A new criterion is introduced for judging the suitability of various fuzzy logics for practical uncertain reasoning in a probabilistic world and the relationship of this criterion to several established criteria, and its consequences for truth functional belief, are investigated.

The paper describes and proves completeness theorems for a series of proof systems formalizing common sense reasoning about uncertain knowledge in the case where this consists of sets of linear constraints on a probability function.

This paper is a sequel to an earlier result of the authors that in making inferences from certain probabilistic knowledge bases the maximum entropy inference process, ME, is the only inference process respecting “common sense.” This result was criticized on the grounds that the probabilistic knowledge bases considered are unnatural and that ignorance of dependence should not be identified with statistical independence. We argue against these criticisms and also against the more general criticism that ME is representation dependent. In a (...) final section, however, we provide a criticism of our own of ME, and of inference processes in general, namely that they fail to satisfy compactness. (shrink)

The paper describes and proves completeness theorems for a series of proof systems formalizing common sense reasoning about uncertain knowledge in the case where this consists of sets of linear constraints on a probability function.

We examine the idea that similar problems should have similar solutions (to paraphrase van Fraassen’s slogan ‘Problems which are essentially the same must receive essentially the same solution’, see van Fraassen in Laws and symmetry, Oxford Univesity Press, Oxford, 1989, p. 236) in the context of symmetries of sentence algebras within Inductive Logic and conclude that by itself this is too generous a notion upon which to found the rational assignment of probabilities. We also argue that within our formulation of (...) symmetry the paradoxes associated with the so called ‘Principle of Indifference’ collapse, but only to be replaced by genuinely irremediable examples of the same phenomenon. (shrink)

A family of symmetries of polyadic inductive logic are described which in turn give rise to the purportedly rational Permutation Invariance Principle stating that a rational assignment of probabilities should respect these symmetries. An equivalent, and more practical, version of this principle is then derived.

We investigate the relative probabilistic support afforded by the combination of two analogies based on possibly different, structural similarity (as opposed to e.g. shared predicates) within the context of Pure Inductive Logic and under the assumption of Language Invariance. We show that whilst repeated analogies grounded on the same structural similarity only strengthen the probabilistic support this need not be the case when combining analogies based on different structural similarities. That is, two analogies may provide less support than each would (...) individually. (shrink)

We present six significant open problems in Pure Inductive Logic, together with their background and current status, with the intention of raising awareness and leading ultimately to their resolution.

We give a unified account of some results in the development of Polyadic Inductive Logic in the last decade with particular reference to the Principle of Spectrum Exchangeability, its consequences for Instantial Relevance, Language Invariance and Johnson's Sufficientness Principle, and the corresponding de Finetti style representation theorems.

B.K.Matilal, and earlier J.F.Staal, have suggested a reading of the `Nyaya five limb schema' (also sometimes referred to as the Indian Schema or Hindu Syllogism) from Gotama's Nyaya-Sutra in terms of a binary occurrence relation. In this paper we provide a rational justification of a version of this reading as Analogical Reasoning within the framework of Polyadic Pure Inductive Logic.

In his 1974 paper “Popper’s qualitative theory of verisimilitude” published in the British Journal for the Philosophy of Science David Miller gave his so called ‘Weather Example’ to argue that the Hamming distance between constituents is flawed as a measure of proximity to truth since the former is not, unlike the latter, translation invariant. In this present paper we generalise David Miller’s Weather Example in both the unary and polyadic cases, characterising precisely which permutations of constituents/atoms can be effected by (...) translations. In turn this suggests a meta-principle of the rational assignment of subjective probabilities, that rational principles should be preserved under translations, which we formalise and give a particular characterisation of in the context of Unary Pure Inductive Logic. (shrink)

We consider two formalizations of the notion of irrelevance as a rationality principle within the framework of (Carnapian) Inductive Logic: Johnson's Sufficientness Principle, JSP, which is classically important because it leads to Carnap's influential Continuum of Inductive Methods and the recently proposed Weak Irrelevance Principle, WIP. We give a complete characterization of the language invariant probability functions satisfying WIP which generalizes the Nix-Paris Continuum. We argue that the derivation of two very disparate families of inductive methods from alternative perceptions of (...) 'irrelevance' is an indication that this notion is imperfectly understood at present. (shrink)

We give a brief account of some de Finetti style representation theorems for probability functions satisfying Spectrum Exchangeability in Polyadic Inductive Logic, together with applications to Non-splitting, Language Invariance, extensions with Equality and Instantial Relevance.

A necessary and sufficient condition in terms of a de Finetti style representation is given for a probability function in Polyadic Inductive Logic to satisfy being part of a Language Invariant family satisfying Spectrum Exchangeability. This theorem is then considered in relation to the unary Carnap and Nix–Paris Continua.

Pure Inductive Logic is the study of rational probability treated as a branch of mathematical logic. This monograph, the first devoted to this approach, brings together the key results from the past seventy years, plus the main contributions of the authors and their collaborators over the last decade, to present a comprehensive account of the discipline within a single unified context.

In the twenty-first century, the debate about life on other worlds is quickly changing from the realm of speculation to the domain of hard science. Within a few years, as a consequence of the rapid discovery by astronomers of planets around other stars, astronomers very likely will have discovered clear evidence of life beyond the Earth. Such a discovery of extraterrestrial life will change everything. Knowing the answer as to whether humanity has company in the universe will trigger one of (...) the greatest intellectual revolutions in history, not the least of which will be a challenge for at least some terrestrial religions. Which religions will handle the discovery of extraterrestrial life with ease and which will struggle to assimilate this new knowledge about our place in the universe? Some religions as currently practiced appear to only be viable on Earth. Other religions could be practiced on distant worlds but nevertheless identify both Earth as a place and humankind as a species of singular spiritual religious importance, while some religions could be practiced equally well anywhere in the universe by any sentient beings. Weintraub guides readers on an invigorating tour of the world's most widely practiced religions. It reveals what, if anything, each religion has to say about the possibility that extraterrestrial life exists and how, or if, a particular religion would work on other planets in distant parts of the universe. (shrink)

Modern scholars have been concerned with the hostility shown to Alexander by the Hellenistic schools of philosophy. Two literary portraits have been distinguished, the Peripatetic and the Stoic, the former deriving from Theophrastus' book on Callisthenes, or starting with this work the Peripatetics worked out a theory of and applied it to Alexander, in order to belittle his achievements. It was a case of giving sophisticated expression to the kind of crude resentment expressed by Demades.

The locus classicus for Plutarch's own views on his methods is in the Alexander He has begun by asking for the indulgence of his readers if they do not find all the exploits of Alexander and Caesar recounted by the biographer or if they discover him not reporting some famous incident in detail (); and he goes on to compare his own search for evidence which will indicate the kind of soul, with the activity of the painter, who, in order (...) to create a likeness, concentrates on the eyes and pays little attention to the other parts. Commentators and critics have been right to take this as a key text for the purpose of understanding Plutarch's attitude towards his biographical work; nevertheless there are other passages in the Lives where we can at least glimpse his attitude to his subject, and we can only see the Alexander-remarks in correct perspective if we take these other passages into account. I propose therefore, starting with the Alexander, to see how far these critical remarks apply to Plutarch's theory and practice elsewhere in the Lives. (shrink)

According to the Ars Amatoria the notorious rape took place on the occasion of a primitive dramatic entertainment staged in a theatre, in which the seats and furnishings were also primitive. There is no time for a description of the arts of the performers—a tibicen and a ludius—before the Romans, impatient for action, receive their signal from Romulus. Nor is there any mention of a god in whose honour the entertainment had been provided.

This paper concerns the question of how to draw inferences common sensically from uncertain knowledge. Since the early work of Shore and Johnson (1980), Paris and Vencovská (1990), and Csiszár (1989), it has been known that the Maximum Entropy Inference Process is the only inference process which obeys certain common sense principles of uncertain reasoning. In this paper we consider the present status of this result and argue that within the rather narrow context in which we work this complete (...) and consistent mode of uncertain reasoning is actually characterised by the observance of just a single common sense principle (or slogan). (shrink)

Trope theory is a leading metaphysical theory in analytic ontology. One of its classic statements is found in the work of Donald C. Williams who argued that tropes qua abstract particulars are the very alphabet of being. The concept of an abstract particular has been repeatedly attacked in the literature. Opponents and proponents of trope theory alike have levelled their criticisms at the abstractness of tropes and the associated act of abstraction. In this paper I defend the concept of a (...) trope qua abstract particular by rejecting arguments that purport to show that tropes should not be understood as abstract and by arguing that the abstractness of tropes plays an indispensable role in one of our more promising trope-theoretic analyses of universals and of concrete objects. (shrink)

In this article, we present, assess and give reasons to reject the popular claim that shame is essentially social. We start by presenting several theses which the social claim has motivated in the philosophical literature. All of them, in their own way, regard shame as displaying a structure in which "others" play an essential role. We argue that while all these theses are true of some important families of shame episodes, none of them generalize so as to motivate the conclusion (...) that shame is an essentially social emotion. We consider each thesis in turn, explaining in the process their connections with one another as well as the constraints on a theory of shame they help uncover. Finally, we show how a non-social picture of shame is not only capable of meeting these constraints, but has the further virtue of shedding light on those situations in which others seem to play no role in why we feel shame. (shrink)

Pursuing Justice, Second Edition, examines the issue of justice by considering the origins of the idea, formal systems of justice, current global issues of justice, and ways in which justice might be achieved by individuals, organizations, and the global community. Part 1 demonstrates how the idea of justice has emerged over time, starting with religion and philosophy, then moving to the justice as a concern of the state, and finally to the concept of social justice. Part 2 outlines the very (...) different mechanisms used by various nations for achieving state justice, including systems based on common law, civil law, and Islamic law, with a separate discussion of the US justice system. Part 3 focuses on four contemporary issues of justice: war, genocide, slavery, and the environment. Finally, Part 4 shows how individuals and organizations can go about pursuing justice, and describes the rise of global justice. This updated timely book helps students understand the complexities and nuances of a society's pursuit of justice. It provides students with the foundations of global justice systems, integrating Greek philosophies and major religious perspectives into a justice perspective, and contributes to undergraduate understanding of international justice bodies, NGOs, and institutions. New edition is completely updated and revised to achieve relevance for today's students Covers concepts of justice as well as ideas for pursuing and achieving justice Examines how our modern laws began, and traces their evolution to today's laws Presents concepts and issues in justice studies as well as a comparison of several systems of law Teaching resources include discussion questions and real-world examples. (shrink)

This essay brings psychoanalytic theory on trauma together with film and television criticism on rape narrative in an analysis of Michael Coel’s 2020 series I May Destroy You. Beyond the limited carceral framework of the police procedural, which dislocates the act of violence from the survivor’s history and context, Coel’s polyvalent, looping narrative metabolizes rape television’s forms and genres in order to stage and restage both trauma and genre again and anew. Contesting common conceptions of vulnerability and susceptibility that prefigure (...) a violent breach of autonomy, Coel’s series and her interviews about it invite an ethics of looking that embraces a curiosity in the unknowable and untreatable kernel of subjective experience and defies and resists a policing of the survivor’s thoughts and emotions. By emphasizing and exploring what psychoanalysis calls the “afterwardness” of trauma, Coel foregrounds her main character’s subjectivity prior to her victimization, widens the sphere of consequence beyond the victim and criminal justice system to the survivor’s larger community, and entreats that community to preserve a space for her to look and look again at everything, without judgment. (shrink)

The concept of instantiation is realized differently across a variety of metaphysical theories. A certain realization of the concept in a given theory depends on what roles are specified and associated with the concept and its corresponding term as well as what entities are suited to fill those roles. In this paper, the classic realization of the concept of instantiation in a one-category ontology of abstract particulars or tropes is articulated in a novel way and defended against unaddressed objections.