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Gregory Landini [73]Gregory C. Landini [1]Gregory Thomas Landini [1]
  1.  70
    Russell's hidden substitutional theory.Gregory Landini - 1998 - New York: Oxford University Press.
    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 The heart of Landini's book is a careful analysis of Russell's largely unpublished "substitutional" theory.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 (...)
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  2.  42
    Russell.Gregory Landini - 2011 - New York: Routledge.
    Landini discusses the second edition of Principia Mathematica, to show Russella (TM)s intellectual relationship with Wittgenstein and Ramsey.
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  3.  47
    Wittgenstein's Apprenticeship with Russell.Gregory Landini - 2007 - Cambridge University Press.
    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 In Wittgenstein's Apprenticeship with Russell, Gregory Landini draws extensively from his work on Russell's unpublished manuscripts to show that the consensus characterises Russell with positions he did not hold.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 (...)
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  4.  28
    Frege's Notations: What They Are and How They Mean.Gregory Landini - 2011 - London and Basingstoke: Palgrave-Macmillan.
    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.
  5.  42
    Stipulations Missing Axioms in Frege's Grundgesetze der Arithmetik.Gregory Landini - 2022 - History and Philosophy of Logic 43 (4):347-382.
    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 (...)
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  6. A new interpretation of russell's multiple-relation theory of judgment.Gregory Landini - 1991 - History and Philosophy of Logic 12 (1):37-69.
    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 (...)
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  7.  57
    How to Russell Another Meinongian.Gregory Landini - 1990 - Grazer Philosophische Studien 37 (1):93-122.
    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 (...)
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  8.  46
    The Philosophy of Logical Atomism: A Centenary Reappraisal.Landon D. C. Elkind & Gregory Landini (eds.) - 2018 - New York, NY, USA: Palgrave Macmillan.
    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 (...)
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  9.  34
    New Evidence concerning Russell's Substitutional Theory of Classes.Gregory Landini - 1989 - Russell: The Journal of Bertrand Russell Studies 9 (1):26.
  10.  19
    Well-Ordering in the Russell–Newman Controversy.Gregory Landini - 2017 - Russell: The Journal of Bertrand Russell Studies 37 (2).
    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.
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  11.  76
    Truth, Predication and a Family of Contingent Paradoxes.Francesco Orilia & Gregory Landini - 2019 - Journal of Philosophical Logic 48 (1):113-136.
    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 (...)
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  12.  56
    Logic in Russell's Principles of Mathematics.Gregory Landini - 1996 - Notre Dame Journal of Formal Logic 37 (4):554-584.
    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 (...)
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  13.  44
    How to Russell Another Meinongian.Gregory Landini - 1990 - Grazer Philosophische Studien 37 (1):93-122.
    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 (...)
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  14.  82
    The Ins and Outs of Frege's Way Out.Gregory Landini - 2006 - Philosophia Mathematica 14 (1):1-25.
    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 (...)
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  15.  91
    Cocchiarella’s Formal Ontology and the Paradoxes of Hyperintensionality.Gregory Landini - 2009 - Axiomathes 19 (2):115-142.
    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.
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  16.  27
    "On Denoting" against Denoting.Gregory Landini - 1998 - Russell: The Journal of Bertrand Russell Studies 18 (1).
  17. Wittgensteinian : Looking at the World From the Viewpoint of Wittgenstein’s Philosophy.A. C. Grayling, Shyam Wuppuluri, Christopher Norris, Nikolay Milkov, Oskari Kuusela, Danièle Moyal-Sharrock, Beth Savickey, Jonathan Beale, Duncan Pritchard, Annalisa Coliva, Jakub Mácha, David R. Cerbone, Paul Horwich, Michael Nedo, Gregory Landini, Pascal Zambito, Yoshihiro Maruyama, Chon Tejedor, Susan G. Sterrett, Carlo Penco, Susan Edwards-Mckie, Lars Hertzberg, Edward Witherspoon, Michel ter Hark, Paul F. Snowdon, Rupert Read, Nana Last, Ilse Somavilla & Freeman Dyson (eds.) - 2019 - Springer Verlag.
    “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 (...)
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  18.  13
    The Paradoxes of Subjectivity and the Projective Structure of Consciousness.Kenneth Williford, David Rudrauf & Gregory Landini - 2012 - In Sofia Miguens & Gerhard Preyer (eds.), Consciousness and Subjectivity. [Place of publication not identified]: Ontos Verlag. pp. 321-354.
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  19.  71
    Decomposition and analysis in Frege’s Grundgesetze.Gregory Landini - 1996 - History and Philosophy of Logic 17 (1-2):121-139.
    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 (...)
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  20.  34
    Russell's Separation of the Logical and Semantic Paradoxes.Gregory Landini - 2004 - Revue Internationale de Philosophie 3:257-294.
  21.  40
    Whitehead's (Badly) Emended Principia.Gregory Landini - 2016 - History and Philosophy of Logic 37 (2):114-169.
    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 (...)
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  22.  58
    Russell's Schema, Not Priest's Inclosure.Gregory Landini - 2009 - History and Philosophy of Logic 30 (2):105-139.
    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 (...)
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  23.  40
    Russell's substitutional theory of classes and relations.Gregory Landini - 1987 - History and Philosophy of Logic 8 (2):171-200.
    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 (...)
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  24.  13
    Showing in Wittgenstein’s ab-Notation.Gregory Landini - 2019 - In Shyam Wuppuluri & Newton da Costa (eds.), Wittgensteinian : Looking at the World From the Viewpoint of Wittgenstein's Philosophy. Springer Verlag. pp. 193-226.
    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 (...)
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  25.  11
    Showing in Wittgenstein’s ab-Notation.Gregory Landini - 2019 - In A. C. Grayling, Shyam Wuppuluri, Christopher Norris, Nikolay Milkov, Oskari Kuusela, Danièle Moyal-Sharrock, Beth Savickey, Jonathan Beale, Duncan Pritchard, Annalisa Coliva, Jakub Mácha, David R. Cerbone, Paul Horwich, Michael Nedo, Gregory Landini, Pascal Zambito, Yoshihiro Maruyama, Chon Tejedor, Susan G. Sterrett, Carlo Penco, Susan Edwards-Mckie, Lars Hertzberg, Edward Witherspoon, Michel ter Hark, Paul F. Snowdon, Rupert Read, Nana Last, Ilse Somavilla & Freeman Dyson (eds.), Wittgensteinian : Looking at the World From the Viewpoint of Wittgenstein’s Philosophy. Springer Verlag. pp. 193-226.
    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 (...)
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  26.  96
    The definability of the set of natural numbers in the 1925 principia mathematica.Gregory Landini - 1996 - Journal of Philosophical Logic 25 (6):597 - 615.
    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 (...)
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  27.  31
    The Evolution of Principia Mathematica; Bertrand Russell's Manuscripts and Notes for the Second Edition.Gregory Landini - 2013 - History and Philosophy of Logic 34 (1):79-97.
    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/£...
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  28.  39
    Typos of Principia Mathematica.Gregory Landini - 2013 - History and Philosophy of Logic 34 (4):306 - 334.
    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.
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  29. Logicism and the Problem of Infinity: The Number of Numbers: Articles.Gregory Landini - 2011 - Philosophia Mathematica 19 (2):167-212.
    Simple-type theory is widely regarded as inadequate to capture the metaphysics of mathematics. The problem, however, is not that some kinds of structure cannot be studied within simple-type theory. Even structures that violate simple-types are isomorphic to structures that can be studied in simple-type theory. In disputes over the logicist foundations of mathematics, the central issue concerns the problem that simple-type theory fails to assure an infinity of natural numbers as objects. This paper argues that the problem of infinity is (...)
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  30.  95
    Frege’s Cardinals as Concept-correlates.Gregory Landini - 2006 - Erkenntnis 65 (2):207-243.
    In his "Grundgesetze", Frege hints that prior to his theory that cardinal numbers are objects he had an "almost completed" manuscript on cardinals. Taking this early theory to have been an account of cardinals as second-level functions, this paper works out the significance of the fact that Frege's cardinal numbers is a theory of concept-correlates. Frege held that, where n > 2, there is a one—one correlation between each n-level function and an n—1 level function, and a one—one correlation between (...)
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  31. Wittgenstein reads Russell.Gregory Landini - 2011 - In Marie McGinn & Oskari Kuusela (eds.), The Oxford Handbook of Wittgenstein. Oxford University Press.
     
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  32.  11
    7 Russell's Substitutional Theory.Gregory Landini - 2003 - In Nicholas Griffin (ed.), The Cambridge Companion to Bertrand Russell. Cambridge University Press. pp. 241.
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  33.  95
    Frege's Cardinals Do Not Always Obey Hume's Principle.Gregory Landini - 2017 - History and Philosophy of Logic 38 (2):127-153.
    Hume's Principle, dear to neo-Logicists, maintains that equinumerosity is both necessary and sufficient for sameness of cardinal number. All the same, Whitehead demonstrated in Principia Mathematica's logic of relations that Cantor's power-class theorem entails that Hume's Principle admits of exceptions. Of course, Hume's Principle concerns cardinals and in Principia's ‘no-classes’ theory cardinals are not objects in Frege's sense. But this paper shows that the result applies as well to the theory of cardinal numbers as objects set out in Frege's Grundgesetze. (...)
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  34. Solving the Conjunction Problem of Russell's Principles of Mathematics.Gregory Landini - 2020 - Journal for the History of Analytical Philosophy 8 (8).
    The quantification theory of propositions in Russell’s Principles of Mathematics has been the subject of an intensive study and in reconstruction has been found to be complete with respect to analogs of the truths of modern quantification theory. A difficulty arises in the reconstruction, however, because it presents universally quantified exportations of five of Russell’s axioms. This paper investigates whether a formal system can be found that is more faithful to Russell’s original prose. Russell offers axioms that are universally quantified (...)
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  35. On the Curious Calculi of Wittgenstein and Spencer Brown.Gregory Landini - 2018 - Journal for the History of Analytical Philosophy 6 (10).
    In his Tractatus, Wittgenstein sets out what he calls his N-operator notation which can be used to calculate whether an expression is a tautology. In his Laws of Form, George Spencer Brown offers what he calls a “primary algebra” for such calculation. Both systems are perplexing. But comparing two blurry images can reduce noise, producing a focus. This paper reveals that Spencer Brown independently rediscovered the quantifier-free part of the N-operator calculus. The comparison sheds a flood light on each and (...)
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  36.  34
    Quantification Theory in *9 of Principia Mathematica.Gregory Landini - 2000 - History and Philosophy of Logic 21 (1):57-77.
    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 (...)
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  37.  29
    Russell to Frege, 24 May 1903: "I Believe That I Have Discovered That Classes Are Completely Superfluous".Gregory Landini - 1992 - Russell: The Journal of Bertrand Russell Studies 12 (2):160-185.
    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 (...)
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  38.  32
    Salvaging 'the f-er is f': The lesson of Clark's paradox.Gregory Landini - 1985 - Philosophical Studies 48 (1):129 - 136.
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  39. Russell: Logic.Gregory Landini - 2018 - Internet Encyclopedia of Philosophy.
    Bertrand Russell: Logic For Russell, Aristotelian syllogistic inference does not do justice to the subject of logic. This is surely not surprising. It may well be something of a surprise, however, to learn that in Russell’s view neither Boolean algebra nor modern quantification theory do justice to the subject. For Russell, logic is a synthetic … Continue reading Russell: Logic →.
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  40.  48
    Putnam's model-theoretic argument, natural realism, and the standard conception of theories.Gregory Landini - 1987 - Philosophical Papers 16 (3):209-233.
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  41.  39
    Quantification Theory in *8 of Principia Mathematica and the Empty Domain.Gregory Landini - 2005 - History and Philosophy of Logic 26 (1):47-59.
    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 (...)
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  42.  50
    Words Without Objects: Semantics, Ontology, and Logic for Non-Singularity.Gregory Landini - 2009 - History and Philosophy of Logic 30 (2):204-208.
    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...
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  43.  7
    Clark’s Paradox of Castañeda’s Guises: A Brief Memoir.Gregory Landini - 2014 - In Adriano Palma (ed.), Castañeda and His Guises: Essays on the Work of Hector-Neri Castañeda. De Gruyter. pp. 67-82.
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  44.  33
    Fictions Are All in the Mind.Gregory Landini - 2012 - Revue Internationale de Philosophie 262 (4):593-614.
    Poetic license is an essential feature of intentionality. The mind is free to think about any objects, even objects with logically incompatible properties. Some philosophers maintain that a theory that embraces an ontology of objects of thought is indispensable to any account of the nature of intentionality. Any such theory, however, must face paradoxes whose solutions conflict with poetic license. In this paper, I propose a theory which rejects the argument from indispensability. The theory maintains that the intentionality of thought (...)
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  45.  30
    Fitch and Mary.Gregory Landini - 2020 - Axiomathes 30 (2):193-199.
    There is a rather famous “Fitch argument” that not everything that is true is knowable. There is a rather famous “Mary argument” that is often used to argue that reductive physicalism is false. This paper sets out the two side by side as the Fitch Knowability Paradox and the Mary Knowability Paradox. It is found that they have the same logical form and thus the question of validity can be evaluated with the same tools. Likening the two is useful, since (...)
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  46.  57
    Gregory Landini. Zermelo and Russell’s Paradox: Is There a Universal Set?: Correction Notice.Gregory Landini - 2014 - Philosophia Mathematica 22 (1):142-142.
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  47. Logicism without Peano 4.Gregory Landini - 2007 - Soochow Journal of Philosophical Studies 16:69 - 91.
     
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  48.  35
    Meinong and Russell: Some Lessons on Quantification.Gregory Landini - 2017 - Axiomathes 27 (5):455-474.
    This paper explores the thesis that de re quantification into propositional attitudes has been wrongly conceived. One must never bind an individual variable in the context of a propositional attitude. Such quantification fails to respect the quantificational scaffolding of discursive thinking. This is the lesson of the Meinong–Russell debate over whether there are objects of thought about which it is true to say they are not. Respecting it helps to see how to solve contingent Liar paradoxes of propositional attitudes such (...)
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  49.  8
    Methodological Cartesianism.Gregory Landini - 2014 - In Guido Bonino, Greg Jesson & Javier Cumpa (eds.), Defending Realism: Ontological and Epistemological Investigations. Boston: De Gruyter. pp. 63-98.
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  50.  62
    Ontology Made Easy By Amie L. Thomasson.Gregory Landini - 2017 - Analysis 77 (1):243-246.
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