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3Are dispositions ultimate-replyPhilosophical Quarterly 38 (150): 86-87. 1988.The original article, 'Are dispositions reducible to categorical properties? (Philosophical Quarterly, 36, 1986), argued that dispositions are not so reducible. The present article defends this view against the criticisms of D M Armstrong (Philosophical Quarterly, 38, 1988). Dispositions are distinguished from fully categorical properties like symmetry.
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613Bayesian Perspectives on Mathematical PracticeIn Bharath Sririman (ed.), Handbook of the History and Philosophy of Mathematical Practice, Springer. pp. 2711-2726. 2020.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 the Riemann hypothesis, have had to be considered in terms of the evidence for and against them. In recent decades, massive increases in computer power have permitted the gathering of huge amounts of numerical evidence, both for conjectures in p…Read more
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584Stove's discovery of the worst argument in the worldPhilosophy 77 (4): 615-624. 2002.The winning entry in David Stove's Competition to Find the Worst Argument in the World was: “We can know things only as they are related to us/insofar as they fall under our conceptual schemes, etc., so, we cannot know things as they are in themselves.” That argument underpins many recent relativisms, including postmodernism, post-Kuhnian sociological philosophy of science, cultural relativism, sociobiological versions of ethical relativism, and so on. All such arguments have the same form as ‘W…Read more
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21Reflections on Kurt Gödel (review)History of European Ideas 13 (5): 637-638. 1991.A review of Hao Wang's Reflections on Kurt Goedel, emphasising Goedel's reaction against his Vienna Circle background.
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557On the parallel between mathematics and moralsPhilosophy 79 (1): 97-119. 2004.The imperviousness of mathematical truth to anti-objectivist attacks has always heartened those who defend objectivism in other areas, such as ethics. It is argued that the parallel between mathematics and ethics is close and does support objectivist theories of ethics. The parallel depends on the foundational role of equality in both disciplines. Despite obvious differences in their subject matter, mathematics and ethics share a status as pure forms of knowledge, distinct from empirical science…Read more
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38Elliptical Orbits and the Aristotelian Scientific Revolution Comment on GroarkeStudia Neoaristotelica 13 (2): 169-179. 2016.The Scientific Revolution was far from the anti-Aristotelian movement traditionally pictured. Its applied mathematics pursued by new means the Aristotelian ideal of science as knowledge by insight into necessary causes. Newton’s derivation of Kepler’s elliptical planetary orbits from the inverse square law of gravity is a central example.
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384The global/local distinction vindicates Leibniz's theodicyTheology and Science 20 (4). 2022.The essential idea of Leibniz’s Theodicy was little understood in his time but has become one of the organizing themes of modern mathematics. There are many phenomena that are possible locally but for purely mathematical reasons impossible globally. For example, it is possible to build a spiral staircase that is rising at any given point, but it is impossible to build one that is rising at all points and comes back to where it started. The necessity is mathematically provable, so not subject to …Read more
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373Resurrecting logical probabilityErkenntnis 55 (2): 277-305. 2001.The logical interpretation of probability, or "objective Bayesianism'' – the theory that (some) probabilities are strictly logical degrees of partial implication – is defended. The main argument against it is that it requires the assignment of prior probabilities, and that any attempt to determine them by symmetry via a "principle of insufficient reason" inevitably leads to paradox. Three replies are advanced: that priors are imprecise or of little weight, so that disagreement about them does …Read more
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26Review of The empire of chance: How probability changed science and everyday life, by Gerd Gigerenzer, Zeno Swijtink, Theodore Porter, Lorraine Daston, John Beatty and Lorenz Krüger (review)History of European Ideas 12 (4): 572-573. 1990.
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81Review of E.T. Jaynes, Probability Theory: The Logic of Science and other books on probability (review)Mathematical Intelligencer 27 (2): 83-85. 2005.Review of Jaynes, Probability Theory: The Logic of Science; Marrison, The Fundamentals of Risk Management; and Hastie, Tibshirani and Friedman, The Elements of Statistical Learning. A standard view of probability and statistics centers on distributions and hypothesis testing. To solve a real problem, say in the spread of disease, one chooses a “model”, a distribution or process that is believed from tradition or intuition to be appropriate to the class of problems in question. One uses data to e…Read more
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294Late scholastic probable arguments and their contrast with rhetorical and demonstrative argumentsPhilosophical Inquiries 10 (2). 2022.Aristotle divided arguments that persuade into the rhetorical (which happen to persuade), the dialectical (which are strong so ought to persuade to some degree) and the demonstrative (which must persuade if rightly understood). Dialectical arguments were long neglected, partly because Aristotle did not write a book about them. But in the sixteenth and seventeenth century late scholastic authors such as Medina, Cano and Soto developed a sound theory of probable arguments, those that have logical …Read more
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432A Hippocratic Oath for mathematicians? Mapping the landscape of ethics in mathematicsScience and Engineering Ethics 28 (5): 1-30. 2022.While the consequences of mathematically-based software, algorithms and strategies have become ever wider and better appreciated, ethical reflection on mathematics has remained primitive. We review the somewhat disconnected suggestions of commentators in recent decades with a view to piecing together a coherent approach to ethics in mathematics. Calls for a Hippocratic Oath for mathematicians are examined and it is concluded that while lessons can be learned from the medical profession, the rela…Read more
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73The Worth of Persons: The Foundation of EthicsEncounter Books. 2022.The death of a person is a tragedy while the explosion of a lifeless galaxy is a mere firework. The moral difference is grounded in the nature of humans: humans have intrinsic worth, a worth that makes their fate really matter. This is the worth proposed as the foundation of ethics. Ethics in the usual sense of right and wrong actions, rights and virtues, and how to live a good life, is founded on something more basic that is not itself about actions, namely the worth of persons. Human moral wor…Read more
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31Review of Keith Hossack, Knowledge and the Philosophy of Number: What Numbers Are and How They Are Known (review)Philosophia Mathematica 30 (1): 127-129. 2022.Hossack presents a clearly argued case that numbers (cardinals, ordinals, and ratios) are not objects (as Platonists think), nor properties of objects, but properties of quantities.
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316David Stove (1927-1994), Sydney philosopher and master of argument: life and workSydney Realist 43 1-8. 2021.David Stove was a philosopher strong on argument and polemic. His work on the logical intepretation of probability led to a defence of induction in The Rationality of Induction (1986). It resulted too in his denunciation of Popper, Kuhn, Lakatos and Feyeraband as irrationalists because of their "deductivism" (the thesis that the only logic is deductive logic). Stove also defended controversial views on the intelligence of women and on Darwinism. The article surveys his life and work.
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1208‘Let No-One Ignorant of Geometry…’: Mathematical Parallels for Understanding the Objectivity of EthicsJournal of Value Inquiry 57 (2): 365-384. 2023.It may be a myth that Plato wrote over the entrance to the Academy “Let no-one ignorant of geometry enter here.” But it is a well-chosen motto for his view in the Republic that mathematical training is especially productive of understanding in abstract realms, notably ethics. That view is sound and we should return to it. Ethical theory has been bedevilled by the idea that ethics is fundamentally about actions (right and wrong, rights, duties, virtues, dilemmas and so on). That is an error like …Read more
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419A Causal-Mentalist View of PropositionsOrganon F: Medzinárodný Časopis Pre Analytickú Filozofiu 29 (1): 47-77. 2022.In order to fulfil their essential roles as the bearers of truth and the relata of logical relations, propositions must be public and shareable. That requirement has favoured Platonist and other nonmental views of them, despite the well-known problems of Platonism in general. Views that propositions are mental entities have correspondingly fallen out of favour, as they have difficulty in explaining how propositions could have shareable, objective properties. We revive a mentalist view of proposi…Read more
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1146Mathematics as a science of non-abstract reality: Aristotelian realist philosophies of mathematicsFoundations of Science 27 (2): 327-344. 2022.There is a wide range of realist but non-Platonist philosophies of mathematics—naturalist or Aristotelian realisms. Held by Aristotle and Mill, they played little part in twentieth century philosophy of mathematics but have been revived recently. They assimilate mathematics to the rest of science. They hold that mathematics is the science of X, where X is some observable feature of the (physical or other non-abstract) world. Choices for X include quantity, structure, pattern, complexity, relatio…Read more
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376D.M. Armstrong: Sydney's most distinguished philosopher: life and workSydney Realist 41 1-6. 2020.David Armstrong (1926-2014) was much the most internationally successful philosopher to come from Sydney. His life moved from a privileged Empire childhood and student of John Anderson to acclaimed elder statesman of realist philosophy. His philosophy developed from an Andersonian realist inheritance to major contributions on materialist theory of mind and the theory of universals. His views on several other topics such as religion and ethics are surveyed briefly.
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856Antitheodicy and the Grading of Theodicies by Moral OffensivenessSophia 59 (3): 563-576. 2020.Antitheodicy objects to all attempts to solve the problem of evil. Its objections are almost all on moral grounds—it argues that the whole project of theodicy is morally offensive. Trying to excuse God’s permission of evil is said to deny the reality of evil, to exhibit gross insensitivity to suffering, and to insult the victims of grave evils. Since antitheodicists urge the avoidance of theodicies for moral reasons, it is desirable to evaluate the moral reasons against theodicies in abstraction…Read more
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550Emergentism as an option in the philosophy of religion: between materialist atheism and pantheismSuri: Journal of the Philosophical Association of the Philippines 7 (2): 1-22. 2019.Among worldviews, in addition to the options of materialist atheism, pantheism and personal theism, there exists a fourth, “local emergentism”. It holds that there are no gods, nor does the universe overall have divine aspects or any purpose. But locally, in our region of space and time, the properties of matter have given rise to entities which are completely different from matter in kind and to a degree god-like: consciousnesses with rational powers and intrinsic worth. The emergentist option …Read more
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465How much of commonsense and legal reasoning is formalizable? A review of conceptual obstaclesLaw, Probability and Risk 11 225-245. 2012.Fifty years of effort in artificial intelligence (AI) and the formalization of legal reasoning have produced both successes and failures. Considerable success in organizing and displaying evidence and its interrelationships has been accompanied by failure to achieve the original ambition of AI as applied to law: fully automated legal decision-making. The obstacles to formalizing legal reasoning have proved to be the same ones that make the formalization of commonsense reasoning so difficult, and…Read more
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8Reasonable science (review)New Criterion 22 (3): 70-73. 2003.Review of Susan Haack, Defending Science - Within Reason. The review suggests that Haack's defense of scientific rationality is correct as far as it goes but could be more enthusiastic.
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22David Stove's Darwinian Fairytales (review)MercatorNet 0-0. 2006.Favourably reviews David Stove's Darwinian Fairytales, which argued that Darwinism is a complex theory with a distant relation to empirical evidence.
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59Philosophy in SydneyIn Graham Robert Oppy & Nick Trakakis (eds.), The Antipodean philosopher, Lexington Books. pp. 61-66. 2011.Let me tell you what philosophy is about, then about how Sydney does it in its own special way. Does life have a meaning, and if so what is it? What can I be certain of, and how should I act when I am not certain? Why are the established truths of my tribe better than the primitive superstitions of your tribe? Why should I do as I’m told? Those are questions it’s easy to avoid, in the rush to acquire goods and prestige. Even for many of a more serious outlook, they are questions easy to dismiss …Read more
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204Last bastion of reason (review)New Criterion 18 (9): 74-78. 2000.Attacks the irrationalism of Lakatos's Proofs and Refutations and defends mathematics as a "last bastion" of reason against postmodernist and deconstructionist currents.
Sydney, New South Wales, Australia
Areas of Specialization
Applied Ethics |
Science, Logic, and Mathematics |
Philosophy of Mathematics |
Interpretation of Probability |
Areas of Interest
Philosophy of Mathematics |
General Philosophy of Science |
PhilPapers Editorships
Mathematical Aristotelianism |