Theory and History of Ontology by Raul Corazzon | e-mail: rc
"Bertrand Russell's Early Philosophy. First Part." 1980. Synthese no. 45.
Contents: Peter Hylton: Russell's Substitutional Theory 1; Rosalind Hursthouse: Denoting in the Principles of Mathematics 33; J. Alberto Coffa: Russell as a Platonic Dialogue: The Matter of Denoting 43; Nino Cocchiarella: The Development of the Theory of Logical Types and the Notion of a Logical Subject in Russell's Early Philosophy 71; Nicholas Griffin: Russell on the Nature of Logic (1903-1913) 117-188.
"Bertrand Russell's Early Philosophy. Second Part." 1981. Synthese no. 46.
The Function of Acquaintance in Russell's Philosophy 149; Jaakko Hintikka: On Denoting What? 167; James Cappio: Russell's Philosophical Development 185; William Lycan: Logical Atomism and Ontological Atom 207; Romane Clark: Acquaintance 231; J. Alberto Coffa: Russell and Kant 247; Jaakko Hintikka: Russell, Kant, and Coffa 265; Richard E. Grandy: Forms of Belief 271-284.
"Antinomies and Paradoxes. Studies in Russell's Early Philosophy." 1988. Russell: the Journal of Bertrand Russell Studies no. 8 (1-2).
Table of Contents: Daniel J. O'Leary: The Propositional Logic of Principia Mathematica and Some of Its Forerunners; Jocelyne Couture: Are Substitutional Quantifiers a Solution to the Problem of the Elimination of Classes in Principia Mathematica?; Michel Seymour:
The Referential Use of Definite Descriptions; Martha Harrell: Extension to Geometry of Principia Mathematica and Related Systems II; John G. Slater: Russell's Conception of Philosophy; Janet Farrell Smith: Russell's Re-Evaluation of Meinong, 1913-14: an Analysis of Acquaintance; Michael Bradie: Russell's Scientific Realism; Robert Tully: Russell's Neutral Monism.
The Tenability of Russell's Early Philosophy.
A. J. Ayer (moderator), I. Grattan-Guinness, Nicholas Griffin, Robert Tully, W. V. O. Quine.
Ian Winchester: Introduction ; Nicholas Griffin: The Tiergarten Programme; Ian Winchester: The Antinomy of Dynamical Causation in Leibniz and the Principles and Russell's Early Picture of Physics; Gregory H. Moore: The Roots of Russell's Paradox; Joan Richards: Bertrand Russell's Essay on the Foundations of Geometry and the Cambridge Mathematical Tradition; I. Grattan-Guinness: Russell's Logical Manuscripts [abstract]; Alasdair Urquhart; Russell's Zigzag Path to the Ramified Theory of Types.
"100 Years of 'on Denoting'." 2005. Mind no. 114.
Stephen Neale: Editorial Introduction. A Century Later 809;
Bertrand Russell: On Denoting 873; Ray Buchanan and Gary Ostertag: Has the Problem of Incompleteness Rested on a Mistake? 889; Richard L. Cartwright: Remarks on Propositional Functions 915; Ólafur Páll Jónsson: The Bike Puzzle 929; David Kaplan: Reading ‘On Denoting’ on its Centenary 933; Saul Kripke: Russell’s Notion of Scope 1005; Alex Oliver and Timothy Smiley: Plural Descriptions and Many-valued Functions 1039; Nathan Salmon: On Designating 1069; Stephen Schiffer: Russell’s Theory of Definite Descriptions 1135; Zoltán Gendler Szabó: The Loss of Uniqueness 1185-1222.
Anderson, Anthony C. 1986. "Some Difficulties Concerning Russellian Intensional Logic." Noûs no. 20:35-43.
Anellis, Irving H. 1995. "Peirce Rustled, Russell Pierced: How Charles Pierce and Bertrand Russell Viewed Each's Other Work in Logic, and an Assessment of Russell's Accuracy and Role in the Historiography of Logic." Modern Logic no. 5 (3):270-328.
———. 2009. "Russell and His Sources for Non-Classical Logics." Logica Universalis no. 2:153-218.
Abstract. "My purpose here is purely historical. It is not an attempt to resolve the question as to whether Russell did or did not countenance nonclassical logics, and if so, which nonclassical logics, and still less to demonstrate whether he himself contributed, in any manner, to the development of nonclassical logic. Rather, I want merely to explore and insofar as possible document, whether, and to what extent, if any, Russell interacted with the various, either the various candidates or their, ideas that Dejnožka and others have proposed as potentially influential in Russell’s intellectual reactions to nonclassical logic or to the philosophical concepts that might contribute to his reactions to nonclassical logics."
Ayer, Alfred Julius. 1971. Russell and Moore: The Analytical Heritage. London: Macmillan.
———. 1972. Russell. London: Fontana.
Beaney, Michael, ed. 2007. The Analytic Turn. Analysis in Early Analytic Philosophy and Phenomenology. New York: Routledge.
———. 2009. "The Early Life of Russell's Notion of a Propositional Function." The Baltic International Yearbook of Cognition, Logic and Communication no. 4:1-25.
———, ed. 2013. The Oxford Handbook of the History of Analytic Philosophy. New York: Oxford University Press.
Bergmann, Gustav. 1947. "Russell on Particulars." Philosophical Review no. 56:59-72.
Reprinted in: Elmer Daniel Klemke (ed.), Essays on Bertrand Russell.
———. 1957. "The Revolt against Logical Atomism (First Part)." Philosophical Quarterly no. 7:323-339.
Reprinted in: Elmer Daniel Klemke (ed.), Essays on Bertrand Russell.
———. 1958. "The Revolt against Logical Atomism (Second Part)." Philosophical Quarterly no. 8:1-13.
Reprinted in: Elmer Daniel Klemke (ed.), Essays on Bertrand Russell.
Bonino, Guido. 2008. The Arrow and the Point. Russell and Wittgenstein's Tractatus. Frankfurt: Ontos Verlag.
Bonomi, Andrea. 1977. "Existence, Presupposition and Anaphoric Space." Journal of Philosophical Logic no. 6:239-267.
Bostock, David. 2012. Russell's Logical Atomism. New York: Oxford University Press.
Bourgeois, Warren. 1981. "Beyond Russell and Meinong." Canadian Journal of Philosophy no. 16:653-666.
Butchvarov, Panayot. 1986. "Our Robust Sense of Reality." Grazer Philosophische Studien no. 25/26:403-421.
———. 1988. "Russell's Views on Reality." Grazer Philosophische Studien no. 32:165-167.
"Russell's account of existence as satisfaction of a propositional function presupposes a more fundamental notion of existence, which we would employ in deciding what to allow as arguments satisfying a function, a notion he never elucidates. Jan Dejnožka has distinguished three ways Russell used the term "exists," one being the phenomenalist's, in which it refers to correlations of sense-data. I argue that this phenomenalist notion cannot be the one Russell needs, since he explicitly held that existence be understood broadly, so that, e.g., the nonexistence of God would not follow by definition."
Candlish, Stewart. 2007. The Russell/Bradley Dispute and Its Significance for Twentieth-Century Philosophy. New York: Palgrave Macmillan.
Cappio, James. 1981. "Russell's Philosophical Development." Synthese no. 46:185-205.
Carey, Rosalind. 2007. Russell and Wittgenstein on the Nature of Judgement. New York: Continuum.
Carey, Rosalind, and Ongley, John. 2009. Historical Dictionary of Bertrand Russell's Philosophy. Lanham: Scarecrow Press.
Cartwright, Richard. 1987. "On the Origins of Russell's Theory of Descriptions." In Philosophical Essays, 95-133. Cambridge: MIT Press.
Casullo, Albert. 1981. "Russell on the Reduction of Particulars." Analysis no. 41:199-205.
Chihara, Charles. 1973. Ontology and the Vicious-Circle Principle. Ithaca: Cornell University Press.
Church, Alonzo. 1976. "Comparison of Russell's Resolution of the Semantical Antinomies with That of Tarski." Journal of Symbolic Logic no. 41:747-760.
———. 1984. "Russell's Theory of Identity of Propositions." Philosophia Naturalis no. 24:513-522.
Clack, Robert J. 1969. Bertrand Russell's Philosophy of Language. The Hague: Martinus Nijhoff.
Cocchiarella, Nino. 1973. "Whither Russell's Paradox of Predication?" In Logic and Ontology, edited by Munitz, Milton K., 133-158. New York University Press.
Contributions to a seminar on ontology held under the auspices of the New York University Institute of Philosophy for the year 1970-1971.
"Russell’s paradox has two forms or versions, one in regard to the class of all classes that are not members of themselves, the other in regard to “the predicate: to be a predicate that cannot be predicated of itself.”(1) The first version is formulable in the ideography of Frege's Grundgesetze der Arithmetik and shows this system to be inconsistent. The second version, however, is not formulable in this ideography, as Frege himself pointed out in his reply to Russell. (2) Nevertheless, it is essentially the second version of his paradox that leads Russell to avoid it (and others of its ilk) through his theory of types.
The first version is of course the relevant version with respect to any formulation of the theory of types in which membership in a class is the fundamental notion, that is, a formulation utilizing 'ε' as a primitive binary predicate constant.(3) However, Russell's theory of types (even ignoring its ramification) is essentially concerned with the notion of predication, and only indirectly through the (philosophically questionable) interpretation of predication as the membership relation is the first version of his paradox relevant to this formulation.
Apparently, Russell saw his paradox as generating an aporetic situation in regard to two fundamental “notions,” namely, the notion of membership (in a class) and the notion of predication (of an attribute).(4) In regard to the notion of membership, the application of Russell’s paradox is not here brought into question. However, in regard to the notion of predication, the applicability of the reasoning grounding Russell’s paradox will here be very much brought into question. Indeed, I shall claim that in this case the paradox fails.(5)" (pp. 133-135)
(1) “Letter to Frege,” reprinted in , p. 125.
(2) “Letter to Russell,” ibid., p. 128.
(3) Cf. , p. 140 for a specific formulation of this kind of type theory.
(4) Gödel (cf. , p. 131f.) distinguishes these two forms of Russell’s paradox by referring to them as the “extensional” and the “intensional” forms, respectively. For the purposes of the present paper, this distinction is preferable to Ramsey’s different but better known distinction between “logical” and “semantical” paradoxes.
(5) With this failure of course goes a primary if not sole motivation for the simple theory of ontological types of third and higher order. The ontological scheme of second-order logic remains unaffected, having as it does a natural motivation of its own. Ramification also has its own motivation, and it may be appended to second-order logic (cf. , §58.) even though historically it was first appended to the simple theory of types.
 Church, A., Introduction to Mathematical Logic. Princeton, N.J.: Princeton University Press, 1956.
 Fraenkel, A., and Y. Bar-Hillel, Foundations of Set Theory. Amsterdam: North-Holland Publishing Company, 1958.
 Gödel, K., “Russell's Mathematical Logic,” The Philosophy of Bertrand Russell. P. A. Schilpp (ed.). Chicago: Northwestern University Press, 1944.
 Van Heijenoort, J., From Frege to Gödel, Cambridge: Harvard University Press, 1967.
———. 1975. "Logical Atomism, Nominalism, and Modal Logic." Synthese no. 31:23-62.
Reprinted as Chapter 7 in Logical Studies in Early Analytic Philosophy, pp. 244-275.
"Logical atomism, through its theory of logical form, provides one of the most coherent formal ontologies in the history of philosophy. It is a coherence which, whether we agree with the ontology or not, renders the framework important and useful as a paradigm by which to compare and better evaluate the coherence of alternative systems based upon alternative theories of logical form and especially alternative theories of predication.
As the basis of a formal ontology, logical atomism, aside from the differences between its realist and nominalist variants, specifies not only a ‘deep structure’ ontological grammar within which all analysis must ultimately be resolved, but determines as well a logistic for that grammar. Both together constitute the formal ontology and serve to indicate how logical atomism views the fundamental structure of reality. Thus, for example, the grammar serves to indicate the formal as well as the material categories of being acknowledged by the ontology, while the logistic, by regulating the proper ‘logico-syntactical employment’ ([TR], 3.327) of the expressions of that grammar serves to indicate not only the logical ‘scaffolding of the world’ ([TR], 6.124) but supplements the grammar in its presentation of the ontological structure of reality.
The distinction between logical scaffolding and ontological structure is fundamental to atomism and pertains to a distinction between material and formal content that grammar alone is insufficient to represent. It is a distinction that any proposed formalization of logical atomism must account for (through the Doctrine of Showing) in order to be an adequate formal representative of that ontology. It is a distinction, however, or so it will be argued here, that cannot be made without the introduction of modal operators for logical necessity and possibility.
The argument for this last claim was already given in chapter 6, but it was there restricted to the level of logical analysis dealing solely with propositional connectives."
"In what follows we shall be concerned with the problematic extension of these results to the level of analysis involving quantifiers for objects as concrete particulars along with some means for expressing their self-identity and mutual difference. On this level, logical atomism’s theory of predication enters our considerations in a fundamental way. For according to that theory, only elementary predications represent or ‘picture’ a structure with material content, and that content is in all cases external to the constituents of the structure. Such a structure is an atomic situation (Sachlage) and the externality of its content to its constituents consists in both it and its complement being logically possible. The difficulty here is that since objects are quantified over, they are part of the world and therefore contribute to the ontological content of the world (cf. [TR] 5.5561); and in that regard their self-identity and mutual difference or nonidentity, and thereby their total number, would prima facie seem to involve material content. Yet, in atomism, an object’s self-identity or nonidentity with any other object is not an external condition of that object, (3) and, as a consequence of the dependence of logical space on reality, it is logically impossible for the totality of objects, no less the number of that totality, to differ from world to world. In other words, in logical atomism, if not in other ontologies, identity and difference, as well as objectual quantification, are formal and not material aspects of reality. Here already we begin to see the paradigmatic role of logical atomism, for in most other systems identity and difference, as well as objectual quantification, are also said to be formal in content, though propositions regarding that content are not also said to be either logically necessary or logically impossible.
Because our considerations will be restricted to quantifying over objects as concrete particulars and not, for example, over material properties and relations as well, the variant of logical atomism we shall discuss here is nominalistic. Several realist alternatives are sketched in order to highlight the significant theses and/or difficulties of nominalism, though it should be noted that not all forms of nominalism need agree with the special ontological theses of nominalist logical atomism.
Finally, it should also be noted that our concern in this chapter is with an adequate formal representation of the ontology of logical atomism and not with its theory of thought, meaning, or philosophy of language. We wish to leave open how these might or must be developed with respect to the system constructed here, especially with regard to how they might or must pertain to the question of its logistic completeness." (pp. 244-247 of the reprint)
(1) The convention adopted here is to use scare-quotes when speaking of what connectives represent as ‘properties’ or ‘relations’. This is done to mark a special philosophical use which is convenient in our informal discussion but which strictly speaking is ontologically misleading. A similar convention applies throughout when we refer to existence (being-the-case) and nonexistence (being-not-the-case) as material ‘properties’ of atomic situations.
(3) That is, an object’s self-identity or nonidentity with any other object is invariant through all the possible worlds of a logical space containing that object. We must distinguish this ontological invariance from the varying semantical relation of denotation (Bedeutung) between an object and a (non-Tractarian) name or definite description of that object. The former must be accounted for within the formal ontology, the latter only within its applications.
[TR] Wittgenstein, L., Tractatus Logico-Philosophicus, D. F. Pears & B. F. McGuinness, trans., 2d. ed. (London: Routledge & Kegan Paul, 1971. first ed. 1921).
———. 1980. "The Development of the Theory of Logical Types and the Notion of a Logical Subject in Russell's Early Philosophy." Synthese no. 45:71-115.
Reprinted as Chapter 1 in Logical Studies in Early Analytic Philosophy, pp. 19-63.
"The development of the theory of logical types in Russell’s early philosophy proceeds along a difficult and rather involuted path; and even the final product, the theory as adumbrated in [Principia Mathematica = PM], remains unclear in its syntax and problematic in its semantics. Indeed, one might well be left with the impression that Russell himself, in the end, remained unsure of which parts of the different views he had held along the way are finally to be adopted.
In what follows, we shall attempt to describe and explain the development of Russell’s early views, at least to the extent to which they are available in published form today, from the perspective of the development in those views of the notion of a logical subject. It is the development of this notion in Russell’s early philosophy, we believe, that holds the key to many of the problems confronting Russell in the development of his theory of logical types and that led to the various, and sometimes conflicting, proposals that he made along the way.
It should be noted, however, that in referring to the development of the theory of logical types in Russell’s early philosophy we have in mind only the views developed by Russell up to, but not subsequent to, the 1910—13 publication of the first edition of [PM]. The subsequent views developed by Russell from 1913—25, that is, between the first and second editions of [PM], and summarized to some extent in his introduction (and added appendices) to the second edition, constitute Russell’s version of logical atomism. Except for some concluding remarks in the final section of this chapter, we delay our discussion of those views until chapter 5." (pp. 19-20 of the reprint)
———. 1982. "Meinong Reconstructed Versus Early Russell Reconstructed." Journal of Philosophical Logic no. 11:183-214.
Reprinted as Chapter 3 in Logical Studies in Early Analytic Philosophy, pp. 119-151.
"Contemporary philosophy is in a rut, according to Terence Parsons in his recent book Nonexistent Objects, ([NO]), and it is one that stems from the (post-1905) work of Bertrand Russell. The main characteristic of this “Russellian rut” ([NO], 1) is strict adherence to the thesis that being, or being something, amounts to being something that exists—or equivalently that ‘there is’ is to be equated with ‘there exists’ ([NO], 6). This view is now so well entrenched, according to Parsons, that it is a main stay of what he also calls the orthodox tradition.
Now the orthodox view is in a rut, according to Parsons, “because it’s a view in which most of us are so entrenched that it’s hard to see over the edges” ([NO], 1). Naturally, if we want “to look over the edge and see how things might be different” ([NO], 8), as any objective seeker of truth would, then “we need to encounter an actual theory about nonexistent objects” (ibid.). It is the construction and presentation of such a theory that is Parsons’s concern in Nonexistent Objects.
"Now we do not object to Parsons’s choice of Meinong’s theory here, nor for that matter to his elegant reconstruction and presentation of that theory. We do think, however, that a more balanced recognition of Russell’s overall view is called for and that perhaps the best way to make the Meinongian notion of a concrete object understandable to the orthodox tradition is to compare it with the general Russellian notion of a concrete individual, i.e., the Russellian notion of an individual that can exist but which might in fact not exist. Indeed, on the basis of the analysis and comparison we shall give here, it is our position that the Meinongian notion of a concrete object, at least as reconstructed by Parsons, is parasitic upon, though in a beneficent way, the Russellian notion of a concrete individual, existent or otherwise." (pp. 119-121)
[NO] Parsons, Terence, Nonexistent Objects, (New Haven and London: Yale University Press, 1980.)
———. 1986. "Frege, Russell and Logicism: A Logical Reconstruction." In Frege Synthesized: Essays on the Philosophical and Foundational Work of Gottlob Frege, edited by Haaparanta, Leila and Hintikka, Jaakko, 197-252. Dordrecht: Reidel.
Reprinted as Chapter 2 in Logical Studies in Early Analytic Philosophy, pp. 64-118.
"Logicism by the end of the nineteenth century was a philosophical doctrine whose time had come, and it is Gottlob Frege to whom we owe its arrival. “Often,” Frege once wrote, “it is only after immense intellectual effort, which may have continued over centuries, that humanity at last succeeds in achieving knowledge of a concept in its pure form, in stripping off the irrelevant accretions which veil it from the eyes of the mind” (Frege, The Foundations of Arithmetic, [Fd], xix). Prior to Frege logicism was just such a concept whose pure form was obscured by irrelevant accretions; and in his life’s work it was Frege who first presented this concept to humanity in its pure form and developed it as a doctrine of the first rank.
That form, unfortunately, has become obscured once again. For today, as we approach the end of the twentieth century, logicism, as a philosophical doctrine, is said to be dead, and even worse, to be impossible. Frege’s logicism, or the specific presentation he gave of it in Die Grundgesetze der Arithmetik, ([Gg]), fell to Russell’s paradox, and, we are told, it cannot be resurrected. Russell’s own subsequent form of logicism presented in [PM], moreover, in effect gives up the doctrine; for in overcoming his paradox, Russell was unable to reduce classical mathematics to logic without making at least two assumptions that are not logically true; namely, his assumption of the axiom of reducibility and his assumption of an axiom of infinity regarding the existence of infinitely many concrete or nonabstract individuals.
Contrary to popular opinion, however, logicism is not dead beyond redemption; that is, if logicism is dead, then it can be easily resurrected. This is not to say that as philosophical doctrines go logicism is true, but only that it can be logically reconstructed and defended or advocated in essentially the same philosophical context in which it was originally formulated. This is true especially of Frege’s form of logicism, as we shall see, and in fact, by turning to his correspondence with Russell and his discussion of Russell’s paradox, we are able to formulate not only one but two alternative reconstructions of his form of logicism, both of which are consistent (relative to weak Zermelo set theory).
In regard to Russell’s form of logicism, on the other hand, our resurrection will not apply directly to the form he adopted in [PM] but rather to the form he was implicitly advocating in his correspondence with Frege shortly after the completion of [POM]. In this regard, though we shall have occasion to refer to certain features of his later form of logicism, especially in our concluding section where a counterpart to the axiom of reducibility comes into the picture, it is Russell’s early form of logicism that we shall reconstruct and be concerned with here.
Though Frege’s and Russell’s early form of logicism are not the same, incidentally, they are closely related; and one of our goals will be to reconstruct or resurrect these forms with their similarity in mind. In particular, it is our contention that both are to be reconstructed as second order predicate logics in which nominalized predicates are allowed to occur as abstract singular terms. Their important differences, as we shall see, will then consist in the sort of object each takes nominalized predicates to denote and in whether the theory of predication upon which the laws of logic are to be based is to be extensional or intensional." (pp. 64-65 of the reprint)
Frege, Gottlob, [Fd] The Foundations of Arithmetic, trans, by J. L. Austin, Harper & Bros., N.Y. 1960.
Frege, Gottlob, [Gg] Die Grundgesetze der Arithmetik, vols. 1 and 2, Hildesheim, 1962.
Russell, Bertrand, [PM] Principia Mathematica, coauthor, A. N. Whitehead, Cambridge University Press, 1913.
Russell, Bertrand, [POM] The Principles of Mathematics, 2nd ed., W. W. Norton & Co., N.Y., 1937.
———. 1989. "Russell's Theory of Logical Types and the Atomistic Hierarchy of Sentences." In Rereading Russell: Essays on Bertrand Russell's Metaphysics and Epistemology, edited by Savage, C.Wade and Anderson, C.Anthony, 41-62. Minneapolis: University of Minnesota Press.
Reprinted as Chapter 5 in Logical Studies in Early Analytic Philosophy, pp. 193-221.
"Russell’s philosophical views underwent a number of changes throughout his life, and it is not always well-appreciated that views he held at one time came later to be rejected; nor, similarly, that views he rejected at one time came later to be accepted. It is not well-known, for example, that the theory of logical types Russell described in his later or post-[PM] philosophy is not the same as the theory originally described in [PM] in 1910-13; nor that some of the more important applications that Russell made of the theory at the earlier time cannot be validated or even significantly made in the framework of his later theory. What is somewhat surprising, however, is that Russell himself seems not to have realized that he was describing a new theory of logical types in his later philosophy, and that as a result of the change some of his earlier logical constructions, including especially his construction of the different kinds of numbers, were no longer available to him.
In the original framework, for example, propositional functions are independently real properties and relations that can themselves have properties and relations of a higher order/type, and all talk of classes, and thereby ultimately of numbers, can be reduced to extensional talk of properties and relations as “single entities,” or what Russell in [POM] had called “logical subjects.” The Platonic reality of classes and numbers was replaced in this way by a more fundamental Platonic reality of propositional functions as properties and relations. In Russell's later philosophy, however, “a propositional function is nothing but an expression. It does not, by itself, represent anything. But it can form part of a sentence which does say something, true or false” (Russell, My Philosophical Development, ([MPD]), 69). Surprisingly. Russell even insists that this was what he meant by a propositional function in [PM]. “Whitehead and I thought of a propositional function as an expression containing an undetermined variable and becoming an ordinary sentence as soon as a value is assigned to the variable: ‘x is human’, for example, becomes an ordinary sentence as soon as we substitute a proper name for V. In this view . . . the propositional function is a method of making a bundle of such sentences” ([MPD], 124). Russell does realize that some sort of change has come about, however, for he admits, “I no longer think that the laws of logic are laws of things; on the contrary, I now regard them as purely linguistic” (ibid., 102).
Now it is not whether [PM] can sustain a nominalistic interpretation that is our concern in this essay, as we have said, but rather how it is that Russell came to be committed in his later philosophy to the atomistic hierarchy and the nominalistic interpretation of propositional functions as expressions generated in a ramified second order hierarchy of languages based on the atomistic hierarchy. We shall pursue this question by beginning with a discussion of the difference between Russell’s 1908 theory of types and that presented in [PM] in 1910. This will be followed by a brief summary of the ontology that Russell took to be implicit in [PM], and that he described in various publications between 1910 and 1913. The central notion in this initial discussion is what Russell in his early philosophy called the notion of a logical subject, or equivalently that of a “term” or “single entity”. (In [PM], this notion was redescribed as the systematically ambiguous notion of an “object.”) As explained in chapter 1 this notion provides the key to the various problems that led Russell in his early philosophy to the development of his different theories of types, including that presented in [PM]. This remains true, moreover, even when we turn to Russell’s later philosophy, i.e., to his post-[PM] views, only then it is described as the notion of what can and cannot be named in a logically perfect language. The ontology of these later views is what Russell called logical atomism, and it is this ontology that determines what Russell described as the atomistic hierarchy of sentences. In other words, it is the notion of what can and cannot be named in the atomistic hierarchy that explains how Russell, however unwittingly, came to replace his earlier theory of logical types by the theory underlying the atomistic hierarchy of sentences as the basis of a logically perfect language." (pp. 193-195 of the reprint)
POM] Russell, Bertrand, The Principles of Mathematics, 2d ed. (NY., Norton & Co., 1938).
[PM] Russell, Bertrand and Alfred Whitehead, Principia Mathematica, vol. 1 (1910), vol. 2 (1912), and vol. 3 (1913) (London: Cambridge Univ. Press,).
———. 2000. "Russell's Paradox of the Totality of Propositions." Nordic Journal of Philosophical Logic no. 5:25-37.
Abstract: "Russell’s ‘‘new contradiction’’ about ‘‘the totality of propositions’’ has been connected with a number of modal paradoxes. M. Oksanen has recently shown how these modal paradoxes are resolved in the set theory NFU. Russell’s paradox of the totality of propositions was left unexplained, however. We reconstruct Russell’s argument and explain how it is resolved in two intensional logics that are equiconsistent with NFU. We also show how different notions of possible worlds are represented in these intensional logics."
"In Appendix B of his 1903 Principles of Mathematics (PoM), Russell described a ‘‘new contradiction’’ about ‘‘the totality of propositions’’ that his ‘‘doctrine of types’’ (as described in Appendix B) was unable to avoid. (1)
In recent years this ‘‘new contradiction’’ has been connected with a number of modal paradoxes, some purporting to show that there cannot be a totality of true propositions, (2) or that even the idea of quantifying over the totality of propositions leads to contradiction. (3) A number of these claims have been discussed recently by Mika Oksanen and shown to be spurious relative to the set theory known as NFU. (4) In other words, if NFU is used instead of ZF as the semantical metalanguage for modal logic, the various ‘‘paradoxes’’ about the totality of propositions (usually construed as the totality of sets of possible worlds) can be seen to fail (generally because of the existence of a universal set and the failure of the general form of Cantor’s power-set theorem in NFU). It is not clear, however, how Russell’s own paradox about the totality of propositions is resolved on this analysis, and although Oksanen quoted Russell’s description of the paradox in detail, he did not show how it is explained in NFU after his resolution of the other related modal paradoxes; in fact, it is not at all clear how this might be done in NFU.
One reason why Russell’s argument is difficult to reconstruct in NFU is that it is based on the logic of propositions, and implicitly in that regard on a theory of predication rather than a theory of membership. A more appropriate medium for the resolution of these paradoxes, in other words, would be a formal theory of predication that is a counterpart to NFU.
Fortunately, there are two such theories, λHST* and HST*λ, that are equiconsistent with NFU and that share with it many of the features that make it a useful framework within which to resolve a number of paradoxes, modal or otherwise. (5)" (pp. 25-26)
(1) PoM, p. 527.
(2) See, e.g., Grim 1991, pp. 92f.
(3) See, e.g., Grim 1991, p. 119 and Jubien 1988, p. 307.
(4) See Oksanen 1999. NFU is a modified version of Quine’s system NF. It was first described in Jensen 1968 and recently has been extensively developed in Holmes 1999.
(5) See Cocchiarella 1986, chapters IV and VI for proofs of the connection of NFU with these systems. Also, see Cocchiarella 1985 for how these systems are related to Quine’s systems NF and ML. For a discussion of the refutation of Cantor’s power-set theorem in
these systems, see Cocchiarella 1992.
Cocchiarella, N. B. 1985. Frege’s double-correlation thesis and Quine’s set theories NF and ML. Journal of Philosophical Logic, vol. 4, pp. 1–39.
Cocchiarella, N. B. 1986. Logical Investigations of Predication Theory and the Problem of Universals. Bibliopolis Press, Naples, 1985.
Cocchiarella, N. B. 1992. Cantor’s Power-Set Theorem Versus Frege’s Double-Correlation Thesis, History and Philosophy of Logic, vol. 13, 179–201.
Holmes, R. 1999. Elementary Set Theory with a Universal Set. Cahiers du Centre de Logique, Bruylant-Academia, Louvain-la-Neuve, Belgium.
Grim, P. 1991. The Incomplete Universe. MIT Press, Cambridge, MA.
Jensen, R. 1968. On the consistency of a slight (?) modification of Quine’s New Foundations. Synthese, vol. 19, pp. 250–263.
Oksanen, M. 1979. The Russell-Kaplan paradox and other modal paradoxes; a new solution. Nordic Journal of Philosophical Logic, vol. 4, no. 1, pp. 73–93.
Russell, B. 1937. The Principles of Mathematics, 2nd edition. W. W. Norton & Co., N.Y.
———. 2017. Epistemological Ontology and Logical Form in Russell's Logical Atomism.
Not yet published.
Preprint available on academia.edu.
Abstract: "Logical analysis, according to Bertrand Russell, leads to and ends with logical atomism, an ontology of atomic facts that is epistemologically founded on sense-data, which Russell claimed are mind-independent physical objects. We first explain how Russell’s 1914–1918 epistemological version of logical atomism is to be understood, and then, because constructing logical forms is a fundamental part of the process of logical analysis, we briefly look at what has happened to Russell’s type theory in this ontology. We then turn to the problem of explaining how the logical forms of Russell’s new logic can explain both the forms of atomic facts and yet also the sentences of natural language. The main problem is to explain the logical forms for belief and desire sentences and how those forms correspond to the logical forms of the facts of logical atomism."
———. 2017. Russell's Logical Atomism 1914-1918: Epistemological Ontology and Logical Form.
Unpublished paper, available on this site.
Abstract: "Logical analysis, according to Bertrand Russell, leads to and ends with logical atomism, an ontology of atomic facts that is epistemologically founded on sense-data, which Russell claimed are mind-independent physical objects. We first explain how Russell's 1914-1918 epistemological version of logical atomism is to be understood, and then, because constructing logical forms is a fundamental part of the process of logical analysis, we briefly look at what has happened to Russell's type theory in this ontology. We then turn to the problem of explaining whether or not the logical forms of Russell's new logic can explain both the forms of atomic facts and yet also the sentences of natural language, especially those about beliefs. The main problem is to explain the logical forms for belief and desire sentences and how those forms do not correspond to the logical forms of the facts of logical atomism."
Coffa, Alberto J. 1980. "Russell as a Platonic Dialogue: The Matter of Denoting." Synthese no. 45:43-70.
Collins, Jordan E. 2012. A History of the Theory of Types: Developments after the Second Edition of Principia Mathematica. Saarbrücken: Lambert Academic Publishing.
Copi, Irving M. 1971. The Theory of Logical Types. London: Routledge.
Crittenden, Charles. 1970. "Ontology and the Theory of Descriptions." Philosophy and Phenomenological Research no. 31:85-96.
Dau, Paolo. 1986. "Russell's First Theory Pf Denoting and Quantification." Notre Dame Journal of Formal Logic no. 27:133-166.
De Rouilhan, Philippe. 1992. "Russell and the Vicious Circle Principle." Philosophical Studies no. 65:169-182.
Dejnožka, Jan. 1984. "Russell's Robust Sense of Reality: A Reply to Butchvarov." Grazer Philosophische Studien no. 32:155-164.
———. 1988. "A Reply to Butchvarov's Russell's Views on Reality." Grazer Philosophische Studien no. 32:181-184.
———. 1988. "A Reply to Umphrey's 'the Meinongian-Antimeinongian Dispute Reviewed." Grazer Philosophische Studien no. 32:185-186.
———. 1990. "The Ontological Foundation of Russell's Theory of Modality." Erkenntnis no. 32:383-418.
———. 1996. The Ontology of the Analytic Tradition and Its Origins. Realism and Identity in Frege, Russell, Wittgenstein, and Quine. Lanham: Littlefield Adams Books.
Paperback edition reprinted with corrections, 2002; reprinted with further corrections, 2003.
———. 1999. Bertrand Russell on Modality and Logical Relevance. Aldershot: Ashgate.
Second edition Ann Arbor, MI: CreateSpace. 2015.
———. 2001. "Origin of Russell's Early Theory of Logical Truth as Purely General Truth: Bolzano, Peirce, Frege, Venn, or Maccoll?" Modern Logic no. 8:21-30.
———. 2001. "Russell and Mccoll: A Reply to Grattan-Guinness, Wolenski, and Read." Nordic Journal of Philosophical Logic no. 6:21-42.
———. 2003. "Russell on Modality: A Reply to Kervick." Bertrand Russell Society Quarterly no. 120:33-38.
———. 2010. "The Concept of Relevance and the Logic Diagram Tradition." Logica Universalis no. 4:67-135.
"What is logical relevance? Anderson and Belnap say that the "modern classical tradition [,] stemming from Frege and Whitehead-Russell, gave no consideration whatsoever to the classical notion of relevance." But just what is this classical notion? I argue that the relevance tradition is implicitly most deeply concerned with the containment of truth-grounds, less deeply with the containment of classes, and least of all with variable sharing in the Anderson-Belnap manner. Thus modern classical logicians such as Peirce, Frege, Russell, Wittgenstein, and Quine are implicit relevantists on the deepest level. In showing this, I reunite two fields of logic which, strangely from the traditional point of view, have become basically separated from each other: relevance logic and diagram logic. I argue that there are two main concepts of relevance, intensional and extensional. The first is that of the relevantists, who overlook the presence of the second in modern classical logic. The second is the concept of truth-ground containment as following from in Wittgenstein's Tractatus. I show that this second concept belongs to the diagram tradition of showing that the premisses contain the conclusion by the fact that the conclusion is diagrammed in the very act of diagramming the premisses. I argue that the extensional concept is primary, with at least five usable modern classical filters or constraints and indefinitely many secondary intensional filters or constraints. For the extensional concept is the genus of deductive relevance, and the filters define species. Also following the Tractatus, deductive relevance, or full truth-ground containment, is the limit of inductive relevance, or partial truth-ground containment. Purely extensional inductive or partial relevance has its filters or species too.
Thus extensional relevance is more properly a universal concept of relevance or summum genus with modern classical deductive logic, relevantist deductive logic, and inductive logic as its three main domains."
Demopoulos, William. 1999. "On the Theory of Meaning of "on Denoting"." Noûs no. 33:439-458.
———. 2013. Logicism and Its Philosophical Legacy. New York: Cambridge Unviersity Press.
Donnellan, Keith. 1966. "Reference and Definite Descriptions." Philosophical Review no. 75:281-304.
Translated in Italian as: Riferimento e descrizioni definite in: Andrea Bonomi (ed.), La struttura logica del linguaggio, Milano, Bompiani, 1973.
Duran, Jane. 1988. "Russell on Names." Philosophy Research Archives no. 13:463-470.
Eames, Elizabeth Ramsden. 1967. Bertrand Russell's Theory of Knowledge. London: Allen and Unwin.
———. 1971. "Russell's Study of Meinong." Russell.The Journal of the Bertrand Russell Archives no. 4:3-7.
"Some commentators have found Russell's treatment of Meinong to be a 'travesty,' but it is argued that the letters between Meinong and Russell and Russell's reading notes (all in the Bertrand Russell archives at McMaster) show Russell to have been a careful student whose interpretation was welcomed by Meinong."
———. 1972. "Russell on "What There Is"." Revue Internationale de Philosophie no. 26:483-498.
Farrell-Smith, Janet. 1985. "The Russell-Meinong Debate." Philosophy and Phenomenological Research no. 45:305-350.
———. 1989. "Russell Re-Evaluation of Meinong, 1913-14: An Analysis of Acquaintance." In Antinomies and Paradoxes. Studies in Russell's Early Philosophy, edited by Winchester, Ian and Blackwell, Kenneth. Hamilton: McMaster University Library Press.
Fritz, Charles A.Jr. 1952. Bertrand Russell's Construction of the External World. New York: Routledge.
Galaugher, Jolen. 2013. Russell's Philosophy of Logical Analysis, 1897-1905. London: Palgrave Macmillan.
Gandon, Sébastien. 2012. Russell's Unknown Logicism: A Study in the History and Philosophy of Mathematics. London: Palgrave Macmillan.
Garciadiego, Alejandro R. 1992. Bertrand Russell and the Origins of the Set-Theoretic 'Paradoxes'. Basel: Birkhäuser Verlag.
Giaretta, Pierdaniele. 1997. "Analysis and Logical Form in Russell: The 1913 Paradigm." Dialectica no. 51:273-293.
Gram, Moltke. 1971. "Ontology and the Theory of Descriptions." In Essays on Bertrand Russell, edited by Klemke, Elmer D. Urbana: University of Illinois Press.
Grattan-Guinness, Ivor. 1974. "The Russell Archives: Some New Light on Russell's Logicism." Annals of Science no. 31:387-406.
———. 1977. Dear Russell - Dear Jourdain: A Commentary on Russell's Logic, Based on His Correspondence with Philip Jourdain. London: Duckworth.
———. 1986. "Bertrand Russell's Logical Manuscripts: An Apprehensive Brief." History and Philosophy of Logic no. 6:53-74.
Grayling, A. C. 2002. Russell: A Very Short Introduction. New York: Oxford University Press.
Green, Keith. 2007. Bertrand Russell, Language and Linguistic Theory. New York: Continuum.
Griffin, Nicholas. 1977. "Russell's "Horrible Travesty" of Meinong." Russell: the Journal of Bertrand Russell Studies no. 25-28:39-51.
———. 1980. "Russell on the Nature of Logic (1903-1913)." Synthese no. 45:117-188.
———. 1985/86. "Russell's Critique of Meinong's Theory of Objects." Grazer Philosophische Studien no. 25/26:375-401.
"Russell brought three arguments forward against Meinong's theory of objects. None of them depend upon a misinterpretation of the theory as is often claimed. In particular, only one is based upon a clash between Meinong's theory and Russell's theory of descriptions, and that did not involve Russell's attributing to Meinong his own ontological assumption. The other two arguments were attempts to find internal inconsistencies in Meinong's theory. But neither was sufficient to refute the theory, though they do require some revisions, viz. a trade-off between freedom of assumption and unlimited characterization. Meinong himself worked out the essentials of the required revisions."
———. 1986. "Wittgenstein's Criticism of Russell's Theory of Judgement." Russell: the Journal of Bertrand Russell Studies no. 5:123-145.
———. 1991. Russell's Idealist Apprenticeship. Oxford: Clarendon Press.
———, ed. 2003. The Cambridge Companion to Russell. Cambridge: Cambridge University Press.
Griffin, Nicholas, and Jacquette, Dale, eds. 2009. Russell Vs. Meinong. The Legacy of "on Denoting". New York: Routledge.
Contents: Preface XI; Acknowledgements XIII; Dale Jacquette and Nicholas Griffin: Introduction 1; 1. Alasdair Urquhart: Logic and denotation 10; 2. Graham Stevens: Antirealism and the theory of descriptions 26; 3. Francis Jeffrey Pelletier and Bernard Linsky: Russell vs. Frege on definite descriptions as singular terms 40; 4. Kevin C. Klement: A Cantorian argument against's Frege and early Russell's theories of descriptions 65; 5. Gideon Makin: 'On denoting' appearance and reality 78; 6. Omar W. Nasim: Explaining G. F. Stout's reaction to Russell's 'On denoting' 101; 7. David Bostock: Russell on 'the' in plural 113; 8. Johann Christian Marek: Psychological content and indeterminacy with respect to Being: two notes on the Russell-Meinong Debate 144; 9. Dale Jacquette: Meditations on Meinong's Golden Mountain 169; 10. Nicholas Griffin: Rethinking Item Theory 204; 11. Peter Loftson: Contra Meinong 233; 12. Gabriele Contessa: Who is afraid of imaginary objects? 248; 13. Gregory Landini: Russell's definite descriptions de re 266; 14. Michael Nelson: Quantifying in and Anti-Essentialism 297; 15. Nathan Salmon: Points, complexes, complex points, and a yacht 343; Contributors 365; Index 369.
Griffin, Nicholas, and Linsky, Bernard, eds. 2013. The Palgrave Centenary Companion to Principia Mathematica. New York: Palgrave Macmillan.
Griffin, Nicholas, Linsky, Bernard, and Blackwell, Kenneth, eds. 2011. Principia Mathematica at 100.
Special issue of Russell: the Journal of Bertrand Russell Studies. N.s. 21, no. 1.
Griffiths, D.A. 1976. "Russell on Existence and Descriptions." Philosophical Quarterly no. 26:157-162.
———. 1981. "A Reconsideration of Russell's Early Ontological Development." Philosophical Quarterly no. 31:145-152.
Hager, Paul J. 1994. Continuity and Change in the Development of Russell's Philosophy. Dordrecht: Kluwer.
Hill, Claire Ortiz. 1991. Word and Object in Husserl, Frege, and Russell. The Roots of Twentieth-Century Philosophy. Athens, Ohio: Ohio University Press.
Contents: Abbreviations IX; Preliminary terminological comments XI; Glossary XIII; Acknowledgments XIV; Introduction 1.
Part One: Logic, realism and the foundations of arithmetic
1. The argument that Frege influenced Husserl 7; 2. Husserl, Frege, and psychologism 13; 3. Sense, meaning, and noema; 4. Husserl's 1891 critique of Frege 43; 5. Frege's review and the development of Husserl's thought 57; Conclusion: analyticity 91.
Part Two: Conceptual clarity
Introduction 99; 6. Intensions and extensions 103; 7. Presentation and ideas 125; 8. Function and concept 137; 9. On denoting 147; Conclusion: The way things are 163; Notes 175; Bibliography 191; Index 215.
From the Introduction: "As a book by the founder of phenomenology that examines Frege's ideas from Brentano's empirical standpoint, Husserl's Philosophy of Arithmetic is both an early work of phenomenology and of logical empiricism. In it Husserl predicted the failure of Frege's attempt to logicize arithmetic and to mathematize logic two years before the publication of the Basic Laws of Arithmetic in 1893. I hope to show that Husserl did so in terms that would prefigure both the account Frege would give of his error after Russell encountered the paradoxes ten years later and the discussions of Principia Mathematica. Moreover, in locating the source of Frege's difficulties in the ambiguous theory of identity, meaning, and denotation that forms the basis of Frege's logical project and generates Russell's contradictions, Husserl's discussions indicate that these contradictions may have as serious consequences for twentieth century philosophy of language as they have had for the philosophy of mathematics.
This book is about these Austro-German roots of twentieth century philosophy. It is mainly about the origins of analytic philosophy, about the transmission of Frege's thought to the English speaking world, and about the relevance of Husserl's early criticism of Frege's Foundations of Arithmetic to some contemporary issues in philosophy. It is more about Husserl the philosopher of logic and mathematics than it is about Husserl the phenomenologist, and it is principally addressed to those members of the philosophical community who, via Russell, have been affected by Frege's logic.
This makes it very different from work on Husserl and Frege that has focused on the importance of Frege's criticism of Husserl's Philosophy of Arithmetic and attendant issues. The goal of this book is quite the opposite. It studies the shortcomings in Frege's thought that Husserl flagged and Russell endeavored to overcome. One possible sequel to this book would be a thorough study of Husserl's successes and failures in remedying the philosophical ills he perceived all about him, but that goes beyond the scope of this work, which follows the issues discussed into the work of Russell and his successors." (pp. 3-4)
———. 1997. Rethinking Identity and Metaphysics. On the Foundations of Analytic Philosophy. New Haven: Yale University Press.
Hintikka, Jaakko. 1981. "On Denoting What?" Synthese no. 46:167-183.
Hiz, Henry. 1977. "Descriptions in Russell's Theory and in Ontology." Studia Logica no. 36:271-283.
Hochberg, Herbert. 1956. "Peano, Russell and Logicism." Analysis no. 16:118-120.
Reprinted in: Elmer Daniel Klemke (ed.), Essays on Bertrand Russell.
———. 1966. "Things and Descriptions." American Philosophical Quarterly no. 3:1-9.
Reprinted in: Elmer Daniel Klemke (ed.), Essays on Bertrand Russell.
———. 1978. Thought, Fact and Reference. The Origins and Ontology of Logical Atomism. Minneapolis: University of Minnesota Press.
———. 1980. "Russell's Proof of Realism Reproved." Philosophical Studies no. 37:37-44.
———. 1995. "Particulars "as" Universals: Russell's Ontological Assay of Particularity and Phenomenological Space-Time." Journal of Philosophical Research no. 20:83-111.
———. 1995. "Abstracts, Functions, Existence and Relations in the Russell-Meinong Dispute, the Bradley Paradox and the Realism-Nominalism Controversy." Grazer Philosophische Studien no. 50:273-291.
———. 1996. "Particulars, Universals and Russell's Late Ontology." Journal of Philosophical Research no. 21:129-137.
———. 1996. "The Role of Subsistent Propositions and Logical Forms in Russell's 1913 Philosophical Logic and in the Russell-Wittgenstein Dispute." In Studies on the History of Logic. Proceedings of the Third Symposium on the History of Logic, edited by Angelelli, Ignacio and Cerezo, Maria, 317-341. Berlin: Walter de Gruyter.
———. 2000. "Facts, Truths and the Ontology of Logical Realism." Grazer Philosophische Studien no. 58-59:23-92.
———. 2000. "Propositions, Truth and Belief: The Wittgenstein-Russell Dispute." Theoria no. 66:3-40.
———. 2001. Russell, Moore, and Wittgenstein. The Revival of Realism. Egelsbach: Hänsel-Hohenhausen.
Hursthouse, Rosalind. 1980. "Denoting in the Principles of Mathematics." Synthese no. 45:33-42.
Hylton, Peter. 1980. "Russell's Substitutional Theory." Synthese no. 45:1-31.
———. 1989. "The Significance of "on Denoting"." In Rereading Russell: Essays in Bertrand Russell's Metaphysics and Epistemology, edited by Savage, Wade C. and Anderson, Anthony C. Minneapolis: University of Minnesota Press.
———. 1990. Russell, Idealism, and the Emergence of Analytic Philosophy. Oxford: Clarendon Press.
———. 1990. "Logic in Russell's Logicism." In The Analytic Tradition. Meaning, Thought and Knowledge, edited by Bell, David and Cooper, Neil, 137-172. Oxford: Basil Blackwell.
———. 2005. Propositions, Functions, and Analysis. Selected Essays on Russell's Philosophy. New York: Oxford University Press.
Irvine, Andrew D. 1999. Bertrand Russell. Critical Assessments. New York: Routledge.
Four volumes: 1. Life, Work and Influence;. 2. Logic and Mathematics; 3. Language, Knowledge and the World; 4. History of Philosophy, Ethics, Education, Religion and Politics.
———. 2009. "Bertrand Russell's Logic." In Handbook of the History of Logic. Volume 5: Logic from Russell to Church, edited by Gabbay, Dov and Woods, John, 1-28. Amsterdam: North-Holland.
"Bertrand Russell is generally recognized as one of the most important English speaking philosophers, logicians and essayists of the twentieth century. Often cited along with G.E. Moore as one of the founders of modern analytic philosophy and along with Kurt Gödel as one of the most influential logicians of his time, Russell is also widely recognized for his sustained public contributions to many of the most controversial social, political and educational issues of his day. Even so, more than anything else, it is Russell's work in logic and the foundations of mathematics that serves as his core contribution to intellectual history and that makes Russell the seminal thinker he is. His most significant achievements include
1. his refining and popularizing of Giuseppe Peano's and Gottlob Frege's first attempts at developing a modern mathematical logic,
2. his discovery of the paradox that bears his name,
3. his introduction of the theory of types (his way of avoiding the paradox),
4. his defense of logicism, the view that mathematics is in some important sense reducible to logic, and his many detailed derivations supporting this view,
5. his ground-breaking advances in technical philosophy, including both his theory of definite descriptions and his theory of logical constructions,
6. his theory of logical relations, including his impressively general theory of relation arithmetic,
7. his formalization of the reals,
8. his theory of logical atomism, and
9. his championing of the many connections between modern logic, mathematics, science, and knowledge in general." (p. 1)
Irvine, Andrew D., and Wedeking, Gary, eds. 1993. Russell and Analytic Philosophy. Toronto: University of Toronto Press.
Jacquette, Dale, Griffin, Nicholas, and Blackwell, Kenneth, eds. 2007. After “on Denoting”: Themes from Russell and Meinong.
Special issue of Russell: the Journal of Bertrand Russell Studies. N.s. 27, no. 1.
Jager, Ronald. 1972. The Development of Bertrand Russell's Philosophy. Lodon: Allen & Unwin.
Kaplan, David. 1970. "What Is Russell's Theory of Descriptions?" In Physics, Logic and History. Based on the First International Colloquium Held at the University of Denver, May 16-20, 1966, edited by Yourgrau, Wolfgang, 227-244. New York: Plenum Press.
Reprinted in David Pears (ed.), Bertrand Russell: A Collection of Critical Essays.
Translated in Italian as: Che cos'è la teoria delle descrizioni di Russell?, in: Andrea Bonomi (ed.), La struttura logica del linguaggio, Milano: Bompaini, 1973.
———. 1975. "How to Russell a Frege-Church." Journal of Philosophy no. 71:716-729.
Klemke, Elmer D., ed. 1970. Essays on Bertrand Russell. Urbana: University of Illinois Press.
———. 1971. "Logic and Ontology in Russell's Philosophy." In Essays on Bertrand Russell, edited by Klemke, Elmer D., 416-444. Urbana: University of Illinois Press.
Korhonen, Anssi. 2013. Logic as Universal Science. Russell's Early Logicism and Its Philosophical Context. New York: Palgrave Macmillan.
Kremer, Michael. 1994. "The Argument of 'on Denoting'." Philosophical Review no. 103:249-297.
Kroon, Frederick W. 2006. "Russell's Descriptions and Meinong's Assumptions." In Modes of Existence. Papers in Ontology and Philosophical Logic, edited by Bottani, Andrea and Davies, Richard, 81-104. Frankfurt: Ontos Verlag.
"The paper is structured as follows. In the next section, I describe a problem for Russell's account of the logical form of negative existentials involving descriptions, and suggest a Russellian solution. This solution is one that no one will care to adopt -- it seems to turn negative existentials into self-contradictions -- but I later argue that, properly interpreted, it constitutes a promising way of reconciling some of Meinong's views about negative existentials with the kind of "robust sense of reality" that informed Russell's own analysis. In section 3 I begin the task of articulating this reading of Meinong by describing Meinong's Assumption View as articulated in the second edition of his On Assumptions (Meinong 1910). Because this view presupposes Meinong's infamous commitment to non-existent objects, it would still offend Russell's "robust sense of reality", and so section 4 considers a weakened version of the view, one that retains the appeal to assumptions while giving up the appeal to non-existent objects. (Meinong defends a similar view in the 1902 edition of On Assumptions, which predates his discovery of non-existents.) Section 5 offers the finale: it shows how Meinong had himself tried to apply such a weakened Assumption View to the case of negative existentials, that Russell had known about the attempt (this arguably solves the first, hermeneutic puzzle), and that, properly interpreted, this way of understanding negative existentials provides Russell with a solution to the problem facing his theory of negative existentials." (pp. 82-83)
Lackey, Douglas. 1975. "Russell's Anticipation of Quine Criterion." Russell: the Journal of Bertrand Russell Studies:27-30.
Lambert, Karel. 1970. "Russell's Theory of Definite Descriptions." Dialectica no. 44:137-152.
———. 1992. "Russell's Version of the Theory of Definite Descriptions." Philosophical Studies no. 65:153-167.
Landini, Gregory. 1987. "Russell's Substitutional Theory of Classes and Relations." History and Philosophy of Logic no. 8:171-200.
———. 1990. "A New Interpretation of Russell's Multiple-Relation Theory of Judgment." History and Philosophy of Logic no. 11:37-69.
———. 1990. "How to Russell Another Meinongian: A Russellian Theory of Fictional Objects Versus Zalta's Theory of Abstract Objects." Grazer Philosophische Studien no. 37:93-122.
———. 1996. "Logic in Russell's Principles of Mathematics." Notre Dame Journal of Formal Logic no. 37:554-584.
———. 1998. Russell's Hidden Substitutional Theory. New York: Oxford University Press.
———. 2009. Wittgenstein's Apprenticeship with Russell. Cambridge: Cambridge University Press.
———. 2010. Russell. New York: Routledge.
Lebens, Samuel. 2017. Bertrand Russell and the Nature of Propositions: A History and Defence of the Multiple Relation Theory of Judgement. New York: Routledge.
Lejewski, Czeslaw. 1980. "A Re-Examination of the Russellian Theory of Descriptions." Philosophy no. 35:14-29.
Link, Godehard, ed. 2004. One Hundred Years of Russell's Paradox: Mathematics, Logic, Philosophy. Berlin: Walter de Gruyter.
Linsky, Bernard. 1999. Russell's Metaphysical Logic. Stanford: CSLI Publications.
———. 2011. Revising Principia Mathematica: Bertrand Russell's Notes and Manuscripts for the Second Edition. New York: Cambridge University Press.
———. 2011. The Evolution of Principia Mathematica: Bertrand Russell's Manuscripts and Notes for the Second Edition. Cambridge: Cambridge University Press.
Linsky, Bernard, and Imaguire, Guido, eds. 2005. "On Denoting", 1905-2005. Munich: Philosophia Verlag.
Linsky, Bernard, and Wishon, Donovan, eds. 2015. Acquaintance, Knowledge, and Logic: New Essays on Bertrand Russell's "the Problems of Philosophy". Stanford, Calif.: Center for the Study of Language and Information.
Linsky, Leonard. 1967. Referring. London: Routledge & Kegan Paul.
———. 1979. Names and Descriptions. Chicago: University of Chicago Press.
Ludlow, Peter, and Neale, Stephen. 1991. "Indefinite Descriptions: In Defense of Russell." Linguistics and Philosophy no. 14:171-202.
Lycan, William. 1981. "Logical Atomism and Ontological Atoms." Synthese no. 46:207-229.
MacLean, Gülberk Ko. 2014. Bertrand Russell's Bundle Theory of Particulars. London: Bloomsbury Academic.
Makin, Gideon. 2000. The Metaphysicians of Meaning. Russell and Frege on Sense and Denotation. London: Routledge & Kegan Paul.
Martinich, Paul. 1976. "Russell's Theory of Meaning and Descriptions (1905-1920)." Journal of the History of Philosophy no. 16:183-201.
Miah, Sajahan. 2006. Russell’s Theory of Perception 1905–1919. London: Continuum.
Miller, Alexander. 2006. "Russell, Multiple Relations, and the Correspondence Theory of Truth." The Monist no. 89:85-101.
Monk, Ray, and Palmer, Anthony, eds. 1996. Bertrand Russell and the Origins of Analytical Philosophy. Bristol: Thoemmes Press.
Moore, George Edward. 1944. "Russell's "Theory of Descriptions"." In The Philosophy of Bertrand Russell, edited by Schilpp, Paul Arthur, 175-225. Lasalle: Open Court.
Nakhnikian, George, ed. 1974. Bertrand Russell's Philosophy. London: Duckworth.
Nasim, Omar W. 2008. Bertrand Russell and the Edwardian Philosophers. New York: Palgrave Macmillan.
Neale, Stephen. 1990. Descriptions. Cambridge: MIT Press.
Oaklander, Nathan, and Miracchi, Silvano. 1980. "Russell, Negative Facts, and Ontology." Philosophy of Science no. 47:434-455.
"Russell's introduction of negative facts to account for the truth of "negative" sentences or beliefs rests on his collaboration with Wittgenstein in such efforts as the characterization of formal necessity, the theory of logical atomism, and the use of the Ideal Language. In examining their views we arrive at two conclusions. First, that the issue of negative facts is distinct from questions of meaning or intentionality; what a sentence or belief means or is about rather than what makes it true or false. Second, that the ontological use of the Ideal Language is incompatible with the requirements of its employment in the logical study of inferences. On this basis we conclude that despite elaboration by recent proponents, the doctrine of negative facts lacks adequate support, and perhaps more importantly, it is proper ontological method to free the Ideal Language from the exigencies of a symbolism constructed for logical investigation."
Ogbozo, Chrysanthus Nnaemeka. 2013. Bertrand Russell's Critiques of Knowledge and Belief as Prolegomena to Complementary Epistemology. Berlin: Rhombos-Verlag.
Preface by Elizabeth Ramsden Eames.
Oksanen, Mika. 1999. "The Russell-Kaplan Paradox and Other Modal Paradoxes: A New Solution." Nordic Journal of Philosophical Logic no. 4:73-95.
Orilia, Francesco. 1991. "Type-Free Property Theory, Bradley's Regress and Meinong and Russell Reconciled." Grazer Philosophische Studien no. 39:103-125.
Ostertag, Gary. 1998. Definite Descriptions: A Reader. Cambridge: MIT Press.
Passmore, John. 1995. "Editing Russell's Papers: A Fragment of Institutional History." Grazer Philosophische Studien no. 49:189-205.
Patterson, Wayne. 1993. Bertrand Russell's Philosophy of Logical Atomism. New York: Peter Lang.
Pears, David. 1967. Bertrand Russell and the British Tradition in Philosophy. New York: Random House.
———. 1972. "Russell's Logical Atomism." In Bertrand Russell. A Collection of Critical Essays, edited by Pears, David, 41-55. Garden City: Anchor Books.
———. 1972. Bertrand Russell: A Collection of Critical Essays. Garden City: Anchor Books.
Pincock, Christopher. 2008. "Russell's Last (and Best) Multiple-Relation Theory of Judgement." Mind no. 117:107-139.
Prior, Arthur Norman. 1965. "Existence in Lesniewski and Russell." In Formal Systems and Recursive Functions, edited by Crossley, John and Dummett, Michael, 149-155. Amsterdam: North-Holland.
Quine, Willard Van Orman. 1966. "Russell's Ontological Development." Journal of Philosophy no. 63:657-667.
Reprinted in: Elmer Daniel Klemke (ed.), Essays on Bertrand Russell.
Rao, A. P. 1998. Understanding Principia and Tractatus: Russell and Wittgenstein Revisited. San Francsico: International Scholars Publications.
Reicher, Maria Elisabeth. 2005. "Russell, Meinong, and the Problem of Existent Nonexistents." In On Denoting 1905-2005, edited by Imaguire, Guido and Linsky, Bernard, 167-193. München: Philosophia Verlag.
"In "On Denoting" Russell attacked Alexius Meinong's so-called "theory of objects" (Gegenstandstheorie), arguing, among other things, that according to Meinong's theory both the sentence "The existent present King of France exists" and "The existent present King of France does not exist" is true, which would render Meinong's theory inconsistent. Some Neo-Meinongians have claimed that one could avoid this consequence by making use of a distinction between two kinds of properties ("nuclear" and "extranuclear" ones), which Meinong worked into his theory several years after "On Denoting". My aim in this paper is to re-evaluate this contemporary attempt to defend Meinong's theory against Russell's attack and to offer an alternative solution."
Ripley, Charles. 1981. "Moore and Russell on Existence as Predicate." Russell: the Journal of Bertrand Russell Studies no. 37-40:17-30.
Rodriguez Consuegra, Francisco. 1987. "Russell's Logicist Definition of Numbers, 1898-1913: Chronology and Significance." History and Philosophy of Logic no. 8:141-189.
———. 1989. "Russell's Theory of Types, 1901-1910: Its Complex Origins in the Unpublished Manuscripts." History and Philosophy of Logic no. 10:131-164.
———. 1991. The Mathematical Philosophy of Bertrand Russell: Origins and Development. Boston: Birkhäuser Verlag.
Rosenberg, Jay. 1972. "Russell on Negative Facts." Noûs no. 6:27-40.
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Sainsbury, Mark. 1979. Russell. New York: Routledge.
Savage, Wade C., and Anderson, Anthony C., eds. 1989. Rereading Russell. Essays in Bertrand Russell's Metaphysics and Epistemology. Minneapolis: University of Minnesota Press.
Schiffer, Stephen. 2005. "Russell’s Theory of Definite Descriptions." mind no. 114:1135-1183.
Schilpp, Paul Arthur, ed. 1944. The Philosophy of Bertrand Russell. La Salle: Open Court.
Schoenman, Ralph, ed. 1967. Bertrand Russell Philosopher of the Century. London: Allen & Unwin.
Schwartz, Stephen P. 2012. A Brief History of Analytic Philosophy: From Russell to Rawls. Hoboken, NJ: Wiley-Blackwell.
Schwerin, Alan, ed. 2010. Russell Revisited, Critical Reflections on the Thought of Bertrand Russell. Newcastle: Cambridge Scholars Publishing.
Simons, Peter M. 1992. "On What There Isn't: The Meinong-Russell Dispute." In Philosophy and Logic in Central Europe from Bolzano to Tarski, 159-191. Dordrecht: Kluwer Academic Publishers.
Translated from: Über das, was es nicht gibt: Die Meinong-Russell Kontroverse - Zeitschrift für Semiotik, 10, 1988 pp. 399-426
Skosnik, Jeffrey. 1980. "Leibniz and Russell on Existence and Quantification Theory." Canadian Journal of Philosophy no. 10:681-720.
Smith, Janet Farrell. 1985. "The Russell-Meinong Debate." Philosophy and Phenomenological Research no. 45:305-350.
"The debates between Bertrand Russell and Alexius Meinong from 1904 to 192.0 dealt with some fundamental issues in philosophy: reference, nonexistent objects, intentionality. Along with the enduring influence of Russell's philosophy, sonic misapprehensions about these exchanges have persisted. One is that Russell's objections to Meinong were definitive. The other stems from taking too seriously Russell's casual remark in 1918 that Meinong's theories evidenced a deficient "sense of reality." Contrary to the impression left by this comment, Russell, during the most intensive years of the debate (1904-1907), felt a real respect for Meinong's theories,' and his main concern lay elsewhere. The exchange did not center on "reality" or "realism," as is often believed, but on the classical laws of logic (noncontradiction, excluded middle) and the correct analysis of logical form, for instance, of existence statements. Russell also took a dim view of the modal concepts Meinong used to support the canons of object theory, but his main concern was that Meinong's overall analysis appeared to threaten the foundation of Russell's philosophical logic. Russell and Meinong's disagreement thus came down to competing logical frameworks tied to different notions of what it is to he an object.
In claiming that Russell's main objection to Meinong's theory was logical, I do not mean to deny that ontology and metaphysics were in the forefront of Russell's concerns up to 1910 or that for him a correct foundational view of logic would tell us much about the way the world is. Russell's motivation for criticizing Meinong may well have been a concern with what is 'real', but his philosophical reasons for rejecting Meinong's object theory in 1905-1907 had to do which logical principles and their reputed violations. Interestingly, during the years Russell was debating with Meinong most intensively (1904-1907) he was also struggling to find the solution to his paradox of classes. With his 1905 invention of the theory of descriptions, Russell believed he had simultaneously found a way to deal with apparent reference to nonexistents in ordinary grammar and a new analysis of classes. It seems that the two difficulties of paradoxical classes and nonexistent objects plagued Russell's sense of consistency in a parallel manner.
In this paper I focus on giving an internal analysis of the objections and replies exchanged by Russell and Meinong to show that Russell's objections failed to be decisive and that the standoff between them came down to fundamentally different frameworks. Some scholarly evidence supports this interpretation as well. Russell's 1904 letter to Meinong emphasizes that what Meinong called "Theory of Objects" Russell had been accustomed to calling "Logic." [See Appendix]' In pressing his contradiction charge, Russell continued to evaluate Meinong's object theory by the standards of his own view of "logic." Lastly, evidence of a more circumstantial nature points to the parallelism of Russell's worries over nonexistent objects and classes."
(1) See the newly published Theory of Knowledge, The 1913 Manuscript, Vol. 7 of Russell's Collected papers, edited by Elizabeth Eames and Kenneth Blackwell (Allen and Unwin, 1983). This manuscript, which contains many accurate references to Meinong's theories, was never published by Russell. He was apparently discouraged by Wittgenstein's criticism of his theory of judgment.
(2) The Appendix contains translations of Russell's three letters to Meinong. See also the chronological Bibliography at the end of this paper.
(3) See Roderick Chisholm, Brentano and Meinong Studies (Amsterdam: Rodopi, 1982.), and The First Person, An Essay on Reference and Intentionality (Minneapolis: University of Minnesota Press, 1981).
(4) Some issues are treated in my "Meinong's Theory of Objects and Assumptions," in Phenomenology: Dialogues and Bridges, ed. R. Bruzina and B. Wilshire (Albany: State University of New York Press, 1982). In a longer study of book length I explore these and other issues in greater depth.
———. 1988. "Russell's Re-Evaluation of Meinong, 1913-14: An Analysis of Acquaintance." Russell.The Journal of the Bertrand Russell Archives no. 8:179-194.
———. 2005. "Russell's "on Denoting", the Laws of Logic and the Refutation of Meinong." In On Denoting 1905-2005, edited by Imaguire, Guido and Linsky, Bernard, 137-166. München: Philosophia Verlag.
Soames, Scott. 2003. Philosophical Analysis in the Twentieth Century, Vol. 1: The Dawn of Analysis. Princeton: Princeton University Press.
Stevens, Graham. 2005. The Russellian Origins of Analytical Philosophy: Bertrand Russell and the Unity of the Proposition. London: Routledge.
———. 2011. The Theory of Descriptions: Russell and the Philosophy of Language. London: Palgrave Macmillan.
Sullivan, Arthur. 2013. Reference and Structure in the Philosophy of Language: A Defense of the Russellian Orthodoxy. New York: Routledge.
Suter, Ronald. 1967. "Russell's 'Refutation' of Meinong in 'on Denoting'." Philosophy and Phenomenological Research no. 27:512-516.
Swanson, Carolyn. 2011. Reburial of Nonexistents. Reconsidering the Meinong-Russell-Debate. Amsterdam: Rodopi.
"Alexius Meinong claimed to uncover a brave new world of nonexistent objects. He contended that unreal objects, such as the golden mountain and the round square, genuinely had properties (such as nonexistence itself) and therefore, deserved a place in an all-inclusive science. Meinong's notion of nonexistents was initially not well-received, largely due to the influence and criticisms of Bertrand Russell. However, it has gained considerable popularity in more recent years as academics have uncovered shortfalls in Russell's philosophy and strived to explain apparent "facts" about the beingless. Some philosophers have continued Meinong's project, further explaining nonexistent objects or formulating logic systems that incorporate them.
The more recent developments beg for a re-examination of Meinongianism. This book does just that, putting the theory on trial. Part One considers if Russell truly defeated Meinongianism. It addresses Meinongian rejoinders in response to Russell's main criticisms and further defends Russell's alternative solution, his Theory of Descriptions. Part Two explores the rationale for nonexistents and their use in interpreting three types of statements: characterization, negative existential, and intentional. The book argues that, despite appearances, Meinongianism cannot plausibly account for its own paradigm claims, whereas Russell's framework, with some further elucidation, can explain these statements quite well. Part Three primarily addresses claims about fiction, exploring the short-comings of Meinongian and Russellian frameworks in interpreting them. The book introduces a contextualization solution and symbolic method for capturing the logical form of such claims - one with the complexity to handle cross-contextual statements, including negative existential and intentional ones. It finally considers where that leaves nonexistent objects, ultimately rejecting such so-called entities."
Umphrey, Stewart. 1988. "The Meinongian-Antimeinongian Dispute Reviewed: A Reply to Dejnožka and Butchvarov." Grazer Philosophische Studien no. 32:169-179.
Vanderveken, Daniel. 1982. "Some Philosophical Remarks on the Theory of Types in Intensional Logic." Erkenntnis no. 17:85-112.
Veatch, Henry. 1971. "The Philosophy of Logical Atomism: A Realism Manqué." In Essays on Bertrand Russell, edited by Klemke, Elmer D., 102-117. Urbana: University of Illinois Press.
Voltolini, Alberto. 2001. "What Is Alive and What Is Dead in Russell's Critique of Meinong." In The School of Alexius Meinong, edited by Albertazzi, Liliana, Jacquette, Dale and Poli, Roberto, 489-516. Aldershot: Ashgate.
Wahl, Russell. 1993. "Russell's Theory on Meaning and Denotation and 'on Denoting'." Journal of the History of Philosophy no. 31:71-94.
———. 2013. Propositions and Facts in the Early Philosophy of Bertrand Russell. Wellington, NZ: Society for Philosophy & Culture.
———, ed. 2018. The Bloomsbury Companion to Bertrand Russell. New York: Bloomsbury.
To be publsihed September 2018.
Weiss, Bernhard. 1994. "On Russell's Argument for Restricting Modes of Specification and Domains of Quantification." History and Philosophy of Logic no. 15:173-188.
Wettstein, Howard. 1990. "Frege-Russell Semantics?" Dialectica no. 44:113-135.
Winslade, William. 1971. "Russell's Theory of Relation." In Essays on Bertrand Russell, edited by Klemke, Elmer D., 81-101. Urbana: University of Illinois Press.
Yu, Yung-ping. 1995. Generality and Reference. An Examination of Denoting in Russell's Principles of Mathematics, University of Iowa.
Available at ProQuest Dissertation Express. Order number: 9603108.
"Bertrand Russell 1872-1970." 1972. Revue internationale de philosophie no. 102.
Sommaire: Gilbert Ryle: Bertrand Russell 1872-1970 436; Brian McGuinness: Bertrand Russell and Ludwig Wittgenstein's 'Notes on Logic' 444; J. R. Leyvraz: Bertrand Russell et l'impact de Wittgenstein 461; Elizabeth R. Ames: Russell on 'What There is' 483; Conrad J. Koehler: Studies in Bertrand Russell's Theory of Knowledge 499; Steen Olaf Welding:Russell's Theory of Definite Descriptions as Opposed to Quine's Singular Terms 513; Jules Vuillemin: Logical Flaws or Philosophical Problems: On Russell's Principia Mathematica 534-556.
"Russell En Héritage / Le Centenaire Des Principles." 2004. Revue internationale de philosophie no. 58:247-372.
Sommaire: Philippe de Rouilhan: Présentation 247; Gregory Landini: Russell's Separation of the Logical and Semantic Paradoxes 257; Geoffrey Hellman: Predicativism as a Philosophical Position 295; Solomon Feferman: Comments on “Predicativity as a philosophical position” by G. Hellman 313; Geoffrey Hellman: Reply to Comments of Solomon Ferferman 325; Philippe de Rouilhan: The Basic Problem of the Logic of Meaning (I) 329-372.
Heijenoort, Jean van. 1987. "Système Et Métasystème Chez Russell." In Logic Colloquium '85, 111-122. Amsterdam: North-Holland.
Proceedings of the Colloquium held in Orsay, France, July 1985. Edited by The Paris Logic Group.
Lepage, Franois. 1983. "Réalisme Et Théorie Russellienne Des Descriptions." Canadian Journal of Philosophy no. 13:209-226.
Vernant, Denis. 1993. La Philosophie Mathématique De Bertrand Russell. Paris: Vrin.
Vuillemin, Jules. 1968. Leons Sur La Première Philosophie De Russell. Paris: Aramand Colin.
———. 1971. La Logique Et Le Monde Sensible. Étude Sur Les Théories Contemporaines De L'abstraction. Paris: Flammarion.
———. 1975. "Le "Platonisme" Dans La Première Philosophe De Russell Et Le "Principe D'abstraction"." Dialogue no. 14:222-240.
Mueller-Goldingen, Christian. 2013. Bertrand Russell. Studien Zu Seinem Philosophischen Werk. Berlin: LIT Verlag.
Rheinwald, Rosemarie. 1998. Semantische Paradoxien, Typentheorie Und Ideale Sprache. Studien Zur Sprachphilosophie Bertrand Russells. Berlin: Walter de Gruyter.
Stepanians, Markus S. 1995. "Russells Kritik an Meinongs Begriff Des Annahmenschlusses." Grazer Philosophische Studien no. 50:415-432.
Tatievskaya, Elena. 2005. Der Begriff Der Logischen Form in Der Analytischen Philosophie. Russell in Auseinandersetzung Mit Frege, Meinong Und Wittgenstein. Frankfurt: Ontos Verlag.
Muguerza, Javier. 1973. "Sobre La Ontologia Del Atomismo Logico De Russell." Pensamiento no. 29:287-312.
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Di Francesco, Michele. 1991. Il Realismo Analitico. Logica, Ontologia E Significato Nel Primo Russell. Milano: Guerini e Associati.
Donati, Stefano. 2003. I Fondamenti Della Matematica Nel Logicismo Di Bertrand Russell. Firenze: Firenze Atheneum.
Granese, Alberto. 1971. Che Cosa Ha Veramente Detto Russell. Roma: Ubaldini.
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