•  27
    Indispensability
    Cambridge University Press. 2023.
    Our best scientific theories explain a wide range of empirical phenomena, make accurate predictions, and are widely believed. Since many of these theories make ample use of mathematics, it is natural to see them as confirming its truth. Perhaps the use of mathematics in science even gives us reason to believe in the existence of abstract mathematical objects such as numbers and sets. These issues lie at the heart of the Indispensability Argument, to which this Element is devoted. The Element's f…Read more
  •  11
    Malebranche on Laws of Nature and God’s General Volitions
    History of Philosophy & Logical Analysis 7 (1): 121-133. 2004.
  •  13
    Malebranche’s Occasionalism
    American Catholic Philosophical Quarterly 79 (2): 251-272. 2005.
    The core thesis of Malebranche’s doctrine of occasionalism is that God is the sole true cause, where a true cause is one that has the power to initiate change and for which the mind perceives a necessary connection between it and its effects. Malebranche gives two separate arguments for his core thesis, T, based on necessary connection and on divine power respectively. The standard view is that these two arguments are necessary to establish T. I argue for a reinterpretation of Malebranche’s stra…Read more
  •  18
    Circularity, indispensability, and mathematical explanation in science
    Studies in History and Philosophy of Science Part A 88 (C): 156-163. 2021.
  •  194
    Simplicity
    Stanford Encyclopedia of Philosophy. 2008.
  •  28
    Bipedal Gait Costs: a new case study of mathematical explanation in science
    European Journal for Philosophy of Science 11 (3): 1-22. 2021.
    In this paper I present a case study of mathematical explanation in science that is new to the philosophical literature, and that arises in the context of estimating the energetic costs of running in bipedal animals. I refer to this as the Bipedal Gait Costs explanation. I argue that it is important for examples of applied mathematics to be driven not just by philosophical and mathematical concerns but also by scientific concerns. After a detailed presentation of the BGC case study, I discuss wa…Read more
  •  32
    Schemas for induction
    Studies in History and Philosophy of Science Part A 82 114-119. 2020.
  •  32
    Quantitative Parsimony and Explanatory Power
    British Journal for the Philosophy of Science 54 (2): 245-259. 2003.
    The desire to minimize the number of individual new entities postulated is often referred to as quantitative parsimony. Its influence on the default hypotheses formulated by scientists seems undeniable. I argue that there is a wide class of cases for which the preference for quantitatively parsimonious hypotheses is demonstrably rational. The justification, in a nutshell, is that such hypotheses have greater explanatory power than less parsimonious alternatives. My analysis is restricted to a cl…Read more
  •  131
    Does the existence of mathematical objects make a difference?
    Australasian Journal of Philosophy 81 (2). 2003.
    In this paper I examine a strategy which aims to bypass the technicalities of the indispensability debate and to offer a direct route to nominalism. The starting-point for this alternative nominalist strategy is the claim that--according to the platonist picture--the existence of mathematical objects makes no difference to the concrete, physical world. My principal goal is to show that the 'Makes No Difference' (MND) Argument does not succeed in undermining platonism. The basic reason why not is…Read more
  •  137
    Mathematical Spandrels
    Australasian Journal of Philosophy 95 (4): 779-793. 2017.
    The aim of this paper is to open a new front in the debate between platonism and nominalism by arguing that the degree of explanatory entanglement of mathematics in science is much more extensive than has been hitherto acknowledged. Even standard examples, such as the prime life cycles of periodical cicadas, involve a penumbra of mathematical features whose presence can only be explained using relatively sophisticated mathematics. I introduce the term ‘mathematical spandrel’ to describe these pe…Read more
  •  1
    Indispensability and the Existence of Mathematical Objects
    Dissertation, Princeton University. 1999.
    According to the so-called "Indispensability Argument", the central role played by mathematics in science gives us sufficient reason to believe in the existence of abstract mathematical objects such as numbers, sets, and functions. The Indispensability Argument may be formulated as follows: We ought rationally to believe our best available scientific theories. Mathematics is indispensable for science. we ought to believe in the existence of mathematical objects. Platonism is the view that there …Read more
  •  186
    Quantitative Parsimony and Explanatory Power
    British Journal for the Philosophy of Science 54 (2): 245-259. 2003.
    The desire to minimize the number of individual new entities postulated is often referred to as quantitative parsimony. Its influence on the default hypotheses formulated by scientists seems undeniable. I argue that there is a wide class of cases for which the preference for quantitatively parsimonious hypotheses is demonstrably rational. The justification, in a nutshell, is that such hypotheses have greater explanatory power than less parsimonious alternatives. My analysis is restricted to a cl…Read more
  •  175
    Science-Driven Mathematical Explanation
    Mind 121 (482): 243-267. 2012.
    Philosophers of mathematics have become increasingly interested in the explanatory role of mathematics in empirical science, in the context of new versions of the Quinean ‘Indispensability Argument’ which employ inference to the best explanation for the existence of abstract mathematical objects. However, little attention has been paid to analysing the nature of the explanatory relation involved in these mathematical explanations in science (MES). In this paper, I attack the only articulated acc…Read more
  •  470
    Many explanations in science make use of mathematics. But are there cases where the mathematical component of a scientific explanation is explanatory in its own right? This issue of mathematical explanations in science has been for the most part neglected. I argue that there are genuine mathematical explanations in science, and present in some detail an example of such an explanation, taken from evolutionary biology, involving periodical cicadas. I also indicate how the answer to my title questi…Read more
  •  551
    Mathematical Explanation in Science
    British Journal for the Philosophy of Science 60 (3): 611-633. 2009.
    Does mathematics ever play an explanatory role in science? If so then this opens the way for scientific realists to argue for the existence of mathematical entities using inference to the best explanation. Elsewhere I have argued, using a case study involving the prime-numbered life cycles of periodical cicadas, that there are examples of indispensable mathematical explanations of purely physical phenomena. In this paper I respond to objections to this claim that have been made by various philos…Read more
  •  83
    Are the laws of nature deductively closed?
    In H. Sankey (ed.), Causation and Laws of Nature, Kluwer Academic Press. pp. 91--109. 1999.
  •  44
    The Foundations of Mathematics in the Theory of Sets
    Australasian Journal of Philosophy 80 (4): 533-534. 2002.
    Book Information The Foundations of Mathematics in the Theory of Sets. The Foundations of Mathematics in the Theory of Sets J. P. Mayberry Cambridge Cambridge University Press 2000 xx + 424 Hardback US$80.00 By J. P. Mayberry. Cambridge University Press. Cambridge. Pp. xx + 424. Hardback:US$80.00
  •  90
    No Reservations Required? Defending Anti-Nominalism
    Studia Logica 96 (2): 127-139. 2010.
    In a 2005 paper, John Burgess and Gideon Rosen offer a new argument against nominalism in the philosophy of mathematics. The argument proceeds from the thesis that mathematics is part of science, and that core existence theorems in mathematics are both accepted by mathematicians and acceptable by mathematical standards. David Liggins (2007) criticizes the argument on the grounds that no adequate interpretation of “acceptable by mathematical standards” can be given which preserves the soundness o…Read more
  •  55
    Complexity, Networks, and Non-Uniqueness
    Foundations of Science 18 (4): 687-705. 2013.
    The aim of the paper is to introduce some of the history and key concepts of network science to a philosophical audience, and to highlight a crucial—and often problematic—presumption that underlies the network approach to complex systems. Network scientists often talk of “the structure” of a given complex system or phenomenon, which encourages the view that there is a unique and privileged structure inherent to the system, and that the aim of a network model is to delineate this structure. I arg…Read more
  •  177
    One recent trend in the philosophy of mathematics has been to approach the central epistemological and metaphysical issues concerning mathematics from the perspective of the applications of mathematics to describing the world, especially within the context of empirical science. A second area of activity is where philosophy of mathematics intersects with foundational issues in mathematics, including debates over the choice of set-theoretic axioms, and over whether category theory, for example, ma…Read more