Critique of instrumental accounts of epistemic rationality.

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

An open U ⊆ ℝ is produced such that (ℝ, +, ·, U) defines a Borel isomorph of (ℝ, +, ·, ℕ) but does not define ℕ. It follows that (ℝ, +, ·, U) defines sets in every level of the projective hierarchy but does not define all projective sets. This result is elaborated in various ways that involve geometric measure theory and working over o-minimal expansions of (ℝ, +, ·). In particular, there is a Cantor set E ⊆ ℝ (...) such that (ℝ, +, ·, E) defines a Borel isomorph of (ℝ, +, ·, ℕ) and, for every exponentially bounded o-minimal expansion $\germ{R}$ of (ℝ, +, ·), every subset of ℝ definable in ( $\germ{R}$ , E) either has interior or is Hausdorff null. (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 this paper, we consider how the four key team emergent states for team learning identified by Bell, Kozlowski and Blawath (2012), namely psychological safety, goal orientation, cohesion, and efficacy, operate as a system that produces the team’s learning climate (TLC). Using the language of systems dynamics, we conceptualize TLC as a stock that rises and falls as a joint function of the psychological safety, goal orientation, cohesion, and efficacy that exists in the team. The systems approach highlights aspects of (...) TLC management that are traditionally overlooked, such as the simultaneous influence of and feedback between the four team emergent states and the inertia that TLC can have as a result. The management of TLC becomes an issue of controlling the system rather than each state as an independent force, especially because changing one part of the system will also affect other parts in sometimes unintended and undesirable ways. Thus the value is to offer a systems view on the leadership function of team monitoring with regards to team emergent states, which we term team state monitoring. This view offers promising avenues for future research as well as practical wisdom. It can help leaders remember that TLC represents an equilibrium that needs balance, in addition to pointing to the various ways in which they can influence such equilibrium. (shrink)

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.

Analysis of Emmy Noether's 1918 theorems provides an illuminating method for testing the consequences of coordinate generality, and for exploring what else must be added to this requirement in order to give general covariance its far-reaching physical significance. The discussion takes us through Noether's first and second theorems, and then a third related theorem due originally to F. Klein. Contact will also be made with the contributions of, principally, J.L. Anderson, A. Trautman, P.A.M. Dirac, R. Torretti and the father of (...) the whole business, A. Einstein. (shrink)

(1995). Innovation and change in the production of knowledge. Social Epistemology: Vol. 9, Knowledge (EX) Change, pp. 211-232. doi: 10.1080/02691729508578789.

The ISI Guides to the Major Disciplines are reader-friendly introductions to the most important fields of knowledge in the liberal arts. Written by leading scholars for both students and the general public, they will be appreciated by anyone desiring a reliable and informative tour of important subject matter. Each title offers an historical overview of a particular discipline, explains the central ideas of each subject, and evaluates the works of thinkers whose ideas have shaped our world. They will aid students (...) seeking to make better decisions about their course of study as well as general readers who wish to supplement their education. All who treasure the world of ideas and liberal learning will be motivated by these original and stimulating presentations. (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.

This article considers the way beneficence was treated in an important journal toward the end of the Old Regime. It finds that the Journal de Paris during the years 1783 and 1784 not only publicized acts of beneficence, but also mediated between members of the public who, on their own initiative, contributed to those in need and officials and organizations which in practice cared for the disadvantaged, especially a committee that freed prisoners for debts to wet nurses and the Société (...) philanthropique of Paris. While the notion of beneficence has sometimes been found to offer a secularized version of the traditional value of charity, this article finds that in practice religious and secular people worked together to support those they deemed worthy of aid. The relation of beneficence to self-interest is also considered, and it is suggested that the initiatives of the better-off members of civil society rather than government opened the way toward something approaching a welfare state. (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.

The notion of interpretation is absolutely fundamental to mathematical logic and the foundations of mathematics. It is also crucial for the foundations and philosophy of science - although here some crucial conditions generally need to be imposed; e.g., “the interpretation leaves the mathematical concepts unchanged”.

This article presents a cross-cultural exploration of the interaction between religion and family in the lives of women. It focuses on elderly Middle Eastern Jewish women who, during the course of their life spans, moved from a conflicting to a complementary experience of family and religion. The author argues that opposition between religion and family seldom arises for women who control their own time or resources, or who control a domestic sphere they themselves see as sacred. Women who wish to (...) conduct their religious lives in the public sphere, especially in the context of an extrafamilial hierarchy or as religious professionals, are likely to come into conflict with their families over issues of competition for their time or allegiance. Official religious doctrines are not likely to determine how particular women experience family and religion; even women who maneuver within the same theological framework may experience the relationship between family and religion in very different ways. (shrink)

Machiavelli's New Modes and Orders is the only full-length interpretive study on Machiavelli's controversial and ambiguous work, Discourses on Livy. These discourses, considered by some to be Machiavelli's most important work, are thoroughly explained in a chapter-by-chapter commentary by Harvey C. Mansfield, one of the world's foremost interpreters of this remarkable philosopher. Mansfield's aim is to discern Machiavelli's intention in writing the book: he argues that Machiavelli wanted to introduce new modes and orders in political philosophy in order to (...) make himself the founder of modern politics. Mansfield maintains that Machiavelli deliberately concealed part of his intentions so that only the most perceptive reader could see beneath the surface of the text and understand the whole of his book. Previously out of print, Mansfield's penetrating study brings to light the hidden thoughts lurking in the details of the Discourses on Livy to inform and challenge its readers at every step along the way. (shrink)

Should advance directives (ADs) such as living wills be employed to direct the care of the severely demented? In considering this question, I focus primarily on the claims of Rebecca Dresser who objects in principle to the use of ADs in this context. Dresser has persuasively argued that ADs are both theoretically incoherent and ethically dangerous. She proceeds to advocate a Best Interest Standard as the best way for deciding when and how the demented ought to be treated. I put (...) forth a compromise position: both ADs and the Best Interest Standard have roles to play in guiding the care of the severely demented. (shrink)

This chapter contains sections titled: Abstract Introduction Arguments Con Arguments Pro Ambivalence Concerning Relativism? The Case of Richard Rorty A Newer Argument Pro: Hales's Defense of Relativism References.

Certainty (and the lack thereof) is a major issue in mathematics and computer science. Mathematicians strongly believe in a special kind of certainty for their theorems.

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)

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)

Dispositionalist accounts of colour concepts are now largely discarded. But a number of recent and influential objections to this type of theory can be readily answered providing the dispositionalist account contains the key elements it should---which actual versions in the literature do not. I explicate some of the conceptual components needed in such an account once we correctly understand the anthropocentricity of the colour concepts involved. When these components are incorporated into dispositionalism, including one crucial distinction in particular, some powerful (...) seeming objections against this revised dispositionalism fail. In addition, dispositionalism has extra advantages over the far more popular physicalist theories, and I therefore contend that we should explore vigorously this kind of enriched dispositionalist account. (shrink)

We give a consistency proof within a weak fragment of arithmetic of elementary algebra and geometry. For this purpose, we use EFA (exponential function arithmetic), and various first order theories of algebraically closed fields and real closed fields.

Each of these theorems and concepts arose from very specific considerations of great general interest in the foundations of mathematics (f.o.m.). They each serve well defined purposes in f.o.m. Naturally, the preferred way to formulate them for mathe-matical logicians is in terms that are close to their roots in f.o.m.

We present several selection theorems for Borel relations, involving only Borel sets and functions, all of which can be obtained as consequences of closely related theorems proved in [DSR 96,99,01,01X] involving coanalytic sets. The relevant proofs given there use substantial set theoretic methods, which were also shown to be necessary. We show that none of our Borel consequences can be proved without substantial set theoretic methods. The results are established for Baire space. We give equivalents of some of the main (...) results for the reals. (shrink)

We have been recently engaged in this search, and have announced a long series of successively simpler and more convincing examples. See [Fr09-10].

This essay argues that it is a matter of vital concern to develop a theoretical apparatus that is adequate to the inherent spatiotemporal dynamics of capital accumulation and the changing practices developed to manage the crisis tendencies of those dynamics. This requires integrating the a-spatial theory of capital accumulation and its internal contradictions with the spatial/geographical theory of imperialism that invokes geopolitical and geo-economic struggles between nation-states. I argue that the two are linked by the way capital deals with the (...) problem of absorbing capital surpluses, namely through geographical fixes. The geographical fix requires imperialist expansionism and the battering down of all barriers to the spatial movement of capital. Such a conception provides the necessary clarity in formulating the relations between capital and state that are sometimes missing from Ellen M. Wood's arguments in Empire of Capital. (shrink)

This is an immediate conse-quence of a more general combinatorial theorem called Ramsey’s theorem, but it is much simpler to state. We call this adjacent Ramsey theory.

I. WKL0 is a conservative extension of PRA for ’-0-2 sentences. II. ACA0 is a conservative extension of PA for arithmetic sentences. III. ATR0 is a conservative extension of IR for arithmetic sentences. IV. ’-1-1-CA0 is a conservative extension of ID(

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The goal is to show that various exotic prefix classes can be "tamed by large cardinals". I.e., every statement in the class is either provable or refutable using presently formulated large cardinals. Some of these exotic prefix classes consist entirely of explicitly P01 sentences.