A succinct introduction to mathematical logic and set theory, which together form the foundations for the rigorous development of mathematics. Suitable for all introductory mathematics undergraduates, Notes on Logic and Set Theory covers the basic concepts of logic: first-order logic, consistency, and the completeness theorem, before introducing the reader to the fundamentals of axiomatic set theory. Successive chapters examine the recursive functions, the axiom of choice, ordinal and cardinal arithmetic, and the incompleteness theorems. Dr. Johnstone has included numerous exercises designed (...) to illustrate the key elements of the theory and to provide applications of basic logical concepts to other areas of mathematics. (shrink)

We show that a morphism of locales is open if and only if all its pullbacks are skeletal in the sense of [P.T. Johnstone, Factorization theorems for geometric morphisms, II, in: Categorical Aspects of Topology and Analysis, in: Lecture Notes in Math., vol. 915, Springer-Verlag, 1982, pp. 216–233], i.e. pulling back along them preserves denseness of sublocales . This result may be viewed as the ‘dual’ of the well-known characterization of proper maps as those which are stably closed. We also (...) investigate the circumstances in which a particular sublocale, or set of sublocales, of a given locale, may be ‘declared closed’. (shrink)

Notices Amer. Math. Sac. 51, 2004). Logically, such a "Grothendieck topos" is something like a universe of continuously variable sets. Before long, however, F.W. Lawvere and M. Tierney provided an elementary axiomatization..

Topos Theory is a subject that stands at the junction of geometry, mathematical logic and theoretical computer science, and it derives much of its power from the interplay of ideas drawn from these different areas. Because of this, an account of topos theory which approaches the subject from one particular direction can only hope to give a partial picture; the aim of this compendium is to present as comprehensive an account as possible of all the main approaches and thereby to (...) demonstrate the overall unity of the subject. The material is organised in such a way that readers interested in following a particular line of approach may do so by starting at an appropriate point in the text. (shrink)

In a project The Hastings Center is now running on the future of prenatal testing, we are encountering clear examples, both in established law and in the practices of individual providers, of failures to respect women's reproductive autonomy: when testing is not offered to certain demographics of women, for instance, or when the choices of women to terminate or continue pregnancies are prohibited or otherwise not supported. But this project also raises puzzles for reproductive autonomy. We have learned that some (...) clinicians and patients do not discuss the fact that prenatal testing can lead to a decision about whether to terminate a pregnancy—they just don't talk about it. And while the decision whether to agree to prenatal screening and diagnostic testing is to be made with women's free and informed consent, many screening tests have been routinized in such a way that some women do not even recall agreeing to testing, while others feel that agreeing to testing is what their clinicians expect of them or that the testing is necessary to protect themselves and their families from the significant financial hardship of raising a child with a disability. In the face of these pressures, can one really say that women are freely choosing to undergo testing or are freely choosing to continue or terminate a pregnancy following receipt of test results? The reality of these pressures is requiring us to consider expanding the scope of our investigation beyond the clinical encounter to the broader context—to think harder about what reproductive autonomy means and how best to enhance it. (shrink)

Immanuel Kant is one of Alain Badiou’s principle philosophical enemies. Kant’s critical philosophy is anathema to Badiou not only because of the latter’s openly aired hatred of the motif of finitude so omnipresent in post-Kantian European intellectual traditions—Badiou blames Kant for inventing this motif—but also because of its idealism. For Badiou-the-materialist, as for any serious philosophical materialist writing in Kant’s wake, transcendental idealism must be dismantled and overcome. In his most recent works, Badiou attempts to invent a non-Kantian notion of (...) the transcendental, a notion compatible with the basic tenets of materialism. However, from 1988’s Being and Event up through the present, Badiou’s oeuvre contains indications that he hasn’t managed fully to purge the traces of Kantian transcendental idealism that arguably continue to haunt his system—with these traces clustering around a concept Badiou christens “counting-for-one”. The result is that, in the end, Kant’s shadow still falls over Badiouian philosophy—this is despite Badiou’s admirable, sophisticated, and instructive attempts to step out from under it—thus calling into question this philosophy’s self-proclaimed status as materialist through and through. (shrink)

Wittgenstein’s Tractarian discussion of solipsism opens with the claim that ‘[t]he limits of my language mean the limits of the world’ (TLP 5.6.) According to this paper, Wittgenstein expresses here a thought that the subject makes no sense of her thinking having content going beyond in kind that which she possesses in thinking. What the subject possesses in thinking is furthermore a truth or falsity, so that the idea is ruled out of truth-independent substance to the world. At the same (...) time, however, thinking is an act of the subject given to her only as such – only as something she does, and so only as a determination of herself. Truth is not therefore independent of the subject; rather, as Wittgenstein puts it, ‘the world is my world’ (TLP 5.62). This conclusion threatens an idealism under which the nature of truth is explained by reference to that of the subject; objectivity is grounded in a deeper subjectivity. This threat is deflected by the recognition that the solipsist’s subject is an essentially undistanceable ‘I’ without content or character, so that ‘solipsism strictly carried out coincides with pure realism’ (TLP 5.64). (shrink)

This chapter contains sections titled: I II III IV V.

This chapter contains sections titled: I II III.

In this essay, I respond to Žižek's charges that my turns to biology risk naturalizing away key features of non-natural subjectivity à la German idealism and Lacanianism. The crux of this dispute between him and me concerns how close to or far from a life-science-based naturalism a materialist theory of the subject with allegiances to Kant, Hegel, Freud, and Lacan should be. I contend that materialism must be closer to naturalism than Žižek allows— while insisting simultaneously that the spontaneous naturalism (...) of the cutting edge of the life sciences isn’t the semi-reductive paradigm Žižek believes it to be. (shrink)

ABSTRACTZalabardo argues that the Tractatus makes an important contribution towards explaining how a representation doesn¹t merely introduce various objects, but furthermore represents them as comb...

Not only is Lacan’s repeatedly advanced assertion that Freud categorically denies the existence of unconscious affects a misleading oversimplification of Freud’s various ambivalent discussions of this issue—Lacan’s own circumnavigations around the topic of affect are much more nuanced and subtle than either he or many of his commentators often acknowledge. What’s more, such complexities aren’t confined solely to the tenth seminar of 1962-1963 devoted to a sustained discussion of anxiety, a seminar to which Lacan sometimes appeals in response to criticisms (...) according to which he reduces the psychoanalytic unconscious to the lifeless formal skeleton of pure linguistic-symbolic units alone. Through analyzing Lacan’s explorations of the distinction between signifiers and affects as articulated across the full span of le Séminaire, this essay seeks to complicate and problematize the standard picture of Lacan’s metapsychology of affective life. In so doing, it strives to clarify hitherto obscure remarks made about affects by Lacan as well as, through this work of clarification, to lay down foundational elements for the construction of a much more accurate and systematic rendition of a Lacanian theory of affects. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Dharma Bums: The Beat Generation and the Making of Countercultural PilgrimageP. J. JohnstonI believe in the sweetness of Jesus And Buddha— I believe, In St. Francis, Avaloki Tesvara, the Saints Of First Century India A D And Scholars Santidevan And Otherwise Santayanan Everywhere.(Kerouac 1959: 15)Preliminary Polemics“PILGRIM, n. A traveler that is taken seriously.”—Ambrose Bierce, The Devil’s Dictionary 2007: 133As Beat commentator Stephen Prothero describes in his article “On the (...) Holy Road: The Beat Movement as Spiritual Protest” (1991), the Beats and their pilgrimages have most emphatically not been taken seriously. Both critics and scholars have been unkind to members of the Beat generation, and this unkindness has manifested itself in relative neglect of the Beats in all possible aspects of scholarly investigation. But nowhere does this appear more pronounced than in the area of Beat religion. Though some recent scholarship has been picking up from this earlier neglect and it is now [End Page 165] possible to find serious biographies of most of the major Beat writers and some belated attention to the movement as a literary phenomenon, the only book-length treatment of Beat Buddhism I was able to locate (Tonkinson 1995) hardly qualifies as a scholarly work and was published not by an academic press but as a special feature of the Buddhist magazine Tricycle. Prothero hypothesizes that this is because of the movement’s reputation as rebellious and antinomian—in its heyday the movement was characterized in identical unsavory terms by publications representing interests as diverse as Life and Playboy, with the latter describing the Beats as “nihilists” and the former claiming that the Beats were at war with “Mom, Dad, Politics, Marriage, the Savings Bank, Organized Religion, Literary Elegance, Law, the Ivy League Suit and Higher Education, to say nothing of the Automatic Dishwasher, the Cellophane-wrapped Soda Cracker, the Split-Level House and the clean, or peace-provoking H-bomb” (Prothero 1991: 206). Norman Podhoretz of Partisan Review went further still, claiming that the Beats were “hostile to civilization” and that the movement as a whole amounted to “a revolt of the spiritually underprivileged and crippled of soul” and “an affirmation of death” (ibid., 206). One couldn’t ask for a more passionate disavowal of the Beats or a more thorough polemic that the movement was profoundly antireligious.This could not contrast more with the Beats’ representation of their movement and its aims, with Jack Kerouac going so far as to reinterpret the crucial term “Beat” (a term for someone down and out originally borrowed from criminal street jive) as a noun derived from the adjective “beatific,” a specifically religious term familiar from such phrases as “the beatific vision” (ibid., 206–207). Several of the representative Beat writers were practicing Buddhists, influencing the entire movement to such an extent that Buddhist ideas and imagery suffused Beat literature as a whole. Ginsberg and Kerouac especially emphasized the positive and constructive elements of their spiritual vision, arguing that literature such as On the Road and Howl should be understood as religious affirmations of what is good and holy rather than as purely critical undertakings: “For the crucifix I speak out, for the Star of Israel I speak out, for the divinest man who ever lived who was German (Bach) I speak out, for sweet Mohammed I speak out, for Buddha I speak out, for Lao-tse and Chuang-tse I speak out” (ibid., 206–207). Or, as Allen Ginsberg put it less lyrically (and rather more bluntly): “Howl is an ‘Affirmation’ by individual experience of God, sex, drugs, and absurdity... the poems are religious and I meant them to be” (ibid., 207).But for the most part, Beat asseverations in no way diminished scholarly wariness about the Beat movement and its spirituality—as Prothero concludes, “the tendency among literary scholars is to see these [religious] concerns as tangential rather than constitutive” while “historians of American religion who have explored beat spirituality have tended to focus almost exclusively on the beats’ engagement with Zen and then to dismiss that engagement as haphazard” (ibid., 207).It is my contention that the mainstream scholarly neglect of Beat spirituality is in some part... (shrink)

The theoretical value of talking to the media isn’t hard to appreciate. Who doesn’t want to shape the public conversation, whether to make it more nuanced and reasoned or to bring injustice and wrongdoing to light? Issues you’ve studied are in the news and you get to be the expert, pointing out what’s wrong, or right, or offering another way of thinking about a difficult question. If you’re lucky, you get your name in print—and in a publication your friends and (...) family actually read. But it can also be intimidating. I used to feel like the hapless witness about to be cross-examined by the wily attorney. I’d heard about the twenty-four-hour news cycle and the push to appeal to the lowest common denominator. .. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Transgressive Translations:Parrhesia and the Politics of Being UnderstoodTim R. JohnstonAuthor And Activist Julia Serano’s spoken word poem “Performance Piece” is a smart and passionate polemic against people who say that “all gender is performance” (Serano 2010, 85). In response to those who treat gender as an endlessly mutable fiction, performance, or facade Serano says:Sure, I can perform gender: I can curtsy, or throw like a girl, or bat my (...) eyelashes. But performance doesn’t explain why certain behaviors and ways of being come to me more naturally than others. It offers no insight into the countless restless nights I spent as a pre-teen wrestling with the inexplicable feeling that I should be female. It doesn’t capture the very real physical and emotional changes that I experienced when I hormonally transitioned from testosterone to estrogen. (Serano 2010, 85–86)My first reaction to this understanding of performativity was to get defensive, immediately thinking of all the ways in which it reflects a poor reading of Judith Butler and is an incorrect use of the concept. Yet, to make that argument would mean arriving late to the party. Many theorists, notably Jay Prosser and Viviane Namaste, have made similar arguments about performativity to which Butler and many others have responded. I am not interested in joining this debate by defending or critiquing performativity; instead, I want to take seriously Serano’s criticism of the way performativity functions as a “mantra” for [End Page 84] “queerer-than-thou hipsters” (Serano 2010, 87). The fact is, concepts that help people make sense of their experience are often taken up piecemeal. They gain traction, get printed on posters, discussed in safe-spaces, taught in intro classes, and yelled at parents. They take on a life of their own and are queered again and again. It may not be anyone’s fault that performativity has come to signify a kind of insincerity, detachment from the body, linguistic constructionism, or a play of surfaces, but for many people this is exactly what it means. What follows is inspired by the questions at the heart of Serano’s poem: “Can’t we find new ways of speaking? Shouldn’t we be championing new slogans that empower all of us, whether trans or non-trans, queer or straight, female and/or male and/ or none of the above?” (Serano 2010, 87). I depart slightly from Serano insofar as I am not interested in replacing performativity as a concept. Instead, I am interested in locating other concepts that could be useful in understanding and communicating our multiple experiences of gender.Serano’s concern is not only the depth and conviction with which she experiences gender, but also the communicability of this conviction. We are social beings. We seek out the company of other people, animals, and objects. In order to flourish we need to feel understood by our surroundings. We are creatures that need to be connected, and connection requires translating our subjective experiences into a communicable, socially understandable register. How does this translation occur? How do we make ourselves understandable? What external forces regulate or influence this translation? And, crucially, how can we construct philosophical concepts that do justice to our need to feel that our interior selves are understood? What concept could we cast out into the world that might answer Serano’s call for new ways of speaking? What follows is an attempt to think through this question by looking at the relationship between the medicalization of trans people, Michel Foucault’s writings on parrhesia, and coming out.The first half of this essay examines the ways in which the medical apparatus that manages transitioning attempts to control transsexual coming-out narratives, an example of what Foucault calls biopower. I argue that the medicalization of transitioning has created a legible transsexual identity structured on the distance between our interiority and the world external to the self. The trans person’s claims about their interior sense of self are the only evidence needed to access medical technologies such as hormone therapy or surgery. But oftentimes such claims are only accepted as valid if they conform to certain scripts—scripts that are... (shrink)

A rhizome may be broken, shattered at a given spot, but it will start up again on one of its old lines, or on new lines. You can never get rid of ants because they form an animal rhizome that can rebound time and again after most of it has been destroyed... There is a rupture in the rhizome whenever segmentary lines explode into a line of flight, but the line of flight is part of the rhizome. That is why (...) one can never posit a dualism or a dichotomy, even in the rudimentary form of the good and the bad. You may make a rupture, draw a line of flight, yet there still is a danger that you will stratify again everything, from Oedipal resurgences to fascist concretions. Groups and individuals contain microfascisms just waiting to crystallize. Yes, couch grass is also a rhizome.Edited by Sylvere Lotringer, On the Line was the first book published in the new "Foreign Agents" series in 1983. It gathers together two seminal texts that Deleuze and Guattari would later elaborate on in A Thousand Plateaus. First delivered in French by Deleuze at the "Schizo-Culture" conference organized by Semiotext at Columbia University in 1975, "Rhizome" introduced a new kind of thinking in philosophy, both non-dialectical and non-hierarchical. The two didn't expect this neo-anarchical blue-print would eventually offer an early template for the understanding of the internet. "Rhizome" substitutes pragmatic, "couch grass," free-floating logic to the binary, oppositional, and exclusive model of the tree.In "Politics," superceding the Marxist concept of class, Deleuze envisages the social macrocosm as a series of lines, and reinvent politics as a process of flux whose outcome will always be unpredictable. It is, he emphasizes, the end of the idea of revolution, but not of the "becoming revolutionary." Throughout, he keeps dispelling the notion of capitalism as a repressive machine only meant to extract surplus value from exploited workers and suggest that it could be opposed from within by redirecting the creativity and multiplicity of its flows.The multiple must be made, not always by adding another dimension, rather in the simplest way, by dint of sobriety... A rhizome as subterranean stem is absolutely different from roots and radices. Bulbs and tubers are rhizomes... Even some animals are, in their pack forms. Rats are rhizomes. Burrows are too, in all their function of shelter, supply, movement, evasion and breakout... The rhizome includes the best and the worst: potato and couch grass. (shrink)

The book roots corruption in the idea of a departure from conventional standards, and thus offers an account not only of its corrosiveness but also of its malleability and controversiality. In the course of a broadranging exploration, it examines various links between private and public corruption, connecting the latter with other social and political structures.

Published one year after Forget Foucault, In the Shadow of the Silent Majorities may be the most important sociopolitical manifesto of the twentieth century: it calls for nothing less than the end of both sociology and politics. Disenfranchised revolutionaries hoped to reach the masses directly through spectacular actions, but their message merely played into the hands of the media and the state. In a media society meaning has no meaning anymore; communication merely communicates itself. Jean Baudrillard uses this last outburst (...) of ideological terrorism in Europe to showcase the end of the "Social." Once invoked by Marx as the motor of history, the masses no longer have sociological reality. In the electronic media society, all the masses can do--and all they will do--is enjoy the spectacle. In the Shadow of the Silent Majorities takes to its ultimate conclusion the "end of ideologies" experienced in Europe after the Soviet invasion of Hungary and the death of revolutionary illusions after May 1968. Ideological terrorism doesn't represent anything anymore, writes Baudrillard, not even itself. It is just the last hysterical reaction to discredited political illusions. (shrink)

The philosophical texts of George Berkeley contain many references to the “relativity” of sensible qualities, that is, to their variation when perceived by different observers; and several of his arguments for immaterialism employ this concept. Many interpreters in this century have minimized the significance and impugned the validity of this argument. Warnock ridicules it as a sophism based on a “fantastic assumption,” and Johnston gives it short shrift. Jessop considers the relativity argument an ad hominem insufficient to demonstrate immaterialism. (...) Indeed, both Jessop and Luce so dilute the entire relativity element in Berkeley that, while he remains an idealist, he comes out assenting, in levelheaded fashion, to nearly absolute sensible objects which persist through time and are available to a plurality of perceivers. (shrink)

Topos Theory is an important branch of mathematical logic of interest to theoretical computer scientists, logicians and philosophers who study the foundations of mathematics, and to those working in differential geometry and continuum physics. This compendium contains material that was previously available only in specialist journals. This is likely to become the standard reference work for all those interested in the subject.

Professor Brian V. Johnstone, CSsR, has been quietly and unobtrusively contributing to the intellectual life of Catholicism, especially in the field of moral theology, for nearly four decades. Having published numerous theological articles on many topics, including biomedical ethics, peace and war, and fundamental moral theology, and directed many doctoral dissertations, it is no exaggeration to say that he has dedicated his entire life to teaching and writing theology. In honor of Johnstone's work, this felicitation volume covers a wide range (...) of themes in the Christian moral life with original articles written by internationally recognized theologians. In the spirit of Johnstone's thought and work, each article challenges the reader to reflect upon the present while contemplating the future of moral theology. (shrink)

This book presents a posthumous collection of previously uncollected works of political theory written by Whittle Johnston. Johnston believed that both the liberal tradition of political thought and the realist tradition of international thought had contributed much to humanity's store of political wisdom, but that each had limitations that could most easily be recognized by its encounter with the other. His method of accomplishing this task was to examine the liberal conception of political life in general and international (...) political life in particular and then to explore the realist critique of the liberal view, particularly as it was expressed by three great twentieth-century realist thinkers, all of whom were, in their various ways, skeptical of liberal assumptions: Reinhold Niebuhr, Hans Morgenthau, and E. H. Carr. In doing so, Johnston reveals the power of the realist outlook, but also the areas in which it remains insufficient, and insufficient particularly where it underestimates the complexity and prudence that liberalism is capable of displaying. There have been studies of both liberalism and realism, but no other work has put them into conversation with each other in the way that this book does. (shrink)

This expanded second edition carries forward the initial insights into the biological and existential significances of animation by taking contemporary research findings in cognitive science and philosophy and in neuroscience into critical and constructive account. It first takes affectivity as its focal point, elucidating it within both an enactive and qualitative affective-kinetic dynamic. It follows through with a thoroughgoing interdisciplinary inquiry into movement from three perspectives: mind, brain, and the conceptually reciprocal realities of receptivity and responsivity as set forth in (...) phenomenology and evolutionary biology, respectively. It ends with a substantive afterword on kinesthesia, pointing up the incontrovertible significance of the faculty to cognition and affectivity. Series A. (shrink)

Like dreaming, hallucination has been a formative trope for modern philosophy. The vivid, often tragic, breakdown in the mind’s apparent capacity to disclose reality has long served to support a paradoxical philosophical picture of sensory experience. This picture, which of late has shaped the paradigmatic empirical understanding the senses, displays sensory acts as already complete without the external world; complete in that the direct objects even of veridical sensory acts do not transcend what we could anyway hallucinate. Hallucination is thus (...) the mother of Representationalism, which insists that it is mental intermediaries that make other.. (shrink)

Critically engaging with thinkers including Slavoj Zizek, Alain Badiou, Catherine Malabou, Jean-Claude Milner, Martin Hagglund, William Connolly and Jane Bennett, Johnston formulates a materialist and naturalist account of subjectivity that does full justice to human beings as irreducible to natural matter alone.

Johnston presents an argument for a form of immortality that divests the notion of any supernatural elements. The book is packed with illuminating philosophical reflection on the question of what we are, and what it is for us to persist over time.

PLoS ONE 3(3): e1897. doi:10.1371/journal.pone.

In this book, Mark Johnston argues that God needs to be saved not only from the distortions of the "undergraduate atheists" but, more importantly, from the idolatrous tendencies of religion itself. Each monotheistic religion has its characteristic ways of domesticating True Divinity, of taming God's demands so that they do not radically threaten our self-love and false righteousness. Turning the monotheistic critique of idolatry on the monotheisms themselves, Johnston shows that much in these traditions must be condemned as (...) false and spiritually debilitating. A central claim of the book is that supernaturalism is idolatry. If this is right, everything changes; we cannot place our salvation in jeopardy by tying it essentially to the supernatural cosmologies of the ancient Near East. Remarkably, Johnston rehabilitates the ideas of the Fall and of salvation within a naturalistic framework; he then presents a conception of God that both resists idolatry and is wholly consistent with the deliverances of the natural sciences. Princeton University Press is publishing Saving God in conjunction with Johnston's forthcoming book Surviving Death, which takes up the crux of supernaturalist belief, namely, the belief in life after death. (shrink)