•  118
    Accountancy as Computational Casuistics
    Business and Professional Ethics Journal 17 (4): 21-37. 1998.
    When a company raises its share price by sacking workers or polluting the environment, it is avoiding paying real costs. Accountancy, which quantifies certain rights, needs to combine with applied ethics to create a "computational casuistics" or "moral accountancy", which quantifies the rights and obligations of individuals and companies. Such quantification has proved successful already in environmental accounting, in health care allocation and in evaluating compensation payments. It is argued …Read more
  •  426
    Caritas in Veritate: Economic activity as personal encounter and the economy of gratuitousness
    Solidarity: The Journal of Catholic Social Thought and Secular Ethics 1 (1). 2011.
    We first survey the Catholic social justice tradition, the foundation on which Caritas in Veritate builds. Then we discuss Benedict’s addition of love to the philosophical virtues (as applied to economics), and how radical a change that makes to an ethical perspective on economics. We emphasise the reality of the interpersonal aspects of present-day economic exchanges, using insights from two disciplines that have recognized that reality, human resources and marketing. Personal encounter really …Read more
  •  696
    Perceiving Necessity
    Pacific Philosophical Quarterly 98 (3). 2017.
    In many diagrams one seems to perceive necessity – one sees not only that something is so, but that it must be so. That conflicts with a certain empiricism largely taken for granted in contemporary philosophy, which believes perception is not capable of such feats. The reason for this belief is often thought well-summarized in Hume's maxim: ‘there are no necessary connections between distinct existences’. It is also thought that even if there were such necessities, perception is too passive or l…Read more
  •  330
    Mathematics, The Computer Revolution and the Real World
    Philosophica 42 (n/a): 79-92. 1988.
    The philosophy of mathematics has largely abandoned foundational studies, but is still fixated on theorem proving, logic and number theory, and on whether mathematical knowledge is certain. That is not what mathematics looks like to, say, a knot theorist or an industrial mathematical modeller. The "computer revolution" shows that mathematics is a much more direct study of the world, especially its structural aspects.
  •  713
    Aristotelianism in the Philosophy of Mathematics
    Studia Neoaristotelica 8 (1): 3-15. 2011.
    Modern philosophy of mathematics has been dominated by Platonism and nominalism, to the neglect of the Aristotelian realist option. Aristotelianism holds that mathematics studies certain real properties of the world – mathematics is neither about a disembodied world of “abstract objects”, as Platonism holds, nor it is merely a language of science, as nominalism holds. Aristotle’s theory that mathematics is the “science of quantity” is a good account of at least elementary mathematics: the ratio …Read more
  •  627
    Uninstantiated Properties and Semi-Platonist Aristotelianism
    Review of Metaphysics 69 (1): 25-45. 2015.
    A problem for Aristotelian realist accounts of universals (neither Platonist nor nominalist) is the status of those universals that happen not to be realised in the physical (or any other) world. They perhaps include uninstantiated shades of blue and huge infinite cardinals. Should they be altogether excluded (as in D.M. Armstrong's theory of universals) or accorded some sort of reality? Surely truths about ratios are true even of ratios that are too big to be instantiated - what is the truthmak…Read more
  •  7
    Philosophy, mathematics and structure
    Philosopher: revue pour tous 1 (2): 31-38. 1995.
    An early version of the work on mathematics as the science of structure that appeared later as An Aristotelian Realist Philosophy of Mathematics (2014)
  •  844
    Review of N. Wildberger, Divine Proportions: Rational Trigonometry to Universal (review)
    Mathematical Intelligencer 28 (3): 73-74. 2006.
    Reviews Wildberger's account of his rational trigonometry project, which argues for a simpler way of doing trigonometry that avoids irrationals.
  •  662
    Throughout history, almost all mathematicians, physicists and philosophers have been of the opinion that space and time are infinitely divisible. That is, it is usually believed that space and time do not consist of atoms, but that any piece of space and time of non-zero size, however small, can itself be divided into still smaller parts. This assumption is included in geometry, as in Euclid, and also in the Euclidean and non- Euclidean geometries used in modern physics. Of the few who have deni…Read more
  •  698
    Just before the Scientific Revolution, there was a "Mathematical Revolution", heavily based on geometrical and machine diagrams. The "faculty of imagination" (now called scientific visualization) was developed to allow 3D understanding of planetary motion, human anatomy and the workings of machines. 1543 saw the publication of the heavily geometrical work of Copernicus and Vesalius, as well as the first Italian translation of Euclid.