My research is primarily in the history of analytic philosophy, focusing on the development of logic and its philosophy, along with mathematics and its philosophy, in the 1920s and 1930s. Particular topics that interest me include:

  • History of analytic philosophy: the interpretation of Carnap's principle of tolerance, the relationship of Carnap's logicism to Frege's, the relationship between Carnap's early investigations into model theory and the Hilbert school. A collection of internet resources for research on Carnap's life and work is here.

  • Philosophy of logic: the nature of logical consequence, logical pluralism and its relationship to other pluralisms (for example, pluralism about truth or about ontology), the possibility of disagreement about logic.

  • Philosophy of mathematics: logicism and neo-logicism, epistemology of mathematics, the epistemic status of mathematical proof, foundations of mathematics.

Refereed Publications

  1. Logical Pluralism and Paradoxical Assertions in the Philosophy of Religion (with Anand Jayprakesh Vaidya), Philosophy Compass

    Many authors show how useful logic can be as a tool for building theories that can account for problems in the philosophy of religion, such as paradoxical assertions. As a consequence, one's philosophy of logic is crucial as well, since it determines which logics, from the set of available and constructible logics, one can use to build a theory. In this paper, we present the relatively recent debate between logical pluralism and monism because the positions in this debate determine which logic(s) can, with justification, be applied to build a theory that addresses problems in the philosophy of religion. We begin by presenting the problem of paradoxical assertions and the debate over logical plural- ism that bears on the addressing paradoxical assertions. We then canvass strategies for arguing in favor of logical monism, and pluralism; ultimately, we conclude that the Western tradition has reached a stalemate on this issue. We then turn our attention to the potential for Indian reli- gious traditions to contribute to the debate. We present the five-step-syllogism from Nyāya-Hindu philosophy, the four corners of reasoning from Buddhist philosophy, and the seven-fold theory of predication from Jaina philosophy. The upshot of our presentation is to lay the groundwork for cross-traditional logical debate by identifying the ways in which Indian discussions of debate and dialogue relate to modern approaches to logic and the philosophy of logic.

  2. Logic and Liberalism, Humanities Bulletin

    What does it take for a society to become enlightened? Kant suggests that the members of it must be free to use their ‘public reason’. Arendt develops this thought, adding that we must be able to recognize the others in our society as worthy of intellectual engagement. But, what happens when we disagree in extreme ways, for example about the laws of logic? On some traditional conceptions of the connection between logic and rationality, disagreements of this kind force us to regard others in our society as irrational. In this paper, I argue that, if we want to maintain a Kantian model of enlightenment, then these kinds of disagreements push us towards a logical pluralism. I examine two forms of pluralism, Beall and Restall’s, and Carnap’s, and show that Beall and Restall’s version conceals a lurking monism, and so cannot be the kind of pluralism needed for enlightenment. But, I argue that Carnap’s pluralism is. I conclude by examining the history of Carnap’s pluralism, and show that using it for political ends – namely, for facilitating discussion in pursuit of enlightenment – is consistent with Carnap’s initial motivations for his work, and clears the way back towards Kantian enlightenment.

  3. Carnap's Tolerance and Friedman's Revenge, Logica Yearbook 2014

    In this paper, I defend Rudolf Carnap’s Principle of Tolerance from an accusation, due to Michael Friedman, that it is self-defeating by prejudicing any debate towards the logically stronger theory. In particular, Friedman attempts to show that Carnap’s reconstruction of the debate between classicists and intuitionists over the foundations of mathematics in his book The Logical Syntax of Language, is biased towards the classical standpoint since the metalanguage he constructs to adjudicate between the rival positions is fully classical. I argue that this criticism is mistaken on two counts: (1) it fails to fully appreciate the freedom with regard to the construction of linguistic frameworks that Carnap intended his Principle to embody, and (2) Friedman’s objection underestimates the extent to which the evaluation of a framework is task-relative. I conclude that Tolerance is not self-undermining in the way that Friedman claims it is. While this is a restricted conclusion – and is not a vindication of Carnap’s views on logic and mathematics tout court – it nonetheless suggests that his tolerant perspective has been dismissed too quickly, even by his supporters.

Other Publications

  1. No Ticket To Ride: A Systematic Definition of Transit Insecurity

    Chen A, Karagoel I, Friedman-Biglin N, Nathan-Roberts D.

    Proceedings of the Human Factors and Ergonomics Society Annual Meeting 2021; 65(1): 1307-1311.

    DOI: 10.1177/1071181321651291

  2. Between Realism and Explication: Review of Mark Colyvan's An Introduction to the Philosophy of Matematics, Metascience 23(2): 269 - 271

    DOI: 10.1007/s11016-013-9855-6

  3. Carnap's Conventionalism: Logic, Science, and Tolerance, Ph.D Thesis, University of St Andrews