•  21
    Rigorous yet engaging and accessible, Introduction to Formal Logic with Philosophical Applications is composed of two parts. The first part provides a focused, "nuts-and-bolts" introduction to formal deductive logic that covers syntax, semantics, translation, and natural deduction forpropositional and predicate logics. The second part presents student-friendly essays on logic and its applications in philosophy and beyond, with writing prompts and suggestions for further reading.
  •  7
    Introduction to Formal Logic
    Oxford University Press. 2018.
    Rigorous yet intuitive and accessible, Introduction to Formal Logic provides a focused, "nuts-and-bolts" introduction to formal deductive logic that covers syntax, semantics, translation, and natural deduction for propositional and predicate logics. For instructors who want to go beyond a basic introduction to explore the connection between formal logic techniques and philosophy, Oxford also publishes Introduction to Formal Logic with Philosophical Applications, an extended version of this text …Read more
  •  10
    Review of Philosophy Camps for Youth: Everything You Wanted to Know about Starting, Organizing, and Running a Philosophy Camp. Edited by Claire Elise Katz
  •  61
    Scaffolding for Fine Philosophical Skills
    American Association of Philosophy Teachers Studies in Pedagogy 5 34-67. 2019.
    Philosophy students often struggle to master the complex skills needed to succeed in their work, especially in writing thesis-driven essays. Research over the past forty years on instructional scaffolding, both generally and as applied in philosophy, has helped teachers to refine both instruction and assignment design to improve students’ performance on complex philosophical tasks. This essay reviews the fundamentals of scaffolding in order to motivate and support some innovative in-class exerci…Read more
  •  38
    Philosophical Method
    The Philosophers' Magazine 85 62-67. 2019.
    Observations on philosophical methods
  •  122
    The Eleatic and the Indispensabilist
    Theoria 30 (3): 415-429. 2015.
    The debate over whether we should believe that mathematical objects exist quickly leads to the question of how to determine what we should believe. Indispensabilists claim that we should believe in the existence of mathematical objects because of their ineliminable roles in scientific theory. Eleatics argue that only objects with causal properties exist. Mark Colyvan’s recent defenses of Quine’s indispensability argument against some contemporary eleatics attempt to provide reasons to favor the …Read more
  •  284
    Structuralism, Indispensability, and the Access Problem
    Facta Philosophica 9 (1): 203-211. 2007.
    The access problem for mathematics arises from the supposition that the referents of mathematical terms inhabit a realm separate from us. Quine’s approach in the philosophy of mathematics dissolves the access problem, though his solution sometimes goes unrecognized, even by those who rely on his framework. This paper highlights both Quine’s position and its neglect. I argue that Michael Resnik’s structuralist, for example, has no access problem for the so-called mathematical objects he posits…Read more
  •  38
    This book includes detailed critical analysis of a wide variety of versions of the indispensability argument, as well as a novel approach to traditional views about mathematics
  •  62
    The debate over whether we should believe that mathematical objects exist quickly leads to the question of how to determine what we should believe. Indispensabilists claim that we should believe in the existence of mathematical objects because of their ineliminable roles in scientific theory. Eleatics argue that only objects with causal properties exist. Mark Colyvan’s recent defenses of Quine’s indispensability argument against some contemporary eleatics attempt to provide reasons to favor the …Read more
  •  64
    How Not to Enhance the Indispensability Argument
    Philosophia Mathematica 22 (3): 345-360. 2014.
    The new explanatory or enhanced indispensability argument alleges that our mathematical beliefs are justified by their indispensable appearances in scientific explanations. This argument differs from the standard indispensability argument which focuses on the uses of mathematics in scientific theories. I argue that the new argument depends for its plausibility on an equivocation between two senses of explanation. On one sense the new argument is an oblique restatement of the standard argument. O…Read more
  •  87
    The holistic presumptions of the indispensability argument
    Synthese 191 (15): 3575-3594. 2014.
    The indispensability argument is sometimes seen as weakened by its reliance on a controversial premise of confirmation holism. Recently, some philosophers working on the indispensability argument have developed versions of the argument which, they claim, do not rely on holism. Some of these writers even claim to have strengthened the argument by eliminating the controversial premise. I argue that the apparent removal of holism leaves a lacuna in the argument. Without the holistic premise, or som…Read more
  •  480
    Numbers without Science
    Dissertation, The Graduate School and University Center of the City University of New York. 2007.
    Numbers without Science opposes the Quine-Putnam indispensability argument, seeking to undermine the argument and reduce its profound influence. Philosophers rely on indispensability to justify mathematical knowledge using only empiricist epistemology. I argue that we need an independent account of our knowledge of mathematics. The indispensability argument, in broad form, consists of two premises. The major premise alleges that we are committed to mathematical objects if science requires th…Read more
  •  109
    Intrinsic Explanation and Field’s Dispensabilist Strategy
    International Journal of Philosophical Studies 21 (2): 163-183. 2013.
    Philosophy of mathematics for the last half-century has been dominated in one way or another by Quine’s indispensability argument. The argument alleges that our best scientific theory quantifies over, and thus commits us to, mathematical objects. In this paper, I present new considerations which undermine the most serious challenge to Quine’s argument, Hartry Field’s reformulation of Newtonian Gravitational Theory
  •  167
    An historical introduction to the philosophy of mathematics (edited book)
    Bloomsbury Academic. 2016.
    Brings together an impressive collection of primary sources from ancient and modern philosophy. Arranged chronologically and featuring introductory overviews explaining technical terms, this accessible reader is easy-to-follow and unrivaled in its historical scope. With selections from key thinkers such as Plato, Aristotle, Descartes, Hume and Kant, it connects the major ideas of the ancients with contemporary thinkers. A selection of recent texts from philosophers including Quine, Putnam, Field…Read more