Zermelo once wrote that he had anticipated Russell's contradiction of the set of all sets that are not members of themselves. Is this sufficient for having anticipated Russell's Paradox — the paradox that revealed the untenability of the logical notion of a set as an extension? This paper argues that it is not sufficient and offers criteria that are necessary and sufficient for having discovered Russell's Paradox. It is shown that there is ample evidence that Russell satisfied the criteria and (...) that Zermelo did not. (shrink)

“Tell me," Wittgenstein once asked a friend, "why do people always say, it was natural for man to assume that the sun went round the earth rather than that the earth was rotating?" His friend replied, "Well, obviously because it just looks as though the Sun is going round the Earth." Wittgenstein replied, "Well, what would it have looked like if it had looked as though the Earth was rotating?” What would it have looked like if we looked at all (...) sciences from the viewpoint of Wittgenstein’s philosophy? Wittgenstein is undoubtedly one of the most influential philosophers of the twentieth century. His complex body of work has been analysed by numerous scholars, from mathematicians and physicists, to philosophers, linguists, and beyond. This volume brings together some of his central perspectives as applied to the modern sciences and studies the influence they may have on the thought processes underlying science and on the world view it engenders. The contributions stem from leading scholars in philosophy, mathematics, physics, economics, psychology and human sciences; all of them have written in an accessible style that demands little specialist knowledge, whilst clearly portraying and discussing the deep issues at hand. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:RUSSELL TO FREGE, 24 MAY 1903: "I BELIEVE I HAVE DISCOVERED THAT CLASSES ARE ENTIRELY SUPERFLUOUS" GREGORY LANDINI Philosophy / University of Iowa Iowa City, IA 52242, USA It was his consideration of Cantor's proof that there is no greatest cardinal, Russell recalls in My Philosophical Development, that led in the spring of 1901 to the discovery of the paradox of the class of all classes not members (...) of themselves. "Never glad confident morning again", were Whitehead's reported words (MPD, p. 58). Whitehead was, of course, wrong. Russell had many new confident mornings. One in particular apparently occurred on 19 May 1903. On 23 May Russell wrote in his journal: "Four days ago 1 solved the Contradiction -the relief of this is unspeakable" (Papm 12: 24). The "solution" was communicated to Whitehead, who responded by telegram: "Heartiest congratulations Aristoteles secundus. 1 am delighted" (Clark, p. III). But it was not long before Russell knew his proposal was inadequate. On the form he would scrawl: "A propos of solVing the Contradiction. [But the solution was wrong]" (ibid; Russell's brackets). The episode is intriguing. What was the proposal? Russell's correspondence with Frege sheds some light. On 20 October 1902 Frege had sent a letter suggesting a way to avoid the contradiction. Frege's suggestion, formulated in a great hurry so that it might appear in the Appendix of Vol. II of the Grundgesetze der Arithmetik, was to abandon his Basic Law V; zcj>z =zez. ==. (x)(x. ==. ex), and to replace it by Russell to Frege, 24 May I903 161 V' zz =zez. ==. (x)(x *zz & x* zez: ~ : x. ==. ex). The underlying idea was to accept that one concept may have the same extension as another even though the two concepts are not coextensive. Though he thought the underlying idea "probably correct",! Russell expressed reservation in a reply of 12 December:... I find it difficult to accept your solution even though it is probably correct. Do you deny, e.g., that all classes form a class? And if this is admitted, then it is possible that - ana. Moreover, the class of non-humans is a. non-human. Otherwise it must be admitted that not ail objects fall either under a or not-a; namely, if a is a range of values, then a fails neither under a nor under not-a. This contradicts the law of excluded middle, which will be inconvenient to say the least.2 (Frege I980, p. 151) Frege's response of 28 December does not mention the contradiction, and Volume II of his Grundgesetze appeared early in 1903. Russell's reservations concerning Frege's solution· continue in a letter to Frege of 20 February 1903: What you say about my contradiction is of the greatest interest to me. Do you believe that the range of values remains unchanged if some subclass of the class is assigned to it as a new member? Extension seems to fit this view better than intension. Bur I fe;el far from clear about this question. (Frege I980, p. 155) Frege replied on 21 May, explaining that in general a class does not remain unchanged when a particular subclass is added to it, but that two concepts may have the same extension (the same class) when the only difference between them is that this class falls under the first concept but not under the second (p. 157). Then on 24 May 1903 Russell excitedly wrote Frege of a solution of the paradox of classes: "I received your letter this morning, and 1 am replying to it at once, for russell: the Journal of the Berrrand Russdl Archives McMasrer University Library Press n.S.•2 (wincer 1992-93): 160-85 ISSN 0036-01631 • The same evaluation appears in Russell's Appendix to The Principles ofMathematics (p. 522). 2 Frege's '\- a II b" is Peano and Russell's "a E b". Russell should have put "~ana". 162 GREGORY LANDINI I believe I have discovered that classes are entirely superfluous. Your designation i(z) can be used for itself, and x E i(z) for (x).... this seems to me to avoid the contradiction" (p. 159). The proposal is also mentioned in a... (shrink)

In lieu of an abstract, here is a brief excerpt of the content:January 22, 2009 (8:41 pm) G:\WPData\TYPE2802\russell 28,2 048red.wpd russell: the Journal of Bertrand Russell Studies n.s. 28 (winter 2008–09): 127–42 The Bertrand Russell Research Centre, McMaster U. issn 0036-01631; online 1913-8032 YABLO’S PARADOX AND RUSSELLIAN PROPOSITIONS Gregory Landini Philosophy / U. of Iowa Iowa City, ia 52242–1408, usa gregory-landini@uiowa.edu Is self-reference necessary for the production of Liar paradoxes? Yablo has given an argument that self-reference is not (...) necessary. He hopes to show that the indexical apparatus of self-reference of the traditional Liar paradox can be avoided by appealing to a list, a consecutive sequence, of sentences correlated one-one withnaturalnumbers.Yabloopens his “Paradox without Self-Reference” (Analysis, 1993) with the assumption that there is a sequence such that: Snz: “(;k)(k > n.!. True Sk)” Each sentence on Yablo’s list is supposed to be correlated one-one with number n. Each sentence is supposed to say that for every natural number kz greater than n, the k-th sentence on the list is not true. By comparing Yablo’s construction to an analogous construction with early Russellian propositions, we show that Yablo has failed to generate a paradox. 1. vicious circularity in yablo’s paradox S elf-reference has been taken to be the source of paradoxes. Poincaré and Russell are commonly associated with this thesis. In an amusing passage, the mathematician Jourdain recalls something of the dialogue between them: Nearly all mathematicians agreed that the way to solve these paradoxes was simply not to mention them; but there was some divergence of opinion as to how they were to be unmentioned. It was clearly unsatisfactory merely not to mention them. Thus Poincaré was apparently of the opinion that the best way of avoiding such awkward subjects was to mention that they were not to be mentioned. But [as Russell put it] “one might as well, in talking to a man with January 22, 2009 (8:41 pm) G:\WPData\TYPE2802\russell 28,2 048red.wpd 128 gregory landini 1 Philip Jourdain, The Philosophy of Mr. B*rtr*nd R*ss*llz (London: Allen & Unwin, 1918), p. 77. Russell is quoted from “Mathematical Logic as Based on the Theory of Types” (1908), LK, p. 63. 2 “On ‘Insolubilia’ and Their Solution By Symbolic Logic”, in B. Russell, Essays in Analysis, ed. Douglas Lackey (London: Allen & Unwin, 1973), p. 196. 3 I believe that this is Russell’s view in 1906. See Gregory Landini, “Russell’s Separation of the Logical and Semantic Paradoxes”, Revue internationale de philosophie 58 (2004): 257–94 (issue titled “Russell en héritage / Le centenaire des Principes”, ed. Philippe de Rouilhan). a long nose, say: ‘When I speak of noses, I except such as are inordinately long’, which would not be a very successful eTort to avoid a painful topic.”1 Poincaré maintained that one should exclude the oTending cases and therebyavoid“viciouscircles”ofself-referencewhichgenerateparadoxes. Russell objected: We may illustrate this by what M. Poincaré says concerning Richard’s paradox. Having Wrst put E = “all numbers deWnable in a Wnite number of words” we arrive at a paradox, due, says M. Poincaré, to our having included a number only deWnable in a Wnite number of words by means of E. This vicious circle he proposes to avoid by deWning E as “all numbers deWnable in a Wnite number of words without mentioning Ey”. To the uninitiated, this deWnition looks more circular than ever.2 Russell held that some paradoxes such as those of classes require, in order to exclude oTending cases without mentioning them, a “reconstruction of logical Wrst principles”. Others, such as Richard’s, are to be dismissed because they involve confused and viciously circular notions of “deWnability ”.3 Is self-reference necessary for paradoxes? The question is not well crafted. There are quite diTerent notions ofz “self-reference” involved in paradoxes. The self-reference involved in the Liar “This sentence is false” is provided by an apparatus of indexicals. This apparatus is quite distinct from the self-reference involved in Russell’s early ontology of propositions (as mind- and language-independent states of aTairs). This is an ontological self... (shrink)

In lieu of an abstract, here is a brief excerpt of the content:_Russell_ journal (home office): E:CPBRRUSSJOURTYPE2502\REVIEWS.252 : 2006-02-27 11:52
eviews WITTGENSTEIN APPROACHED G L Philosophy / U. of Iowa Iowa City,  ,  -@. Brian McGuinness. Approaches to Wittgenstein: Collected Papers. London and New York: Routledge, . Pp. xv, . .. his book is a joy to read. Brian McGuinness is among the foremost Tscholars of Wittgenstein’s life and work. For better than  years, his papers have given (...) perhaps the most clear and authoritative account of the complex intellectual and personal journey of Wittgenstein. The collection of these important papers in one book is an outstanding gift to all who are interested in early analytic philosophy. The papers are not presented diachronically, but topically, starting with McGuinness’s discussions of the interplay between Wittgenstein’s philosophy and his conception of himself, as Austrian patriot, as teacher, as Jew, as architect, as penitent. There is much controversy in all of this. It is upsetting to learn that Wittgenstein remarked (likely sometime shortly after the events of Pearl Harbor in ) that “Things will be terrible when the war is over, whoever wins. Of course very terrible if the Nazis won, but terribly slimy if the Allies win” (p. ). In spite of McGuinness’s attempts at charitable explanation, it is hard to excuse this remark. Wittgenstein should have recognized that it was imperative that the Allies win, for surely he could not, by then, have been blind to the pogroms of Nazism (if not the implementation of their Final Solution to the Jewish question). It is just disappointing to discover Wittgenstein’s dalliance with anti-Semitism or with Weininger’s deplorable Sex and Gender. Nonetheless, McGuinness offers a wonderful and balanced portrait of Wittgenstein with a welcome minimum of hyperbole either concerning his genius, achievements and influences, or his eccentricities and failings.  As also in McGuinness’s Wittgenstein, a Life: Young Ludwig (London: Duckworth, and Berkeley : U. of California P., ; reprinted as Young Ludwig: Wittgenstein’s Life, – with a new Preface [Oxford: Clarendon P., ]) russell: the Journal of Bertrand Russell Studies n.s.  (winter –): – The Bertrand Russell Research Centre, McMaster U.  - _Russell_ journal (home office): E:CPBRRUSSJOURTYPE2502\REVIEWS.252 : 2006-02-27 11:52  Reviews In a second part, the book delves into the origins and nature of Wittgenstein ’s Tractatus Logico-Philosophicus. Since the papers in this part do not come diachronically, it would be nice for each to have a date by its title, so that if there is an historical development of McGuinness’s ideas it could be more easily tracked. But evolving or not, the interpretations in McGuinness’s papers are of the very highest quality. I know of no one else who has come closer to unravelling the often cryptic entries in the Tractatus. Though some of McGuinness’s assumptions about Russell’s philosophy are now challenged by new interpretations —in particular, it seems that Russell never held a theory of types of entities —there remain a great many gems in these papers. Among them are the following: Wittgenstein’s conception of solipsism is not Cartesian and epistemic, but concerns the limits of logical form and the proper ethical attitude towards life (p. ); the Notes on Logic were offered as satisfying the dissertation requirement for Wittgenstein’s .. degree (p. ); Wittgenstein included among the “logical constants” such notions as that of a “predicate” and a “dual complex”, not just logical particles such as “not”, “or”, “all” and “some” (p. ); Wittgenstein’s Grundgedanke was independent of his “picture theory” (p. ); Wittgenstein’s “logical atomism” was to be a purified form of Russell’s so that it forms “true logical atomism” with no differences of type and with the unification provided by neutral monism of mental and physical particulars (p. ); Wittgenstein and Russell had similar attractions to Spinozistic ethics, the conception of the world sub specie aeternitatis and the “mystical” as what inspires the scientific attitude (pp. , ); Hertz’s elimination of the concept of “force” in physics was an inspiration for Wittgenstein’s elimination of “classes”, “probability”, and the logical constants (p. ); structured variables were central to Wittgenstein’s Tractarian programme (p. ); Wittgenstein’s conception of philosophical analysis has important ties to Kuhn’s concept of a paradigm (pp. , , ). These... (shrink)

A. Kenny, Frege, an introduction to the founder of modern analytic philosophy. London:Penguin, 1995. viii-h223pp. £7.99 T. Willamson, Vagueness. London:Routledge, 1994. xiii-f-325 pp. £35.00 TOM BU...

Landini discusses the second edition of Principia Mathematica, to show Russella (TM)s intellectual relationship with Wittgenstein and Ramsey.

EbertPhilip A and RossbergMarcus, eds.* * _ Essays on Frege’s Basic Laws of Arithmetic_. Oxford: Oxford University Press, 2019. Pp. xii + 673. ISBN: 978-0-19-871208-4 ; 978-0-19-102005-6, 978-0-19-178024-0. doi: 10.1093/oso/9780198712084.001.0001.

In truth theory one aims at general formal laws governing the attribution of truth to statements. Gupta’s and Belnap’s revision-theoretic approach provides various well-motivated theories of truth, in particular T* and T#, which tame the Liar and related paradoxes without a Tarskian hierarchy of languages. In property theory, one similarly aims at general formal laws governing the predication of properties. To avoid Russell’s paradox in this area a recourse to type theory is still popular, as testified by recent work in (...) formal metaphysics by Williamson and Hale. There is a contingent Liar that has been taken to be a problem for type theory. But this is because this Liar has been presented without an explicit recourse to a truth predicate. Thus, type theory could avoid this paradox by incorporating such a predicate and accepting an appropriate theory of truth. There is however a contingent paradox of predication that more clearly undermines the viability of type theory. It is then suggested that a type-free property theory is a better option. One can pursue it, by generalizing the revision-theoretic approach to predication, as it has been done by Orilia with his system P*, based on T*. Although Gupta and Belnap do not explicitly declare a preference for T# over T*, they show that the latter has some advantages, such as the recovery of intuitively acceptable principles concerning truth and a better reconstruction of informal arguments involving this notion. A type-free system based on T# rather than T* extends these advantages to predication and thus fares better than P* in the intended applications of property theory. (shrink)

This paper offers an interpretation of Russell's multiple-relation theory of judgment which characterizes it as direct application of the 1905 theory of definite descriptions. The paper maintains that it was by regarding propositional symbols (when occurring as subordinate clauses) as disguised descriptions of complexes, that Russell generated the philosophical explanation of the hierarchy of orders and the ramified theory of types of _Principia mathematica (1910). The interpretation provides a new understanding of Russell's abandoned book _Theory of Knowledge (1913), the 'direction (...) problems' and Wittgenstein's criticisms. (shrink)

This paper describes the semiotic process by which parents, as attachment figures, enable infants to learn to make meaning. It also applies these ideas to psychotherapy, with the therapist functioning as transitional attachment figures to patients where therapy attempts to change semiotic processes that have led to maladaptive behavior. Three types of semiotic processes are described in attachment terminology and these are offered as possible precursors of a neuro-behavioral nosology tying mental illness to adaptation. Non-conscious biosemiotic processes in infant-parent attachment (...) are the basis for early adaptation as well as adaptation or maladaptation in adulthood. Mother-infant interaction can be described as a series of signs, each interpreted so as to dispose the behavior of the other interactant towards the goal of protecting the infant from danger and distress. Regulating arousal, scaffolding infants’ behavior in the infants’ zone of proximal development, and repairing ruptures in the interaction are crucial to infants’ development and adaptation. In semiotic terms, each person activates multiple interpretants to make meaning of sensory stimulation. Non-verbal semiotic synchrony establishes the relationship whereas shared repair of ruptures promotes change. Attachment strategies, as learned adaptations to threat, are neuro-psychological strategies for making meaning of sensory information so as to dispose protective behavior. Type A privileges cognitive-temporal information, Type C affective information, Type B has no bias. Type A and C limit semiotic freedom by using ‘short-cuts’ in processing that produce quick protective behavior in the short-term. Type B includes more representations, and thus more semiotic freedom, resulting in slower responses and long-term flexibility. Attachment strategies function as meta-interpretants for applying one semiotic process to most incoming information about danger. A, B, and C case examples are analyzed in semiotic terms. Psychotherapy can be considered a helping process embedded in a transitional attachment relationship. For psychotherapy to be successful, both somatic stabilization and a therapeutic relationship are needed. Treatment that uses scaffolded semiotic processes in each patient’s ZPD to repair moment-to-moment ruptures holds the potential to reorganize attachment strategies and transfer that potential to reflective language and relationships outside the therapy. The outcome should be greater semiotic freedom such that the individual can trust their own mental processes and use them to establish safe relationships. Language can speed the process, but premature reliance on verbal transformations of non-conscious information can carry misattributions into a second layer of misconstrued meaning and maladaptive behavior. Even when dangerous family relationships and external danger cannot be changed, patients can come to know their own minds and use information to regulate their behavior. The goal of psychotherapy is to free patients from their past by enabling them to be secure about the functioning of their own minds, so that they can both avoid eliciting harm and also establish supportive relationships. (shrink)

Unaware of Frege's 1879 Begriffsschrift, Russell's 1903 The Principles of Mathematics set out a calculus for logic whose foundation was the doctrine that any such calculus must adopt only one style of variables–entity (individual) variables. The idea was that logic is a universal and all-encompassing science, applying alike to whatever there is–propositions, universals, classes, concrete particulars. Unfortunately, Russell's early calculus has appeared archaic if not completely obscure. This paper is an attempt to recover the formal system, showing its philosophical background (...) and its semantic completeness with respect to the tautologies of a modern sentential calculus. (shrink)

Frege seems to hold two incompatible theses:(i) that sentences differing in structure can yet express the same sense; and (ii) that the senses of the meaningful parts of a complex term are determinate parts of the sense of the term. Dummett offered a solution, distinguishing analysis from decomposition. The present paper offers an embellishment of Dummett?s distinction by providing a way of depicting the internal structures of complex senses?determinate structures that yield distinct decompositions. Decomposition is then shown to be adequate (...) as a foundation for the informativity and analyticity of logic. (shrink)

This book explores an important central thread that unifies Russell's thoughts on logic in two works previously considered at odds with each other, the Principles of Mathematics and the later Principia Mathematica. This thread is Russell's doctrine that logic is an absolutely general science and that any calculus for it must embrace wholly unrestricted variables. The heart of Landini's book is a careful analysis of Russell's largely unpublished "substitutional" theory. On Landini's showing, the substitutional theory reveals the unity (...) of Russell's philosophy of logic and offers new avenues for a genuine solution of the paradoxes plaguing Logicism. (shrink)

This is a welcome reprint of a book that continues to grow in importance.

On investigating a theorem that Russell used in discussing paradoxes of classes, Graham Priest distills a schema and then extends it to form an Inclosure Schema, which he argues is the common structure underlying both class-theoretical paradoxes (such as that of Russell, Cantor, Burali-Forti) and the paradoxes of ?definability? (offered by Richard, König-Dixon and Berry). This article shows that Russell's theorem is not Priest's schema and questions the application of Priest's Inclosure Schema to the paradoxes of ?definability?.1 1?Special thanks to (...) Francesco Orilia for criticisms of an early draft of this article. (shrink)

This paper examines Russell's substitutional theory of classes and relations, and its influence on the development of the theory of logical types between the years 1906 and the publication of Principia Mathematica (volume I) in 1910. The substitutional theory proves to have been much more influential on Russell's writings than has been hitherto thought. After a brief introduction, the paper traces Russell's published works on type-theory up to Principia. Each is interpreted as presenting a version or modification of the substitutional (...) theory. New motivations for Russell's 1908 axiom of infinity and axiom of reducibility are revealed. (shrink)

This book offers a comprehensive critical survey of issues of historical interpretation and evaluation in Bertrand Russell's 1918 logical atomism lectures and logical atomism itself. These lectures record the culmination of Russell's thought in response to discussions with Wittgenstein on the nature of judgement and philosophy of logic and with Moore and other philosophical realists about epistemology and ontological atomism, and to Whitehead and Russell’s novel extension of revolutionary nineteenth-century work in mathematics and logic. Russell's logical atomism lectures have had (...) a lasting impact on analytic philosophy and on Russell's contemporaries including Carnap, Ramsey, Stebbing, and Wittgenstein. Comprised of 14 original essays, this book will demonstrate how the direct and indirect influence of these lectures thus runs deep and wide. (shrink)

Norbert Elias has been recognized as one of the key social scientists of the 20th century at least in sociology, political science and history. This book will address Norbert Elias's approach to empirical research, the use of his work in empirical research, and compare him with other theorists.

Wittgenstein's Tractatus has generated many interpretations since its publication in 1921, but over the years a consensus has developed concerning its criticisms of Russell's philosophy. In Wittgenstein's Apprenticeship with Russell, Gregory Landini draws extensively from his work on Russell's unpublished manuscripts to show that the consensus characterises Russell with positions he did not hold. Using a careful analysis of Wittgenstein's writings he traces the 'Doctrine of Showing' and the 'fundamental idea' of the Tractatus to Russell's logical atomist research program, (...) which dissolves philosophical problems by employing variables with structure. He argues that Russell and his apprentice Wittgenstein were allies in a research program that makes logical analysis and reconstruction the essence of philosophy. His sharp and controversial study will be essential reading for all who are interested in this rich period in the history of analytic philosophy. (shrink)

This paper examines the quantification theory of *9 of Principia Mathematica. The focus of the discussion is not the philosophical role that section *9 plays in Principia's full ramified type-theory. Rather, the paper assesses the system of *9 as a quantificational theory for the ordinary predicate calculus. The quantifier-free part of the system of *9 is examined and some misunderstandings of it are corrected. A flaw in the system of *9 is discovered, but it is shown that with a minor (...) repair the system is semantically complete. Finally, the system is contrasted with the system of *8 of Principia's second edition. (shrink)

HENRY LAYCOCK, Words Without Objects: Semantics, Ontology, and Logic for Non-Singularity. Oxford: Clarendon Press, 2006. xvi + 202pp. £35.00. ISBN 0‐19‐928171‐8. Gregory Landini, Department of Phil...

The second printing of Principia Mathematica in 1925 offered Russell an occasion to assess some criticisms of the Principia and make some suggestions for possible improvements. In Appendix A, Russell offered *8 as a new quantification theory to replace *9 of the original text. As Russell explained in the new introduction to the second edition, the system of *8 sets out quantification theory without free variables. Unfortunately, the system has not been well understood. This paper shows that Russell successfully antedates (...) Quine's system of quantification theory without free variables. It is shown as well, that as with Quine's system, a slight modification yields a quantification theory inclusive of the empty domain. (shrink)

Gregory Landini offers a detailed historical account of Frege's notations and the philosophical views that led Frege from Begriffssscrhrift to his mature work Grundgesetze, addressing controversial issues that surround the notations.

Frege's Grundgesetze der Arithmetik offers a conception of cpLogic as the study of functions. Among functions are included those that are concepts, i.e. characteristic functions whose values are the logical objects that are the True/the False. What, in Frege's view, are the objects the True/the False? Frege's stroke functions are themselves concepts. His stipulation introducing his negation stroke mentions that it yields [...]. But curiously no accommodating axiom is given, and there is no such theorem. Why is it that some (...) of Frege's informal stipulations never made appearances as axioms? I offer an explanation that sheds new light on the Grundgesetze. No axioms should over-determination the True as a logical object. Perhaps the True = 0, as would be common in the mathematics of characteristic functions. But the logical objects that are cardinal numbers are value ranges correlated with second-level numerical concepts by a non-homogeneous second-level value-range function [...]. The existence of concepts would be ontologically circular if the True is itself a number. We find this circularity perfectly agreeable to Frege, and suggest that he had accepted that the existence of functions that are concepts in his cpLogic may well be ontologically inseparable from the existence of his value-range function. His cpLogic itself stands or falls with the viability of some value-range function. (shrink)

This article compares the theory of Meinongian objects proposed by Edward Zalta with a theory of fiction formulated within an early Russellian framework. The Russellian framework is the second-order intensional logic proposed by Nino B. Cocchiarelly as a reconstruction of the form of Logicism Russell was examining shortly after writing The Principles of Mathematics. A Russellian theory of denoting concepts is developed in this intensional logic and applied as a theory of the "objects' of fiction. The framework retains the Orthodox (...) early Russellian ontology of existents, possible non-existents, and properties and relations in intension. This avoids the assumption, found in Meinongian theories, of impossible and incomplete objects. It also obviates the need to preserve consistency by distinguishing a new "mode of predication", or a "distinction in kinds of predicates". Thus, it is argued that an early Russellian theory forms a powerful rival to a Meinongian theory of objects. (shrink)

There is a curious letter of 24 April 1928, reproduced in Russell’s Autobiography. It is from Russell to Max Newman. It is my thesis that there is a crucial “not” missing from the text and interpretations of the letter. This small point, if it is correct, has a very large impact for clarifying how Russell saw Newman’s challenge to his structural realism according to which all of our empirical knowledge in physics concerns structure alone.

This article compares the theory of Meinongian objects proposed by Edward Zalta with a theory of fiction formulated within an early Russellian framework. The Russellian framework is the second-order intensional logic proposed by Nino B. Cocchiarelly as a reconstruction of the form of Logicism Russell was examining shortly after writing The Principles of Mathematics. A Russellian theory of denoting concepts is developed in this intensional logic and applied as a theory of the "objects' of fiction. The framework retains the Orthodox (...) early Russellian ontology of existents, possible non-existents, and properties and relations in intension. This avoids the assumption, found in Meinongian theories, of impossible and incomplete objects. It also obviates the need to preserve consistency by distinguishing a new "mode of predication", or a "distinction in kinds of predicates". Thus, it is argued that an early Russellian theory forms a powerful rival to a Meinongian theory of objects. (shrink)

Confronted with Russell's Paradox, Frege wrote an appendix to volume II of his _Grundgesetze der Arithmetik_. In it he offered a revision to Basic Law V, and proclaimed with confidence that the major theorems for arithmetic are recoverable. This paper shows that Frege's revised system has been seriously undermined by interpretations that transcribe his system into a predicate logic that is inattentive to important details of his concept-script. By examining the revised system as a concept-script, we see how Frege imagined (...) that minor modifications of his former proofs would recover arithmetic. (shrink)

This is a critical discussion of Nino B. Cocchiarella’s book “Formal Ontology and Conceptual Realism.” It focuses on paradoxes of hyperintensionality that may arise in formal systems of intensional logic.

There are many wonderful puzzles concerning Principia Mathematica, but none are more striking than those arising from the crisis that befell Whitehead in November of 1910. Volume 1 appeared in December of 1910. Volume 2 on cardinal numbers and Russell's relation arithmetic might have appeared in 1911 but for Whitehead's having halted the printing. He discovered that inferences involving the typically ambiguous notation ‘Nc‘α’ for the cardinal number of α might generate fallacies. When the volume appeared in 1912, it was (...) extensively emended by Whitehead and accompanied by a Prefatory Statement of Symbolic Conventions. This paper endeavors to recover from Whitehead's bad emendations—including his bewildering thesis that since ‘‘α’ is ‘true whenever significant,’ ‘α is to be accepted. It is supposedly a fallacy to apply Modus Ponens and infer Nc‘α from ‘α and‘‘α. (shrink)

Perhaps it is not overly pedantic to say that one will find Wittgenstein’s Tractatus Logico-Philosophicus very difficult even if one first understands Russell’s philosophical logic. But the question remains as to whether the work is intended in alliance with Russell’s research program for a scientific method in philosophy or splits from that program. This paper endeavors to answer the question by revealing new evidence that Wittgenstein held his Doctrine of Showing in 1913 and that it was a demand he imposed (...) in criticizing Russell’s multiple relation theory of judgment. (shrink)

Perhaps it is not overly pedantic to say that one will find Wittgenstein’s Tractatus Logico-Philosophicus very difficult even if one first understands Russell’s philosophical logic. But the question remains as to whether the work is intended in alliance with Russell’s research program for a scientific method in philosophy or splits from that program. This paper endeavors to answer the question by revealing new evidence that Wittgenstein held his Doctrine of Showing in 1913 and that it was a demand he imposed (...) in criticizing Russell’s multiple relation theory of judgment. (shrink)

In his new introduction to the 1925 second edition of Principia Mathematica, Russell maintained that by adopting Wittgenstein's idea that a logically perfect language should be extensional mathematical induction could be rectified for finite cardinals without the axiom of reducibility. In an Appendix B, Russell set forth a proof. Godel caught a defect in the proof at *89.16, so that the matter of rectification remained open. Myhill later arrived at a negative result: Principia with extensionality principles and without reducibility cannot (...) recover mathematical induction. The finite cardinals are indefinable in it. This paper shows that while Gödel and Myhill are correct, Russell was not wrong. The 1925 system employs a different grammar than the original Principia. A new proof for *89.16 is given and induction is recovered. (shrink)

Bernard Linsky, The Evolution of Principia Mathematica; Bertrand Russell's Manuscripts and Notes for the Second Edition. Cambridge: Cambridge University Press. 2011. 407 pp. + two plates. $150.00/£...

Principia Mathematic goes to great lengths to hide its order/type indices and to make it appear as if its incomplete symbols behave as if they are singular terms. But well-hidden as they are, we cannot understand the proofs in Principia unless we bring them into focus. When we do, some rather surprising results emerge ? which is the subject of this paper.