
8Quine, New Foundations, and the Philosophy of Set Theory by Sean Morris (review)Journal of the History of Philosophy 59 (2): 342343. 2021.This book has two main goals: first, to show that Quine's New Foundations set theory is better motivated than often assumed; and second, to defend Quine's philosophy of set theory. It is divided into three parts. The first concerns the history of set theory and argues against readings that see the iterative conception of set being the dominant notion of set from the very beginning. The second part concerns Quine's philosophy of set theory. Part 3 is a contemporary assessment of the philosophical…Read more

1Book Reviews (review)Hopos: The Journal of the International Society for the History of Philosophy of Science 10 (1): 357361. 2020.

18Did Frege Solve One of Zeno’s Paradoxes?In Maria Zack & Dirk Schlimm (eds.), Research in History and Philosophy of Mathematics: The CSHPM 2018 Volume, Springer Verlag. pp. 99107. 2020.Of Zeno’s book of forty paradoxes, it was the first that attracted Socrates’ attention. This is the paradox of the like and the unlike. On contemporary assessments, this paradox is largely considered to be Zeno’s weakest surviving paradox. All of these assessments, however, rely heavily on reconstructions of the paradox. It is only relative to these reconstructions that there is nothing paradoxical involved, or that there is some rather obvious mistake being made. This paper puts forward and def…Read more

1Waismann: From Wittgenstein's Tafelrunde to His Writings on AnalyticityIn Dejan Makovec & Stewart Shapiro (eds.), Friedrich Waismann: The Open Texture of Analytic Philosophy. pp. 131158. 2019.Gregory Lavers gives us a timeline of Waismann’s career, an overview of Waismann’s most significant publications in this later period and a detailed walkthrough from the first to the last paper of Waismann’s series on analyticity, “Analytic  Synthetic”. Lavers closes his paper with comparisons of Waismann and Quine as well as Waismann and Carnap. Both Waismann and Quine argue that the concept of analyticity is vague and both reject reductionism. However, behind these superficial similarities we…Read more

41Hitting a Moving Target: Gödel, Carnap, and Mathematics as Logical SyntaxPhilosophia Mathematica 27 (2): 219243. 2019.From 1953 to 1959 Gödel worked on a response to Carnap’s philosophy of mathematics. The drafts display Gödel’s familiarity with Carnap’s position from The Logical Syntax of Language, but they received a dismissive reaction on their eventual, posthumous, publication. Gödel’s two principal points, however, will here be defended. Gödel, though, had wished simply to append a few paragraphs to show that the same arguments apply to Carnap’s later views. Carnap’s position, however, had changed signific…Read more

28Øystein Linnebo*. Philosophy of Mathematics (review)Philosophia Mathematica 26 (3): 413417. 2018.Øystein Linnebo*. Philosophy of Mathematics. Princeton University Press, 2017. ISBN: 9780691161402 ; 9781400885244. Pp. xviii + 203.

130Carnap, semantics and ontologyErkenntnis 60 (3): 295316. 2004.This paper will deal with three questions regarding Carnap's transition from the position he held at the time of writing Syntax to the doctrines he held during his semantic phase: (1) What was Carnap's attitude towards truth at the time of writing Syntax? (2) What was Carnap's position regarding questions of reference and ontology at the time of writing Syntax? (3) Was Carnap's acceptance of Tarski's analysis of truth and reference detrimental to his philosophical project? Section 1 of this pape…Read more

154On the Quineananalyticity of mathematical propositionsPhilosophical Studies 159 (2): 299319. 2012.This paper investigates the relation between Carnap and Quine’s views on analyticity on the one hand, and their views on philosophical analysis or explication on the other. I argue that the stance each takes on what constitutes a successful explication largely dictates the view they take on analyticity. I show that although acknowledged by neither party (in fact Quine frequently expressed his agreement with Carnap on this subject) their views on explication are substantially different. I argue t…Read more

129Benacerraf’s dilemma and informal mathematicsReview of Symbolic Logic 2 (4): 769785. 2009.This paper puts forward and defends an account of mathematical truth, and in particular an account of the truth of mathematical axioms. The proposal attempts to be completely nonrevisionist. In this connection, it seeks to satisfy simultaneously both horns of Benacerrafs work on informal rigour. Kreisel defends the view that axioms are arrived at by a rigorous examination of our informal notions, as opposed to being stipulated or arrived at by trial and error. This view is then supplemented by a…Read more

68Frege and numbers as selfsubsistent ObjectsDiscusiones Filosóficas 11 (16): 97118. 2010.This paper argues that Frege is not the metaphysical platonist about mathematics that he is standardly taken to be. It is shown that Frege’s project has two distinct stages: the identification of what is true of our ordinary notions, and then the provision of a systematic account that shares the identified features. Neither of these stages involves much metaphysics. The paper criticizes in detail Dummett’s interpretation of §§5561 of Grundlagen. These sections fall under the heading ‘Every num…Read more

22Review of Mary Leng, Mathematics and Reality (review)Notre Dame Philosophical Reviews 2010 (9). 2010.

Carnap’s ‘Empiricism, Semantics, and Ontology’ (Carnap (1950a), ESO hereafter) is certainly a classic of twentieth century analytic philosophy. For decades now, most undergraduates are expected to read it at some point in their studies. Lately, it is being seen as the inspiration for a host of positions in the field of metaontology. Despite the widespread agreement on the importance of the paper, there is a lack of agreement on what Carnap attempts to do in the paper. My main aim in this chapter…Read more

19Frege the Carnapian and Carnap the FregeanIn Early Analytic Philosophy – New Perspectives on the Tradition, Springer Verlag. pp. 353373. 2016.In this paper I examine the fundamental views on the nature of logical and mathematical truth of both Frege and Carnap. I argue that their positions are much closer than is standardly assumed. I attempt to establish this point on two fronts. First, I argue that Frege is not the metaphysical realist that he is standardly taken to be. Second, I argue that Carnap, where he does differ from Frege, can be seen to do so because of mathematical results proved in the early twentieth century. The differe…Read more

744Frege, Carnap, and Explication: ‘Our Concern Here Is to Arrive at a Concept of Number Usable for the Purpose of Science’History and Philosophy of Logic 34 (3): 22541. 2013.This paper argues that Carnap both did not view and should not have viewed Frege's project in the foundations of mathematics as misguided metaphysics. The reason for this is that Frege's project was to give an explication of number in a very Carnapian sense — something that was not lost on Carnap. Furthermore, Frege gives pragmatic justification for the basic features of his system, especially where there are ontological considerations. It will be argued that even on the question of the independ…Read more

49Review of Richard Creath, Michael Friedman (eds.), The Cambridge Companion to Carnap (review)Notre Dame Philosophical Reviews 2008 (9). 2008.

26Carnap, Quine, Quantification and OntologyIn Alessandro Torza (ed.), Quantifiers, Quantifiers, and Quantifiers: Themes in Logic, Metaphysics, and Language, Springer. 2015.Abstract At the time of The Logical Syntax of Language (Syntax), Quine was, in his own words, a disciple of Carnap’s who read this work page by page as it issued from Ina Carnap’s typewriter. The present paper will show that there were serious problems with how Syntax dealt with ontological claims. These problems were especially pronounced when Carnap attempted to deal with higher order quantification. Carnap, at the time, viewed all talk of reference as being part of the misleading material mod…Read more

82Carnap, formalism, and informal rigourPhilosophia Mathematica 16 (1): 424. 2008.Carnap's position on mathematical truth in The Logical Syntax of Language has been attacked from two sides: Kreisel argues that it is formalistic but should not be, and Friedman argues that it is not formalistic but needs to be. In this paper I argue that the Carnap of Syntax does not eliminate our ordinary notion of mathematical truth in favour of a formal analogue; so Carnap's notion of mathematical truth is not formalistic. I further argue that there is no conflict between Carnap's use of inf…Read more
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Quantification and Ontology 