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581Arguments Whose Strength Depends on Continuous VariationInformal Logic 33 (1): 33-56. 2013.Both the traditional Aristotelian and modern symbolic approaches to logic have seen logic in terms of discrete symbol processing. Yet there are several kinds of argument whose validity depends on some topological notion of continuous variation, which is not well captured by discrete symbols. Examples include extrapolation and slippery slope arguments, sorites, fuzzy logic, and those involving closeness of possible worlds. It is argued that the natural first attempts to analyze these notions and …Read more
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413The formal sciences discover the philosophers' stoneStudies in History and Philosophy of Science Part A 25 (4): 513-533. 1994.The formal sciences - mathematical as opposed to natural sciences, such as operations research, statistics, theoretical computer science, systems engineering - appear to have achieved mathematically provable knowledge directly about the real world. It is argued that this appearance is correct.
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490Mathematical necessity and realityAustralasian Journal of Philosophy 67 (3). 1989.Einstein, like most philosophers, thought that there cannot be mathematical truths which are both necessary and about reality. The article argues against this, starting with prima facie examples such as "It is impossible to tile my bathroom floor with regular pentagonal tiles." Replies are given to objections based on the supposedly purely logical or hypothetical nature of mathematics
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43Accountancy and the quantification of rights: Giving moral values legal teethCentre for an Ethical Society Papers. 2007.If a company’s share price rises when it sacks workers, or when it makes money from polluting the environment, it would seem that the accounting is not being done correctly. Real costs are not being paid. People’s ethical claims, which in a smaller-scale case would be legally enforceable, are not being measured in such circumstances. This results from a mismatch between the applied ethics tradition and the practice of the accounting profession. Applied ethics has mostly avoided quantification of…Read more
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166Global justice: an anti-collectivist and pro-causal ethicSolidarity 2 (1). 2012.Both philosophical and practical analyses of global justice issues have been vitiated by two errors: a too-high emphasis on the supposed duties of collectives to act, and a too-low emphasis on the analysis of causes and risks. Concentrating instead on the duties of individual actors and analysing what they can really achieve reconfigures the field. It diverts attention from individual problems such as poverty or refugees or questions on what states should do. Instead it shows that there are diff…Read more
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564Proof in Mathematics: An IntroductionQuakers Hill Press. 1996.A textbook on proof in mathematics, inspired by an Aristotelian point of view on mathematics and proof. The book expounds the traditional view of proof as deduction of theorems from evident premises via obviously valid steps. It deals with the proof of "all" statements, "some" statements, multiple quantifiers and mathematical induction.
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638An Aristotelian Realist Philosophy of Mathematics: Mathematics as the science of quantity and structurePalgrave MacMillan. 2014.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
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118Accountancy as Computational CasuisticsBusiness 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
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426Caritas in Veritate: Economic activity as personal encounter and the economy of gratuitousnessSolidarity: 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
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696Perceiving NecessityPacific 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
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 |