•  3
    Leonard, Goodman, and the Development of the Calculus of Individuals
    In Gerhard Ernst, Jakob Steinbrenner & Oliver R. Scholz (eds.), From Logic to Art: Themes from Nelson Goodman, Ontos. pp. 51-70. 2009.
  • Destroying artworks
    In Christy Mag Uidhir (ed.), Art and Abstract Objects, Oxford University Press. 2013.
  •  3
    The Cambridge Handbook of Analytic Philosophy (edited book)
    Cambridge University Press. forthcoming.
  •  131
    Logic and science: science and logic
    Synthese 199 (3-4): 6429-6454. 2021.
    According to Ole Hjortland, Timothy Williamson, Graham Priest, and others, anti-exceptionalism about logic is the view that logic “isn’t special”, but is continuous with the sciences. Logic is revisable, and its truths are neither analytic nor a priori. And logical theories are revised on the same grounds as scientific theories are. What isn’t special, we argue, is anti-exceptionalism about logic. Anti-exceptionalists disagree with one another regarding what logic and, indeed, anti-exceptionalis…Read more
  •  507
    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 quantier `there exists' varies in such debates: according to one opponent in this dispute, some existential statement claim…Read more
  •  116
    Somehow Things Do Not Relate: On the Interpretation of Polyadic Second-Order Logic
    Journal of Philosophical Logic 44 (3): 341-350. 2015.
    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 argue…Read more
  •  31
    Essays on Frege's Basic Laws of Arithmetic (edited book)
    Oxford University Press. 2019.
    The volume is the first collection of essays that focuses on Gottlob Frege's Basic Laws of Arithmetic (1893/1903), highlighting both the technical and the philosophical richness of Frege's magnum opus. It brings together twenty-two renowned Frege scholars whose contributions discuss a wide range of topics arising from both volumes of Basic Laws of Arithmetic. The original chapters in this volume make vivid the importance and originality of Frege's masterpiece, not just for Frege scholars but for…Read more
  •  2
    Destroying Artworks
    In Christy Mag Uidhir (ed.), Art & Abstract Objects, Oxford University Press. 2013.
    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…Read more
  •  54
    Gottlob Frege: Basic Laws of Arithmetic (edited book)
    Oxford University Press. 1964.
    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
  •  231
    Logical Consequence for Nominalists
    Theoria 24 (2): 147-168. 2009.
    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.
  •  103
    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, how…Read more
  •  87
    First-order logic, second-order logic, and completeness
    In Vincent Hendricks, Fabian Neuhaus, Stig Andur Pedersen, Uwe Scheffler & Heinrich Wansing (eds.), First-Order Logic Revisited, Logos. pp. 303-321. 2004.
    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.
  •  127
    Blanchette on Frege on Analysis and Content
    Journal for the History of Analytical Philosophy 3 (7). 2015.
    All contributions included in the present issue were originally presented at an ‘Author Meets Critics’ session organised by Richard Zach at the Pacific Meeting of the American Philosophical Association in San Diego in the Spring of 2014.
  •  78
    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 "episte…Read more
  •  493
    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 defect…Read more
  •  98
    Too Good to be “Just True”
    Thought: A Journal of Philosophy 2 (1): 1-8. 2013.
    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 ind…Read more
  •  8
    Basic Laws of Arithmetic (edited book)
    Oxford University Press UK. 2013.
    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.
  •  168
    Ed Zalta's Version of Neo-Logicism: a friendly letter of complaint
    In Hannes Leitgeb & Alexander Hieke (eds.), Reduction – Abstraction – Analysis, Ontos. pp. 11--305. 2009.
    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).
  •  27
    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 epistemolo…Read more
  •  46
    Nelson Goodman
    The Stanford Encyclopedia of Philosophy. 2014.
    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 Goo…Read more
  •  60
    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 …Read more
  •  47
    Nelson Goodman
    Routledge. 2006.
    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 Goo…Read more