only Cantor's set theory but also ordinary arithmetic and the theory of measurement are treated from this abstract relational standpoint. | |
| From: report of B Russell/AN Whitehead (Principia Mathematica [1913]) by Kurt Gödel - Russell's Mathematical Logic p.448 | |
| A reaction: I presume this is accounting for relations in terms of ordered sets. |
| 18941 | Names don't have a sense, but are disguised definite descriptions [Russell, by Sawyer] |
| Full Idea: Russell proposed that names do not express a Fregean sense, ...but are disguised definite descriptions, of the form 'the F'. | |
| From: report of Bertrand Russell (On Denoting [1905]) by Sarah Sawyer - Empty Names 3 | |
| A reaction: Of course, Russell then has a famous theory about definite descriptions, which turns them into quantifications. |
| 4945 | Russell says names are not denotations, but definite descriptions in disguise [Russell, by Kripke] |
| Full Idea: Russell (and Frege) thought that Mill was wrong about names: really a proper name, properly used, simply was a definite description abbreviated or disguised. | |
| From: report of Bertrand Russell (On Denoting [1905]) by Saul A. Kripke - Naming and Necessity lectures Lecture 1 | |
| A reaction: It is tempting to oversimplify this issue, one way or the other, but essentially one has to agree with Kripke that naming does not inherently involve description, but is a 'baptism', without initial content. Connotations and descriptions accrue to a name. |
| 18942 | Russell says a name contributes a complex of properties, rather than an object [Russell, by Sawyer] |
| Full Idea: Russell's view of names, understood as a definite description, which is understood as a quantificational phrase, is not to contribute an object to propositions, but to contribute a complex of properties. | |
| From: report of Bertrand Russell (On Denoting [1905]) by Sarah Sawyer - Empty Names 3 | |
| A reaction: This seems to contradict the role of constants in first-logic, which are the paradigm names, picking out an object in the domain. Kripke says names and definite descriptions have different modal profiles. |
| 7745 | Are names descriptions, if the description is unknown, false, not special, or contains names? [McCullogh on Russell] |
| Full Idea: Russell's proposal that a natural name is an abbreviated description invites four objections: not all speakers can produce descriptions; the description could be false; no one description seems special; and descriptions usually contain names. | |
| From: comment on Bertrand Russell (On Denoting [1905]) by Gregory McCullogh - The Game of the Name 8.74 | |
| A reaction: The best reply on behalf of Russell is probably to concede all of these points, but deny that any of them are fatal. Most replies will probably say that they are possible true descriptions, rather than actual limited, confused or false ones. |
| 15159 | The meaning of a logically proper name is its referent, but most names are not logically proper [Russell, by Soames] |
| Full Idea: Russell defined a logically proper name to be one the meaning of which is its referent. However, his internalist epistemology led him to deny that the words we ordinarily call names are logically proper. | |
| From: report of Bertrand Russell (On Denoting [1905]) by Scott Soames - Philosophy of Language 1.25 |
| 10449 | Logically proper names introduce objects; definite descriptions introduce quantifications [Russell, by Bach] |
| Full Idea: For Russell, a logically proper name introduces its referent into the proposition, whereas a description introduces a certain quantificational structure, not its denotation. | |
| From: report of Bertrand Russell (On Denoting [1905]) by Kent Bach - What Does It Take to Refer? 22.2 L0 | |
| A reaction: I have very strong resistance to the idea that the actual referent could ever become part of a proposition. I am not, and never have been, part of a proposition! Russell depended on narrow 'acquaintance', which meant that few things qualified. |
| 7757 | "Nobody" is not a singular term, but a quantifier [Russell, by Lycan] |
| Full Idea: Though someone just beginning to learn English might take it as one, "nobody" is not a singular term, but a quantifier. | |
| From: report of Bertrand Russell (On Denoting [1905]) by William Lycan - Philosophy of Language Ch.1 | |
| A reaction: If someone replies to "nobody's there" with "show him to me!", presumably it IS a singular term - just one that doesn't work very well. If you want to get on in life, treat it as a quantifier; if you just want to have fun... |
| 2612 | Russell rewrote singular term names as predicates [Russell, by Ayer] |
| Full Idea: Russell's theory used quantification to eliminate singular terms, which could be meaningful without denoting anything. He reparsed such sentences so they appeared as predicates instead of names. | |
| From: report of Bertrand Russell (On Denoting [1905]) by A.J. Ayer - The Central Questions of Philosophy IX.A.2 |
| 18943 | Russell implies that all sentences containing empty names are false [Sawyer on Russell] |
| Full Idea: Russell's account implies that all sentences composed of an empty name and a predicate are false, including 'Pegasus was a mythical creature'. | |
| From: comment on Bertrand Russell (On Denoting [1905]) by Sarah Sawyer - Empty Names 4 | |
| A reaction: Russell insists that such sentences contain a concealed existence claim, which they clearly don't. |
| 6411 | Critics say definite descriptions can refer, and may not embody both uniqueness and existence claims [Grayling on Russell] |
| Full Idea: The main objections to Russell's theory of descriptions are to say that definite descriptions sometime are referring expressions, and disputing the claim that definite descriptions embody both uniqueness and existence claims. | |
| From: comment on Bertrand Russell (On Denoting [1905]) by A.C. Grayling - Russell Ch.2 | |
| A reaction: The first one seems particularly correct, as you can successfully refer with a false description. See Colin McGinn (Idea 6067) for criticism of the existence claim made by the so-called 'existential' quantifier. |
| 10433 | Definite descriptions fail to refer in three situations, so they aren't essentially referring [Russell, by Sainsbury] |
| Full Idea: Russell's reasons for saying that definite descriptions are not referring expressions are: some definite descriptions have no referent, and they cannot be referring when used in negative existential truths, or in informative identity sentences. | |
| From: report of Bertrand Russell (On Denoting [1905]) by Mark Sainsbury - The Essence of Reference 18.5 | |
| A reaction: The idea is that by 'parity of form', if they aren't referring in these situations, they aren't really referring in others. Sainsbury notes that if there are two different forms of definite description (referential and attributive) these arguments fail. |
| 11009 | Russell's theory must be wrong if it says all statements about non-existents are false [Read on Russell] |
| Full Idea: Russell's theory makes an exciting distinction between logical and grammatical form, but any theory which says that every positive statement, without distinction, about objects which don't exist is false, has to be wrong. | |
| From: comment on Bertrand Russell (On Denoting [1905]) by Stephen Read - Thinking About Logic Ch.5 |
| 1608 | The theory of descriptions eliminates the name of the entity whose existence was presupposed [Russell, by Quine] |
| Full Idea: When a statement of being or non-being is analysed by Russell's theory of descriptions it ceases to contain any expression which even purports to name the alleged entity, so the being of such an entity is no longer presupposed. | |
| From: report of Bertrand Russell (On Denoting [1905]) by Willard Quine - On What There Is p.6 |
| 7754 | Russell's theory explains non-existents, negative existentials, identity problems, and substitutivity [Russell, by Lycan] |
| Full Idea: Russell showed that his theory of definite descriptions affords solutions to each of four vexing logical problems: the Problems of Apparent Reference to Non-existents and Negative existentials, Frege's Puzzle about Identity, and Substitutivity. | |
| From: report of Bertrand Russell (On Denoting [1905]) by William Lycan - Philosophy of Language 2.Over | |
| A reaction: You must seek elsewhere for the explanations of the four problems, but this gives some indication of why Russell's theory was famous, and was felt to be a breakthrough in explaining logical forms. |
| 21529 | Russell showed how to define 'the', and thereby reduce the ontology of logic [Russell, by Lackey] |
| Full Idea: With the devices of the Theory of Descriptions at hand, it was no longer necessary to take 'the' as indefinable, and it was possible to diminish greatly the number of entities to which a logical system is ontologically committed. | |
| From: report of Bertrand Russell (On Denoting [1905]) by Douglas Lackey - Intros to Russell's 'Essays in Analysis' p.13 | |
| A reaction: Illuminating, because it shows that ontology is what drove Russell at this time, and really they were all searching for Quine's 'desert landscapes', which minimalise commitment. |
| 6333 | The theory of definite descriptions reduces the definite article 'the' to the concepts of predicate logic [Russell, by Horwich] |
| Full Idea: Russell's theory of definite descriptions reduces the definite article 'the' to the notions of predicate logic - specifically, 'some', 'every', and 'same as'. | |
| From: report of Bertrand Russell (On Denoting [1905]) by Paul Horwich - Truth (2nd edn) Ch.2.7 | |
| A reaction: This helpfully clarifies Russell's project - to find the logical form of every sentence, expressed in terms which are strictly defined and consistent. This huge project now looks rather too optimistic. Artificial Intelligence would love to complete it. |
| 6412 | Russell implies that 'the baby is crying' is only true if the baby is unique [Grayling on Russell] |
| Full Idea: Russell's analysis of 'the baby is crying' seems to imply that this can only be true if there is just one baby in the world; ..to dispose of the objection, it seems necessary to appeal implicitly or explicitly to a 'domain of discourse'. | |
| From: comment on Bertrand Russell (On Denoting [1905]) by A.C. Grayling - Russell Ch.2 | |
| A reaction: This objection leads to ordinary language philosophy, and the 'pragmatics' of language. It is standard in modern predicate logic to specify the domain over which an expression is quantified. |
| 7743 | Russell explained descriptions with quantifiers, where Frege treated them as names [Russell, by McCullogh] |
| Full Idea: Russell proposed that descriptions be treated along with the quantifiers, which departs from Frege, who treated descriptions as proper names. ...the problem was that names invoke objects, and there is no object in failed descriptions. | |
| From: report of Bertrand Russell (On Denoting [1905]) by Gregory McCullogh - The Game of the Name 2.16 | |
| A reaction: Maybe we just allow intentional objects (such as unicorns) into our ontology? Producing a parsimonious ontology seems to be the main motivation of most philosophy of language. Or maybe names are just not committed to actual existence? |
| 7310 | Russell avoids non-existent objects by denying that definite descriptions are proper names [Russell, by Miller,A] |
| Full Idea: Russell attempted to avoid Meinong's strategy (of saying 'The present King of France' refers to a 'non-existent object') by denying that definite descriptions are proper names. | |
| From: report of Bertrand Russell (On Denoting [1905]) by Alexander Miller - Philosophy of Language 2.7 | |
| A reaction: Russell claimed that there was a covert existence claim built into a definite description. What about descriptions in known counterfactual situations ('Queen of the Fairies')? |
| 12006 | Denying definite description sentences are subject-predicate in form blocks two big problems [Russell, by Forbes,G] |
| Full Idea: Since Russell did not want to introduce non-existent objects, or declare many sentences meaningless, he prevented the problem from getting started, by denying that 'the present King of France is bald' is really a subject-predicate sentence. | |
| From: report of Bertrand Russell (On Denoting [1905]) by Graeme Forbes - The Metaphysics of Modality 4.1 |
| 4569 | Russell says apparent referring expressions are really assertions about properties [Russell, by Cooper,DE] |
| Full Idea: Russell's theory says that sentences which apparently serve to refer to particulars are really assertions about properties. | |
| From: report of Bertrand Russell (On Denoting [1905]) by David E. Cooper - Philosophy and the Nature of Language §4.1 | |
| A reaction: Right. Which is why particulars get marginalised in Russell, and universals take centre stage. I can't help suspecting that talk of de re/de dicto reference handles this problem better. |
| 21549 | The theory of descriptions lacks conventions for the scope of quantifiers [Lackey on Russell] |
| Full Idea: Some logicians charge that the theory of descriptions as it stands is formally inadequate because it lacks explicit conventions for the scope of quantifiers, and that when these conventions are added the theory becomes unduly complex. | |
| From: comment on Bertrand Russell (On Denoting [1905]) by Douglas Lackey - Intros to Russell's 'Essays in Analysis' p.97 | |
| A reaction: [Especially in modal contexts, apparently] I suppose if the main point is to spell out the existence commitments of the description, then that has to include quantification, for full generality. |
| 12796 | Non-count descriptions don't threaten Russell's theory, which is only about singulars [Laycock on Russell] |
| Full Idea: It is sometimes claimed that the behaviour of definite non-count descriptions shows Russell's Theory of Descriptions itself to be false. ....but it isn't a general theory of descriptions, but precisely a theory of singular descriptions. | |
| From: comment on Bertrand Russell (On Denoting [1905]) by Henry Laycock - Words without Objects 3.1 |
| 7532 | Denoting is crucial in Russell's account of mathematics, for identifying classes [Russell, by Monk] |
| Full Idea: Denoting phrases are central to mathematics, especially in Russell's 'logicist' theory, in which they are crucial to identifying classes ('the class of all mortal beings', 'the class of natural numbers'). | |
| From: report of Bertrand Russell (On Denoting [1905]) by Ray Monk - Bertrand Russell: Spirit of Solitude Ch.6 | |
| A reaction: This explains the motivation for Russell's theory of definite descriptions, since he thinks reference is achieved by description. Russell nearly achieved an extremely complete philosophical system. |
| 11988 | Russell's analysis means molecular sentences are ambiguous over the scope of the description [Kaplan on Russell] |
| Full Idea: Russell's analysis of sentences containing definite descriptions has as an immediate consequence the doctrine that molecular sentences containing definite descriptions are syntactically ambiguous as regards the scope of the definite description. | |
| From: comment on Bertrand Russell (On Denoting [1905]) by David Kaplan - How to Russell a Frege-Church I | |
| A reaction: Presumably this is a virtue of Russell's account, and an advert for analytic philosophy, because it reveals an ambiguity which was there all the time. |
| 6061 | Existence is entirely expressed by the existential quantifier [Russell, by McGinn] |
| Full Idea: Nowadays Russell's position is routinely put by saying that existence is what is expressed by the existential quantifier and only by that. | |
| From: report of Bertrand Russell (On Denoting [1905]) by Colin McGinn - Logical Properties Ch.2 | |
| A reaction: We must keep separate how you express existence, and what it is. Quantifiers seem only to be a style of expressing existence; they don't offer any insight into what existence actually is, or what we mean by 'exist'. McGinn dislikes quantifiers. |
| 18248 | A real number is the class of rationals less than the number [Russell/Whitehead, by Shapiro] |
| Full Idea: For Russell the real number 2 is the class of rationals less than 2 (i.e. 2/1). ...Notice that on this definition, real numbers are classes of rational numbers. | |
| From: report of B Russell/AN Whitehead (Principia Mathematica [1913]) by Stewart Shapiro - Thinking About Mathematics 5.2 |
| 18152 | Russell takes numbers to be classes, but then reduces the classes to numerical quantifiers [Russell/Whitehead, by Bostock] |
| Full Idea: Although Russell takes numbers to be certain classes, his 'no-class' theory then eliminates all mention of classes in favour of the 'propositional functions' that define them; and in the case of the numbers these just are the numerical quantifiers. | |
| From: report of B Russell/AN Whitehead (Principia Mathematica [1913]) by David Bostock - Philosophy of Mathematics 9.B.4 |
| 10025 | Russell and Whitehead took arithmetic to be higher-order logic [Russell/Whitehead, by Hodes] |
| Full Idea: Russell and Whitehead took arithmetic to be higher-order logic, ..and came close to identifying numbers with numerical quantifiers. | |
| From: report of B Russell/AN Whitehead (Principia Mathematica [1913]) by Harold Hodes - Logicism and Ontological Commits. of Arithmetic p.148 | |
| A reaction: The point here is 'higher-order'. |
| 8683 | Russell and Whitehead were not realists, but embraced nearly all of maths in logic [Russell/Whitehead, by Friend] |
| Full Idea: Unlike Frege, Russell and Whitehead were not realists about mathematical objects, and whereas Frege thought that only arithmetic and analysis are branches of logic, they think the vast majority of mathematics (including geometry) is essentially logical. | |
| From: report of B Russell/AN Whitehead (Principia Mathematica [1913]) by Michèle Friend - Introducing the Philosophy of Mathematics 3.1 | |
| A reaction: If, in essence, Descartes reduced geometry to algebra (by inventing co-ordinates), then geometry ought to be included. It is characteristic of Russell's hubris to want to embrace everything. |
| 10037 | 'Principia' lacks a precise statement of the syntax [Gödel on Russell/Whitehead] |
| Full Idea: What is missing, above all, in 'Principia', is a precise statement of the syntax of the formalism. | |
| From: comment on B Russell/AN Whitehead (Principia Mathematica [1913]) by Kurt Gödel - Russell's Mathematical Logic p.448 |
| 10093 | The ramified theory of types used propositional functions, and covered bound variables [Russell/Whitehead, by George/Velleman] |
| Full Idea: Russell and Whitehead's ramified theory of types worked not with sets, but with propositional functions (similar to Frege's concepts), with a more restrictive assignment of variables, insisting that bound, as well as free, variables be of lower type. | |
| From: report of B Russell/AN Whitehead (Principia Mathematica [1913]) by A.George / D.J.Velleman - Philosophies of Mathematics Ch.3 | |
| A reaction: I don't fully understand this (and no one seems much interested any more), but I think variables are a key notion, and there is something interesting going on here. I am intrigued by ordinary language which behaves like variables. |
| 8691 | The Russell/Whitehead type theory was limited, and was not really logic [Friend on Russell/Whitehead] |
| Full Idea: The Russell/Whitehead type theory reduces mathematics to a consistent founding discipline, but is criticised for not really being logic. They could not prove the existence of infinite sets, and introduced a non-logical 'axiom of reducibility'. | |
| From: comment on B Russell/AN Whitehead (Principia Mathematica [1913]) by Michèle Friend - Introducing the Philosophy of Mathematics 3.6 | |
| A reaction: To have reduced most of mathematics to a founding discipline sounds like quite an achievement, and its failure to be based in pure logic doesn't sound too bad. However, it seems to reduce some maths to just other maths. |
| 10305 | In 'Principia Mathematica', logic is exceeded in the axioms of infinity and reducibility, and in the domains [Bernays on Russell/Whitehead] |
| Full Idea: In the system of 'Principia Mathematica', it is not only the axioms of infinity and reducibility which go beyond pure logic, but also the initial conception of a universal domain of individuals and of a domain of predicates. | |
| From: comment on B Russell/AN Whitehead (Principia Mathematica [1913], p.267) by Paul Bernays - On Platonism in Mathematics p.267 | |
| A reaction: This sort of criticism seems to be the real collapse of the logicist programme, rather than Russell's paradox, or Gödel's Incompleteness Theorems. It just became impossible to stick strictly to logic in the reduction of arithmetic. |
| 8684 | Russell and Whitehead consider the paradoxes to indicate that we create mathematical reality [Russell/Whitehead, by Friend] |
| Full Idea: Russell and Whitehead are particularly careful to avoid paradox, and consider the paradoxes to indicate that we create mathematical reality. | |
| From: report of B Russell/AN Whitehead (Principia Mathematica [1913]) by Michèle Friend - Introducing the Philosophy of Mathematics 3.1 | |
| A reaction: This strikes me as quite a good argument. It is certainly counterintuitive that reality, and abstractions from reality, would contain contradictions. The realist view would be that we have paradoxes because we have misdescribed the facts. |
| 8746 | To avoid vicious circularity Russell produced ramified type theory, but Ramsey simplified it [Russell/Whitehead, by Shapiro] |
| Full Idea: Russell insisted on the vicious circle principle, and thus rejected impredicative definitions, which resulted in an unwieldy ramified type theory, with the ad hoc axiom of reducibility. Ramsey's simpler theory was impredicative and avoided the axiom. | |
| From: report of B Russell/AN Whitehead (Principia Mathematica [1913]) by Stewart Shapiro - Thinking About Mathematics 5.2 | |
| A reaction: Nowadays the theory of types seems to have been given up, possibly because it has no real attraction if it lacks the strict character which Russell aspired to. |
| 18775 | Russell showed that descriptions may not have ontological commitment [Russell, by Linsky,B] |
| Full Idea: Russell's theory of definite descriptions allows us to avoid being ontologically committed to objects simply by virtue of using descriptions which seemingly denote them. | |
| From: report of Bertrand Russell (On Denoting [1905]) by Bernard Linsky - Quantification and Descriptions 1.1.2 | |
| A reaction: This I take to be why Russell's theory is a famous landmark. I personally take ontological commitment to be independent of what we specifically say. Others, like Quine, prefer to trim what we say until the commitments seem sound. |
| 7533 | The Theory of Description dropped classes and numbers, leaving propositions, individuals and universals [Russell, by Monk] |
| Full Idea: The real Platonic entities left standing after the Theory of Descriptions were propositions (not classes or numbers), and their constituents did not include denoting concepts or classes, but only individuals (Socrates) and universals (mortality). | |
| From: report of Bertrand Russell (On Denoting [1905]) by Ray Monk - Bertrand Russell: Spirit of Solitude Ch.6 | |
| A reaction: Propositions look like being the problem here. If we identify them with facts, it is not clear how many facts there are in the universe, independent of human thought. Indeed, how many universals are there? Nay, how many individuals? See Idea 7534. |
| 6063 | Russell can't attribute existence to properties [McGinn on Russell] |
| Full Idea: Russell's view makes it impossible to attribute existence to properties, and this would have to be declared ill-formed and meaningless. | |
| From: comment on Bertrand Russell (On Denoting [1905]) by Colin McGinn - Logical Properties Ch.2 | |
| A reaction: This strikes me as a powerful criticism, used to support McGinn's view that existence cannot be analysed, using quantifiers or anything else. |
| 18777 | If the King of France is not bald, and not not-bald, this violates excluded middle [Linsky,B on Russell] |
| Full Idea: Russell says one won't find the present King of France on the list of bald things, nor on the list of things that are not bald. It would seem that this gives rise to a violation of the law of excluded middle. | |
| From: comment on Bertrand Russell (On Denoting [1905]) by Bernard Linsky - Quantification and Descriptions 2 | |
| A reaction: It's a bit hard to accuse the poor old King of violating a law when he doesn't exist. |
| 12033 | An object is identical with itself, and no different indiscernible object can share that [Russell/Whitehead, by Adams,RM] |
| Full Idea: Trivially, the Identity of Indiscernibles says that two individuals, Castor and Pollux, cannot have all properties in common. For Castor must have the properties of being identical with Castor and not being identical with Pollux, which Pollux can't share. | |
| From: report of B Russell/AN Whitehead (Principia Mathematica [1913], I p.57) by Robert Merrihew Adams - Primitive Thisness and Primitive Identity 2 | |
| A reaction: I suspect that either the property of being identical with itself is quite vacuous, or it is parasytic on primitive identity, or it is the criterion which is actually used to define identity. Either way, I don't find this claim very illuminating. |
| 10040 | Russell showed, through the paradoxes, that our basic logical intuitions are self-contradictory [Russell/Whitehead, by Gödel] |
| Full Idea: By analyzing the paradoxes to which Cantor's set theory had led, ..Russell brought to light the amazing fact that our logical intuitions (concerning such notions as truth, concept, being, class) are self-contradictory. | |
| From: report of B Russell/AN Whitehead (Principia Mathematica [1913]) by Kurt Gödel - Russell's Mathematical Logic p.452 | |
| A reaction: The main intuition that failed was, I take it, that every concept has an extension, that is, there are always objects which will or could fall under the concept. |
| 21725 | The multiple relations theory says assertions about propositions are about their ingredients [Russell/Whitehead, by Linsky,B] |
| Full Idea: The multiple relations theory of judgement proposes that assertions about propositions are dependent upon genuine facts involving belief and other attitude relations, subjects of those attitudes, and the constituents of the belief. | |
| From: report of B Russell/AN Whitehead (Principia Mathematica [1913]) by Bernard Linsky - Russell's Metaphysical Logic 7.2 | |
| A reaction: This seems to require a commitment to universals (especially relations) with which we can be directly acquainted. I prefer propositions, but as mental entities, not platonic entities. |
| 23474 | A judgement is a complex entity, of mind and various objects [Russell/Whitehead] |
| Full Idea: When a judgement occurs, there is a certain complex entity, composed of the mind and the various objects of the judgement. | |
| From: B Russell/AN Whitehead (Principia Mathematica [1913], p.44) | |
| A reaction: This is Russell's multiple-relation theory of judgement, which replaced his earlier belief in unified propositions (now 'false abstractions'). He seems to have accepted Locke's view, that the act of judgement produces the unity. |
| 23455 | The meaning of 'Socrates is human' is completed by a judgement [Russell/Whitehead] |
| Full Idea: When I judge 'Socrates is human', the meaning is completed by the act of judging. | |
| From: B Russell/AN Whitehead (Principia Mathematica [1913], p.44), quoted by Michael Morris - Guidebook to Wittgenstein's Tractatus | |
| A reaction: Morris says this is Russell's multiple-relations theory of judgement. The theory accompanies the rejection of the concept of the unified proposition. When I hear 'Socrates had a mole on his shoulder' I get the meaning without judging. |
| 23480 | The multiple relation theory of judgement couldn't explain the unity of sentences [Morris,M on Russell/Whitehead] |
| Full Idea: When Russell moved to his multiple relation theory of judgement he then faced difficulties making sense of the unity of sentences. | |
| From: comment on B Russell/AN Whitehead (Principia Mathematica [1913], p.44) by Michael Morris - Guidebook to Wittgenstein's Tractatus 3A | |
| A reaction: Roughly, he seems committed to saying that there is only unity if you think there is unity; there is no unity in a sentence prior to the act of judgement. |
| 18275 | Only the act of judging completes the meaning of a statement [Russell/Whitehead] |
| Full Idea: When I judge 'Socrates is human', the meaning is completed by the act of judging, and we no longer have an incomplete symbol. | |
| From: B Russell/AN Whitehead (Principia Mathematica [1913], p.44), quoted by J. Alberto Coffa - The Semantic Tradition from Kant to Carnap | |
| A reaction: Personally I would have thought that you needed to know the meaning properly before you could make the judgement, but then he is Bertrand Russell and I'm not. |
| 4567 | Russell argued with great plausibility that we rarely, if ever, refer with our words [Russell, by Cooper,DE] |
| Full Idea: Russell argued with great plausibility that we rarely, if ever, refer with our words. | |
| From: report of Bertrand Russell (On Denoting [1905]) by David E. Cooper - Philosophy and the Nature of Language §4 | |
| A reaction: I'm not sure if I understand this. Presumably phrases which appear to refer actually point at other parts of language rather than the world. |
| 5810 | Referring is not denoting, and Russell ignores the referential use of definite descriptions [Donnellan on Russell] |
| Full Idea: If I am right, referring is not the same as denoting and the referential use of definite descriptions is not recognised on Russell's view. | |
| From: comment on Bertrand Russell (On Denoting [1905]) by Keith Donnellan - Reference and Definite Descriptions §I | |
| A reaction: This introduces a new theory of reference, which goes beyond the mere contents of linguistic experessions. It says reference is an 'external' and 'causal' affair, and so a definite description is not sufficient to make a reference. |
| 5774 | Denoting phrases are meaningless, but guarantee meaning for propositions [Russell] |
| Full Idea: Denoting phrases never have any meaning in themselves, but every proposition in whose verbal expression they occur has a meaning. | |
| From: Bertrand Russell (On Denoting [1905], p.43) | |
| A reaction: This is the important idea that the sentence is the basic unit of meaning, rather than the word. I'm not convinced that this dispute needs to be settled. Words are pretty pointless outside of propositions, and propositions are impossible without words. |
| 5775 | In 'Scott is the author of Waverley', denotation is identical, but meaning is different [Russell] |
| Full Idea: If we say 'Scott is the author of Waverley', we assert an identity of denotation with a difference of meaning. | |
| From: Bertrand Russell (On Denoting [1905], p.46) | |
| A reaction: This shows Russell picking up Frege's famous distinction, as shown in 'Hesperus is Phosphorus'. To distinguish the meaning from the reference was one of the greatest (and simplest) clarifications ever offered of how language works. |
| 16385 | A definite description 'denotes' an entity if it fits the description uniquely [Russell, by Recanati] |
| Full Idea: In Russell's definition of 'denoting', a definite description denotes an entity if that entity fits the description uniquely. | |
| From: report of Bertrand Russell (On Denoting [1905]) by François Recanati - Mental Files 17.2 | |
| A reaction: [Recanati cites Donnellan for this] Hence denoting is not the same thing as reference. A description can denote beautifully, but fail to refer. Donnellan says if denoting were reference, someone might refer without realising it. |
| 16987 | By eliminating descriptions from primitive notation, Russell seems to reject 'sense' [Russell, by Kripke] |
| Full Idea: Russell, since he eliminates descriptions from his primitive notation, seems to hold in 'On Denoting' that the notion of 'sense' is illusory. | |
| From: report of Bertrand Russell (On Denoting [1905]) by Saul A. Kripke - Naming and Necessity notes and addenda note 04 | |
| A reaction: Presumably we can eliminate sense from formal languages, but natural languages are rich in connotations (or whatever we choose to call them). |
| 4570 | Russell assumes that expressions refer, but actually speakers refer by using expressions [Cooper,DE on Russell] |
| Full Idea: Russell assumes that it is expressions which refer if anything does, but strictly speaking it is WE who refer with the use of expressions. | |
| From: comment on Bertrand Russell (On Denoting [1905]) by David E. Cooper - Philosophy and the Nature of Language §4.1 | |
| A reaction: This sounds right. Russell is part of the overemphasis on language which plagued philosophy after Frege. Words are tools, like searchlights or pointing fingers. |
| 16349 | Russell rejected sense/reference, because it made direct acquaintance with things impossible [Russell, by Recanati] |
| Full Idea: Russell rejected Frege's sense/reference distinction, on the grounds that, if reference is mediated by sense, we lose the idea of direct acquaintance and succumb to Descriptivism. | |
| From: report of Bertrand Russell (On Denoting [1905]) by François Recanati - Mental Files 1.1 | |
| A reaction: [15,000th IDEA in the DB!! 23/3/2013, Weymouth] Recanati claims Russell made a mistake, because you can retain the sense/reference distinction, and still keep direct acquaintance (by means of 'non-descriptive senses'). |
| 7313 | 'Sense' is superfluous (rather than incoherent) [Russell, by Miller,A] |
| Full Idea: Russell does not claim that Frege's notion of sense is incoherent, but rather that it is superfluous. | |
| From: report of Bertrand Russell (On Denoting [1905]) by Alexander Miller - Philosophy of Language 2.9 | |
| A reaction: My initial reaction to this is that the notion of strict and literal meaning (see Idea 7309) is incredibly useful. Some of the best jokes depend on the gap between implications and strict meaning. How could metaphors be explained without it? |
| 7767 | The theory of definite descriptions aims at finding correct truth conditions [Russell, by Lycan] |
| Full Idea: Russell's theory of definite descriptions proceeds by sketching the truth conditions of sentences containing descriptions, and arguing on various grounds that they are the correct truth conditions. | |
| From: report of Bertrand Russell (On Denoting [1905]) by William Lycan - Philosophy of Language Ch.9 | |
| A reaction: It seems important to see both where Russell was going, and where Davidson has come from. The whole project of finding the logical form of sentences (which starts with Frege and Russell) implies that truth conditions is what matters. |
| 21726 | In graspable propositions the constituents are real entities of acquaintance [Russell] |
| Full Idea: In every proposition that we can apprehend, ...all the constituents are real entities with which we have immediate acquaintance. | |
| From: Bertrand Russell (On Denoting [1905], p.56), quoted by Bernard Linsky - Russell's Metaphysical Logic 7.2 | |
| A reaction: This is the clearest statement of the 'Russellian' concept of a proposition. It strikes me as entirely wrong. The examples are always nice concrete objects like Mont Blanc, but as an account of sophisticated general propositions it seem hopeless. |
| 23453 | Propositions as objects of judgement don't exist, because we judge several objects, not one [Russell/Whitehead] |
| Full Idea: A 'proposition', in the sense in which a proposition is supposed to be the object of a judgement, is a false abstraction, because a judgement has several objects, not one. | |
| From: B Russell/AN Whitehead (Principia Mathematica [1913], p.44), quoted by Michael Morris - Guidebook to Wittgenstein's Tractatus 2E | |
| A reaction: This is the rejection of the 'Russellian' theory of propositions, in favour of his multiple-relations theory of judgement. But why don't the related objects add up to a proposition about a state of affairs? |
| 7903 | The six perfections are giving, morality, patience, vigour, meditation, and wisdom [Nagarjuna] |
| Full Idea: The six perfections are of giving, morality, patience, vigour, meditation, and wisdom. | |
| From: Nagarjuna (Mahaprajnaparamitashastra [c.120], 88) | |
| A reaction: What is 'morality', if giving is not part of it? I like patience and vigour being two of the virtues, which immediately implies an Aristotelian mean (which is always what is 'appropriate'). |
| 5773 | The ontological argument begins with an unproven claim that 'there exists an x..' [Russell] |
| Full Idea: 'There is one and only one entity x which is most perfect; that one has all perfections; existence is a perfection; therefore that one exists' fails as a proof because there is no proof of the first premiss. | |
| From: Bertrand Russell (On Denoting [1905], p.54) | |
| A reaction: This is the modern move of saying that existence (which is 'not a predicate', according to Kant) is actually a quantifier, which isolates the existence claim being made about a variable with a bunch of predicates. McGinn denies Russell's claim. |