66 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 |
| 10170 | While true-in-a-model seems relative, true-in-all-models seems not to be [Reck/Price] |
| Full Idea: While truth can be defined in a relative way, as truth in one particular model, a non-relative notion of truth is implied, as truth in all models. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §4) | |
| A reaction: [The article is actually discussing arithmetic] This idea strikes me as extremely important. True-in-all-models is usually taken to be tautological, but it does seem to give a more universal notion of truth. See semantic truth, Tarski, Davidson etc etc. |
| 10166 | ZFC set theory has only 'pure' sets, without 'urelements' [Reck/Price] |
| Full Idea: In standard ZFC ('Zermelo-Fraenkel with Choice') set theory we deal merely with pure sets, not with additional urelements. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §2) | |
| A reaction: The 'urelements' would the actual objects that are members of the sets, be they physical or abstract. This idea is crucial to understanding philosophy of mathematics, and especially logicism. Must the sets exist, just as the urelements do? |
| 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. |
| 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. |
| 10175 | Three types of variable in second-order logic, for objects, functions, and predicates/sets [Reck/Price] |
| Full Idea: In second-order logic there are three kinds of variables, for objects, for functions, and for predicates or sets. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §5) | |
| A reaction: It is interesting that a predicate seems to be the same as a set, which begs rather a lot of questions. For those who dislike second-order logic, there seems nothing instrinsically wicked in having variables ranging over innumerable multi-order types. |
| 10165 | 'Analysis' is the theory of the real numbers [Reck/Price] |
| Full Idea: 'Analysis' is the theory of the real numbers. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §2) | |
| A reaction: 'Analysis' began with the infinitesimal calculus, which later built on the concept of 'limit'. A continuum of numbers seems to be required to make that work. |
| 10174 | Mereological arithmetic needs infinite objects, and function definitions [Reck/Price] |
| Full Idea: The difficulties for a nominalistic mereological approach to arithmetic is that an infinity of physical objects are needed (space-time points? strokes?), and it must define functions, such as 'successor'. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §4) | |
| A reaction: Many ontologically austere accounts of arithmetic are faced with the problem of infinity. The obvious non-platonist response seems to be a modal or if-then approach. To postulate infinite abstract or physical entities so that we can add 3 and 2 is mad. |
| 10164 | Peano Arithmetic can have three second-order axioms, plus '1' and 'successor' [Reck/Price] |
| Full Idea: A common formulation of Peano Arithmetic uses 2nd-order logic, the constant '1', and a one-place function 's' ('successor'). Three axioms then give '1 is not a successor', 'different numbers have different successors', and induction. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §2) | |
| A reaction: This is 'second-order' Peano Arithmetic, though it is at least as common to formulate in first-order terms (only quantifying over objects, not over properties - as is done here in the induction axiom). I like the use of '1' as basic instead of '0'! |
| 10172 | Set-theory gives a unified and an explicit basis for mathematics [Reck/Price] |
| Full Idea: The merits of basing an account of mathematics on set theory are that it allows for a comprehensive unified treatment of many otherwise separate branches of mathematics, and that all assumption, including existence, are explicit in the axioms. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §4) | |
| A reaction: I am forming the impression that set-theory provides one rather good model (maybe the best available) for mathematics, but that doesn't mean that mathematics is set-theory. The best map of a landscape isn't a landscape. |
| 10242 | I apply structuralism to concrete and abstract objects indiscriminately [Quine] |
| Full Idea: My own line is a yet more sweeping structuralism (than David Lewis's account of classes), applying to concrete and abstract objects indiscriminately. | |
| From: Willard Quine (Structure and Nature [1992], p.6), quoted by Stewart Shapiro - Philosophy of Mathematics 4.9 | |
| A reaction: Shapiro calls this 'breathtaking', and retreats from it, but it is something like my own view, starting from Mill's pebbles and working up. |
| 10167 | Structuralism emerged from abstract algebra, axioms, and set theory and its structures [Reck/Price] |
| Full Idea: Structuralism has emerged from the development of abstract algebra (such as group theory), the creation of axiom systems, the introduction of set theory, and Bourbaki's encyclopaedic survey of set theoretic structures. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §2) | |
| A reaction: In other words, mathematics has gradually risen from one level of abstraction to the next, so that mathematical entities like points and numbers receive less and less attention, with relationships becoming more prominent. |
| 10169 | Relativist Structuralism just stipulates one successful model as its arithmetic [Reck/Price] |
| Full Idea: Relativist Structuralism simply picks one particular model of axiomatised arithmetic (i.e. one particular interpretation that satisfies the axioms), and then stipulates what the elements, functions and quantifiers refer to. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §4) | |
| A reaction: The point is that a successful model can be offered, and it doesn't matter which one, like having any sort of aeroplane, as long as it flies. I don't find this approach congenial, though having a model is good. What is the essence of flight? |
| 10179 | There are 'particular' structures, and 'universal' structures (what the former have in common) [Reck/Price] |
| Full Idea: The term 'structure' has two uses in the literature, what can be called 'particular structures' (which are particular relational systems), but also what can be called 'universal structures' - what particular systems share, or what they instantiate. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §6) | |
| A reaction: This is a very helpful distinction, because it clarifies why (rather to my surprise) some structuralists turn out to be platonists in a new guise. Personal my interest in structuralism has been anti-platonist from the start. |
| 10181 | Pattern Structuralism studies what isomorphic arithmetic models have in common [Reck/Price] |
| Full Idea: According to 'pattern' structuralism, what we study are not the various particular isomorphic models of arithmetic, but something in addition to them: a corresponding pattern. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §7) | |
| A reaction: Put like that, we have to feel a temptation to wield Ockham's Razor. It's bad enough trying to give the structure of all the isomorphic models, without seeking an even more abstract account of underlying patterns. But patterns connect to minds.. |
| 10182 | There are Formalist, Relativist, Universalist and Pattern structuralism [Reck/Price] |
| Full Idea: There are four main variants of structuralism in the philosophy of mathematics - formalist structuralism, relativist structuralism, universalist structuralism (with modal variants), and pattern structuralism. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §9) | |
| A reaction: I'm not sure where Chihara's later book fits into this, though it is at the nominalist end of the spectrum. Shapiro and Resnik do patterns (the latter more loosely); Hellman does modal universalism; Quine does the relativist version. Dedekind? |
| 10168 | Formalist Structuralism says the ontology is vacuous, or formal, or inference relations [Reck/Price] |
| Full Idea: Formalist Structuralism endorses structural methodology in mathematics, but rejects semantic and metaphysical problems as either meaningless, or purely formal, or as inference relations. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §3) | |
| A reaction: [very compressed] I find the third option fairly congenial, certainly in preference to rather platonist accounts of structuralism. One still needs to distinguish the mathematical from the non-mathematical in the inference relations. |
| 10178 | Maybe we should talk of an infinity of 'possible' objects, to avoid arithmetic being vacuous [Reck/Price] |
| Full Idea: It is tempting to take a modal turn, and quantify over all possible objects, because if there are only a finite number of actual objects, then there are no models (of the right sort) for Peano Arithmetic, and arithmetic is vacuously true. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §5) | |
| A reaction: [compressed; Geoffrey Hellman is the chief champion of this view] The article asks whether we are not still left with the puzzle of whether infinitely many objects are possible, instead of existent. |
| 10176 | Universalist Structuralism is based on generalised if-then claims, not one particular model [Reck/Price] |
| Full Idea: Universalist Structuralism is a semantic thesis, that an arithmetical statement asserts a universal if-then statement. We build an if-then statement (using quantifiers) into the structure, and we generalise away from any one particular model. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §5) | |
| A reaction: There remains the question of what is distinctively mathematical about the highly generalised network of inferences that is being described. Presumable the axioms capture that, but why those particular axioms? Russell is cited as an originator. |
| 10177 | Universalist Structuralism eliminates the base element, as a variable, which is then quantified out [Reck/Price] |
| Full Idea: Universalist Structuralism is eliminativist about abstract objects, in a distinctive form. Instead of treating the base element (say '1') as an ambiguous referring expression (the Relativist approach), it is a variable which is quantified out. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §5) | |
| A reaction: I am a temperamental eliminativist on this front (and most others) so this is tempting. I am also in love with the concept of a 'variable', which I take to be utterly fundamental to all conceptual thought, even in animals, and not just a trick of algebra. |
| 10171 | The existence of an infinite set is assumed by Relativist Structuralism [Reck/Price] |
| Full Idea: Relativist Structuralism must first assume the existence of an infinite set, otherwise there would be no model to pick, and arithmetical terms would have no reference. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §4) | |
| A reaction: See Idea 10169 for Relativist Structuralism. They point out that ZFC has an Axiom of Infinity. |
| 10243 | My ontology is quarks etc., classes of such things, classes of such classes etc. [Quine] |
| Full Idea: My tentative ontology continues to consist of quarks and their compounds, also classes of such things, classes of such classes, and so on. | |
| From: Willard Quine (Structure and Nature [1992], p.9), quoted by Stewart Shapiro - Philosophy of Mathematics 4.9 | |
| A reaction: I would call this the Hierarchy of Abstraction (just coined it - what do you think?). Unlike Quine, I don't see why its ontology should include things called 'sets' in addition to the things that make them up. |
| 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. |
| 10173 | A nominalist might avoid abstract objects by just appealing to mereological sums [Reck/Price] |
| Full Idea: One way for a nominalist to reject appeal to all abstract objects, including sets, is to only appeal to nominalistically acceptable objects, including mereological sums. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §4) | |
| A reaction: I'm suddenly thinking that this looks very interesting and might be the way to go. The issue seems to be whether mereological sums should be seen as constrained by nature, or whether they are unrestricted. See Mereology in Ontology...|Intrinsic Identity. |
| 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. |
| 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. |
| 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. |