Pascal’s wager and the origins of decision theory: decision-making by real decision-makers

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

Feature selection methods for solving the reference class problem

Probabilistic inference from frequencies, such as "Most Quakers are pacifists; Nixon is a Quaker, so probably Nixon is a pacifist" suffer from the problem that an individual is typically a member of many "reference classes" (such as Quakers, Republicans, Californians, etc) in which the frequency of the target attribute varies. How to choose the best class or combine the information? The article argues that the problem can be solved by the feature selection methods used in contemporary Big Data science: the correct reference class is that determined by the features relevant to the target, and relevance is measured by correlation (that is, a feature is relevant if it makes a difference to the frequency of the target)

Science by Conceptual Analysis: The Genius of the Late Scholastics

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

Diagrammatic Reasoning and Modelling in the Imagination: The Secret Weapons of the Scientific Revolution

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

How much of commonsense and legal reasoning is formalizable? A review of conceptual obstacles

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 are most evident where legal reasoning has to meld with the vast web of ordinary human knowledge of the world. Underlying many of the problems is the mismatch between the discreteness of symbol manipulation and the continuous nature of imprecise natural language, of degrees of similarity and analogy, and of probabilities

Quantity and number

Quantity is the first category that Aristotle lists after substance. It has extraordinary epistemological clarity: "2+2=4" is the model of a self-evident and universally known truth. Continuous quantities such as the ratio of circumference to diameter of a circle are as clearly known as discrete ones. The theory that mathematics was "the science of quantity" was once the leading philosophy of mathematics. The article looks at puzzles in the classification and epistemology of quantity

The objective Bayesian conceptualisation of proof and reference class problems

The objective Bayesian view of proof (or logical probability, or evidential support) is explained and defended: that the relation of evidence to hypothesis (in legal trials, science etc) is a strictly logical one, comparable to deductive logic. This view is distinguished from the thesis, which had some popularity in law in the 1980s, that legal evidence ought to be evaluated using numerical probabilities and formulas. While numbers are not always useful, a central role is played in uncertain reasoning by the ‘proportional syllogism’, or argument from frequencies, such as ‘nearly all aeroplane flights arrive safely, so my flight is very likely to arrive safely’. Such arguments raise the ‘problem of the reference class’, arising from the fact that an individual case may be a member of many different classes in which frequencies differ. For example, if 15 per cent of swans are black and 60 per cent of fauna in the zoo is black, what should I think about the likelihood of a swan in the zoo being black? The nature of the problem is explained, and legal cases where it arises are given. It is explained how recent work in data mining on the relevance of features for prediction provides a solution to the reference class problem

Mathematics, core of the past and hope of the future

Mathematics has always been a core part of western education, from the medieval quadrivium to the large amount of arithmetic and algebra still compulsory in high schools. It is an essential part. Its commitment to exactitude and to rigid demonstration balances humanist subjects devoted to appreciation and rhetoric as well as giving the lie to postmodernist insinuations that all “truths” are subject to political negotiation. In recent decades, the character of mathematics has changed – or rather broadened: it has become the enabling science behind the complexity of contemporary knowledge, from gene interpretation to bank risk. Mathematical understanding is all the more necessary for future jobs, as well as remaining, as ever, a prophylactic against the more corrosive philosophical views emanating from the humanities

Emergentism as an option in the philosophy of religion: between materialist atheism and pantheism

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 is compared with the standard alternatives and the arguments for and against it are laid out. It is argued that, among options in the philosophy of religion, it involves the minimal reworking of the manifest image of common sense. Hence it deserves a place at the table in arguments as to the overall nature of the universe

Stove's anti-darwinism

Stove's article, 'So you think you are a Darwinian?'[ 1] was essentially an advertisement for his book, Darwinian Fairytales.[ 2] The central argument of the book is that Darwin's theory, in both Darwin's and recent sociobiological versions, asserts many things about the human and other species that are known to be false, but protects itself from refutation by its logical complexity. A great number of ad hoc devices, he claims, are used to protect the theory. If co operation is observed where the theory predicts competition, then competition is referred to the time of the cavemen, or is reinterpreted as competition between some hidden entities like genes or abstract entities like populations. In a characteristic sally, Stove writes of the sociobiologists' oscillation on the meaning of kin altruism: Any discussion of altruism with an inclusive fitness theorist is, in fact, exactly like dealing with a pair of balloons connected by a tube, one balloon being the belief that kin altruism is an illusion, the other being the belief that kin altruism is caused by shared genes. If a critic puts pressure on the illusion balloon - perhaps by ridiculing the selfish theory of human nature - air is forced into the causal balloon. There is then an increased production of earnest causal explanations of why we love our children, why hymenopteran workers look after their sisters, etc., etc. Then, if the critic puts pressure on the causal balloon - perhaps about the weakness of sibling altruism compared with parental, or the absence of sibling altruism in bacteria - then the illusion balloon is forced to expand. There will now be an increased production of cynical scurrilities about parents manipulating their babies for their own advantage, and vice versa, and in general, about the Hobbesian bad times that are had by all. In this way critical pressure, applied to the theory of inclusive fitness at one point, can always be easily absorbed at another point, and the theory as a whole is never endangered.[ 3] Now, it is uncontroversial to assert that Darwinism is a logically complex theory, and that its relation to empirical evidence is distant and multi faceted. One does not directly observe chance genetic variations leading to the development of new species, or even continuous variations in the fossil record, but must rely on subtle arguments to the best explanation, scaling up from varieties to species, and so on.