Most scholars think of David Hilbert's program as the most demanding and ideologically motivated attempt to provide a foundation for mathematics, and because they see technical obstacles in the way of realizing the program's goals, they regard it as a failure. Against this view, Curtis Franks argues that Hilbert's deepest and most central insight was that mathematical techniques and practices do not need grounding in any philosophical principles. He weaves together an original historical account, philosophical analysis, and his (...) own development of the meta-mathematics of weak systems of arithmetic to show that the true philosophical significance of Hilbert's program is that it makes the autonomy of mathematics evident. The result is a vision of the early history of modern logic that highlights the rich interaction between its conceptual problems and technical development. (shrink)

Attempts to articulate the real meaning or ultimate significance of a famous theorem comprise a major vein of philosophical writing about mathematics. The subfield of mathematical logic has supplie...

The papers where Gerhard Gentzen introduced natural deduction and sequent calculi suggest that his conception of logic differs substantially from the now dominant views introduced by Hilbert, Gödel, Tarski, and others. Specifically, (1) the definitive features of natural deduction calculi allowed Gentzen to assert that his classical system nk is complete based purely on the sort of evidence that Hilbert called ?experimental?, and (2) the structure of the sequent calculi li and lk allowed Gentzen to conceptualize completeness as a question (...) about the relationships among a system's individual rules (as opposed to the relationship between a system as a whole and its ?semantics?). Gentzen's conception of logic is compelling in its own right. It is also of historical interest, because it allows for a better understanding of the invention of natural deduction and sequent calculi. (shrink)

In his Philosophical Investigations, Wittgenstein said that “turning our whole investigation around” is the only way to shake the illusion of a “preconceived idea of crystalline purity.” Commentators have built sweeping descriptions of Wittgenstein’s general approach to philosophy out of their interpretations of this slogan. For his own part, Wittgenstein specified a particular subject. “For,” he wrote, “the crystalline purity of logic was…not a result of investigation: it was a requirement.” In asking what Wittgenstein could have meant by reversing the (...) direction of the investigation of logic and of what he called its apparent “hardness,” I propose to follow his own advice: to look around before thinking. Two episodes from logic’s history serve as illustrative examples of concepts being dislodged from their original position as theorems or discoveries and relocated as starting points of an investigation (and vice-versa). The details of the cases showcase how “turning our whole investigation around” has proven its practical utility in the growth and development of logic in the last century. Further, it suggests that Wittgenstein might have intended something at once humbler and, for logic, more important than a grand reconceptualization of the nature of necessity: the science of logic itself relies on a continuous inversion of discoveries and requirements. (shrink)

The exegesis of sacred rites in the Talmud is subject to a restriction on the iteration and composition of inference rules. In order to determine the scope and limits of that restriction, the sages of the Talmud deploy those very same inference rules. We present the remarkable features of this early use of self-reference to navigate logical constraints and uncover the hidden complexity behind the sages? arguments. Appendix 11 contains a translation of the relevant sugya. 1Hebrew and Aramaic transliteration approximates (...) traditional Sephardic pronunciation, which is closer to academic standard transliteration than the various Ashkenazic pronunciations, yet is legible. Specific references follow the convention of folio (number), side (a or b), number of lines from the top or (if negative) bottom of the page. (shrink)

There is an ambiguity in the concept of deductive validity that went unnoticed until the middle of the twentieth century. Sometimes an inference rule is called valid because its conclusion is a theorem whenever its premises are. But often something different is meant: The rule's conclusion follows from its premises even in the presence of other assumptions. In many logical environments, these two definitions pick out the same rules. But other environments are context-sensitive, and in these environments the second notion (...) is stronger. Sorting out this ambiguity has led to profound mathematical investigations with applications in complexity theory and computer science. The origins of this ambiguity and the history of its resolution deserve philosophical attention, because our understanding of logic stands to benefit from their details. I am eager to examine together with you, Crito, whether this argument will appear in any way different to me in my present circumstances, or whether it remains the same, whet... (shrink)

I attribute an 'intensional reading' of the second incompleteness theorem to its author, Kurt G del. My argument builds partially on an analysis of intensional and extensional conceptions of meta-mathematics and partially on the context in which G del drew two familiar inferences from his theorem. Those inferences, and in particular the way that they appear in G del's writing, are so dubious on the extensional conception that one must doubt that G del could have understood his theorem extensionally. However, (...) on the intensional conception, the inferences are straightforward. For that reason I conclude that G del had an intensional understanding of his theorem. Since this conclusion is in tension with the generally accepted view of G del's understanding of mathematical truth, I explain how to reconcile that view with the intensional reading of the theorem that I attribute to G del. The result is a more detailed account of G del's conception of meta-mathematics than is currently available. (shrink)

The focus here will be on the tension between architecture’s symbolic role and its function as a space to house and present art. ‘Symbolic’ refers both to a building as an aesthetic or sculptural form and secondly to its role in expressing civic identity. ‘Function’ refers to the intended purpose or practical use apart from its role as a form of art. As an art form, it serves important symbolic purposes; its practical purposes are linked to serving individual and community (...) functions requiring the delineation of space. In the present context of museum architecture, certain museum buildings are more likely to be seen as a sculptural object than as functioning buildings. The reasons for this development derive in part from unresolved issues pertaining to the respective roles of symbolic and practicalfunction as is seen in the analysis of architecture provided by G. W. F. Hegel, Rudolf Arnheim and Nelson Goodman. The vocabularies of contemporary architects such Frank Gehry and Santiago Calatrava do not follow the abstract geometrical patterns of Le Corbusier or Louis Kahn who envisioned a universal vocabulary of architectural forms derived from industrial technical forms that underscored Modernist conventions in architecture.By looking at this issue in the contexts provided by the theoretical discussions of Hegel, Arnheim and Goodman, it is possible to see more clearly the importance of examining with a critical eye the relative place of symbolism and function in museum architecture, and to question whether current museum practice has gone astray in allowing the sculptural symbolism to become the dominant element. When either its symbolic or its practical aspects are out of balance the result is sure to be unsatisfactory architecture. If the past is a reliable guide, it works best when the symbolic (sculptural) and the practical in architecture are worked out in harmony with each other. (shrink)

Recent financial fraud legislation such as the Dodd–Frank Act and the Sarbanes–Oxley Act (U.S. House of Representatives, Dodd-Frank Wall Street Reform and Consumer Protection Act of 2010, [H.R. 4173], 2010 ; U.S. House of Representatives, The Sarbanes–Oxley Act of 2002, Public Law 107-204 [H.R. 3763], 2002 ) relies heavily on whistleblowers for enforcement, and offers protection and incentives for whistleblowers. However, little is known about many aspects of the whistleblowing decision, especially the effects of contextual and wrongdoing attributes on organizational (...) members’ willingness to report fraud. We extend the ethics literature by experimentally investigating how the nature of the wrongdoing and the awareness of those surrounding the whistleblower can influence whistleblowing. As predicted, we find that employees are less likely to report: (1) financial statement fraud than theft; (2) immaterial than material financial statement fraud; (3) when the wrongdoer is aware that the potential whistleblower has knowledge of the fraud; and (4) when others in addition to the wrongdoer are not aware of the fraud. Our findings extend whistleblowing research in several ways. For instance, prior research provides little evidence concerning the effects of fraud type, wrongdoer awareness, and others’ awareness on whistleblowing intentions. We also provide evidence that whistleblowing settings represent an exception to the well-accepted theory of diffusion of responsibility. Our participants are professionals who represent the likely pool of potential whistleblowers in organizations. (shrink)

History and Philosophy of Logic, Volume 32, Issue 2, Page 177-183, May 2011.

Die {raquo}Revolution der Denkart{laquo} hat nicht nur den Anlauf genommen, welchem sie ihren Namen verdankt.! Gezahlt werden noch weitere Umstellungen der Theorie bildung als bloG die kopernikanische Kants. Hier interessieren gleich zwei. Die eine liefert den Gegenstand, die entsprechende, RevolutionPhanomenologie.

Does the universe embody beautiful ideas? Artists as well as scientists throughout human history have pondered this "beautiful question." With Nobel laureate Frank Wilczek as your guide, embark on a voyage of related discoveries, from Plato and Pythagoras up to the present. Wilczek's groundbreaking work in quantum physics was inspired by his intuition to look for a deeper order of beauty in nature. In fact, every major advance in his career came from this intuition: to assume that the universe embodies (...) beautiful forms, forms whose hallmarks are symmetry--harmony, balance, proportion--and economy. There are other meanings of "beauty," but this is the deep logic of the universe--and it is no accident that it is also at the heart of what we find aesthetically pleasing and inspiring. As he reveals here, this has been the heart of scientific pursuit from Pythagoras, the ancient Greek who was the first to argue that "all things are number," to Galileo, Newton, Maxwell, Einstein, and into the deep waters of twentieth-century physics. Gorgeously illustrated, A Beautiful Question is a mind-shifting book that braids the age-old quest for beauty and the age-old quest for truth into a thrilling synthesis. Yes: the world is a work of art, and its deepest truths are ones we already feel, as if they were somehow written in our souls.--From publisher description. (shrink)

One of our great contemporary scientists presents ten insights that illuminate what every thinking person needs to know about what the world is and how it works. Nobel Prize winner Frank Wilczek's Fundamentals is built around a simple but profound idea: the models of the world we construct as children are practical and adequate for everyday life, but they do not bring in the surprising and mind-expanding revelations of modern science. To do that, we must look at the world anew, (...) combining clear thinking with an openness to wonder. This "born again" world is in many ways larger, fuller, and much stranger than it appears. Through an exploration of space, time, matter, and ideas--and equipped with facts, questions, and brilliant speculations--Wilczek guides us through the past, present, and future of fundamental science. Readers will emerge with an expanded vision of our universe. Author Bio: Frank Wilczek won the Nobel Prize in Physics in 2004 for work he did as a graduate student. He was among the earliest MacArthur fellows, and has won many awards both for his scientific work and his writing. He is the author of A Beautiful Question, The Lightness of Being, Fantastic Realities, Longing for the Harmonies, and hundreds of articles in leading scientific journals. His "Wilczek's Universe" column appears regularly in the Wall Street Journal. Wilczek is the Herman Feshbach Professor of Physics at the Massachusetts Institute of Technology, founding director of the T. D. Lee Institute and chief scientist at the Wilczek Quantum Center in Shanghai, China, and a distinguished professor at Arizona State University and Stockholm University. (shrink)

Der Übergang vom Verhältnisbewußtsein zum Selbstbewußtsein kann unmöglich nur vom Verhältnisbewußtsein aus gedacht werden, weil wir uns eine Welt, in der das Bewubtsein unserer selbst verteilt ist auf die Dimensionen der Handlung vor deren Zentrierung in uns, gar nicht vorstellen können. Jedes Tableau der Handlungsmöglichkeiten, so abstrakt es auch abgefaßt sein mag, ist gebunden an Vorstellungen möglicher Handlungssubjekte, denen wir Handlungsmöglichkeiten zuschreiben. Handlungstheorie ist daher notwendig Reflexion unserer Praxis, in der wir uns selbst als Selbstbewußtsein erfahren, das seinem Verhältnisbewubtsein enthoben (...) ist, ohne dieses dadurch selbst schon aufzuheben zu können. Daß uns Freiheit im Handeln unaufhebbar prekär und problematisch bleiben mub, ist die Grundvoraussetzung dafür, dab wir Handlungstheorien historisch und bereichsbezogen ständig neu entwerfen müssen. Das Verhältnis von Handlungsphilosophie zu Handlungstheorien kann daher so gefaßt werden, daß Handlungsphilosophie die Grundbegrifflichkeit in kritischer Absicht bereitstellt, die den bereichsorientierten, mehr oder weniger deskriptiven Handlungstheorien abgehen muß. Dazu muß die ontologische Differenz von Handlung und Interpretation methodologisch ernst genommen werden. Die radikale Andersheit der hier zu begründenden Konzeption liegt vor allem in der Ansicht, daß Handlungen nicht als isolierbare Ereignis-Entitäten aufgefaßt werden können, die gegenüber der »Welt der Tatsachen des Bewußtseins« eine kausale, d.h. von der Welt des Bewußtseins abgetrennte Rolle übernehmen. (shrink)

A number of studies have tested the relationship between a corporation's social and ethical performance and its financial performance. In contrast, this is the first study to demonstrate a link between overall financial performance and an emphasis on ethics as an aspect of corporate governance. It identifies the 26.8 percent of the 500 largest U.S. public corporations that, in their annual report to shareholders, commit to ethical behavior toward their stakeholders or emphasize compliance with their code of conduct. The financial (...) performance of these corporations ranks higher than that of those who do not at a significance level of p = < 0.005, using the 1997 Business Week ranking which averages eight publicly-reported measures of historical financial performance. These findings should motivate more corporations to utilize the principles of Social and Ethical Accounting, Auditing and Reporting (SEAAR). (shrink)

The confounding effects of heterogeneity in biological psychiatry and psychiatric genetics have been widely discussed in the literature. We suggest an approach in which heterogeneity may be put to use in hypothesis testing, and may find application in evaluation of the Crespi & Badcock (C&B) imprinting hypothesis. Here we consider three potential sources of etiologic subtypes for analysis.

The target article by Charney on behavior genetics/genomics discusses how numerous molecular factors can inform heritability estimations and genetic association studies. These factors find application in the search for genes for behavioral phenotypes, including neuropsychiatric disorders. We elaborate upon how single causal factors can generate multiple phenotypes, and discuss how multiple causal factors may converge on common neurodevelopmental mechanisms.

**** Reprint of the Indiana U. Press edition of 1966--which is cited in BCL3. Annotation copyright by Book News, Inc., Portland, OR.

Although declarations of the death of God seem to be provocations announcing the end of the era of theology, this announcement is actually central to the Christian revelation in its most classic forms, as well as to its reworkings in contemporary religious thought. Indeed provocative new possibilities for thinking theologically open up precisely in the wake of the death of God. Already Hegel envisaged a revolutionary new realization of divinity emerging in and with the secular world through its establishment of (...) a total order of immanence. However, in postmodern times this comprehensive order aspired to by modern secularism implodes or cracks open towards the wholly Other. A hitherto repressed demand for the absolute difference of the religious, or for “transcendence”, returns with a vengeance. This difference is what could not be stated in terms of the Hegelian System, for reasons that poststructuralist writers particularly have insisted on: all representations of God are indeed dead. Yet this does not mean that they cannot still be powerful, but only that they cannot assign God any stable identity. Nietzsche’s sense of foreboding concerning the death of God is coupled with his intimations of the demise of representation and “grammar” as epistemologically bankrupt, but also with his vision of a positive potential for creating value in the wake of this collapse of all linguistically articulated culture. He points the way towards the emergence of a post-secular religious thinking of what exceeds thought and representation. (shrink)

Much of the debate about identity in recent decades has been about personal identity, and specifically about personal identity over time, but identity generally, and the identity of things of other kinds, have also attracted attention. Various interrelated problems have been at the centre of discussion, but it is fair to say that recent work has focussed particularly on the following areas: the notion of a criterion of identity; the correct analysis of identity over time, and, in particular, the disagreement (...) between advocates of perdurance and advocates of endurance as analyses of identity over time; the notion of identity across possible worlds and the question of its relevance to the correct analysis of de re modal discourse; the notion of contingent identity; the question of whether the identity relation is, or is similar to, the composition relation; and the notion of vague identity. A radical position, advocated by Peter Geach, is that these debates, as usually conducted, are void for lack of a subject matter: the notion of absolute identity they presuppose has no application; there is only relative identity. Another increasingly popular view is the one advocated by Lewis: although the debates make sense they cannot genuinely be debates about identity, since there are no philosophical problems about identity. Identity is an utterly unproblematic notion. What there are, are genuine problems which can be stated using the language of identity. But since these can be restated without the language of identity they are not problems about identity. (For example, it is a puzzle, an aspect of the so-called “problem of personal identity”, whether the same person can have different bodies at different times. But this is just the puzzle whether a person can have different bodies at different times. So since it can be stated without the language of personal “identity”, it is not a problem about identity, but about personhood.) This article provides an overview of the topics indicated above, some assessment of the debates and suggestions for further reading. (shrink)

Human interaction and communication involve space in multiple ways. This paper examines the spatial and interactional order of a covertly video-taped police interrogation. When the participants enter the interrogation room and become engaged in the interrogation process, the room itself is a constraint and a resource for interaction. While interacting within a built environment, the participants appropriate their material surroundings in ways that constitute a spatial order and make possible certain arguments. This paper examines how the physical structure of the (...) interrogation room is differentially appropriated, used, and filled in by the participants''; territorial and postural manoeuvers over the course of their interaction; and how the spatial structures thus created by the bodily appropriation of the physical locale are subsequently formulated by talk and thereby used as a metaphorical resource to frame the participants'' situated experience. Through this embedded process, the interrogators move the suspect toward confession. (shrink)

Heidegger and East-Asian thought have traditionally been strongly correlated. However, although still largely unrecognized, significant differences between the political and metaphysical stance of Heidegger and his perceived counterparts in East-Asia most certainly exist. One of the most dramatic discontinuities between East-Asian thought and Heidegger is revealed through an investigation of Kitarō Nishida’s own vigorous criticism of Heidegger. Ironically, more than one study of Heidegger and East-Asian thought has submitted that Nishida is that representative of East-Asian thought whose philosophy most closely (...) resembles Heideggerian thought. In words that then and now resound discordantly within the enshrined, established view of Heidegger’s relationship to East-Asian thought, Nishida stated uninhibitedly his own view of Heidegger in the noteworthy statement: “Heidegger is not worth your time… He…does not recognize that which is indispensible and decisive, namely, God.” This present study lays out for the first time in English, the significant differences between the metaphysical and political stances of Nishida and Heidegger, Nishida’s own critique of Heidegger, and Heidegger’s own rather dismal assessment of non-Western philosophy, all of which demonstrate a remarkable, hitherto unrecognized discontinuity between Heidegger and East-Asian thought. (shrink)

This article considers the war against terror in relation to classical tragedy. It uses Heidegger's analysis of Sophocles's play Antigone to argue that human beings are essentially `homeless' and yet our destiny lies in the continual attempt to overcome this homelessness by establishing foundational principles that might bring our journeying to an end. The tragedy of this situation is that the search for foundations and a search for a home invariably bring differing worlds in conflict with each other as their (...) paths to truth collide. Lucien Goldmann's analysis of the tragedy of refusal is also considered in relation to a non-foundational politics that may permit us not only to endure, but actually to affirm our homelessness as an attempt to resist the terror and anabolic militarism that marks the current age. (shrink)

This paper uses argumentation tools such as argument diagrams and argumentation schemes to analyze four examples of argument from analogy, and argues that to proceed from there to evaluating these arguments, features of the context of dialogue need to be taken into account. The evidence drawn from these examples is taken to support a pragmatic approach to studying argument from analogy, meaning that identifying the logical form of the argument by building an argument diagram of the premises and conclusion is (...) not by itself sufficient for argument evaluation. To get further, it is argued, the argument evaluator needs to take into account how this particular argument was used in context to support a conversational goal.Cet article utilise des outils d'argumentation tels que des diagrammes d'argument et des schèmes d'argumentation pour analyser trois exemples d'argument par analogie, et soutient que pour évaluer ces arguments de manière adéquate, il est nécessaire de tenir compte du contexte d'utilisation de l'argument. Ces exemples suggèrent que l’étude des arguments par analogie à partir de seulement l’identification de leur forme logique n'est pas adéquate. Pour aller plus loin, on avance que l'analyste d'argument doit prendre en compte comment un argument particulier a été utilisé dans un contexte pour soutenir un but conversationnel. (shrink)

This chapter describes the Danish church, with the focus centered primarily on its life during the years 1835 to 1855 when Søren Kierkegaard was productive. The beginnings of the church up to 1835 are briskly examined, and then contributions of Jacob Peter Mynster, Nicolai Frederik Severin Grundtvig, and Hans Lassen Martensen are delineated. These three figures have been chosen because of their importance both for the Danish church and for Kierkegaard. The chapter ends with a few comments on some creative (...) thinkers who find in Kierkegaard's critique a resource for critically reforming the church so that it might more appropriately serve its intended purpose. At points in the chapter, the analysis utilizes the Kierkegaardian categories of the objective and the subjective. (shrink)

In this paper, I shed light on Kant’s notion of Erkenntnis or cognition by focusing on texts pertaining to Kant’s thoughts on logic. Although a passage from Kant’s Logik is widely referred to for understanding Kant’s conception of Erkenntnis, this work was not penned by Kant himself but rather compiled by Benjamin Jäsche. So, it is imperative to determine its fidelity to Kant’s thought. I compare the passage with other sources, including Reflexionen and students’ lecture notes. I argue that several (...) of the text’s peculiarities stem from Jäsche rather than Kant, but that nevertheless Jäsche largely got Kant's view right, with two major exceptions. First, Jäsche’s text fails to reproduce Kant’s key thesis that kennen and verstehen are jointly sufficient for Erkenntnis. Second, Jäsche’s text gives the false impression that Kant holds that animals have consciousness. (shrink)

The paper was read at a symposium in Eastern International Meeting of the American Academcy of Religion, Alfred, N.Y. April 16–17, 1993.