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Marcus Rossberg
University of Connecticut
Marcus Rossberg
University of Connecticut
  1. Basic Laws of Arithmetic.Philip A. Ebert & Marcus Rossberg (eds.) - 2013 - Oxford University Press UK.
    This is the first complete English translation of Gottlob Frege's Grundgesetze der Arithmetik, with introduction and annotation. The importance of Frege's ideas within contemporary philosophy would be hard to exaggerate. He was, to all intents and purposes, the inventor of mathematical logic, and the influence exerted on modern philosophy of language and logic, and indeed on general epistemology, by the philosophical framework.
     
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  2.  17
    Nelson Goodman.Daniel Cohnitz & Marcus Rossberg - 2006 - Routledge.
    Nelson Goodman's acceptance and critique of certain methods and tenets of positivism, his defence of nominalism and phenomenalism, his formulation of a new riddle of induction, his work on notational systems, and his analysis of the arts place him at the forefront of the history and development of American philosophy in the twentieth-century. However, outside of America, Goodman has been a rather neglected figure. In this first book-length introduction to his work Cohnitz and Rossberg assess Goodman's lasting contribution to philosophy (...)
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  3. On the Logic of Quantifier Variance.Marcus Rossberg - manuscript
    Eli Hirsch recently suggested the metaontological doctrine of so-called "quantifier variance", according to which ontological disputes—e.g. concerning the question whether arbitrary, possibly scattered, mereological fusions exist, in the sense that these are recognised as objects proper in our ontology—can be defused as insubstantial. His proposal is that the meaning of the quanti er `there exists' varies in such debates: according to one opponent in this dispute, some existential statement claiming the existence of, e.g., a scattered object is true, according to (...)
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  4.  67
    Too Good to Be “Just True”.Marcus Rossberg - 2013 - Thought: A Journal of Philosophy 2 (1):1-8.
    Paraconsistent and dialetheist approaches to a theory of truth are faced with a problem: the expressive resources of the logic do not suffice to express that a sentence is just true—i.e., true and not also false—or to express that a sentence is consistent. In his recent book, Spandrels of Truth, Jc Beall proposes a ‘just true’-operator to identify sentences that are true and not also false. Beall suggests seven principles that a ‘just true’-operator must fulfill, and proves that his operator (...)
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  5. Cantor on Frege's Foundations of Arithmetic : Cantor's 1885 Review of Frege's Die Grundlagen der Arithmetik.Marcus Rossberg & Philip A. Ebert - 2009 - History and Philosophy of Logic 30 (4):341-348.
    In 1885, Georg Cantor published his review of Gottlob Frege's Grundlagen der Arithmetik . In this essay, we provide its first English translation together with an introductory note. We also provide a translation of a note by Ernst Zermelo on Cantor's review, and a new translation of Frege's brief response to Cantor. In recent years, it has become philosophical folklore that Cantor's 1885 review of Frege's Grundlagen already contained a warning to Frege. This warning is said to concern the defectiveness (...)
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  6.  35
    The Convenience of the Typesetter; Notation and Typography in Frege’s Grundgesetze der Arithmetik.Jim J. Green, Marcus Rossberg & A. Ebert Philip - 2015 - Bulletin of Symbolic Logic 21 (1):15-30.
    We discuss the typography of the notation used by Gottlob Frege in his Grundgesetze der Arithmetik.
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  7.  72
    Open-Endedness, Schemas and Ontological Commitment.Nikolaj Jang Lee Linding Pedersen & Marcus Rossberg - 2010 - Noûs 44 (2):329-339.
    Second-order axiomatizations of certain important mathematical theories—such as arithmetic and real analysis—can be shown to be categorical. Categoricity implies semantic completeness, and semantic completeness in turn implies determinacy of truth-value. Second-order axiomatizations are thus appealing to realists as they sometimes seem to offer support for the realist thesis that mathematical statements have determinate truth-values. The status of second-order logic is a controversial issue, however. Worries about ontological commitment have been influential in the debate. Recently, Vann McGee has argued that one (...)
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  8.  11
    Blanchette on Frege on Analysis and Content.Marcus Rossberg - 2015 - Journal for the History of Analytical Philosophy 3 (7).
  9.  85
    Logical Consequence for Nominalists.Marcus Rossberg & Daniel Cohnitz - 2009 - Theoria: Revista de Teoría, Historia y Fundamentos de la Ciencia 24 (2):147-168.
    It is often claimed that nominalistic programmes to reconstruct mathematics fail, since they will at some point involve the notion of logical consequence which is unavailable to the nominalist. In this paper we use an idea of Goodman and Quine to develop a nominalistically acceptable explication of logical consequence.
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  10.  15
    Gottlob Frege: Basic Laws of Arithmetic.Philip A. Ebert & Marcus Rossberg (eds.) - 2013 - Oxford University Press.
    This is the first complete English translation of Gottlob Frege's Grundgesetze der Arithmetik (1893 and 1903), with introduction and annotation. As the culmination of his ground-breaking work in the philosophy of logic and mathematics, Frege here tried to show how the fundamental laws of arithmetic could be derived from purely logical principles.
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  11. First-Order Logic, Second-Order Logic, and Completeness.Marcus Rossberg - 2004 - In Vincent Hendricks, Fabian Neuhaus, Stig Andur Pedersen, Uwe Scheffler & Heinrich Wansing (eds.), First-Order Logic Revisited. Logos. pp. 303-321.
    This paper investigates the claim that the second-order consequence relation is intractable because of the incompleteness result for SOL. The opponents’ claim is that SOL cannot be proper logic since it does not have a complete deductive system. I argue that the lack of a completeness theorem, despite being an interesting result, cannot be held against the status of SOL as a proper logic.
     
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  12. Ed Zalta's Version of Neo-Logicism: A Friendly Letter of Complaint.Philip A. Ebert & Marcus Rossberg - 2009 - In Hannes Leitgeb & Alexander Hieke (eds.), Reduction – Abstraction – Analysis. Ontos. pp. 11--305.
    In this short letter to Ed Zalta we raise a number of issues with regards to his version of Neo-Logicism. The letter is, in parts, based on a longer manuscript entitled “What Neo-Logicism could not be” which is in preparation. A response by Ed Zalta to our letter can be found on his website: http://mally.stanford.edu/publications.html (entry C3).
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  13.  79
    Somehow Things Do Not Relate: On the Interpretation of Polyadic Second-Order Logic.Marcus Rossberg - 2015 - Journal of Philosophical Logic 44 (3):341-350.
    Boolos has suggested a plural interpretation of second-order logic for two purposes: to escape Quine’s allegation that second-order logic is set theory in disguise, and to avoid the paradoxes arising if the second-order variables are given a set-theoretic interpretation in second-order set theory. Since the plural interpretation accounts only for monadic second-order logic, Rayo and Yablo suggest an new interpretation for polyadic second-order logic in a Boolosian spirit. The present paper argues that Rayo and Yablo’s interpretation does not achieve the (...)
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  14.  78
    Monism, Pluralism and Relativism: New Essays on the Status of Logic.Daniel Cohnitz, Peter Pagin & Marcus Rossberg - 2014 - Erkenntnis 79 (S2):201-210.
  15. Destroying Artworks.Marcus Rossberg - 2013 - In Christy Mag Uidhir (ed.), Art & Abstract Objects. Oxford University Press.
    This paper investigates feasible ways of destroying artworks, assuming they are abstract objects, or works of a particular art-form, where the works of at least this art-form are assumed to be abstracta. If artworks are eternal, mind-independent abstracta, and hence discovered, rather than created, then they cannot be destroyed, but merely forgotten. For more moderate conceptions of artworks as abstract objects, however, there might be logical space for artwork destruction. Artworks as abstracta have been likened to impure sets (i.e., sets (...)
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  16.  43
    Second-Order Logic : Ontological and Epistemological Problems.Marcus Rossberg - unknown
    In this thesis I provide a survey over different approaches to second-order logic and its interpretation, and introduce a novel approach. Of special interest are the questions whether second-order logic can count as logic in some proper sense of logic, and what epistemic status it occupies. More specifically, second-order logic is sometimes taken to be mathematical, a mere notational variant of some fragment of set theory. If this is the case, it might be argued that it does not have the (...)
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  17.  14
    Nelson Goodman.Daniel Cohnitz & Marcus Rossberg - 2014 - The Stanford Encyclopedia of Philosophy.
    Nelson Goodman's acceptance and critique of certain methods and tenets of positivism, his defence of nominalism and phenomenalism, his formulation of a new riddle of induction, his work on notational systems, and his analysis of the arts place him at the forefront of the history and development of American philosophy in the twentieth-century. However, outside of America, Goodman has been a rather neglected figure. In this first book-length introduction to his work Cohnitz and Rossberg assess Goodman's lasting contribution to philosophy (...)
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  18. Leonard, Goodman, and the Development of the Calculus of Individuals.Marcus Rossberg - 2009 - In G. Ernst, O. Scholz & J. Steinbrenner (eds.), Nelson Goodman: From Logic to Art. Ontos.
    This paper investigates the relation of the Calculus of Individuals presented by Henry S. Leonard and Nelson Goodman in their joint paper, and an earlier version of it, the so-called Calculus of Singular Terms, introduced by Leonard in his Ph.D. dissertation thesis Singular Terms. The latter calculus is shown to be a proper subsystem of the former. Further, Leonard’s projected extension of his system is described, and the definition of an intensional part-relation in his system is proposed. The final section (...)
     
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  19.  60
    What is the Purpose of Neo-Logicism?Marcus Rossberg & Philip A. Ebert - 2007 - Traveaux de Logique 18:33-61.
    This paper introduces and evaluates two contemporary approaches of neo-logicism. Our aim is to highlight the differences between these two neo-logicist programmes and clarify what each projects attempts to achieve. To this end, we first introduce the programme of the Scottish school – as defended by Bob Hale and Crispin Wright1 which we believe to be a..
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  20. McGee on Open-Ended Schemas.Nikolaj Jang Lee Linding Pedersen & Marcus Rossberg - 2007 - In Helen Bohse & Sven Walter (eds.), Selected Contributions to GAP.6: Sixth International Conference of the German Society for Analytical Philosophy, Berlin, 11–14 September 2006. mentis.
    Vann McGee claims that open-ended schemas are more innocuous than ordinary second-order quantification, particularly in terms of ontological commitment. We argue that this is not the case.
     
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  21.  1
    Logical Consequence for Nominalists.Marcus Rossberg & Daniel Cohnitz - 2009 - Theoria : An International Journal for Theory, History and Fundations of Science 24 (2):147-168.
    It is often claimed that nominalistic programmes to reconstruct mathematics fail, since they will at some point involve the notion of logical consequence which is unavailable to the nominalist. In this paper we use an idea of Goodman and Quine to develop a nominalistically acceptable explication of logical consequence.
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  22.  1
    Logical Consequence for Nominalists.Marcus Rossberg & Daniel Cohnitz - 2009 - Theoria: Revista de Teoría, Historia y Fundamentos de la Ciencia 24 (2):147-168.
    It has repeatedly been argued that nominalistic programmes in the philosophy of mathematics fail, since they will at some point or other involve the notion of logical consequence which is unavailable to the nominalist. In this paper we will argue that this is not the case. Using an idea of Nelson Goodman andW.V. Quine’s which they developed in Goodman and Quine and supplementing it with means that should be nominalistically acceptable, we present a way to explicate logical consequence in a (...)
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  23. Abstractionism: Essays in Philosophy of Mathematics.Philip A. Ebert & Marcus Rossberg - 2016 - Oxford University Press UK.
    Abstractionism, which is a development of Frege's original Logicism, is a recent and much debated position in the philosophy of mathematics. This volume contains 16 original papers by leading scholars on the philosophical and mathematical aspects of Abstractionism. After an extensive editors' introduction to the topic of abstractionism, the volume is split into 4 sections. The contributions within these sections explore the semantics and meta-ontology of Abstractionism, abstractionist epistemology, the mathematics of Abstractionis, and finally, Frege's application constraint within an abstractionist (...)
     
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  24. Essays on Frege's Basic Laws of Arithmetic.Philip A. Ebert & Marcus Rossberg (eds.) - forthcoming - Oxford University Press.
  25. Introduction to Abstractionism.Philip A. Ebert & Marcus Rossberg - 2016 - In Philip A. Ebert & Marcus Rossberg (eds.), Abstractionism. Oxford: Oxford University Press. pp. 3-33.
  26. Translators' Introduction.Philip A. Ebert & Marcus Rossberg - 2013 - In Gottlob Frege (ed.), Basic Laws of Arithmetic, Derived Using Concept-Script: Volumes I & II. Oxford: Oxford University Press.
  27. Die Vertreibung aus dem Platonischen Paradies.Marcus Rossberg - 2006 - Erwägen – Wissen – Ethik 17 (Naturalism in Mathematics):387–389.