Reasoning under uncertainty, that is, making judgements with only partial knowledge, is a major theme in artificial intelligence. Professor Paris provides here an introduction to the mathematical foundations of the subject. It is suited for readers with some knowledge of undergraduate mathematics but is otherwise self-contained, collecting together the key results on the subject, and formalising within a unified framework the main contemporary approaches and assumptions. The author has concentrated on giving clear mathematical formulations, analyses, justifications and consequences of the (...) main theories about uncertain reasoning, so the book can serve as a textbook for beginners or as a starting point for further basic research into the subject. It will be welcomed by graduate students and research workers in logic, philosophy, and computer science as a textbook for beginners, a starting point for further basic research into the subject, and not least, an account of how mathematics and artificial intelligence can complement and enrich each other. (shrink)

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"The Laws", Plato's most lengthy dialogue, has longbeen regarded as the most comprehensive explanation of the possible consequences of a practical application of his philosophy.We might expect the first question Plato ponders to be "What is Law?" Instead, the question posed is "Who is given the credit for laying down your laws?"We are privy to an interaction between a powerfulstatesman and an Athenian philosopher on theisland of Crete. We watch as a plan for a new political order is worked out (...) that embodiesmany of the issues that we still struggle withtoday, such as the status of women, the statusof homosexuals, the family, criminal law, andthe role of religion in a healthy society.We at Timeless Classic Books hope that you enjoy this ancient thought-provoking story that may change the way you think about modern day issues.(Timeless Classic Books). (shrink)

J. B. Schneewind's "The Invention of Autonomy" has been hailed as a major interpretation of modern moral thought. Schneewind's narrative, however, elides several serious interpretive issues, particularly in the transition from late medieval to early modern thought. This results in potentially distorted accounts of Thomas Aquinas, Hugo Grotius, and G. W. Leibniz. Since these thinkers play a crucial role in Schneewind's argument, uncertainty over their work calls into question at least some of Schneewind's larger agenda for the history of ethics.

A supertask is a task that consists in infinitely many component steps, but which in some sense is completed in a finite amount of time. Supertasks were studied by the pre-Socratics and continue to be objects of interest to modern philosophers, logicians and physicists. The term “super-task” itself was coined by J.F. Thomson (1954). Here we begin with an overview of the analysis of supertasks and their mechanics. We then discuss the possibility of supertasks from the perspective of general relativity.

We examine the closure conditions of the probabilistic consequence relation of Hawthorne and Makinson, specifically the outstanding question of completeness in terms of Horn rules, of their proposed (finite) set of rules O. We show that on the contrary no such finite set of Horn rules exists, though we are able to specify an infinite set which is complete.

We give an account of some relationships between the principles of Constant and Atom Exchangeability and various generalizations of the Principle of Instantial Relevance within the framework of Inductive Logic. In particular we demonstrate some surprising and somewhat counterintuitive dependencies of these relationships on ostensibly unimportant parameters, such as the number of predicates in the overlying language.

In the paper I offer a brief sketch of one of the sources of utilitarianism. Our biological ancestry is a matter of fact that is not altered by the way we describe ourselves. With philosophical theories it is otherwise. Utilitarianism can be described in ways that make it look as if it is as old as moral philosophy – as J. S. Mill thought it was. For my historical purposes, it is more useful to have an account that brings out (...) what is specific about Benthamism and its descendants. Let us try to make do with the following. First, utilitarianism asserts that the fundamental requirement of morality is that we are to maximize good, for everyone and not just for the agent. This basic principle presupposes that it makes sense to think of aggregating goods to make a total, and of comparing amounts of good thus aggregated. Second, the good to be brought about is located in feelings of pleasure, and the evil to be avoided in feelings of pain. These feelings have inherent value or disvalue regardless of how they are caused to exist and regardless of their own consequences. Third, all moral principles can be derived from the requirement that good be maximized. The principles involved in evaluating agents as well as in giving moral direction to action are nothing but applications of the basic principle. (shrink)

This article shows a clear sense in which general relativity allows for a type of ‘machine’ that can bring about a spacetime structure suitable for the implementation of ‘supertasks’. 1Introduction2Preliminaries3Malament–Hogarth Spacetimes4Machines5Malament–Hogarth Machines6Conclusion.

In this era of increased polarization of opinion and contentious disagreement, CRITICAL REASONING presents a cooperative approach to critical thinking and formation of beliefs. CRITICAL REASONING emphasizes the importance of developing and applying analytical skills in real life contexts. This book is unique in providing multiple, diverse examples of everyday arguments, both textual and visual, including hard to find long argument passages from real-life sources. The book provides clear, step-by-step procedures to help you decide for yourself what to believe--to be (...) a consumer of information in our contemporary "world of experts.". (shrink)

We give a complete characterization of Priest's Finite Inconsistent Arithmetics observing that his original putative characterization included arithmetics which cannot in fact be realized.

Part I of this two-part paper provided a broad overview of clinical and experimental findings bearing on the neural correlates of conscious processes. It was argued that several neurocognitive models related to: orienting to the outer world, dream sleep, and the integration of sensory-motor representations, converge upon a core ‘conscious system’, dubbed the extended reticular-thalamic activating system . The functions of the ERTAS, which shares extensive projections with the cerebral cortex, are mostly ‘implicit’, in contrast to the explicit representation of (...) conscious content within the neocortex. Part II expands this ERTAS model to encompass: the generation of coherent patterns of EEG activation, the integration of distributed cortical processes into a stream of unified percepts , and selective attention, as well as links between the ERTAS and systems providing the neural substrates for episodic memory and volition. (shrink)

We answer some problems set by Priest in [11] and [12], in particular refuting Priest's Conjecture that all LP-models of Th(N) essentially arise via congruence relations on classical models of Th(N). We also show that the analogue of Priest's Conjecture for I δ₀ + Exp implies the existence of truth definitions for intervals [0,a] ⊂ₑ M ⊨ I δ₀ + Exp in any cut [0,a] ⊂e K ⊆ M closed under successor and multiplication.

One usually identifies a particular collection of geometric objects with the models of general relativity. But within this standard collection lurk ‘physically unreasonable’ models of spacetime. If such models are ruled out, attention can be restricted to some sub-collection of ‘physically reasonable’ models which can be considered a variant theory of general relativity. Since we have yet to identify a privileged sub-collection of ‘physically reasonable’ models, it is helpful to think of ‘general relativity’ in a pluralistic way; we can study (...) a collection of such ‘physically reasonable’ collections of models. (shrink)

It is generally believed that the uncertainty relation Δq Δp≥1/2ħ, where Δq and Δp are standard deviations, is the precise mathematical expression of the uncertainty principle for position and momentum in quantum mechanics. We show that actually it is not possible to derive from this relation two central claims of the uncertainty principle, namely, the impossibility of an arbitrarily sharp specification of both position and momentum (as in the single-slit diffraction experiment), and the impossibility of the determination of the path (...) of a particle in an interference experiment (such as the double-slit experiment).The failure of the uncertainty relation to produce these results is not a question of the interpretation of the formalism; it is a mathematical fact which follows from general considerations about the widths of wave functions.To express the uncertainty principle, one must distinguish two aspects of the spread of a wave function: its extent and its fine structure. We define the overall widthW Ψ and the mean peak width wψ of a general wave function ψ and show that the productW Ψ w φ is bounded from below if φ is the Fourier transform of ψ. It is shown that this relation expresses the uncertainty principle as it is used in the single- and double-slit experiments. (shrink)

Here we discuss the challenge posed by self-organization to the Darwinian conception of evolution. As we point out, natural selection can only be the major creative agency in evolution if all or most of the adaptive complexity manifest in living organisms is built up over many generations by the cumulative selection of naturally occurring small, random mutations or variants, i.e., additive, incremental steps over an extended period of time. Biological self-organization—witnessed classically in the folding of a protein, or in the (...) formation of the cell membrane—is a fundamentally different means of generating complexity. We agree that self-organizing systems may be fine-tuned by selection and that self-organization may be therefore considered a complementary mechanism to natural selection as a causal agency in the evolution of life. But we argue that if self-organization proves to be a common mechanism for the generation of adaptive order from the molecular to the organismic level, then this will greatly undermine the Darwinian claim that natural selection is the major creative agency in evolution. We also point out that although complex self-organizing systems are easy to create in the electronic realm of cellular automata, to date translating in silico simulations into real material structures that self-organize into complex forms from local interactions between their constituents has not proved easy. This suggests that self-organizing systems analogous to those utilized by biological systems are at least rare and may indeed represent, as pre-Darwinists believed, a unique ascending hierarchy of natural forms. Such a unique adaptive hierarchy would pose another major challenge to the current Darwinian view of evolution, as it would mean the basic forms of life are necessary features of the order of nature and that the major pathways of evolution are determined by physical law, or more specifically by the self-organizing properties of biomatter, rather than natural selection. (shrink)

I analyze a number of the quantum no-signalling proofs (Ghirardi et al. 1980, Bussey 1982, Jordan 1983, Shimony 1985, Redhead 1987, Eberhard and Ross 1989, Sherer and Busch 1993). These purport to show that the EPR correlations cannot be exploited for transmitting signals, i.e., are not causal. First, I show that these proofs can be mathematically unified; they are disguised versions of a single theorem. Second, I argue that these proofs are circular. The essential theorem relies upon the tensor product (...) representation for combined systems, which has no physical basis in the von Neumann axioms. Historically, the construction of this representation scheme by von Neumann and Weyl built no-signalling assumptions into the quantum theory. Signalling between the wings of the EPR-Bell experiments is unlikely but is not ruled out empirically by the class of proofs considered. (shrink)

This study investigates specific behavioral perceptual differences of ethics between practitioners and students enrolled in sales classes. Respondents were asked to indicate their beliefs to issues related to ethics in sales. A highly significant difference was found between mean responses of students and sales personnel. Managers indicated a greater concern for ethical behavior and less attention to sales than did the students. Students indicated a strong desire for success regardless of ethical constraints violated.

A splendid edition. Schneewind's illuminating introduction succinctly situates the _Enquiry_ in its historical context, clarifying its relationship to Calvinism, to Newtonian science, and to earlier moral philosophers, and providing a persuasive account of Hume's ethical naturalism. --Martha C. Nussbaum, Brown University.