Physical Relativity explores the nature of the distinction at the heart of Einstein's 1905 formulation of his special theory of relativity: that between kinematics and dynamics. Einstein himself became increasingly uncomfortable with this distinction, and with the limitations of what he called the 'principle theory' approach inspired by the logic of thermodynamics. A handful of physicists and philosophers have over the last century likewise expressed doubts about Einstein's treatment of the relativistic behaviour of rigid bodies and clocks in motion in (...) the kinematical part of his great paper, and suggested that the dynamical understanding of length contraction and time dilation intimated by the immediate precursors of Einstein is more fundamental. Harvey Brown both examines and extends these arguments, after giving a careful analysis of key features of the pre-history of relativity theory. He argues furthermore that the geometrization of the theory by Minkowski in 1908 brought illumination, but not a causal explanation of relativistic effects. Finally, Brown tries to show that the dynamical interpretation of special relativity defended in the book is consistent with the role this theory must play as a limiting case of Einstein's 1915 theory of gravity: the general theory of relativity.Appearing in the centennial year of Einstein's celebrated paper on special relativity, Physical Relativity is an unusual, critical examination of the way Einstein formulated his theory. It also examines in detail certain specific historical and conceptual issues that have long given rise to debate in both special and general relativity theory, such as the conventionality of simultaneity, the principle of general covariance, and the consistency or otherwise of the special theory with quantum mechanics. Harvey Brown' s new interpretation of relativity theory will interest anyone working on these central topics in modern physics. (shrink)

My paper addresses a number of questions raised in the Statesman by the Eleatic Visitor’s identification of certain ontological conditions for the existence of art of due measure, and therefore of all the technai. My view is that evidence relevant to these questions can be found in the Philebus, and specifically, in an ontological doctrine presented at 23c–27c. What emerges from an examination of the Statesman and Philebus is a highly developed conception of technê, one that affords a place for (...) such ordinary human activities within the broader framework of Plato’s philosophy. (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)

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 now fix A ⊆ Q. We study a fundamental class of digraphs associated with A, which we call the A-digraphs. An A,kdigraph is a digraph (Ak,E), where E is an order invariant subset of A2k in the following sense. For all x,y ∈ A2k, if x,y have the same order type then x ∈ E ↔ y ∈ E.

We address the general problem of determining the validity of boolean combinations of equalities and inequalities between real-valued expressions. In particular, we consider methods of establishing such assertions using only restricted forms of distributivity. At the same time, we explore ways in which “local'’ decision or heuristic procedures for fragments of the theory of the reals can be amalgamated into global ones. Let $Tadd[QQ]$ be the first-order theory of the real numbers in the language with symbols $0, 1, +, -.

Most of my intellectual efforts have focused around a single general question in the foundations of mathematics (f.o.m.). I became keenly aware of this question as a student at MIT around 40 years ago, and readily adopted it as the principal driving force behind my research.

There are two kinds of such limiting results that must be carefully distinguished. Results of the first kind state the nonexistence of any algorithm for determining whether any statement among a given set of statements is true or false.

An unprovable theorem is a mathematical result that can-not be proved using the com-monly accepted axioms for mathematics (Zermelo-Frankel plus the axiom of choice), but can be proved by using the higher infinities known as large cardinals. Large car-dinal axioms have been the main proposal for new axioms originating with Gödel.

We discuss enormous integers and rates of growth after [PH77]. This breakthrough was based on a variant of the classical finite Ramsey theorem. Since then, examples have been given of greater relevance to a number of standard mathematical and computer science contexts, often involving even more enormous integers and rates of growth.

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.

there are mathematical statements that cannot be proved or refuted using the usual axioms and rules of inference of mathematics.

Most of the research in foundations of mathematics that I do in some way or another involves the use of nonstandard models. I will give a few examples, and indicate what is involved.

This is an introduction to the most primitive form of the new Boolean relation theory, where we work with only one function and one set. We give eight complete classifications. The thin set theorem (along with a slight variant), and the complementation theorem are the only substantial cases that arise in these classifications.

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).

The main powerful method for establishing termination of term rewriting systems was discovered by Nachum Dershowitz through the introduction of certain natural well founded orderings (lexicographic path orderings). This leads to natural decision problems which may be of the highest computational complexity of any decidable problems appearing in a natural established computer science context.

Provide a formal system that is a conservative extension of PA for Π02 sentences, and even a conservative extension of HA, that supports the worry free smooth development of constructive analysis in the style of Errett Bishop.

Gödel's legacy is still very much in evidence. We will not attempt to properly discuss the full impact of his work and all of the ongoing important research programs that it suggests. This would require a book length manuscript. Indeed, there are several books discussing the Gödel legacy from many points of view, including, for example, (Wang 1987, 1996), (Dawson 2005), and the historically comprehensive five volume set (Gödel 1986-2003).

The equation P = NP concerns algorithms for deciding membership in sets. The consensus is that P ≠ NP, although some prominent experts guess otherwise.

I don’t remember if I got as high as 2-390, but I distinctly remember taking my first logic course - as a Freshman - with Hartley Rogers, in Fall 1964 - here in 2-190. Or was it in 2-290?

Normal mathematical culture is overwhelmingly concerned with finite structures, finitely generated structures, discrete structures (countably infinite), continuous and piecewise continuous functions between complete separable metric spaces, with lesser consideration of pointwise limits of sequences of such functions, and Borel measurable functions between complete separable metric spaces.

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.

We can look at this model theoretically as follows. By the linearly ordered predicate calculus, we simply mean ordinary predicate calculus with equality and a special binary relation symbol <. It is required that in all interpretations, < be a linear ordering on the domain. Thus we have the usual completeness theorem provided we add the axioms that assert that < is a linear ordering.

It is not yet clear just what the most illuminating ways of rigorously stating the Incompleteness Theorems are. This is particularly true of the Second. Also I believe that there are more illuminating proofs of the Second that have yet to be uncovered.

In this essay Charles Harvey offers a worried reflection on the range, extent, depth, affects, and effects of the perpetual assessment of the person in industrial nations in the contemporary world. Harvey begins his analysis by appealing to the work of Martin Heidegger, Michel Foucault, and Jean Baudrillard to provide an interpretive framework of our situation. He then focuses and concretizes these ideas through examples from his own life and, by extension, the readers. Finally, in light of Pierre (...) Bourdieu's concept of the habitus, Harvey speculates on the implications for selfhood in the contemporary world. Throughout the essay, Harvey uses assessment procedures in higher and public education as exemplary instances of his thesis. (shrink)

ARISTOTLE often claims that words are "homonymous" or "multivocal". He claims this about some of the crucial words and concepts of his own philosophy—"cause," "being," "one," "good," "justice," "friendship." Often he claims it with a polemical aim; other philosophers have wrongly overlooked homonymy and supposed that the same word is always said in the same way. Plato made this mistake; his accounts of being, good, and friendship are rejected because they neglect homonymy and multivocity. In Aristotle’s view Plato shared the (...) Socratic assumption about words and definitions. Socrates thought that when he asked "What is F?" some single definition of F could always be found to match the name "F." Aristotle thinks the Socratic question is important, but argues that it must be controlled by awareness of homonymy and multivocity. (shrink)

The paper describes the approach by which ethics are integrated into the undergraduate curriculum at Northern Illinois University''s College of Business. Literature is reviewed to identify conceptual frameworks for, and issues associated with, the teaching of business ethics. From the review, a set of guidelines for teaching ethics is developed and proposed. The objectives and strategies implemented for teaching ethics is discussed. Foundation and follow-up coursework, measurement issues and ancillary programs are also discussed.

Large Language Models (LLMs) have been transformative. They are pre-trained foundational models that are self-supervised and can be adapted with fine tuning to a wide range of natural language tasks, each of which previously would have required a separate network model. This is one step closer to the extraordinary versatility of human language. GPT-3 and more recently LaMDA can carry on dialogs with humans on many topics after minimal priming with a few examples. However, there has been a wide range (...) of reactions and debate on whether these LLMs understand what they are saying or exhibit signs of intelligence. This high variance is exhibited in three interviews with LLMs reaching wildly different conclusions. A new possibility was uncovered that could explain this divergence. What appears to be intelligence in LLMs may in fact be a mirror that reflects the intelligence of the interviewer, a remarkable twist that could be considered a Reverse Turing Test. If so, then by studying interviews we may be learning more about the intelligence and beliefs of the interviewer than the intelligence of the LLMs. As LLMs become more capable they may transform the way we interact with machines and how they interact with each other. Increasingly, LLMs are being coupled with sensorimotor devices. LLMs can talk the talk, but can they walk the walk? A road map for achieving artificial general autonomy is outlined with seven major improvements inspired by brain systems. LLMs could be used to uncover new insights into brain function by downloading brain data during natural behaviors. (shrink)

By recourse to the fundamentals of preference orderings and their numerical representations through linear utility, we address certain questions raised in Nover and Hájek 2004, Hájek and Nover 2006, and Colyvan 2006. In brief, the Pasadena and Altadena games are well-defined and can be assigned any finite utility values while remaining consistent with preferences between those games having well-defined finite expected value. This is also true for the St Petersburg game. Furthermore, the dominance claimed for the Altadena game over the (...) Pasadena game, and that would have been claimed for the St Petersburg game over the Altadena, can be contradicted without fear of inconsistency with the axioms of utility theory. However, insistence upon dominance can be made to yield a contradiction of the Archimedean axiom of utility theory. CiteULike Connotea Del.icio.us What's this? (shrink)

Professional Ethics: A Trust-Based Approach explores the unique nature of professional duty and virtue in light of the trust that professionals must invite, develop, and honor from those they intend to serve.

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)