We introduce a reducibility preordering between classes of countable structures, each class containing only structures of a given similarity type (which is allowed to vary from class to class). Though we sometimes work in a slightly larger context, we are principally concerned with the case where each class is an invariant Borel class (i.e. the class of all models, with underlying set $= \omega$, of an $L_{\omega_1\omega}$ sentence; from this point of view, the reducibility can be thought of as a (...) (rather weak) sort of $L_{\omega_1\omega}$-interpretability notion). We prove a number of general results about this notion, but our main thrust is to situate various mathematically natural classes with respect to the preordering, most notably classes of algebraic structures such as groups and fields. (shrink)

The purpose of this paper is to evaluate the `Lorentzian Pedagogy' defended by J.S. Bell in his essay ``How to teach special relativity'', and to explore its consistency with Einstein's thinking from 1905 to 1952. Some remarks are also made in this context on Weyl's philosophy of relativity and his 1918 gauge theory. Finally, it is argued that the Lorentzian pedagogy---which stresses the important connection between kinematics and dynamics---clarifies the role of rods and clocks in general relativity.

PREFACE. We present a variety of basic theories involving fundamental concepts of naive thinking, of the sort that were common in "natural philosophy" before the dawn of physical science. The most extreme forms of infinity ever formulated are embodied in the branch of mathematics known as abstract set theory, which forms the accepted foundation for all of mathematics. Each of these theories embodies the most extreme forms of infinity ever formulated, in the following sense. ZFC, and even extensions of ZFC (...) with the so called large cardinal axioms, are mutually interpretable with these theories. This is an extended abstract. Proofs of the claims will appear elsewhere. (shrink)

We introduce insertion domains that support the placement of new, higher, vertices into finite trees. We prove that every nonincreasing insertion domain has an element with simple structural properties in the style of classical Ramsey theory. This result is proved using standard large cardinal axioms that go well beyond the usual axioms for mathematics. We also establish that this result cannot be proved without these large cardinal axioms. We also introduce insertion rules that specify the placement of new, higher, vertices (...) into finite trees. We prove that every insertion rule greedily generates a tree with these same structural properties; and every decreasing insertion rule generates (or admits) a tree with these same structural properties. It is also necessary and sufficient to use the same large cardinals (in the precise sense of Corollary D.25). The results suggest new areas of research in discrete mathematics called "Ramsey tree theory" and "greedy Ramsey theory" which demonstrably require more than the usual axioms for mathematics. (shrink)

The subtle, almost ineffable, and ineffable cardinals were introduced in an unpublished 1971 manuscript of R. Jensen and K. Kunen. The concepts were extended to that of k-subtle, k-almost ineffable, and k-ineffable cardinals in 1975 by J. Baumgartner. In this paper we give a self contained treatment of the basic facts about this level of the large cardinal hierarchy, which were established by J. Baumgartner. In particular, we give a proof that the k-subtle, k-almost ineffable, and k-ineffable cardinals define three (...) properly intertwined hierarchies with the same limit, lying strictly above “total indescribability” and strictly below “arrowing ω”. The innovation here is presented in Section 2, where we take a distinctly minimalist approach. Here the subtle cardinal hierarchy is characterized by very elementary properties that do not mention closed unbounded or stationary sets. This development culminates in a characterization of the hierarchy by means of a striking universal second-order property of linear orderings. (shrink)

The purpose of the paper is to explore different aspects of the covariance of non-relativistic quantum mechanics. First, doubts are expressed concerning the claim that gauge fields can be 'generated' by way of imposition of gauge covariance of the single-particle wave equation. Then a brief review is given of Galilean covariance in the general case of external fields, and the connection between Galilean boosts and gauge transformations. Under time-dependent translations the geometric phase associated with Schrödinger evolution is non-invariant, and the (...) significance of this result is briefly analysed. The covariance properties of Schrödinger dynamics are then brought to bear on certain versions of the modal interpretation of quantum mechanics. The conclusion that it is only relational properties that can be considered coordinate- or gauge-independent elements of reality is reinforced by appeal to the theory of quantum reference frames due to Aharonov and Kauffher. , Cambridge University Press ; pp. 45-70.). (shrink)

Let k ≥ 2 and f:Nk Æ [1,k] and n ≥ 1 be such that there is no x1 < ... < xk+1 £ n such that f(x1,...,xk) = f(x1,...,xk+1). Then we want to find g:Nk+1 Æ [1,3] such that there is no x1 < ... < xk+2 £ n such that g(x1,...,xk+1) = g(x2,...,xk+2). This reducees adjacent Ramsey in k dimensions with k colors to adjacent Ramsey in k+1 dimensions with 3 colors.

Philosophy of education has an honored place in the history of Western philosophical thought. Its questions are as vital now, both philosophically and practically, as they have ever been. In recent decades, however, philosophical thinking about education has largely fallen off the philosophical radar screen. Philosophy of education has lost intimate contact with the parent discipline to a regrettably large extent--to the detriment of both. The Oxford Handbook of Philosophy of Education is intended to serve as a general introduction to (...) key issues in the field, to further the philosophical pursuit of those issues, and to bring philosophy of education back into closer contact with general philosophy. Distinguished philosophers and philosophers of education, most of whom have made important contributions to core areas of philosophy, turn their attention in these 28 essays to a broad range of philosophical questions concerning education. The chapters are accessible to readers with no prior exposure to philosophy of education, and provide both surveys of the general domain they address, and advance the discussion in those domains in original and fruitful ways. Together their authors constitute a new wave of general philosophers taking up fundamental philosophical questions about education--the first such cohort of outstanding general philosophers to do so (in English) in a generation. (shrink)

We consider a number of statements involving restrictions and extensions of algebras, and derive connections with large cardinal axioms.

Religion is more than a matter of worshipping a deity or spirit. For many people, religion pervades every part of their lives and is not separated off into some purely private and personal realm. Religion is integral to many people's relationship with the wider world, an aspect of their dwelling among other beings - both human and other-than-human - and something manifested in the everyday world of eating food, having sex and fearing strangers. Food, Sex and Strangers offers alternative ways (...) of thinking about what religion involves and how we might better understand it. Drawing on studies of contemporary religions, especially among indigenous peoples, the book argues that religion serves to maintain and enhance human relationships in and with the larger-than-human world. Fundamentally, religion can be better understood through the ways we negotiate our lives than in affirmations of belief - and it is best seen when people engage in intimate acts with themselves and others. (shrink)

We axiomatize EFA in strictly mathematical terms, involving only the ring operations, without extending the language by either exponentiation, finite sets of integers, or polynomials.

In mathematics, we back up our discoveries with rigorous deductive proofs. Mathematicians develop a keen instinctive sense of what makes a proof rigorous. In logic, we strive for a *theory* of rigorous proofs.

An assignment is a function f that assigns subsets of N to some atoms. Then f is extended to f* which sends every formula A of HPC to a subset of S(A).

Gödel's definitive results and his essays leave us with a rich legacy of philosophical programs that promise to be subject to mathematical treatment. After surveying some of these, we focus attention on the program of circumventing his demonstrated impossibility of a consistency proof for mathematics by means of extramathematical concepts.

For digraphs G, we write V(G) for the set of all vertices of G, and E(G) for the set of all edges of G. A digraph on a set E is a digraph G where V(G) = E.

Mathematical Logic had a glorious period in the 1930s, which was briefly rekindled in the 1960s. Any Shock Value, such as it is, has surrounded unprovability from ZFC.

An extreme kind of logic skeptic claims that "the present formal systems used for the foundations of mathematics are artificially strong, thereby causing unnecessary headaches such as the Gödel incompleteness phenomena". The skeptic continues by claiming that "logician's systems always contain overly general assertions, and/or assertions about overly general notions, that are not used in any significant way in normal mathematics. For example, induction for all statements, or even all statements of certain restricted forms, is far too general - mathematicians (...) only use induction for natural statements that actually arise. If logicians would tailor their formal systems to conform to the naturalness of normal mathematics, then various logical difficulties would disappear, and the story of the foundations of mathematics would look radically different than it does today. In particular, it should be possible to give a convincing model of actual mathematical practice that can be proved to be free of contradiction using methods that lie within what Hilbert had in mind in connection with his program”. Here we present some specific results in the direction of refuting this point of view, and introduce the Strict Reverse Mathematics (SRM) program. (shrink)

It has been accepted since the early part of the Century that there is no problem formalizing mathematics in standard formal systems of axiomatic set theory. Most people feel that they know as much as they ever want to know about how one can reduce natural numbers, integers, rationals, reals, and complex numbers to sets, and prove all of their basic properties. Furthermore, that this can continue through more and more complicated material, and that there is never a real problem.

Abstract The Suttas indicate physical conditions for success in meditation, and also acceptance of a not?Self life?principle (primarily viññana) which is (usually) dependent on the mortal physical body. In the Abhidhamma and commentaries, the physical acts on the mental through the senses and through the ?basis? for mind?organ and mind?consciousness, which came to be seen as the ?heart?basis?. Mind acts on the body through two ?intimations?: fleeting modulations in the primary physical elements. Various forms of r?pa are also said to (...) originate dependent on citta and other types of r?pa. Meditation makes possible the development of a ?mind?made body? and control over physical elements through psychic powers. The formless rebirths and the state of cessation are anomalous states of mind?without?body, or body?without?mind, with the latter presenting the problem of how mental phenomena can arise after being completely absent. Does this twin?category process pluralism avoid the problems of substance?dualism? (shrink)

Since then we have been engaged in the development of such results of greater relevance to mathematical practice. In January, 1997 we presented some new results of this kind involving what we call “jump free” classes of finite functions. This Jump Free Theorem is treated in section 2.

Is 'education' a thick epistemic concept? The answer depends, of course, on the viability of the 'thick/thin' distinction, as well as the degree to which education is an epistemic concept at all. I will concentrate mainly on the latter, and will argue that epistemological matters are central to education and our philosophical thinking about it; and that, insofar, education is indeed rightly thought of as an epistemic concept. In laying out education's epistemological dimensions, I hope to clarify the degree to (...) which it makes sense to regard the concept as 'thick'. I also discuss the relationship between philosophy of education and virtue epistemology and the sense in which being educated might itself be thought to be an epistemic virtue. Finally, I urge virtue epistemologists in particular and epistemologists generally to turn their attention to questions of education, to further both the philosophy of education and epistemology itself. (shrink)

There are many contemporary sources and defenders of epistemological relativism which have not been considered thus far. I have, for example, barely touched on the voluminous literature regarding frameworks, conceptual schemes, and Wittgensteinian forms of life. Davidson's challenge to the scheme/content distinction and thereby to conceptual relativism, Rorty's acceptance of the Davidsonian argument and his use of it to defend a relativistic position, Winchian and other sociological and anthropological arguments for relativism, recent work in the sociology of science, and Goodman's (...) novel articulation of a relativism of worlds and of worldmaking, to mention just some of the contemporary loci of debate, all need to be addressed. So also do the plethora of relativistic arguments spawned by Kuhn and related literature in recent philosophy of science. Therefore, it cannot be said that there is no more to be said on behalf of epistemological relativism. Moreover, the positive task of delineating a defensible version of absolutism remains to be accomplished.Nevertheless, the defenses of relativism considered above do seem to have been successfully undercut. More specifically, the arguments for the incoherence of relativism are as compelling as ever, and have manifestly not been laid to rest by contemporary relativists. The basic Socratic insight that relativism is self-refuting, and so incoherent, remains a fundamental difficulty for those who would resuscitate and defend the ancient Protagorean doctrine or a modern variant of it. (shrink)

Notwithstanding that there is now widespread interest in the rights of victims, little has been written about the theoretical justification of state compensation. Here we offer an initial exploration of the field in the hope that others might venture further and examine the points at which issues of compensation connect with other general and specific themes in social and political philosophy. For example, there has been much discussion about communitarian conceptions of civil society but the practical implications of such views, (...) other than those relating to multiculturalism, have been largely ignored. The application of theory to social policy needs to take account of existing laws and institutions and these vary from one society and jurisdiction to another. In what follows we are principally concerned with the situation obtaining in the United Kingdom but the underlying issues are general ones [1]. (shrink)

AT the conclusion of his recently published paper on Corinna1 Professor Page leaves open the question whether the poetess was a contemporary of Pindar or of Moschus-whether she belongs to the middle of the fifth century or the end of the third. He gives excellent reasons for believing that these two dates exhaust the possibilities: they are far more probable than a date either outside or between them; but there seems to be no sure criterion by which we can decide (...) between the two, and Professor Page has to end his researches with a suspension of judgement. (shrink)

This article argues that the quantitative and quasi-experimental approach to evaluating public participation exercises is deficient in at least two respects. First, casting participants in instrumental terms excludes that participants have an experience and that this may be dramatic and emotional. If people are to be invited, even obliged, to participate, then this experience should be considered in event evaluation. Second, current evaluation frameworks tend not to be sensitive to what actually happened in terms of the actions of participants and (...) how these influenced the proceedings and outcome, thus ignoring that such events are fora where positions, values, decisions, and so forth are constructed and constrained rather than simply reported. This article considers the possible contribution of dramaturgical, discourse and conversation analytic, and ethnographic and phenomenological approaches to evaluating participation exercises and illustrates their potential with data gathered during the U.K. “GM Nation?” public debate. (shrink)

Cells can transit between a range of stable epithelial and mesenchymal states and this has allowed the evolution of complex body forms. Epithelial to mesenchymal transition (EMT) and its reverse, mesenchymal to epithelial transition (MET), occur sequentially in development and organogenesis. EMT often accompanies transitions between stem‐like cells and their more differentiated progeny, as occurs at gastrulation, although the relevance of this had not been clarified. New findings from the cancer and cell reprogramming fields suggest that EMT and MET can (...) act as essential portals to stem cell character. Here, we review these findings in the broader context of EMT and MET with emphasis on stem cell biology. Using the heart as an example, we also explore the potential role of EMT/MET in organ regeneration. Understanding EMT and MET at a network level will give us new tools to probe stem cell character and enhance tissue repair. (shrink)

The cognitive and behavioral functions of the frontal lobes have been of great interest to neuroscientists, neurologists, psychologists and psychiatrists. Recent technical advances have made it possible to trace their neuroanatomical connections more precisely and to conduct evoked potential and neuroimaging studies in patients. This book presents a broad and authoritative synthesis of research progress in this field. It encompasses neuroanatomical studies; experiments involving temporal organization and working memory tasks in non-human primates; clinical studies of patients following frontal lobe excisions (...) for intractable epilepsy; metabolic imaging in schizophrenia and affective disorder; neurobehavioral studies of patients with dementia, frontal lobe tumors, and head injuries; magnetic resonance imaging methods for studying human frontal lobe anatomy; theoretical approaches to describing frontal lobe functions; and rehabilitation of patients with frontal lobe damage including their core problem of diminished awareness. Written by a distinguished group of neuroscientists, psychologists and clinicians, Frontal Lobe Function and Dysfunction provides the best current source of information on this region of the brain and its role in cognition, behavior and clinical disorders. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:Plato's Utopia Recast: His Later Ethics and PoliticsGeorge HarveyChristopher Bobonich. Plato's Utopia Recast: His Later Ethics and Politics. Oxford: Clarendon Press of Oxford University Press, 2002. Pp. xi + 643. Cloth, $49.95.In tracing developments in Plato's views between his middle- and late-period dialogues, Plato's Utopia Recast focuses on the differences between philosophers and non-philosophers with respect to their capacities to become genuinely virtuous. The central thesis of this (...) extensive work is that the Laws reveals a degree of optimism about the prospects for non-philosophers in attaining virtue and happiness not found in dialogues of the middle period. Specifically, Bobonich describes this development in terms of four claims that he thinks Plato denies in the Phaedo and Republic but later affirms in the Laws: first, that at least some non-philosophers are capable of being virtuous; second, that they can value virtue for its own sake; third, that they can value the virtue and happiness in others for its own sake; and fourth, that these non-philosophers are capable of living happy lives.Bobonich devotes most of the first chapter to describing Plato's pessimism about non-philosophers in the middle period. The cause for this pessimism is both epistemic and psychological. In the Phaedo, non-philosophers are incapable of knowing what is genuinely valuable. Failure to grasp non-sensible value properties means that in non-philosophers, reason simply takes over the ends defined by bodily impulses. The Republic is less pessimistic, but even here, Plato's tripartitioning of the soul makes clear that the rational part of the soul in non-philosophers fails to fulfill its proper ruling function. Bobonich's claim is that the more optimistic view presented in the Laws is indicative of developments not only in Plato's political theory, but also in the areas of psychology and epistemology.The central feature of the political theory advanced in the Laws is that the proper goal of legislation is not victory in war, but the cultivation of virtue in all citizens. More importantly for Bobonich, it suggests that all citizens, both philosophers and non-philosophers, are capable of attaining some degree of genuine virtue. For evidence of this, he points to the preludes that accompany each piece of legislation designed to provide a rational justification for what the laws command. In identifying virtue as the aim of legislation, Bobonich observes that the Laws endorses a dependency thesis about goods, making the value of a dependent good such as wealth, honor or military victory dependent upon its possessor being virtuous. His position is that Plato's endorsement of this dependency thesis in the Laws implies that ordinary citizens are capable of at least a partial grasp of what is genuinely valuable, making some degree of virtue and happiness attainable.Bobonich's view that this optimism about non-philosophers has implications for Plato's later epistemology and psychology is developed in the third and fourth chapters. He argues that the Republic's partitioning of the soul into three distinct, agent-like parts is abandoned in the later dialogues in favor of a more unified conception. This approach in the [End Page 334] middle period served to account for akratic action and the formation of non-rational desires, but Bobonich believes that Plato came to see this doctrine as ultimately flawed. By contrast, the Laws offers an account of akratic action and non-rational desire that maintains a unified subject and avoids the problems found in partitioning. In chapter four, Bobonich considers how the Laws' unified conception of the subject, supported by the Phaedrus, Philebus and Timaeus, reveals how all human aims and desires, both rational and non-rational, are structured and conceptualized through the soul's rational faculty. In this unified conception of the subject, Bobonich sees important implications for the role of non-rational elements in the ethical education of even ordinary human beings.In the fifth and final chapter, Bobonich returns to politics, and considers how Plato's conception of citizenship in the Laws reflects the more optimistic view of human nature. He examines how citizens in the Laws develop non-instrumental concerns for the happiness... (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)

The one sphere of life where a claimed right to privacy is most sympathetically received is in the inner realm of the mind. I will look briefly at Joseph Tussman’s claim that a government is not only entitled but morally required to be concerned with and involved in the minds of the nation’s citizens. I then further explore reasons why the realm of the mind matters not only morally but politically. There are consequentialist reasons, but more interestingly there are non-consequentialist (...) reasons on the basis of which I introduce the concept of “authentic social justice.” In particular, there are relevant insights to be gainedby reflecting on forms of oppression that are subtle but serious in nature, forms that involve neither violence nor the use of law. (shrink)

This paper proposes a model of human uniqueness based on an unusual distinction between two contrasted kinds of political competition and political status: (1) antagonistic competition, in quest of dominance (antagonistic status), a zero-sum, self-limiting game whose stake—who takes what, when, how—summarizes a classical definition of politics (Lasswell 1936), and (2) synergistic competition, in quest of merit (synergistic status), a positive-sum, self-reinforcing game whose stake becomes “who brings what to a team’s common good.” In this view, Rawls’s (1971) famous virtual (...) “veil of ignorance” mainly conceals politics’ antagonistic stakes so as to devise the principles of a just, egalitarian society, yet without providing any means to enforce these ideals (Sen 2009). Instead, this paper proposes that human uniqueness flourished under a real “adapted veil of ignorance” concealing the steady inflation of synergistic politics which resulted from early humans’ sturdy egalitarianism. This proposition divides into four parts: (1) early humans first stumbled on a purely cultural means to enforce a unique kind of within-team antagonistic equality—dyadic balanced deterrence thanks to handheld weapons (Chapais 2008); (2) this cultural innovation is thus closely tied to humans’ darkest side, but it also launched the cumulative evolution of humans’ brightest qualities—egalitarian team synergy and solidarity, together with the associated synergistic intelligence, culture, and communications; (3) runaway synergistic competition for differential merit among antagonistically equal obligate teammates is the single politically selective mechanism behind the cumulative evolution of all these brighter qualities, but numerous factors to be clarified here conceal this mighty evolutionary driver; (4) this veil of ignorance persists today, which explains why humans’ unique prosocial capacities are still not clearly understood by science. The purpose of this paper is to start lifting this now-ill-adapted veil of ignorance, thus uncovering the tight functional relations between egalitarian team solidarity and the evolution of human uniqueness. (shrink)

In the course of his studies on Kabbalah, Moshe Idel has written on the influence of Kabbalists on philosophy. He suggests that Spinoza was influenced by the Kabbalah regarding his expressions “Deus sive Natura“ and “amor Dei intellectualis.” The 13th-century ecstatic Kabbalist Rabbi Abraham Abulafia and many authors after him cited the numerical equivalence of the Hebrew words for God and Nature: elohim = ha-teba` = 86. This striking numerical equivalence may be one of the sources of Spinoza’s expression “Deus (...) sive Natura.” The same Kabbalist used the Hebrew expression “ahabah elohit sikhlit“ (“divine intellectual love”), which may underlie Spinoza’s expression “amor Dei intellectualis.” Abulafia’s expression “ahabah elohit sikhlit“ is repeated by the popular 15th-century Maimonidean philosopher, Rabbi Abraham Shalom. (shrink)