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Gregory Landini [67]Gregory Thomas Landini [1]Gregory C. Landini [1]
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Gregory Landini
University of Iowa
  1.  48
    Russell’s Hidden Substitutional Theory.Gregory Landini - 1998 - 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 The heart of Landini's book is a careful analysis of Russell's largely unpublished "substitutional" theory.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.  27
    Russell.Gregory Landini - 2010 - 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.  32
    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 In Wittgenstein's Apprenticeship with Russell, Gregory Landini draws extensively from his work on Russell's unpublished manuscripts to show that the consensus characterises Russell with positions he did not hold.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. Frege's Notations: What They Are and How They Mean.Gregory Landini - 2012 - Palgrave-Macmillan.
  5.  4
    Philip A. Ebert and Marcus Rossberg, Eds.Essays on Frege’s Basic Laws of Arithmetic. [REVIEW]Gregory Landini - forthcoming - Philosophia Mathematica:nkaa013.
    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.
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  6. 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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  7.  43
    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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  8.  78
    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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  9.  57
    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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  10.  21
    Russell's Separation of the Logical and Semantic Paradoxes.Gregory Landini - 2004 - Revue Internationale de Philosophie 3:257-294.
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  11.  23
    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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  12. The Paradoxes of Subjectivity and the Projective Structure of Consciousness.Kenneth Williford, David Rudrauf & Gregory Landini - 2012 - In Miguens & Preyer (eds.), Consciousness and Subjectivity. Ontos Verlag. pp. 47--321.
     
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  13.  19
    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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  14.  21
    New Evidence Concerning Russell's Substitutional Theory of Classes.Gregory Landini - 1989 - Russell: The Journal of Bertrand Russell Studies 9 (1):26.
  15.  35
    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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  16.  35
    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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  17.  9
    "On Denoting" Against Denoting.Gregory Landini - 1998 - Russell: The Journal of Bertrand Russell Studies 18 (1).
  18.  13
    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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  19.  41
    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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  20.  57
    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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  21. Logicism without Peano 4.Gregory Landini - 2007 - Soochow Journal of Philosophical Studies 16:69 - 91.
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  22.  64
    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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  23.  4
    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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  24.  20
    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.
  25.  19
    How to Russell Another Meinongian: A Russellian Theory of Fictional Objects Versus Zalta's Theory of Abstract Objects.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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  26.  69
    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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  27. 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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  28.  48
    Ontology Made Easy By Amie L. Thomasson.Gregory Landini - 2017 - Analysis 77 (1):243-246.
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  29.  20
    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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  30.  26
    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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  31.  20
    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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  32.  29
    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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  33.  32
    Erik C. Banks, The Realistic Empiricism of Mach, James and Russell. [REVIEW]Gregory Landini - 2016 - Hopos: The Journal of the International Society for the History of Philosophy of Science 6 (2):329-333.
  34.  31
    Reviews of 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 Burke, Dewey's New Logic: A Reply to Russell. Chicago: University of Chicago, 1994. XII+288 Pp. £25.50/$36.75 M. Pinkal Logic and Lexicon: The Semantics of the Indefinite. Translated From the German by G.Simmons. Dordrecht: Kluwer, 1995. XVIII + 378 Pp. £74.00/ $93/175 Dfl M. Pinkal Logic and Lexicon: The Semantics of the Indefinite. Translated From the German by G.Simmons. Dordrecht: Kluwer, 1995. XVIII + 378 Pp. £74.00/ $93/175 Dfl Nicholas Rescher, Essays in the History of Philosophy. Aldershot: Avebury, 1995. VII + 373 Pp. £42.50 Christian Thiel, Philosophie Und Mathematik. Eine Einführung in Ihre Wechsel-Wirkungen Und in Die Philosophie der Mathematik. Darmstadt: Wissenschaftliche Buchgesellschaft, 1995. 364 Pp. Isbn 3-534 05990-5. No Price Stated Jon Barwise and John Etchemen. [REVIEW]C. Hill, Bertil Rolf, Gregory Landini, Timothy Williamson & Desmond Henry - 1996 - History and Philosophy of Logic 17 (1 & 2):85-119.
  35.  7
    Yablo’s Paradox and Russellian Propositions.Gregory Landini - 2008 - Russell: The Journal of Bertrand Russell Studies 28 (2).
    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 with natural numbers. Yablo opens his “Paradox without Self-Reference” with the assumption that there is a sequence such that: Sn: “” Each sentence on Yablo’s list is supposed to be correlated one-one (...)
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  36.  86
    Wittgenstein's Notes on Logic – Michael Potter. [REVIEW]Gregory Landini - 2010 - Philosophical Quarterly 60 (240):645-648.
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  37.  28
    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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  38.  26
    Gregory Landini. Zermelo and Russell’s Paradox: Is There a Universal Set?: Correction Notice.Gregory Landini - 2014 - Philosophia Mathematica 22 (1):142-142.
  39.  7
    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.
  40.  9
    On the Curious Calculi of Wittgenstein and Spencer Brown.Gregory Landini - 2018 - Journal for the History of Analytical Philosophy 6 (10).
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  41.  41
    The Persistence of Counterexample: Re-Examining the Debate Over Leibniz Law.Gregory Landini & Thomas R. Foster - 1991 - Noûs 25 (1):43-61.
  42.  17
    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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  43.  37
    Russellian Facts About the Slingshot.Gregory Landini - 2014 - Axiomathes 24 (4):533-547.
    The so-called “Slingshot” argument purports to show that an ontology of facts is untenable. In this paper, we address a minimal slingshot restricted to an ontology of physical facts as truth-makers for empirical physical statements. Accepting that logical matters have no bearing on the physical facts that are truth-makers for empirical physical statements and that objects are themselves constituents of such facts, our minimal slingshot argument purportedly shows that any two physical statements with empirical content are made true by one (...)
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  44.  18
    Russell and the Ontological Argument: It is Well Known That in Principia Mathematica Russell Offers a Theory of Definite Descriptions and Holds That ‘Existence’ is Not a Property. It is Less Well Known That in “On Denoting” He Discusses the Version of Anselm’s Ontological Argument for God Formulated by Descartes, Accepting the Premiss “Existence is a Perfection” and Assessing the Argument as Valid but Question-Begging. This is Different From His Later Comments in A History of Western Philosophy Which Find the Argument Invalid. Indeed, Given the Sanctions of Principia, One Might Have Thought He Would Find the Argument Logically Ungrammatical. This Paper Shows How Russell Might Formulate and Evaluate Anselm’s Ontological Argument and the Version Offered by Descartes in a Way That Avoids the Conflict.Gregory Landini - 2009 - Russell: The Journal of Bertrand Russell Studies 29 (2).
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  45.  2
    Wittgenstein's Tractarian Apprenticeship.Gregory Landini - 2003 - Russell: The Journal of Bertrand Russell Studies 23 (2).
    The years since the publication of Wittgenstein's Tractatus have produced a good many interpretations of its central tenets. Time has produced something of a consensus concerning the nature of the Tractarian criticisms of Russell's philosophy. Recent work on Russell's philosophy of logic reveals, however, that the agreed account of Tractarian criticisms relies upon characterizing Russell with positions he did not hold.
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  46.  22
    The Collected Papers of Bertrand Russell, Volume 5: Toward Principia Mathematica, 1905–1908.Gregory Landini - 2015 - History and Philosophy of Logic 36 (2):162-178.
  47.  38
    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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  48.  27
    Review: D. Bostock. Russell’s Logical Atomism. [REVIEW]Gregory Landini - 2013 - Journal for the History of Analytical Philosophy 2 (1).
    This is review of D. David Bostock. Russell’s Logical Atomism.
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  49.  9
    Well-Ordering in the Russell–Newman Controversy.Gregory Landini - 2017 - Russell: The Journal of Bertrand Russell Studies 37 (2).
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  50.  32
    Words Without Objects: Semantics, Ontology, and Logic for Non-Singularity.Gregory Landini - 2009 - History and Philosophy of Logic 30 (2):204-208.
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