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The Cambridge Companion to Analytic Philosophy (edited book)Cambridge University Press. forthcoming.
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6Leonard, Goodman, and the Development of the Calculus of IndividualsIn Gerhard Ernst, Jakob Steinbrenner & Oliver R. Scholz (eds.), From Logic to Art: Themes from Nelson Goodman, Ontos. pp. 51-70. 2009.
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6Ed Zalta’s Version of Neo-Logicism – a Friendly Letter of ComplaintIn Alexander Hieke & Hannes Leitgeb (eds.), Reduction, abstraction, analysis: proceedings of the 31th International Ludwig Wittgenstein-Symposium in Kirchberg, 2008, De Gruyter. pp. 305-310. 2009.
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Destroying artworksIn Christy Mag Uidhir (ed.), Art & Abstract Objects, Oxford University Press. 2013.
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33Frege's Concept-Script (Grundgesetze der Arithmetik)In Bruno Woltzenlogel Paleo & Giselle Reis (eds.), Encyclopedia of Proof Systems, College Publications. 2022.
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3The Cambridge Handbook of Analytic Philosophy (edited book)Cambridge University Press. forthcoming.
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147Logic and science: science and logicSynthese 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
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333Translators' IntroductionIn Gottlob Frege (ed.), Basic Laws of Arithmetic, Oxford University Press. 1893.
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Contemporary Reviews of Frege’s GrundgesetzeIn Philip A. Ebert & Marcus Rossberg (eds.), Essays on Frege's Basic Laws of Arithmetic, Oxford University Press. pp. 637-652. 2019.
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Mathematical Creation in Frege's GrundgesetzeIn Philip A. Ebert & Marcus Rossberg (eds.), Essays on Frege's Basic Laws of Arithmetic, Oxford University Press. pp. 325-342. 2019.
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45Essays 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
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39Review of Richard G. Heck, Jr: Reading Frege’s Grundgesetze. Oxford: Oxford University Press, 2012 (review)Notre Dame Philosophical Review 11. 2014.Scathing review of Heck's book.
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2Destroying ArtworksIn 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
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510Eli 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
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126Somehow Things Do Not Relate: On the Interpretation of Polyadic Second-Order LogicJournal 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
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57Gottlob 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
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249Logical Consequence for NominalistsTheoria 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.
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498Cantor on Frege's Foundations of Arithmetic : Cantor's 1885 Review of Frege's Die Grundlagen der ArithmetikHistory and Philosophy of Logic 30 (4): 341-348. 2009.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
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104Too 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
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Die Vertreibung aus dem Platonischen ParadiesErwägen – Wissen – Ethik 17 (Naturalism in Mathematics). 2006.
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122Open-endedness, schemas and ontological commitmentNoûs 44 (2): 329-339. 2010.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
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87First-order logic, second-order logic, and completenessIn 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.
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156Blanchette on Frege on Analysis and ContentJournal 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.
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83Second-order logic : ontological and epistemological problemsDissertation, St Andrews. 2006.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
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177Ed Zalta's Version of Neo-Logicism: a friendly letter of complaintIn 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).
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34Abstractionism: Essays in Philosophy of MathematicsOxford University Press UK. 2016.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
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14Basic 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.
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1Introduction to AbstractionismIn Philip A. Ebert & Marcus Rossberg (eds.), Abstractionism: Essays in Philosophy of Mathematics, Oxford University Press Uk. pp. 3-33. 2016.
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70What is the purpose of neo-logicism?Traveaux de Logique 18 33-61. 2007.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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120Monism, Pluralism and Relativism: New Essays on the Status of LogicErkenntnis 79 (S2): 201-210. 2014.