We provide a new interpretation of Zeno’s Paradox of Measure that begins by giving a substantive account, drawn from Aristotle’s text, of the fact that points lack magnitude. The main elements of this account are (1) the Axiom of Archimedes which states that there are no infinitesimal magnitudes, and (2) the principle that all assignments of magnitude, or lack thereof, must be grounded in the magnitude of line segments, the primary objects to which the notion of linear magnitude applies. Armed (...) with this account, we are ineluctably driven to introduce a highly constructive notion of (outer) measure based exclusively on the total magnitude of potentially infinite collections of line segments. The Paradox of Measure then consists in the proof that every finite or potentially infinite collection of points lacks magnitude with respect to this notion of measure. We observe that the Paradox of Measure, thus understood, troubled analysts into the 1880’s, despite their knowledge that the linear continuum is uncountable. The Paradox was ultimately resolved by Borel in his thesis of 1893, as a corollary to his celebrated result that every countable open cover of a closed line segment has a finite sub-cover, a result he later called the “First Fundamental Theorem of Measure Theory.” This achievement of Borel has not been sufficiently appreciated. We conclude with a metamathematical analysis of the resolution of the paradox made possible by recent results in reverse mathematics. (shrink)

The presence of nonobservational vocabulary is shown to be necessary for wide application of a conservative principle of theory revision.

We describe a logic of preference in which modal connectives reflect reasons to desire that a sentence be true. Various conditions on models are introduced and analyzed.

Alternative models of idealized scientific inquiry are investigated and compared. Particular attention is devoted to paradigms in which a scientist is required to determine the truth of a given sentence in the structure giving rise to his data.

A model of idealized scientific inquiry is presented in which scientists are required to infer the nature of the structure that makes true the data they examine. A necessary and sufficient condition is presented for scientific success within this paradigm.

This chapter contains sections titled: Validity in the Finite Model Theory in the Finite? Definability and Complexity First‐Order Definability Second‐Order Definability Inductive Definability Infinitary Logics Random Graphs and 0–1 Laws.

We consider drawbacks to scientific methods that prefer simple hypotheses to complex ones that cover the same data. The discussion proceeds in the context of a precise model of scientific inquiry.

This paper provides a mathematical model of scientific discovery. It is shown in the context of this model that any discovery problem that can be solved by a computable scientist can be solved by a computable scientist all of whose conjectures are finitely axiomatizable theories.

Criteria of approximate scientific success are defined within a formal paradigm of empirical inquiry. One consequence of aiming for less than perfect truth is examined.

A criterion of adequacy is proposed for theories of relevant consequence. According to the criterion, scientists whose deductive reasoning is limited to some proposed subset of the standard consequence relation must not thereby suffer a reduction in scientific competence. A simple theory of relevant consequence is introduced and shown to satisfy the criterion with respect to a formally defined paradigm of empirical inquiry.

This note investigates the class of finite initial segments of the cumulative hierarchy of pure sets. We show that this class is first-order definable over the class of finite directed graphs and that this class admits a first-order definable global linear order. We apply this last result to show that FO = FO.

This book gives a comprehensive overview of central themes of finite model theory – expressive power, descriptive complexity, and zero-one laws – together with selected applications relating to database theory and artificial intelligence, especially constraint databases and constraint satisfaction problems. The final chapter provides a concise modern introduction to modal logic, emphasizing the continuity in spirit and technique with finite model theory. This underlying spirit involves the use of various fragments of and hierarchies within first-order, second-order, fixed-point, and infinitary logics (...) to gain insight into phenomena in complexity theory and combinatorics. The book emphasizes the use of combinatorial games, such as extensions and refinements of the Ehrenfeucht-Fraissé pebble game, as a powerful way to analyze the expressive power of such logics, and illustrates how deep notions from model theory and combinatorics, such as o-minimality and treewidth, arise naturally in the application of finite model theory to database theory and AI. Students of logic and computer science will find here the tools necessary to embark on research into finite model theory, and all readers will experience the excitement of a vibrant area of the application of logic to computer science. (shrink)

A paradigm of scientific discovery is defined within a first-order logical framework. It is shown that within this paradigm there exists a formal scientist that is Turing computable and universal in the sense that it solves every problem that any scientist can solve. It is also shown that universal scientists exist for no regular logics that extend first-order logic and satisfy the Löwenheim-Skolem condition.

We examine the prospects for finding “best possible” or “ideal” computing machines for various learning tasks. For this purpose, several precise senses of “ideal machine” are considered within the context of formal learning theory. Generally negative results are provided concerning the existence of ideal learning‐machines in the senses considered.

Response to Mark Weinstein's "Reason and the Child." Questions the connection between "rationality" and children's moral status.

ON DECEMBER 10, 1991 Charles Shonubi, a Nigerian citizen but a resident of the USA, was arrested at John F. Kennedy International Airport for the importation of heroin into the United States.1 Shonubi's modus operandi was ``balloon swallowing.'' That is, heroin was mixed with another substance to form a paste and this paste was sealed in balloons which were then swallowed. The idea was that once the illegal substance was safely inside the USA, the smuggler would pass the balloons and (...) recover the heroin. On the date of his arrest, Shonubi was found to have swallowed 103 balloons containing a total of 427.4 grams of heroin. There was little doubt about Shonubi's guilt. In fact, there was considerable evidence that he had made at least seven prior heroin-smuggling trips to the USA (although he was not tried for these). In October 1992 Shonubi was convicted in a United States District Court for possessing and importing heroin. Although the conviction was only for crimes associated with Shonubi's arrest date of December 10, 1991, the sentencing judge, Jack B. Weinstein, also made a ®nding that Shonubi had indeed made seven prior drug-smuggling trips to the USA. The interesting part of this case was in the sentencing. According to the federal sentencing guidelines, the sentence in cases such as this should depend on the total quantity of heroin involved. This instruction was interpreted rather broadly.. (shrink)

This is a review of the film Big Eyes. Adapted from a true story about artist Margaret Keane, the overarching theme of the movie is plagiarism. While most people think of written works such as books and articles being plagiarized, Big Eyes gives viewers insight into the world of stolen works of visual art, namely paintings. The victim finds moral courage through religion, while the thief lives in denial until death. Anyone with an interest in art, law, or psychiatry will (...) enjoy what Big Eyes has to offer. (shrink)

Fitouchi et al.'s moral disciplining approach highlights the significant role social evaluations of self-control appear to play in human moral judgment. At the same time, attributing the wide range of puritanical concerns to a singular focus on self-control seems unwarranted. A more pluralistic approach would enrich understanding of moral judgment in all its cultural and historical diversity.

From very early on, Western philosophers have been obsessed with the understanding of a relatively few works of philosophy which have played a disproportionately large and fundamental role in developing the Western philosophical canon, dominating the curriculum in the past and in the present; there is no indication that they will not do so in the future.Uses and Abuses of the Classics examines the various ways in which the different periods of the history of philosophy have approached these texts. The (...) editors have chosen for analysis some of the major philosophers from periods of the history of philosophy in which the interpretation of the classics has been particularly significant.Contributions to this book include entries on: Aristotle's reading of Plato; Averroes on Aristotle; Nietzsche on the Beginnings of Western Philosophy; and Thomas Aquinas's Commentary on Aristotle's Metaphysics. (shrink)

Why We Argue : A Guide to Political Disagreement in an Age of Unreason presents an accessible and engaging introduction to the theory of argument, with special emphasis on the way argument works in public political debate. The authors develop a view according to which proper argument is necessary for one's individual cognitive health; this insight is then expanded to the collective health of one's society. Proper argumentation, then, is seen to play a central role in a well-functioning democracy. Written (...) in a lively style and filled with examples drawn from the real world of contemporary politics, and questions following each chapter to encourage discussion, Why We Argue reads like a guide for the participation in, and maintenance of, modern democracy. An excellent student resource for courses in critical thinking, political philosophy, and related fields, Why We Argue is an important contribution to reasoned debate. What's New in the Second Edition: Updated examples throughout the book, including examples from the 2016 U.S. election and first years of the Trump presidency; Expanded coverage of dialectical fallacies, including coverage of new types of fallacies and of sites where such fallacies thrive ; Revised For Further Thought questions and definitions of Key Terms, included at the end of each chapter; The addition of five new chapters: Deep Disagreement Argument by Analogy Argument between the Ads The Owl of Minerva Argumentative Responsibility and Repair. (shrink)

From the beginning of the scientific revolution, scientists, philosophers, and laypersons have been concerned about the effects of knowledge on social relations. Although views differ about the details of this knowledge-society interface, most observers have understood that the kind of knowledge that emanates from establishedscience can indeed be quite powerful in practice. In exploring both the nature of race science discourse and selected features of the practical context within which it resonates effectively, the authors' investigationsof this field and its contribution (...) to the Holocaust represent an effort to specify some of the things that make knowledge powerful. (shrink)

Critical explorations of the key thinkers in the New World. Intersecting biography and history, individual monographs in New World Perspectives examine the central intellectual vision of leading contributors to politics, culture and society.

Physicians have an ethical responsibility to their patients to offer the best available medical care. This responsibility conflicts with their role as gatekeepers of the limited health care resources available for all patients collectively. It is ethically untenable to expect doctors to face this trade-off during each patient encounter; the physician cannot be expected to compromise the wellbeing of the patient in the office in favour of anonymous patients elsewhere. Hence, as in other domains of public policy where individual and (...) collective interests conflict, some form of collective solution is required. Collective solutions may take the form of placing explicit resource constraints on resources available to physicians, or clinical practice guidelines that recognise cost-effective care as acceptable. Such solutions will be politically and ethically sustainable only if patients as citizens of the larger population accept the need for rationing of limited resources in health care. (shrink)

In the following paper, Annemiek Richters of the University of Leiden in the Netherlands addresses the dilemmas faced by health professionals who are asked to evaluate and provide supporting documentation for those refugees who seek political asylum in the countries of Europe. It is in the politically charged arena of asylum applications, government regulations, and public policy where bioethics, human rights, and health converge. Despite the 1951 Convention on Refugees, a treaty signed by nations around the world to safeguard the (...) rights of those who are displaced, and other treaties that protect the rights of vulnerable populations, refugee and asylum policies have become increasingly strict in an effort to deter those who would seek safety. This tightening of borders in the countries of the West challenges physicians who find themselves caught between obligations to treat, to advocate, and to challenge policies that make treatment a potentially dangerous proposition. Unfortunately, the World Trade Center attacks have exacerbated the problem by labeling asylees and refugees as potential terrorists and subject to deportation. (shrink)

Science and the originality of life -- Christian facticity -- Grasping life as a topic -- Ruinance -- The retrieval of history -- Facticity and ontology -- Factical speaking -- Rhetoric -- Sophistry.

In Group Psychology and the Analysis of the Ego Freud addresses the problem of how groups are formed or of how society is possible. The question of the possibility of society presupposes that in some sense human beings are not thoroughly social beings, that they must agree to or be made to participate in a common life in which they submit to general principles regulating their conduct towards one another. The notion that the grounds for social order cannot be taken (...) for granted originates in the beginnings of modern thought, particularly in Hobbes’ Leviathan, in which the classical idea that human beings are essentially social and political animals is rejected in favor of the view that the individual is in a basic sense independent of society and opposed to it, and that society is merely a conventional unity. For Hobbes, society is primarily a defensive alliance guaranteed by fear of a sovereign who constitutes a legal order. Social order, then, is imposed externally on the individual, who submits to regulation only on the basis of prudence. The history of thought about the problem of order after Hobbes’ initial attempt to resolve it is a development of more refined motives for obedience, which culminates in Kant's notion of a self-legislated moral law. The importance of Kant's solution is that it provides a positive ground for society. Human beings do not merely submit to standards because they are inclined to, either out of fear or out of desire, but because they acknowledge a rational principle to which they give their voluntary assent. For Hobbes, society is at least an imposition and at most an expedient. For Kant, society may, indeed, be both an imposition and an expedient, but it is also an order of life that might be perfected. In Kant's view, human beings are imperfectly rational beings, not organisms entirely ruled by pleasure and pain, as they were for Hobbes. (shrink)

This ambitious, interdisciplinary book seeks to explain the origins of religion using our knowledge of the evolution of cognition. A cognitive anthropologist and psychologist, Scott Atran argues that religion is a by-product of human evolution just as the cognitive intervention, cultural selection, and historical survival of religion is an accommodation of certain existential and moral elements that have evolved in the human condition.