James Franklin

Pascal’s Wager does not exist in a Platonic world of possible gods, abstract probabilities and arbitrary payoffs. Real decision-makers, such as Pascal’s “man of the world” of 1660, face a range of religious options they take to be serious, with fixed probabilities grounded in their evidence, and with utilities that are fixed quantities in actual minds. The many ingenious objections to the Wager dreamed up by philosophers do not apply in such a real decision matrix. In the situation Pascal addresses, the Wager is a good bet. In the situation of a modern Western intellectual, the reasoning of the Wager is still powerful, though the range of options and the actions indicated are not the same as in Pascal’s day.

Programs of drug testing welfare recipients are increasingly common in US states and have been considered elsewhere. Though often intensely debated, such programs are complicated to evaluate because their aims are ambiguous – aims like saving money may be in tension with aims like referring people to treatment. We assess such programs using a proportionality approach, which requires that for ethical acceptability a practice must be: reasonably likely to meet its aims, sufficiently important in purpose as to outweigh harms incurred, and lower in costs than feasible alternatives. In the light of empirical findings, we argue that the programs fail the three requirements. Pursuing recreational drug users is not important in the light of costs incurred, while dependent users who may require referral are usually identifiable without testing and typically need a broader approach than one focussing on drugs. Drug testing of welfare recipients is therefore not ethically acceptable policy.

• It would be a moral disgrace for God (if he existed) to allow the many evils in the world, in the same way it would be for a parent to allow a nursery to be infested with criminals who abused the children. • There is a contradiction in asserting all three of the propositions: God is perfectly good; God is perfectly powerful; evil exists (since if God wanted to remove the evils and could, he would). • The religious believer has no hope of getting away with excuses that evil is not as bad as it seems, or that it is all a result of free will, and so on. Piper avoids mentioning the best solution so far put forward to the problem of evil. It is Leibniz’s theory that God does not create a better world because there isn’t one — that is, that (contrary to appearances) if one part of the world were improved, the ramifications would result in it being worse elsewhere, and worse overall. It is a “bump in the carpet” theory: push evil down here, and it pops up over there. Leibniz put it by saying this is the “Best of All Possible Worlds”. That phrase was a public relations disaster for his theory, suggesting as it does that everything is perfectly fine as it is. He does not mean that, but only that designing worlds is a lot harder than it looks, and determining the amount of evil in the best one is no easy matter. Though humour is hardly appropriate to the subject matter, the point of Leibniz’s idea is contained in the old joke, “An optimist is someone who thinks this is the best of all possible worlds, and a pessimist thinks..

The late twentieth century saw two long-term trends in popular thinking about ethics. One was an increase in relativist opinions, with the “generation of the Sixties” spearheading a general libertarianism, an insistence on toleration of diverse moral views (for “Who is to say what is right? – it’s only your opinion.”) The other trend was an increasing insistence on rights – the gross violations of rights in the killing fields of the mid-century prompted immense efforts in defence of the “inalienable” rights of the victims of dictators, of oppressed peoples, of refugees. The obvious incompatibility of those ethical stances, one anti-objectivist, the other objectivist in the extreme, proved no obstacle to their both being held passionately, often by the same people.

Greek, Latin and Ancient History. Instead, after a good result in mathematics, I decided to pursue that instead. That left me with an extra subject to choose to fill up first year. What was this "Philosophy" on offer? I couldn't understand where there was something in the spectrum of knowledge for philosophy to be about. Biology was about cats, English was about language and literature, mathematics was about numbers (I was not yet philosophically smart enough to realise there was a problem as to what numbers were, given that you can't observe them like cats.) But what topics were left over for philosophy?

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, qualitative reasoning, and adversary and advocacy models. The document includes a supplementary report as an appendix, providing an overview of the quantification of bank operational risks.

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 in the social sciences. In legal theory they developed, for example, the ethical analyses of the conditions of validity of contracts, and natural rights theory. In political theory, they introduced constitutionalism and the thought experiment of a “state of nature”. Their contributions to economics included concepts still regarded as basic, such as demand, capital, labour, and scarcity. Faculty psychology and semiotics are other areas of significance. In such disciplines, later developments rely crucially on scholastic concepts and vocabulary.

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 international general-purpose political and legal regime to develop. We survey the new global regulatory systems in the actuarial, banking and accounting fields, with a view to showing how the need to deal reasonably with risk has resulted in an international de facto law solidly based on correct abstract principles of probability.

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 democratically elected body or to any legal system. Although by and large they have acted for good, the dangers of long-term unaccountability are illustrated by the travesties of justice perpetrated by the International Labour Organisation Administrative Tribunal.

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 the ways in which the brain can transform and organize its perceptual intake. It is not necessary for a geometrical form to be perfectly instantiated in order for perception of such a form to be the basis of a geometrical concept

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 central issue in the applicable mathematics of the last hundred years. This article explains the distinction and why it has proved to be one of the great organizing themes of mathematics.

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 is a major factor in economic exchanges in professional services, such as law and medicine. Finally, we examine the prospects for an economics of gratuitousness at a level higher than the individual, that is, for businesses devoted to social ends more than profit.

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 localized a faculty to register them. We defend the perception of necessity against such Humeanism, drawing on examples from mathematics.

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 of two heights, for example, is a perceivable and measurable real relation between properties of physical things, a relation that can be shared by the ratio of two weights or two time intervals. Ratios are an example of continuous quantity; discrete quantities, such as whole numbers, are also realised as relations between a heap and a unit-making universal. For example, the relation between foliage and being-a-leaf is the number of leaves on a tree,a relation that may equal the relation between a heap of shoes and being-a-shoe. Modern higher mathematics, however, deals with some real properties that are not naturally seen as quantity, so that the “science of quantity” theory of mathematics needs supplementation. Symmetry, topology and similar structural properties are studied by mathematics, but are about pattern, structure or arrangement rather than quantity.

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 truthmaker of such truths? It is argued that Aristotelianism can answer the question, but only a semi-Platonist form of it.

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 denied that space and time are infinitely divisible, the most notable are the ancient atomists, and Berkeley and Hume. All of these assert not only that space and time might be atomic, but that they must be. Infinite divisibility is, they say, impossible on purely conceptual grounds.