The calculus of relations was created and developed in the second half of the nineteenth century by Augustus De Morgan, Charles Sanders Peirce, and Ernst Schröder. In 1940 Alfred Tarski proposed an axiomatization for a large part of the calculus of relations. In the next decade Tarski's axiomatization led to the creation of the theory of relation algebras, and was shown to be incomplete by Roger Lyndon's discovery of nonrepresentable relation algebras. This paper introduces the calculus of relations and (...) the theory of relation algebras through a review of these historical developments. (shrink)
The set of equations which use only one variable and hold in all representable relation algebras cannot be derived from any finite set of equations true in all representable relation algebras. Similar results hold for cylindric algebras and for logic with finitely many variables. The main tools are a construction of nonrepresentable one-generated relation algebras, a method for obtaining cylindric algebras from relation algebras, and the use of relation algebras in defining algebraic semantics for first-order logic.
Sound and complete semantics for classical propositional logic can be obtained by interpreting sentences as sets. Replacing sets with commuting dense binary relations produces an interpretation that turns out to be sound but not complete for R. Adding transitivity yields sound and complete semantics for RM, because all normal Sugihara matrices are representable as algebras of binary relations.
This book is intended as an equivalent to or substitute for that "more reflective reading" which Rousseau considered essential to an understanding of his ideas. It is designed to complement perusal of the texts themselves, and the arrangement is such that chapters on each of Rousseau's major writings can be consulted separately or the commentary may be read through in sequence. The author's purpose is not to present a "key" to Rousseau's political philosophy, but rather to explore the works themselves (...) in an effort to reveal Rousseau's "system," from which the reader may then draw his own conclusions. Originally published in 1976. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905. (shrink)
Conjecture (1) of [Ma83] is confirmed here by the following result: if $3 \leq \alpha < \omega$, then there is a finite relation algebra of dimension α, which is not a relation algebra of dimension α + 1. A logical consequence of this theorem is that for every finite α ≥ 3 there is a formula of the form $S \subseteq T$ (asserting that one binary relation is included in another), which is provable with α + 1 variables, but not (...) provable with only α variables (using a special sequent calculus designed for deducing properties of binary relations). (shrink)
Most people are familiar with the traditional view of the role of ethics in the auditing profession – the need for auditors with integrity and objectivity. This essay addresses a second dimension of ethics in the auditing profession – the demand for auditors to assess the integrity and ethical values of clients. This second dimension is a difficult task for auditors in practice and demands a deep and robust understanding of ethics, ethical infrastructures, and the products of those infrastructures. The (...) essay proposes how educators and researchers might facilitate that understanding. (shrink)
Most people are familiar with the traditional view of the role of ethics in the auditing profession - the need for auditors with integrity and objectivity. This essay addresses a second dimension of ethics in the auditing profession - the demand for auditors to assess the integrity and ethical values of clients. This second dimension is a difficult task for auditors in practice and demands a deep and robust understanding of ethics, ethical infrastructures, and the products of those infrastructures. The (...) essay proposes how educators and researchers might facilitate that understanding. (shrink)
Molecular genetic testing has increasingly been incorporated into clinical medicine, and this trend is likely to accelerate in the future. The introduction of genetic testing into medical practice is beginning to collide head on with patents that claim ownership of correlations between human genetic variants and predisposition to disease, response to therapeutic drugs, and susceptibility to pharmacologic side effects. Patent holders or licensees of genes, genetic variants, and their genotype-phenotype correlations are already using the threat of litigation to monopolize genetic (...) tests for important well-known syndromes like Duchenne Muscular Dystrophy and inherited breast and ovarian cancer, in addition to a host of less commonly discussed conditions. (shrink)
If K is a class of semiassociative relation algebras and K contains the relation algebra of all binary relations on a denumerable set, then the word problem for the free algebra over K on one generator is unsolvable. This result implies that the set of sentences which are provable in the formalism Lwx is an undecidable theory. A stronger algebraic result shows that the set of logically valid sentences in Lwx forms a hereditarily undecidable theory in Lwx. These results generalize (...) similar theorems, due to Tarski, concerning relation algebras and the formalism Lx. (shrink)
This monograph introduces the functional characteristics and conceptual significance of a simulation software system called CyberRat (Ray, 1996a, 2003a, 2012a, 2012b). CyberRat expands upon prior illustrations (Ray & Delprato, 1989; Ray, 1992) of how such computer-based simulations can serve to formatively enhance, and eventually validate, the descriptive research methodology upon which their development relies. To illustrate this process I also review highlights of previous publications (cf. Ray & Brown, 1975, 1976; Ray & Delprato, 1989), detailing the unique research methodology used (...) to collect data that guided CyberRat’s development. This methodology integrates interbehavioral psychology (Kantor, 1959) and general systems analysis (von Bertalanffy, 1968), and thus is referred to as interbehavioral systems analysis (IBSA). CyberRat’s validation of IBSA methods involves a process analogous to Turing’s (1950) famous test for simulation authenticity, in that it relies upon “phenomenological equivalence” criteria for observers to compare experiences of real vs. simulated events. And because IBSA stresses three convergent strategies for research, including structural analysis, functional analysis, and operations analysis, my organizing theme addresses how closely CyberRat comes to passing a trilogy of hypothetical Turing tests—one for each of these three analytic strategies. (shrink)
Speculations about the role of consciousness in physical systems are frequently observed in the literature concerned with the interpretation of quantum mechanics. While only three experimental investigations can be found on this topic in physics journals, more than 800 relevant experiments have been reported in the literature of parapsychology. A well-defined body of empirical evidence from this domain was reviewed using meta-analytic techniques to assess methodological quality and overall effect size. Results showed effects conforming to chance expectation in control conditions (...) and unequivocal non-chance effects in experimental conditions. This quantitative literature review agrees with the findings of two earlier reviews, suggesting the existence of some form of consciousness-related anomaly in random physical systems. (shrink)
The value of Abraham Kuyper’s thought is presently being discovered by a growing body of readers. Herman Dooyeweerd’s thought is appreciated by a smaller number. Yet he was trained in the Kuyperian tradition and conceived many of his most characteristic insights by building on Kuyper’s. What did he learn from Abraham and what can be learned by reflecting on their shared ideas? A view of the coherence, the gum and wire holding society and the cosmos together is the first of (...) their common themes, considered in this essay. The second is religion and its root, namely, the human heart in its encounter with the Eternal. This involves a discussion of time and whether human existence can be said to extend beyond time in some respect. Observations are made and questions are raised about the contrasting and comparative accessibility of the two authors’ thoughts and writings. The second half of the essay focuses on the earliest statements of Dooyeweerd’s germinating philosophy — in relationship to Kuyper’s thought. At the most fundamental level these two thinkers share basic principles, and in light of these they developed their most distinctive ideas. An implicit reassessment of this intellectual tradition is offered here with the hope of finding hints and motivation to open new vistas on some key insights and principles. (shrink)
Les chercheurs disputent depuis longtemps pour savoir si Machiavel est le "premier moderne", le chef de file du "républicanisme classique" ou un penseur laïc dans une perspective médiévale ou pré-moderne. Les rapports personnels entre Léonard de Vinci et Machiavel, dont les théoriciens politiques sont généralement inconscients, permettent de mieux comprendre le rôle de Machiavel dans la transition vers la modernité. La conception vincinienne d'une science de la nature et les possibilités qu'elle ouvrait aux innovations technologiques ont représenté un grand pas (...) dans le passage de la philosophie antique ou médiévale à la science naturelle moderne. Après avoir été l'ingénieur militaire de Ludovic Sforza puis de César Borgia, Vinci est rentré à Florence en 1503. Machiavel, qui l'avait apparemment rencontré en 1502, s'est assuré son aide technique pour diriger le cours de l'Arno afin de vaincre Pise, l'auteur du Prince semble aussi être lié à la commande du tableau de la Bataille d'Anghiari et il s'est arrangé pour que Vinci dirige une mission technique à Piombino en 1504. Les textes prouvent que Machiavel a été nettement influencé par ces expériences, ce qui suggère une réponse plausible aux controverses sur la "modernité" de Machiavel. La différence entre les approches des mathématiques et de la physique par Vinci puis par Galilée ou Newton illustre particulièrement bien les étapes ultérieurement nécessaires pour le développement complet d'une approche moderne de la politique comme celle de Hobbes ou Locke dans la tradition anglo-saxonne, ou de Descartes et des "philosophes" sur le continent. (shrink)
Relation algebras were invented by Tarski and his collaborators in the middle of the 20th century. The concept of integrality arose naturally early in the history of the subject, as did various constructions of finite integral relation algebras. Later the concept of finite-dimensionality was introduced for classifying nonrepresentable relation algebras. This concept is closely connected to the number of variables used in proofs in first-order logic. Some results on these topics are presented in chronological order.
A brief preface to the Cambridge Companion to Nietzsche announces the aims of the ambitious series of which this volume is a part: to provide students and nonspecialists with a handy reference volume and to help them overcome the “intimidation” they often feel when encountering a difficult thinker for the first time. Unlike the other volumes that I have seen in the Companion series, this one truly is pitched to the undergraduate and/or popular market. Of the 11 articles, only 4 (...) are grouped under the rubric “Nietzsche as Philosopher,” although Tracy B. Strong’s essay, “Nietzsche’s Political Misappropriation,” and Jörg Salaquarda’s “Nietzsche and the Judeo-Christian Tradition”—both listed under part II, “The Use and Abuse of Nietzsche’s Life and Works”—in their analysis of Nietzsche’s politics and his critique of religion certainly strike philosophical, or at least theoretical, poses. So, we have 6 articles out of eleven, roughly 191 out of 403 pages, that are devoted to the analysis, or at least discussion, of Nietzsche’s philosophy as such. The remaining articles treat broadly biographical topics and Nietzsche’s reception: in the 20th Century in general, in France, and in East Asia. This proportion, sadly, echoes the larger structure of the Nietzsche legend, which often expresses a desire to explain Nietzsche’s philosophy by means of certain biographical details, and which is in fact the central topic of R.J. Hollingdale’s contribution to this volume, “The Hero as Outsider.” That the devotion of such a disproportionate amount of space to what are arguably tangential issues is not inevitable is proven by the splendid Cambridge Companion to Spinoza, edited by Don Garrett, in which one article each is devoted to Spinoza’s life and his reception, with the remaining eight articles organized according to major topics in Spinoza’s philosophy: metaphysics, philosophy of mind, politics, critique of religion, et cetera, thus giving us a proper 8/2 proportion in favor of philosophy—and this vis-à-vis a philosopher with his own “extra-philosophical” legend. Of course, the Nietzsche question is complicated by National Socialism, among other things. (shrink)
In the United States, a longstanding legal rule exists against patenting natural phenomena. The Supreme Court recently had an opportunity to help define the boundaries and clarify the implications of this “natural phenomenon doctrine” in Laboratory Corporation of America v. Metabolite Labs., dismissed as improvidently granted. This article argues that the natural phenomenon doctrine renders both the patent claim at issue in LabCorp, and the patents that directly or indirectly claim biological correlations between genotypes and medical phenotypes, invalid or unenforceable (...) under U.S. patent law. (shrink)