•  55
    Assessment of strategies for evaluating extreme risks
    with James Franklin and Scott Sisson
    Australian Centre of Excellence for Risk Analysis Reports. 2007.
    The report begins by outlining several case studies with varying levels of data, examining the role for extreme event risk analysis. The case studies include BA’s analysis of fire blight and New Zealand apples, bank operational risk and several technical failures. The report then surveys recent developments in methods relevant to evaluating extreme risks and evaluates their properties. These include methods for fraud detection in banks, formal extreme value theory, Bayesian approaches, qualitati…Read more
  •  43
    Talk about ethics involves a great number of different sorts of concepts – rules, virtues, values, outcomes, rights, etc … Ethics is about all those things, but it is not fundamentally about them. Let’s review them with a view to seeing why they are not basic.
  •  403
    Science by Conceptual Analysis
    Studia Neoaristotelica 9 (1): 3-24. 2012.
    The late scholastics, from the fourteenth to the seventeenth centuries, contributed to many fields of knowledge other than philosophy. They developed a method of conceptual analysis that was very productive in those disciplines in which theory is relatively more important than empirical results. That includes mathematics, where the scholastics developed the analysis of continuous motion, which fed into the calculus, and the theory of risk and probability. The method came to the fore especially i…Read more
  •  168
    Powerful, technically complex international compliance regimes have developed recently in certain professions that deal with risk: banking (the Basel II regime), accountancy (IFRS) and the actuarial profession. The need to deal with major risks has acted as a strong driver of international co-operation to create enforceable international semilegal systems, as happened earlier in such fields as international health regulations. This regulation in technical fields contrasts with the failure of an in…Read more
  •  26
    Is philosophy irrelevant to science?
    Philosopher's Zone (ABC Radio National) 0-0. 2009.
    Scientists get on with the job – they do stuff with test tubes or with computers – but can philosophers help them? Do they need help and, if so, do they think they need help? This week, we examine what philosophers of science talk about and what effect it might have on what scientists actually do.
  •  241
    Thomas Kuhn's irrationalism
    New Criterion 18 (10): 29-34. 2000.
    Criticizes the irrationalist and social constructionist tendencies in Kuhn's Structure of Scientific Revolutions.
  •  488
    Aristotle on Species Variation
    Philosophy 61 (236). 1986.
    Explains Aristotle's views on the possibility of continuous variation between biological species. While the Porphyrean/Linnean classification of species by a tree suggests species are distributed discretely, Aristotle admitted continuous variation between species among lower life forms.
  •  46
    Species in Aristotle
    Philosophy 64 (247). 1989.
    Reply to H. Granger, Aristotle and the finitude of natural kinds, Philosophy 62 (1987), 523-26, which discussed J. Franklin, Aristotle on species variation, Philosophy 61 (1986), 245-52.
  •  173
    The Sokal hoax
    The Philosopher 1 (4): 21-24. 1996.
    Describes the Sokal hoax and defends it against attacks by postmodernists.
  •  65
    The renaissance myth
    Quadrant 26 (11): 51-60. 1982.
    THE HISTORY OF IDEAS is full of more tall stories than most other departments of history. Here are three which manage to combine initial implausibility with impregnability to refutation: that in the Middle Ages it was believed that the world was flat; that medieval philosophers debated as to how many angels could dance on the head of a pin; that Galileo revolutionised physics by dropping weights from the Leaning Tower of Pisa. None of these stories is true, and no competent historian has asserte…Read more
  •  284
    International compliance regimes: a public sector without restraints
    Australian Journal of Professional and Applied Ethics 9 (2): 86-95. 2007.
    Though there is no international government, there are many international regimes that enact binding regulations on particular matters. They include the Basel II regime in banking, IFRS in accountancy, the FIRST computer incident response system, the WHO’s system for containing global epidemics and many others. They form in effect a very powerful international public sector based on technical expertise. Unlike the public services of nation states, they are almost free of accountability to any de…Read more
  •  1038
    The Epistemology of Geometry I: the Problem of Exactness
    Proceedings of the Australasian Society for Cognitive Science 2009. 2010.
    We show how an epistemology informed by cognitive science promises to shed light on an ancient problem in the philosophy of mathematics: the problem of exactness. The problem of exactness arises because geometrical knowledge is thought to concern perfect geometrical forms, whereas the embodiment of such forms in the natural world may be imperfect. There thus arises an apparent mismatch between mathematical concepts and physical reality. We propose that the problem can be solved by emphasizing th…Read more
  •  858
    Discrete and continuous: a fundamental dichotomy in mathematics
    Journal of Humanistic Mathematics 7 (2): 355-378. 2017.
    The distinction between the discrete and the continuous lies at the heart of mathematics. Discrete mathematics (arithmetic, algebra, combinatorics, graph theory, cryptography, logic) has a set of concepts, techniques, and application areas largely distinct from continuous mathematics (traditional geometry, calculus, most of functional analysis, differential equations, topology). The interaction between the two – for example in computer models of continuous systems such as fluid flow – is a centr…Read more
  •  638
    An Aristotelian Philosophy of Mathematics breaks the impasse between Platonist and nominalist views of mathematics. Neither a study of abstract objects nor a mere language or logic, mathematics is a science of real aspects of the world as much as biology is. For the first time, a philosophy of mathematics puts applied mathematics at the centre. Quantitative aspects of the world such as ratios of heights, and structural ones such as symmetry and continuity, are parts of the physical world and are…Read more
  •  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.
  •  280
    Non-deductive logic in mathematics
    British Journal for the Philosophy of Science 38 (1): 1-18. 1987.
    Mathematicians often speak of conjectures as being confirmed by evidence that falls short of proof. For their own conjectures, evidence justifies further work in looking for a proof. Those conjectures of mathematics that have long resisted proof, such as Fermat's Last Theorem and the Riemann Hypothesis, have had to be considered in terms of the evidence for and against them. It is argued here that it is not adequate to describe the relation of evidence to hypothesis as `subjective', `heuristic' …Read more
  •  481
    Indispensability Without Platonism
    In Alexander Bird, Brian David Ellis & Howard Sankey (eds.), Properties, Powers and Structures: Issues in the Metaphysics of Realism, Routledge. pp. 81-97. 2013.
    According to Quine’s indispensability argument, we ought to believe in just those mathematical entities that we quantify over in our best scientific theories. Quine’s criterion of ontological commitment is part of the standard indispensability argument. However, we suggest that a new indispensability argument can be run using Armstrong’s criterion of ontological commitment rather than Quine’s. According to Armstrong’s criterion, ‘to be is to be a truthmaker (or part of one)’. We supplement this …Read more
  •  73
    Structure and domain-independence in the formal sciences
    Studies in History and Philosophy of Science Part A 30 721-723. 1999.
    Replies to Kevin de Laplante’s ‘Certainty and Domain-Independence in the Sciences of Complexity’ (de Laplante, 1999), defending the thesis of J. Franklin, ‘The formal sciences discover the philosophers’ stone’, Studies in History and Philosophy of Science, 25 (1994), 513-33, that the sciences of complexity can combine certain knowledge with direct applicability to reality.
  •  42
    Homomorphisms between Verma modules in characteristic P
    Journal of Algebra 112 58-85. 1988.
    The composition series of Verma modules and homomorphisms between Verma modules in the case of a complex semisimple Lie algebra were studied by Verma and by Bernstein, Gelfand and Gelfand. The author studies homomorphisms between the Verma modules in characteristic p.
  •  547
    If Tahiti suggested to theorists comfortably at home in Europe thoughts of noble savages without clothes, those who paid for and went on voyages there were in pursuit of a quite opposite human ideal. Cook's voyage to observe the transit of Venus in 1769 symbolises the eighteenth century's commitment to numbers and accuracy, and its willingness to spend a lot of public money on acquiring them. The state supported the organisation of quantitative researches, employing surveyors and collecting stat…Read more