This junior/senior level text is devoted to a study of first-order logic and its role in the foundations of mathematics: What is a proof? How can a proof be justified? To what extent can a proof be made a purely mechanical procedure? How much faith can we have in a proof that is so complex that no one can follow it through in a lifetime? The first substantial answers to these questions have only been obtained in this century. The most (...) striking results are contained in Goedel's work: First, it is possible to give a simple set of rules that suffice to carry out all mathematical proofs; but, second, these rules are necessarily incomplete - it is impossible, for example, to prove all true statements of arithmetic. The book begins with an introduction to first-order logic, Goedel's theorem, and model theory. A second part covers extensions of first-order logic and limitations of the formal methods. The book covers several advanced topics, not commonly treated in introductory texts, such as Trachtenbrot's undecidability theorem. Fraissé's elementary equivalence, and Lindstroem's theorem on the maximality of first-order logic. (shrink)

The German term “Antiziganismus” could be translated as “antigypsyism”, but the semantic roots are, in fact, different. Coined in the 1980s, “Antiziganismus” might be misconceived as a sheer abstraction: a “close reading” of the term's context could indeed partially justify the assumption that it in many ways reproduces certain impacts and implications of its better known equivalent – an actively employed anti-Semitism. However, the article's main thesis is that “Antiziganismus” denotes a term in its own right. This status cannot be (...) challenged even by the most recent development, which is an interest group's attempt to internationalize the scope of the term by coining the derivative “antiziganism”. (shrink)

In examining Hegel's and Kierkegaard's theories of language, I argue that both entail conceptions of the therapeutic power of language to heal us from madness and despair. I show that whereas Hegel quite straightforwardly celebrates the emancipatory power of language, Kierkegaard is more ambivalent; on the one hand, he devotes his life to a maieutic authorship in service of aiding the reader, but on the other, he believes that ultimately it is only faith in God that can cure us, and (...) that faith requires silence. I use Lacan's psychoanalytic account of the role of language to explore Hegel's view that language constitutes the self and Kierkegaard's experimentation with an indirect form of communication that he hopes will enable him to fulfill each of his apparently conflicting goals, to write and yet to remain silent. (shrink)

In Flip Thinking, Berthold Gunster, the founder of the Dutch omdenken--or flip thinking--philosophy, presents fifteen strategies to transform your thinking away from limitations and negativities and towards possibilities and opportunities. From disrupting (turn all the rules upside down) to flaunting (play up what you want to hide) and from importing (get the enemy on board) to amplifying (do more of what works), Gunster's strategies and stories will have you approaching even the most challenging problems--from an annoying neighbor to an (...) angry colleague to an unhappy partner--in a whole new way. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Talking Cures, the Clinic, and the Value of the IneffableDaniel Berthold (bio)KeywordsMadness, disease, the normal, the abnormal, the ineffable, Hegel, Kierkegaard, LacanI am most grateful to my readers, James Phillips and Louis Sass, who have led me to several new insights by suggesting ways of complicating my reading of a Lacanian approach to Hegel's and Kierkegaard's conceptions of madness. I am a Kierkegaard and Hegel scholar, with very (...) little pretense to expertise about Lacan and regrettably even less about the theory and practice of psychiatry. In submitting my essay to Philosophy, Psychiatry, & Philosophy, I was hoping to entice a community of practitioners and theoreticians I have great respect for to consider the musings of a philosopher on topics which engage them as thinkers and actors in their professions. I could not possibly have hoped for more intelligent and provocative replies than I have been given by my two respondents.Phillips' framing of his response in terms of the distinction between the "madness of the philosophers" and the "madness of the clinic" is very helpful. It is a distinction that is indeed central to the question of the possibility of dialogue between philosophers and clinicians—so central, in fact, that it is generous of Phillips not to reproach me for failing to mention it. On the one hand, the challenge for philosophers is to show that their descriptions are not merely metaphoric and that their preoccupation with the dark side of human experience connects in some way with the reality of disease, so that there is some way for clinicians to translate their language into the language of psychiatry. Otherwise, philosophers will have only poetic or literary interest for the psychiatrist or psychologist.On the other hand, the challenge for clinicians is the extent to which they are open to moving beyond a reduction of "mental illness" to a purely biological conception of disease. One needn't go so far—nor should we—as Thomas Szasz or Michel Foucault in seeing "mental disease" as itself merely a metaphor. But granting the evidence of underlying organic disorder, symptoms nevertheless display themselves as mental and behavioral states (what Hegel calls "shapes of consciousness") that, as Hegel argued, are paralleled in "normal" experience, so that the distinction between disease and normality (and hence illness and metaphor) is often elusive. Madness "has the healthy consciousness for its presupposition," Hegel writes, because the healthy mind is still grappling with the same sorts of contradictions and feelings of alienation, the same "infinite pain" which characterizes insanity. Madness is not the absolute "other" of rationality, but an echo of it (1978, 3:382, 408).Hegel himself accepted the medicalization of madness that began to occur in the late eighteenth [End Page 325] century, and rejected the metaphysical and theological categories of what was called "romantic medicine." But he also cautioned against the narrowness of the "somatic" school which he felt lacked sufficient explanatory value if not connected to a "speculative" (i.e., philosophic) framework (see Berthold-Bond 1995, ch. 2).It might even be argued that every person seeking therapy is first of all suffering from "philosophic" madness, at least in the sense that initially she does not understand her own suffering as "disease," but experiences her torment in the vocabulary of the philosopher. Thus the philosopher's descriptions are the closest to the subject's own self-understanding, and while the therapist must seek to rephrase these descriptions into the vocabulary of the clinic (just as Hegel, for example, translated his own philosophic description of the madness of his friend Hölderlin in the Phenomenology as the "lost soul" whose "light dies away within it" into the medical category of Wahnsinn—mania or frenzy, which today we would call schizophrenia—in the classificatory scheme of mental disorder he gives in the Encyclopaedia; 1977, 400; 1978, 408)—there is a real question about which vocabulary is a metaphor for the other.The second main point Phillips addresses, which is taken up in different ways by Sass as well, has to do with the relation between speech and silence in madness. Phillips finds that Kierkegaard offers a more complex and subtle view than... (shrink)

In Thomas Thomson's System of chemistry of 1802 Bergman and Scheele are actually considered as creators of the analytical concept of an element. With regard to this, a detailed investigation of the work of Bergman and Scheele shows that Thomson's statement contains mistakes as well as inadmissable simplifications and generalizations. It is correct, however, that Bergman in 1774–1777 specifically anticipated in essential aspects the analytical element concept proposed by Lavoisier in 1787–1789.

The idea of “place” has become a topic of growing interest in environmental ethics literature. I explore a variety of issues surrounding the conceptualization of “place” in bioregional theory. I show that there is a necessary vagueness in bioregional definitions of region or place because these concepts elude any purely objective, geographically literal categorization. I argue that this elusiveness is in fact a great meritbecause it calls attention to a more essential “subjective” and experiential geography of place. I use a (...) reading of Aldo Leopold’s Sand Country Almanac as an example of the value of a non-literalistic geography for the understanding of place. (shrink)

While ideals of racial purity may be out of fashion, other sorts of purity ideals are increasingly popular in the United States today. The theme of purity is noticeable everywhere, but it is especially prominent in our contemporary fixation on health and hygiene. This may seem totally unrelated to issues of racism and classism, but in fact, the purveyors of purity draw upon the same themes of physical and moral purity that have helped produce white identity and dominance in the (...) US. Historically, this is where the purity rhetoric gets its power. To invoke purity ideals in the US is to mobilize this genealogy of racialized associations. Today's zealous preoccupation with hygiene is part of our living heritage in a racist culture.Just as ideas of race and racial purity were debunked by biologists long before the public would begin to question them, ideals of extreme hygienic purity linger with us, even flourish, despite scientific evidence of their futility and harm. Why are we still so enamored with purity? Because, to some extent, our very self-conceptions are at stake. Other scholars have described how our process of self individuation is based upon exclusion. The unique contribution of a genealogical approach to this issue is that, instead of merely locating the problem in ideologies held by others, it can evoke self-recognition and self-transformation. We will tend to assume the problem lies elsewhere until we learn to recognize ourselves in practices that reproduce cultural ideals. As inheritors of this racist culture, we are all lovers of purity, and we are all responsible for rethinking this value. (shrink)

When Humpty-Dumpty had his great fall nobody could put him together again. A vastly more moderate challenge is to reunite the two partial beams of a Stern-Gerlach apparatus with such precision that the original spin state is recovered. Nevertheless, as we demonstrate, a substantial loss of spin coherence always occurs, unless the experimenter is able to control the magnetic field's inhomogeneity with an accuracy of at least one part in 105.

Knapp sechs Jahre nach Rudolf Heinz' sechzigstem Geburtstag und dem auf dieses Ereignis ausgerichteten Erscheinen der Festschrift "Kontiguitäten. Texte-Festival für Rudolf Heinz" (Christoph Weismüller [Hg.] unter Mitarbeit von Ralf Bohn, Wien: Passagen 1997) folgt die Nachbearbeitung der "Kontiguitäten" und deren Produktion. Die Post-Skripts zum Texte-Festival für Rudolf Heinz setzen ein mit den Dokumenten der Feierlichkeit der Festschriftüberreichung: Laudatio, Geburtstagskomposition - inklusive Audio-CD -, Photographien der Festschriftübergabe. Unter dem topos Festschrift-Mechané folgt diesen Initialien die Korrespondenz von Heide (...) class='Hi'>Heinz und Christoph Weismüller nebst notwendigen Paraphrasen und Hinweisen. Die Après nehmen einschlägige Kontiguitäts-Effekte auf, die mit der Fertigstellung der Festschrift, der Feierlichkeit der Übergabe, ihrer Distribution und ersten Nachbearbeitungen ihrer Konstitution einhergingen oder diesen folgten. Die Katamnese von Heide Heinz und Rudolf Heinz sowie weitere Korrespondenzen - Heide Heinz mit Ralf Bohn, Doris Dorner, Axel Schünemann; Rudolf Heinz mit Manfred Pohlen - finden sich als Zuträge ein. (shrink)

This is one of the most important books on quantum mechanics ever written for lay readers, in which an eminent physicist and successful science writer, Heinz Pagels, discusses and explains the core concepts of physics without resorting to complicated mathematics. "Can be read by anyone. I heartily recommend it!" -- New York Times Book Review. 1982 edition.

Perspective, Symbol, and Symbolic Form: Concerning the Relationship between Cassirer and Panofsky During the last two decades of the twentieth century, there was a sudden surge of interest in Ernst Cassirer’s major work, The Philosophy of Symbolic Forms (1923–29), and Erwin Panofsky’s essay, ‘Perspective as Symbolic Form’ (1927), an interest that has continued uninterrupted to the present day. Particularly amongst art historians, however, a serious misunderstanding remains evident here – the confusing of ‘symbolic form’ with ‘symbol’. Cultural and perceptual mediations, (...) in which objects (and subjects) are only just in the process of forming, are carelessly turned into arbitrary, isolated objects of art history or pictorial history. Every work, in this view, is regarded as a ‘symbolic form’ to the extent that a representation of the world is ‘expressed’ in it. This article initially reviews Panofsky’s essay in order to establish the context in which the art historian uses the term ‘symbolic form’. His use of it is then compared with Cassirer’s original understanding of the term. A careful distinction is made between ‘symbol’, ‘symbolic pregnance’, and ‘symbolic form’, and this is followed by an analysis of scattered remarks in Cassirer’s writings, and particularly in his posthumous manuscripts and notes, on ‘art’ as symbolic form and on the spatial form that is prior to all perception and art production, as well as his call for a kind of art history that conceives of itself as a scholarly discipline. The article concludes with the recognition that Panofsky not only deliberately, but justifiably – that is, in the spirit of Cassirer, at least – transferred the expression ‘symbolic form’ to ‘perspective’. (shrink)

Berthold-Bond (philosophy, Bard College) traces the project through Hegel's epistemology, metaphysics, and philosophy of history. Paper edition ($18.95) not seen. Annotation copyrighted by Book News, Inc., Portland, OR.

In this article I will discuss various aspects of Hegel’s radical critique of metaphilosophy. This critique announces a clear-cut departure from the widely held conviction in the philosophic tradition that in order to gain a firm foundation for science, a preliminary examination of the capacity and nature of knowledge is required. Hegel’s position is that such a propaedeutic is impossible. In the first part of this article, I will show how Hegel’s position can be illuminated in terms of his criticism (...) of Kant’s philosophic methodology and in terms of a comparison with Plato’s solution to the Meno paradox. In the second part, I will ask the question whether Hegel’s own philosophic method is consistent with his criticism of metaphilosophy. This question arises most clearly when we reflect on Hegel’s frequent claim that in order for the philosopher to write the science of knowledge, he or she needs “only to watch” or “merely to look on” at the way consciousness develops its knowledge of objects. We must consider whether such a “language of spectatorship,” as we might call it, does not contradict the evident conclusion of Hegel’s critique of metaphilosophy, viz., that the philosopher cannot attain a distanced perspective from knowledge without at the same time abandoning knowledge. (shrink)

This chapter situates Kierkegaard's commitment to death in companionship with a similar, if not identical, commitment on the part of Friedrich Nietzsche. Both conceptualize the relation between self and other as occurring across an abyss of difference that dissolves the authority of the author, and adhere to a philosophy of language in which the author's text becomes infinitely interpretable according to the position occupied by the reader. But notwithstanding the inventiveness with which Kierkegaard and Nietzsche practice the art of dying, (...) we can discern a fundamental ambivalence: With every intention of dying, they have recurring second thoughts; at the entrance to the tomb they hesitate, giving in to a certain nostalgia for the privileged position of the author. (shrink)

The article engages the current debate between humanistic' and anti-humanistic' alternatives for an ecological philosophy by putting Heidegger and Hegel into dialogue. It is argued that Heidegger's portrait of Hegel's philosophy as a form of humanism' which foreshadows the modern logic of domination and exploitation of nature is highly misleading. Hegel's humanistic' position can allow for a genuinely ecological vision of nature, which, while not as radically ecological as Heidegger's, may in fact avoid some of the problems of Heidegger's view.

While neither Hegel nor Marx can be called “ecologists” in any strict sense of the term, they both present views of the human-nature relationship which offer important insights for contemporary debates in philosophical ecology. Further, while Marx and Engels began a tradition of sharply distinguishing their own views of nature from those of Hegel, careful examination reveals a substantial commonality of sentiment. The essay compares Hegel and Marx (and Engels) in terms of their basic conceptions of nature, their critiques of (...) Romanitic nature-worship, their notions of how a meaningful unity with nature requires the act of socially transforming nature, their respective calls for a new science of nature, and their attitudes towards technology. I argue that we can uncover a largely shared humanistic orientation toward nature, and I situate this view within contemporary debates about the anthropocentric or non-anthropocentric foundation of ecological thinking. (shrink)

While neither Hegel nor Marx can be called “ecologists” in any strict sense of the term, they both present views of the human-nature relationship which offer important insights for contemporary debates in philosophical ecology. Further, while Marx and Engels began a tradition of sharply distinguishing their own views of nature from those of Hegel, careful examination reveals a substantial commonality of sentiment. The essay compares Hegel and Marx (and Engels) in terms of their basic conceptions of nature, their critiques of (...) Romanitic nature-worship, their notions of how a meaningful unity with nature requires the act of socially transforming nature, their respective calls for a new science of nature, and their attitudes towards technology. I argue that we can uncover a largely shared humanistic orientation toward nature, and I situate this view within contemporary debates about the anthropocentric or non-anthropocentric foundation of ecological thinking. (shrink)

A unitary transformation replaces the given description of a quantum system by an equivalent one. It is observed, however, that not all members of a set of unitarily equivalent Hamilton operators are equally well suited for identifying the corresponding classical systems. A criterion is proposed for recognizing the privileged representatives of the set. A few explicit examples are reported that show the criterion at work.

There is a strongly entrenched ambiguity in Hegel's philosophy between two opposed ways of describing the End, or "completion" of history: the "absolutist" and the "epochal" readings. Either Hegel's eschatological vision is of a completely final End, where no further progress in history or knowledge is possible, or it is an epochal conception, where the completion he speaks of is the fulfillment of an historical epoch. Passages in Hegel's texts may be found to support either of these alternatives. A non-absolutist (...) reading of Hegel's philosophy is shown to be preferable through a consideration of 1) his unorthodoxly historical interpretation of the Christian eschatological End, to which he lends great importance; 2) the implication that if Christianity were to usher in a radical completion of history and time, spirit would cease to be spirit and God would cease to be God, since for Hegel God is irreducibly the logos, or Word, or spirit; and 3) a closer look at Hegel's conception of the "new world," which shows the paralyzing sacrifice of the dialectical soul necessary to an absolutist reading of Hegel's philosophy. Any attempt to harmonize the absolutist and epochal readings must inevitably fall into confusion. (shrink)