We show that a statement HIL, which is motivated by a lemma of Hilbert and close in formulation to Hindman’s theorem, is actually much weaker than Hindman’s theorem. In particular, HIL is finitistically reducible in the sense of Hilbert’s program, while Hindman’s theorem is not.

For over forty years, Leland Ryken has championed and modeled a Christian liberal arts education. His scholarship and commitment to integrating faith with learning in the classroom have influenced thousands of students who have sat under his winsome teaching. Published in honor of Professor Ryken and presented on the occasion of his retirement from Wheaton College, this compilation carries on his legacy of applying a Christian liberal arts education to all areas of life. Five sections explore the background of a (...) Christian liberal arts education, its theological basis, habits and virtues, differing approaches, and ultimate aims. Contributors including Philip Ryken, Jeffry Davis, Duane Litfin, John Walford, Alan Jacobs, and Jim Wilhoit analyze liberal arts as they relate to the disciplines, the Christian faith, and the world. Also included are a transcript of a well-known 1984 chapel talk delivered by Leland Ryken on the student's calling and practical chapters on how to read, write, and speak well. Comprehensive in scope, this substantial volume will be a helpful guide to anyone involved in higher education, as well as to students, pastors, and leaders looking for resources on the importance of faith in learning. - Publisher. (shrink)

This book focuses on the degree to which certain moral and legal doctrines are rooted in specific passions that are then institutionalised in the form of criminal law. A philosophical analysis is developed of the following questions: when, if ever, should hatred be overcome by sympathy or compassion? What are forgiveness and mercy and to what degree do they require - both conceptually and morally - the overcoming of certain passions and the motivation by other passions? If forgiveness and mercy (...) indeed are moral virtues, what role, if any, should they play in the law? (shrink)

In this revised edition, two distinguished philosophers have extended and strengthened the most authoritative text available on the philosophy of law and jurisprudence. While retaining their comprehensive coverage of classical and modern theory, Murphy and Coleman have added new discussions of the Critical Legal Studies movement and feminist jurisprudence, and they have strengthened their treatment of natural law theory, criminalization, and the law of torts. The chapter on law and economics remains the best short introduction to that difficult, controversial, and (...) influential topic.Students will appreciate the careful organization and clear presentation of complicated issues as well as the emphasis on the relevance of both law and legal theory to contemporary society. (shrink)

The prevalence of social pathologies in contemporary societies has triggered many critical theorists to challenge or even disrupt the status quo in the hope for a better society. Thus, the notion of social transformation or, better yet, emancipation has become one of the central themes in critical social theory. This paper aims to contribute to this scholarship through an exposition of Herbert Marcuse's attempt to socialize Georg Hegel's ontology. Inparticular, this paper aims to show how Marcuse explains the possibility of (...) social transformation by appropriating key concepts in Hegel's huge philosophical system, most particularly from Hegel's Logic and the phenomenology of mind. (shrink)

Scientists employ a variety of procedures to eliminate degrees of freedom from computationally and/or analytically intractable equations. In the process, they often construct new models and discover new concepts, laws and functional relations. I argue these procedures embody a central notion of reduction, namely, the containment of one structure within another. However, their inclusion in the philosophical concept of reduction necessitates a reevaluation of many standard assumptions about the ontological, epistemological and functional features of a reduction. On the basis of (...) the reevaluation, I advocate a continuum of reduction which proceeds from the eliminative to the constructive. The metaphysical aspects of theory use in constructive reductions are sketched. (shrink)

Achilles is vindictive; he wants to get even with Agamemnon. Being so disposed, he sounds rather like many current crime victims who angrily complain that the American system of criminal justice will not allow them the satisfactions they rightfully seek. These victims often feel that their particular injuries are ignored while the system addresses itself to some abstract injury to the state or to the rule of law itself – a focus that appears to result in wrongdoers being treated with (...) much greater solicitation and respect than their victims receive. If the actual victims are noticed at all, they will likely be told that there is another branch of law – tort law – that has the job of dealing with private injuries and grievances and that, if they pursue this route at their own expense, they might ultimately get some financial compensation for the wrongs done to them. However, just as Achilles felt that mere compensation was inadequate to the kind of injury done to him by Agamemnon, many of these victims will often claim that the injuries they have suffered do not admit of financial compensation. How, they might ask, can a dollar value be set on the humiliation and degradation they have experienced? They might also note that those who injure them tend, unlike Agamemnon, to be judgment-proof – so lacking in resources as to be unable to make any meaningful contribution to any compensation package that the victim may win. (shrink)

Jeffry H. Morrison offers readers the first comprehensive look at the political thought and career of John Witherspoon—a Scottish Presbyterian minister and one of America’s most influential and overlooked founding fathers. Witherspoon was an active member of the Continental Congress and was the only clergyman both to sign the Declaration of Independence and to ratify the federal Constitution. During his tenure as president of the College of New Jersey at Princeton, Witherspoon became a mentor to James Madison and influenced (...) many leaders and thinkers of the founding period. He was uniquely positioned at the crossroads of politics, religion, and education during the crucial first decades of the new republic. Morrison locates Witherspoon in the context of early American political thought and charts the various influences on his thinking. This impressive work of scholarship offers a broad treatment of Witherspoon’s constitutionalism, including his contributions to the mediating institutions of religion and education, and to political institutions from the colonial through the early federal periods. This book will be appreciated by anyone with an interest in American political history and thought and in the relation of religion to American politics. “I have been waiting a long time for such a book on John Witherspoon. This book is not only well-researched, but well-written. The story Morrison tells is quite wonderful.” —_Michael Novak, American Enterprise Institute for Public Policy Research_ _ _ "Dr. John Witherspoon is at once an exceptionally influential figure in Early American history, and a sadly neglected one. Professor Morrison's book fills this gap in American political history brilliantly. It is especially revealing of 18th century views on the interrationships between education, religion, and society. Morrison presents new insights into the Early American understanding of balancing faith, government, and society. It will change our conceptions of this period and provide fresh perspectives on contemporary problems. Everyone interested in the American Founding era is indebted to Morrison for this illuminating book." —_Garrett Ward Sheldon, University of Virginia's College at Wise_ "At last we have a full and learned account, as the title states, of _JOHN WITHERSPOON aND THE FOUNDING OF THE AMERICAN REPUBLIC_. Including discussion of Witherspoon's direct role in the crucial events of 1775-1790 as an advocate of Independence and friend of the Constitution, as a contributor to early American religious and political thought, and most important, as a mentor to James Madison and other Princeton revolutionairies and nation-builders, Morrison reveals Witherspoon's high standing in American religious, educational, and political history. Madison remembered Witherspoon's injunction to his students to 'Lead useful Lives;' he provided an excellent role model." —_Ralph Ketcham, Syracuse University_. (shrink)

Prediction is more than testing established theory by examining whether the prediction matches the data. To show this, I examine the practices of a community of scientists, known as threaders, who are attempting to predict the final, folded structure of a protein from its primary structure, i.e., its amino acid sequence. These scientists employ a careful and deliberate methodology of prediction. A key feature of the methodology is calibration. They calibrate in order to construct better models. The construction leads to (...) knowledge of how to construct or build an object. Thus, prediction serves a cognitive goal of model construction and not just model or theory testing. The kind of knowledge that results is relevantly different than theoretical knowledge. (shrink)

If α and β are ordinals, α ≤ β, and $\beta \nleq \alpha$ , then α + 1 ≤ β. The first result of this paper shows that the restriction of this statement to countable well orderings is provably equivalent to ACA 0 , a subsystem of second order arithmetic introduced by Friedman. The proof of the equivalence is reminiscent of Dekker's construction of a hypersimple set. An application of the theorem yields the equivalence of the set comprehension scheme ACA (...) 0 and an arithmetical transfinite induction scheme. (shrink)

The authors present a balanced critique of the adaptation/exaptation debate and specify some of the hard evidentiary criteria that are needed to advance our understanding of human evolution. Investigators must build more “special design” criteria into their theorizing and research. By documenting that certain traits meet these rigorous criteria, the evolutionary sciences will ultimately rest on a firmer theoretical foundation.

Human mating and parenting are more complex than has been implied by many evolutionarily based theories of sex differences. While focusing on sex differences might shed some light on the evolution of mating and parenting, this level of analysis is rather imprecise. More important, it ignores several ecological variables that should have influenced mating/parenting decisions and behaviors in both sexes.

We have all been victims of wrongdoing. Forgiving that wrongdoing is one of the staples of current pop psychology dogma; it is seen as a universal prescription for moral and mental health in the self-help and recovery section of bookstores. At the same time, personal vindictiveness as a rule is seen as irrational and immoral. In many ways, our thinking on these issues is deeply inconsistent; we value forgiveness yet at the same time now use victim-impact statements to argue for (...) harsher penalties for criminals. Do we have a right to hate others for what they have done to us? Providing a nuanced approach to a proper understanding of the place of our strongest emotions in moral, political, and personal life, and using lucid, easily understood prose, this volume is a classic example of philosophical thinking applied to a thorny, everyday problem. (shrink)

Philosophers disagree how abstract, theoretical principles can be applied to instances. This paper generates a puzzle for law theorists, causal theorists and inductivists alike. Intractability can force scientists to use a "semi-empirical" method, in which some of an equation's theoretically-determinable parameters are replaced with values taken directly from the data. This is not a purely deductive or inductive process, nor does it involve causes and capacities in any simple way (Humphreys 1995). I argue the predictive successes of such methods require (...) us to reanalyze our views about the nature of prediction, the status of models, and the goal(s) of science. When laws and experimental evidence are neither individually nor jointly sufficient for prediction, models become the locus of understanding. I analyze an historically important debate about the use of semi-empirical methods to construct potential energy surfaces. (shrink)

Chemists take mechanisms to be an important way of explaining chemical change. I examine the usefulness of the mechanism approach in the recent philosophical literature in explicating the explanatory use of mechanisms by organic chemists. I argue that chemists consider a mechanism to be explanatory because it accounts for the “dynamic process of bringing about” (Tabery 2004 , 10) chemical change. For chemists, mechanisms are causal explanations based on interventions that show “how some possibilities depend on others” (Woodward 2003 , (...) 375). Only possibilities are achievable because chemists face a number of challenges when they explain by means of a mechanism. †To contact the author, please write to: Department of Philosophy, Smith College, Northampton, MA 01063; e‐mail: [email protected]. (shrink)

By stressing the act rather than the relation of approximation, I argue that the magnitude of the error introduced should not be used as the sole criterion for judging the worth of the approximation. Magnitude is a necessary but not sufficient condition for such a judgement. Controllability, the absence of cancelling errors, and the approximation's justification are also important criteria to consider when praising or blaming an approximation. Boltzmann's discussion of the types of approximations used in the kinetic theory of (...) gases at the turn of the century illustrates the use of these criteria. (shrink)

Simpson has claimed that “ATR0 is the weakest set of axioms which permits the development of a decent theory of countable ordinals” [8]. This paper provides empirical support for Simpson's claim. In particular, Cantor's Normal Form Theorem and Sherman's Inequality for countable well-orderings are both equivalent to ATR0. The proofs of these results require a substantial development of ordinal exponentiation and a strengthening of the comparability result in [3].

One of the earliest applications of transfinite numbers is in the construction of derived sequences by Cantor [2]. In [6], the existence of derived sequences for countable closed sets is proved in ATR0. This existence theorem is an intermediate step in a proof that a statement concerning topological comparability is equivalent to ATR0. In actuality, the full strength of ATR0 is used in proving the existence theorem. To show this, we will derive a statement known to be equivalent to ATR0, (...) using only RCA0 and the assertion that every countable closed set has a derived sequence. We will use three of the subsystems of second order arithmetic defined by H. Friedman , which can be roughly characterized by the strength of their set comprehension axioms. RCA0 includes comprehension for Δmath image definable sets, ACA0 includes comprehension for arithmetical sets, and ATR0 appends to ACA0 a comprehension scheme for sets defined by transfinite recursion on arithmetical formulas. MSC: 03F35, 54B99. (shrink)

If there is a homeomorphic embedding of one set into another, the sets are said to be topologically comparable. Friedman and Hirst have shown that the topological comparability of countable closed subsets of the reals is equivalent to the subsystem of second order arithmetic denoted byATR 0. Here, this result is extended to countable closed locally compact subsets of arbitrary complete separable metric spaces. The extension uses an analogue of the one point compactification of ℝ.

Psychologist Sharon Lamb and philosopher Jeffrie Murphy argue that forgiveness has been accepted as a therapeutic strategy without serious, critical examination. Chapters by both psychologists and philosophers ask: Why is forgiveness so popular now? What exactly does it entail? When might it be appropriate for a therapist not to advise forgiveness? When is forgiveness in fact harmful?

We prove that the statement “there is aksuch that for everyfthere is ak-bounded diagonally nonrecursive function relative tof” does not imply weak König’s lemma over${\rm{RC}}{{\rm{A}}_0} + {\rm{B\Sigma }}_2^0$. This answers a question posed by Simpson. A recursion-theoretic consequence is that the classic fact that everyk-bounded diagonally nonrecursive function computes a 2-bounded diagonally nonrecursive function may fail in the absence of${\rm{I\Sigma }}_2^0$.

In an interesting experimental study, Bonini et al. (1999) present partial support for truth-gap theories of vagueness. We say this despite their claim to find theoretical and empirical reasons to dismiss gap theories and despite the fact that they favor an alternative, epistemic account, which they call ‘vagueness as ignorance’. We present yet more experimental evidence that supports gap theories, and argue for a semantic/pragmatic alternative that unifies the gappy supervaluationary approach together with its glutty relative, the subvaluationary approach.

Based on a series of lectures delivered at the University of Virginia in October 1981. Includes bibliographical references and index.

A critique of Richard Posner's suggestion that notions of economic efficiency can serve as ethical foundations.

Grand Hotel Abyss investigates the lives and afterlives of the critical theorists who formed the Frankfurt School.

Abstract Philosophers have paid little attention to the kind of reduction involved in transforming an analytically intractable equation into solvable form. I argue that this practice is important because it involves the design of a basic level theory for use in a specific domain. The design process can lead to the construction of a new theory. As a result of my analysis, theory design emerges as an important category of analysis for scientific methodology. Similarities between design in technology and science (...) are explored to illuminate the heuristic function of such reductions. (shrink)

Natural deduction is the type of logic most familiar to current philosophers, and indeed is all that many modern philosophers know about logic. Yet natural deduction is a fairly recent innovation in logic, dating from Gentzen and Jaśkowski in 1934. This article traces the development of natural deduction from the view that these founders embraced to the widespread acceptance of the method in the 1960s. I focus especially on the different choices made by writers of elementary textbooks—the standard conduits of (...) the method to a generation of philosophers—with an eye to determining what the ‘essential characteristics’ of natural deduction are. (shrink)