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Artykuły w czasopismach na temat "Totally primitive elements"

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Dong, Jingcheng, Linwei Lu, Jingjing Le, Chen Yan, Hongying Zhang i Lulu Li. "Philosophical thinking of Chinese Traditional Medicine". Traditional Medicine and Modern Medicine 01, nr 01 (marzec 2018): 1–10. http://dx.doi.org/10.1142/s2575900018100018.

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Traditional medicine is often an integration of ancient philosophy, clinical experiences, primitive knowledge of medicine, regional cultures and religious beliefs. Chinese Traditional Medicine (CTM) is the general appellation of all the traditional medicines of different ethnicities in China, which share great similarities of basic concept and philosophical basis, and conform to the development of empirical medicine, among which the medicine of Han ethnicity (Han medicine) is the most mature. The development of CTM is totally different from that of modern medicine, always revolving around the center of disease diagnosis and treatment, establishing the core theoretical system of Yin and Yang, Five Elements, Zang and Fu and Humoralism with the theoretical foundation of ancient Chinese philosophy, which represents the highest achievement of worldwide empirical medicine and philosophy form at that time. In general, the basic structure of CTM mainly consists of three parts as follows: the part that has already reached consensus with modern medicine, the part that is unconsciously ahead of modern medicine, and the part that needs to be reconsidered or abandoned.
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Delihas, Nicholas. "An ancestral genomic sequence that serves as a nucleation site for de novo gene birth". PLOS ONE 17, nr 5 (12.05.2022): e0267864. http://dx.doi.org/10.1371/journal.pone.0267864.

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The process of gene birth is of major interest with current excitement concerning de novo gene formation. We report a new and different mechanism of de novo gene birth based on the finding and the characteristics of a short non-coding sequence situated between two protein genes, termed a spacer sequence. This non-coding sequence is present in genomes of Mus musculus, the house mouse and Philippine tarsier, a primitive ancestral primate. The ancestral sequence is highly conserved during primate evolution with certain base pairs totally invariant from mouse to humans. By following the birth of the sequence of human lincRNA BCRP3 (BCR activator of RhoGEF and GTPase 3 pseudogene) during primate evolution, we find diverse genes, long non-coding RNA and protein genes (and sequences that do not appear to encode a gene) that all stem from the 3’ end of the spacer, and all begin with a similar sequence. During primate evolution, part of the BCRP3 sequence initially formed in the Old World Monkeys and developed into different primate genes before evolving into the BCRP3 gene in humans. The gene developmental process consists of the initiation of DNA synthesis at spacer 3’ ends, addition of a complex of tandem transposable elements and the addition of a segment of another gene. The findings support the concept of the spacer sequence as a starting site for DNA synthesis that leads to formation of different genes with the addition of other sequences. These data suggest a new process of de novo gene birth.
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ZAÏMI, T., M. J. BERTIN i A. M. ALJOUIEE. "ON NUMBER FIELDS WITHOUT A UNIT PRIMITIVE ELEMENT". Bulletin of the Australian Mathematical Society 93, nr 3 (11.01.2016): 420–32. http://dx.doi.org/10.1017/s0004972715001410.

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We characterise number fields without a unit primitive element, and we exhibit some families of such fields with low degree. Also, we prove that a noncyclotomic totally complex number field $K$, with degree $2d$ where $d$ is odd, and having a unit primitive element, can be generated by a reciprocal integer if and only if $K$ is not CM and the Galois group of the normal closure of $K$ is contained in the hyperoctahedral group $B_{d}$.
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"The Effects of E – Waste Elements and Management Strategies on Human Health in India Using R-Studio". International Journal of Innovative Technology and Exploring Engineering 8, nr 11 (10.09.2019): 432–39. http://dx.doi.org/10.35940/ijitee.k1386.0981119.

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Electronic equipments contain several venturous silver contaminants like Lead(Pb), Cadmium(Cd), and Beryllium(Be) and brominated flame-retardants. The parts as well as iron, copper, Aluminium(Al), Gold(AU), and alternative metals in e-waste is over hour, whereas plastics account for regarding half-hour and also the venturous pollutants comprise solely regarding two.70%. of the many noxious serious metals, lead is that the most generally employed in electronic devices for numerous functions, leading to a range of health hazards thanks to environmental contamination. Lead enters biological systems via food, water, air, and soil. Youngsters are significantly prone to illness – a lot of therefore than adults as a result of they absorb a lot of lead from their setting and their nervous system and blood get affected. It’s found that the e-waste deployment activities had contributed to the elevated blood lead levels in youngsters living in India, that is one amongst the favoured destinations of e-waste. This was thanks to that undeniable fact that the processes and techniques used throughout the utilization activities were terribly primitive.8 It absolutely was found that ewaste utilization operations were inflicting higher levels of polychlorinated di-benzo-p-dioxins and polychlorinated Dibenzofuran(PCDD/Fs) within the setting moreover as in humans. an outsized range of employees as well as babies ar exposed to totally different disassembly activities of e-waste. though findings of those studies can't be generalized to India however these are enough to alarm and powerfully counsel to be replicating in activity settings in India. There are not any knowledge offered regarding the health implications of those employees. They could be ruin their lives within the lack of applicable information. During this study models for estimation and prediction is given and located the intensity of impacts of the many by-products throughout sorting and utilization of E-Waste by R-Studio.
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Sutherland, Thomas. "Counterculture, Capitalism, and the Constancy of Change". M/C Journal 17, nr 6 (18.09.2014). http://dx.doi.org/10.5204/mcj.891.

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In one of his final pieces of writing, Timothy Leary—one of the most singularly iconic and influential figures of the 1960s counterculture, known especially for his advocacy of a “molecular revolution” premised upon hallucinogenic self-medication—proposes that [c]ounterculture blooms wherever and whenever a few members of a society choose lifestyles, artistic expressions, and ways of thinking and being that wholeheartedly embrace the ancient axiom that the only true constant is change itself. The mark of counterculture is not a particular social form or structure, but rather the evanescence of forms and structures, the dazzling rapidity and flexibility with which they appear, mutate, and morph into one another and disappear. (ix) But it is not just radical activists and ancient philosophers who celebrate the constancy of change; on the contrary, it is a basic principle of post-industrial capitalism, a system which relies upon the constant extraction of surplus value—this being the very basis of the accumulation of capital—through an ever-accelerating creation of new markets and new desires fostered via a perpetual cycle of technical obsolescence and social destabilisation. Far from being unambiguously aligned with a mode of resistance then (as seemingly inferred by the quote above), the imperative for change would appear to be a basic constituent of that which the latter seeks to undermine. The very concept of “counterculture” as an ideal and a practice has been challenged and contested repeatedly over the past fifty or so years, both inside and outside of the academy. For the most part, the notion of counterculture is understood to have emerged out of the tumultuous cultural shifts of the 1960s, and yet, at the same time, as Theodore Roszak—who first coined the term—notes, the intellectual heritage of such a movement draws upon a “stormy Romantic sensibility, obsessed from first to last with paradox and madness, ecstasy and spiritual striving” (91) that dates back to nineteenth century Idealist philosophy and its critique of a rapidly industrialising civilisation. My purpose in this paper is not to address these numerous conceptualisations of counterculture but instead to analyse specifically the enigmatic definition given by Leary above, whereby he conflates counterculture with the demand for continual change or novelty, arguing that the former appears precisely at the point when “equilibrium and symmetry have given way to a complexity so intense as to appear to the eye as chaos” (ix). Concerned that this definition is internally inconsistent given Leary’s understanding of counterculture as a profoundly anti-capitalist force, I will cursorily illustrate the contradictions that proceed when the notion of counterculture as resistance to capitalist hegemony is combined with the identification of counterculture as an authentic and repeated irruption of the new, albeit one that is inevitably domesticated by and subsumed into the dominant culture against which it is posed, as occurs in Leary’s account. The claim that I make here is that this demand for change as an end in itself is inextricably capitalist in its orientation, and as such, cannot be meaningfully understood as a structural externality to the capitalist processes that it strives to interrupt. Capitalism and Growth The study of counterculture is typically, and probably inevitably premised upon an opposition between a dominant culture and those emergent forces that seek to undermine it. In the words of Roszak, the American counterculture of the 1960s arose in defiance of the “modernizing, up-dating, rationalizing, planning” tendencies of technocracy, “that social form in which an industrial society reaches the peak of its organizational integration” (5). Similarly, for Herbert Marcuse, the philosopher perhaps most closely associated with this counterculture, and whose writings formed the intellectual lynchpin of the student protest movement at that time, “intensified progress seems to be bound up with intensified unfreedom,” and as a consequence, we must strive for “a non-repressive civilization, based on a fundamentally different experience of being, a fundamentally different relation between man [sic] and nature, and fundamentally different existential relations” (Eros 4-5). In both cases, the dominant culture is associated with a particular form of repression, based upon the false sense of freedom imposed by the exigencies of the market. “Free choice among a wide variety of goods and services does not signify freedom,” argues Marcuse, “if these goods and services sustain social controls over a life of toil and fear” (One-Dimensional 10). Most importantly, Marcuse observes that this facile freedom of choice is propped up by processes of continual renewal, transformation, and rationalisation—“advertising, public relations, indoctrination, planned obsolescence”—operating on the basis of a “relentless utilization of advanced techniques and science,” such that “a rising standard of living is the almost unavoidable by-product of the politically manipulated industrial society” (One-Dimensional 52-53). Writing at a time when the Keynesian welfare state was still a foregone conclusion, Marcuse denounces the way in which an increase in the quality of life associated with the rise of consumerism and lifestyle culture “reduces the use-value of freedom”, for “there is no reason to insist on self-determination if the administered life is the comfortable and even the ‘good’ life” (One-Dimensional 53). The late industrial society, in other words, is presented as driven by a repressive desublimation which does not merely replace the objects of a so-called “high culture” with those of an inferior mass culture, but totally liquidates any such distinction, reducing all culture to a mere process of consumption, divorced from any higher goals or purposes. This desublimation is able to maintain growth through the constant production of novelty—providing new objects for the purposes of consumption. This society is not stagnant then; rather, “[i]ts productivity and efficiency, its capacity to increase and spread comforts, to turn waste into need, and destruction into construction” all represent the demand for a continual production of the new that undergirds its own stability (One-Dimensional 11). This necessary dynamism, and the creative destruction that goes along with it, is a result of the basic laws of competition: the need not only to generate profit, but to maintain this profitability means that new avenues for growth must constantly be laid down. This leads to both a geographical expansion in search of new markets, and a psychological manipulation in order to cultivate needs, desires, and fantasies in consumers that they never knew they had, combined with a dramatic shift in the search for both raw materials and labour power toward the developing economies of Asia. The result, notes David Harvey, is to “exacerbate insecurity and instability, as masses of capital and workers shift from one line of production to another, leaving whole sectors devastated, while the perpetual flux in consumer wants, tastes, and needs becomes a permanent locus of uncertainty and struggle” (106). What we are seeing then, as these processes of production and demands for consumption accelerate, is not so much the maintenance of the comfortable and carefree life that Marcuse sees as destructive to culture; conversely, this acceleration is engendering a sense of disorientation and even groundlessness that leaves us in a state of continual anxiety and disquietude. Although these processes have certainly accelerated in recent years—not least because of the rise of high-speed digital networking and telecommunications—they were prominent throughout the second-half of the twentieth century (in varying degrees), and indicate a general logic of rationalisation and technical efficiency that has been the focus of critique from the proto-countercultural romanticism of the nineteenth century onward. It is Marx who observes that “[t]he driving motive and determining purpose of capitalist production is the self-valorization of capital to the greatest possible extent,” and it is precisely this seemingly unstoppable impetus toward accumulation that finds its most acute manifestation in our age of digital, post-industrial capitalism (449). What needs to be kept in mind is that capitalism is not opposed to those exteriorities that resist its logic; on the contrary, it is through its ability to appropriate them in a double movement whereby it simultaneously claims to act as the condition of their production and claims the right to represent them on its terms (through the universal sign of money) that capitalism is able to maintain its continual growth. Put simply, capitalism as an economic system and an ideological constellation has proved itself time and time again to be remarkably resilient not only to intellectual critique, but also to the concrete production of new forms of living seemingly contrary to its principles, precisely because it is able to incorporate and thus nullify such threats. The production of the new does not harm capitalism; on the contrary, capitalism thrives on such production. The odd contradiction of the mass society, writes Walter Benjamin, coheres in the way that “the novelty of products—as a stimulus to demand—is accorded an unprecedented importance,” whilst at the same time, “‘the eternal return of the same’ is manifest in mass production” (331). This production of novelty is, in other words, restricted by the parameters of the commodity form—the necessity that it be exchangeable under the terms of capital (as money)—such that its potential heterogeneity is restrained by its identity as a commodity. Capitalism is perfectly capable of creating new modes of living, but it does so specifically according to its terms. This poses a difficulty then for the study and advocacy of counterculture in the terms for which Leary advocates above, because the progressivism of the latter—referring to its demand for continual change and innovation (a demand that admittedly runs counter to the nostalgic romanticism that has motivated a great deal of countercultural thought and praxis, and is certainly not a universally accepted definition of counterculture more broadly)—is not necessarily easily distinguishable from the dominant culture against which it is counterposed. Raymond Williams expresses this frustration well when he observes that “it is exceptionally difficult to distinguish between those which are really elements of some new phase of the dominant culture […] and those which are substantially alternative or oppositional to it” (123). In other words, given that capitalism as an economic system and hegemonic cultural formation is so effective in producing the novelty that we crave—creating objects, ideas, and practices often vastly different to those residual traditions that preceded them—there is no obvious metric for determining when we are looking at a genuine alternative to this hegemony, and when we are looking at yet another variegated product of it. Williams makes a distinction here, whereby the emergence (in the strict sense of coming-into-being or genesis) of a new culture is presumed to be qualitatively different to mere novelty. What is not adequately considered is the possibility that this distinction is entirely illusory—that holding out hope for a qualitatively different mode of existence that will mark a distinct break from capitalist hegemony is in fact the chimera by which this hegemony is sustained, and its cycle of production perpetuated. There is an anxiety here that is present within (and one might suggest even constitutive of) present-day debates over counterculture, particularly in regard to the question of resistance, and what form it might take under the conditions of late capitalism. From Williams’s perspective, it can be argued that “all or nearly all initiatives and contributions, even when they take on manifestly alternative or oppositional forms, are in practice tied to the hegemonic,” such that “the dominant culture, so to say, at once produces and limits its own forms of counter-culture” (114). To argue this though, he goes on to suggest, would: overlook the importance of works and ideas which, while clearly affected by hegemonic limits and pressures, are at least in part significant breaks beyond them, which may again in part be neutralized, reduced, or incorporated, but which in their most active elements nevertheless come through as independent and original. (114)Authentic breaks in specific social conditions are not just a fantasy, he correctly observes, but have occurred many times across history—and not merely in the guise of violent revolutionary activity. What is needed, therefore, is the development of “modes of analysis which instead of reducing works to finished products, and activities to fixed positions, are capable of discerning, in good faith, the finite but significant openness of many actual initiatives and contributions” (114). For Williams, this openness is located chiefly within the semiotic indeterminacy of the artwork, and the resultant potentiality contained within it for individuals to develop resistant readings contrary to any dominant interpretation. These divergent readings become the sites upon which we might imagine new worlds and new ways of living. There is a sense of resignation in his solution though: an appeal to the autonomy of an artwork, and a momentary sublime glimpse of another world, that will inevitably be domesticated by capital. The difficulty that comes with understanding counterculture as an uncompromising demand for the new, over and against the mundane repetitions of commodity culture and lifestyle consumerism, is that it must reckon with the seemingly inevitable appropriation of these new creations by the system against which they are opposed. In such cases, the typical result is a tragic and fundamentally romantic defeatism, in which the creative individual (or community, etc.) must continue to create anew, knowing full well that their output will immediately find itself domesticated and enervated by the forces of capital. This specific conception of counterculture as perpetual change knows that it is doomed to failure, but takes pleasure in the struggle that nonetheless ensues. The Subsumption of Counterculture “Marx and Freud, perhaps, do represent the dawn of our culture,” writes philosopher Gilles Deleuze, “but Nietzsche is something entirely different: the dawn of counterculture” (142). Friedrich Nietzsche seems like an unlikely candidate for the originator of counterculture—his writings certainly bear little overt resemblance to the premises of the various movements that emerged in the 1960s, even though, as Roszak remarks, these movements actually largely issued forth from “the work of Freud and of Nietzsche, the major psychologists of the Faustian soul” (91)—but what he does share with Leary is a belief, expressed most clearly in his posthumous text The Will to Power (1967), in the political and ethical power of becoming, and the need to celebrate and affirm, rather than resist, a world that appears to be in constant, ineluctable flux. Rather than seeking merely to improve the status quo, Nietzsche works toward total and perpetual upheaval—a transvaluation of all values. In Deleuze’s words, he “made thought into a machine of war—a battering ram—into a nomadic force” (149). At a time when resistance to capitalism seems futile; when the possibility of capitalism ending seems more and more distant (which is not to say that it is unlikely to end anytime soon, but merely that its plausible alternatives have been evacuated from the popular imagination), such a claim can seem rather appealing. But how might we distinguish this conception of perpetual revolution of values from the creative destruction of capitalism itself? Why do we presume that there is such a distinction to be made? Why should Leary’s call for rapidity and flexibility—and more broadly, a celebration of change over constancy—be seen as anything other than an acknowledgement and reinforcement of capitalism’s accelerating cycle of obsolescence? The uncomfortable reality we must consider is that the countercultural, as an apparent exteriority waiting to be appropriated, plays an essential role in the accumulation of capital that drives our economic system, and that accordingly, it cannot be plausibly understood as external to the structural conditions that it opposes. This is not to suggest that counterculture does not produce new possibilities, new opportunities, and new ways of living, but simply that its production is always already structured by capitalist relations—the precise anxiety acknowledged by Williams. Once again, this is not a dismissal of counterculture, just the opposite in fact. It is a rejection of the conflation that Leary makes between counterculture and novelty, the combination of which is supposed to provide a potent threat to capitalist hegemony. “The naive supposition of an unambiguous development towards increased production,” argues German philosopher Theodor Adorno, “is itself a piece of that bourgeois outlook which permits development because […] it is hostile to qualitative difference” (156). Capitalism produces many different types of commodities (within which we can include ideas, beliefs, means of communication, as well as physical goods in the traditional sense), but what unites them is their shared identity under the regime of exchange value (money). This exchange value masks their genuine heterogeneity. But what use is it simply reassuring us that if we continue to produce, we may eventually produce something so new, so different that it will evade capture by this logic? Does this not merely reinforce a complicity between the appeal of the countercultural as a force of change and the continuous accumulation of capital? I would contend that to define counterculture as the production of the new underwrites the inexhaustible productivism of the capitalist hegemony that it seeks to challenge. What if, then, this qualitative difference was created not through the production of the new, but the total rejection of this production as the means to resistance? This would not be to engender or encourage a state of total stasis (which is definitely not a preferable or plausible scenario), but rather, to detach the hope for a better world from the idea that we must achieve this by somehow adding to the world that we already have—to recognise, as Adorno would have it, that “the forces of production are not the deepest substratum of man [sic], but represent his historical form adapted to the production of commodities” (156). Leary’s peculiar conception of counterculture that we have been examining throughout this paper refuses to give countenance to any kind of stability or equilibrium, instead proffering an essentially Nietzschean mode of resistance in which incessant creativity becomes the means to the contrivance of a new world—this is part of what Roszak records as the rejection of Marx’s “compulsive hard-headedness” and the embrace of “[m]yth, religion, dreams, visions” which mark the fundamental romanticism of (post-)1960s counterculture, and its heritage in nineteenth century bourgeois sensibilities. For all the benefits that such a conception of counterculture has provided, it would seem misguided to ignore the ways in which Leary’s rhetoric is undermined by the simple fact that it presumes a hierarchy between a dominant culture (capitalism) and its resistant periphery that is already structured by and given through a capitalist mode of thought that presumes its own self-sufficiency (that is, it assumes the adequacy of the logic of exchange to homogenise all products under the commodity form). The postulate that grounds Leary’s understanding of counterculture is a covert identification of man/woman as a restless, alienated being who will never reach a state of stability or actualisation, and must instead continue to produce in the vain hope that this might finally and definitely change things for the better. Instead of embracing the constancy of change, an ideology that ends up justifying the excesses of a capitalist order that knows nothing other than production, perhaps it is possible to begin reconceptualising counterculture in terms that resist precisely this demand for novelty. As Alexander Galloway declares, “[i]t is time now to subtract from this world, not add to it,” for the “political does not arise from the domain of production” (138-139). We do not need more well-intentioned ideas regarding how the world could be a better place or what new possibilities are on offer—we know these things already, we hear about them every day. What we need, and what perhaps counterculture can offer, is to affirm the truth of that which does not need to be produced, which is always already given to us through the immanence of human thought. In the words of François Laruelle, this is an understanding of human individuals as ordinary, “stripped of qualities or attributes by a wholly positive sufficiency,” such that “they lack nothing, are not alienated,” whereby the identity of the individual “is defined by characteristics that are absolutely original, primitive, internal, and without equivalent in the World […] not ideal essences, but finite, inalienable (and consequently irrecusable) lived experiences” (48-49). The job of counterculture then becomes not so much creating that which did not exist prior, but of realising “what we already know to be true” (Galloway 139). References Adorno, Theodor. Minima Moralia: Reflections on a Damaged Life. London and New York: Verso, 1974. Benjamin, Walter. The Arcades Project. Ed. Rolf Tiedemann. Cambridge and London: The Belknapp Press, 1999. Deleuze, Gilles. “Nomad Thought.” The New Nietzsche: Contemporary Styles of Interpretation. Ed. David B. Allison. New York City: Dell Publishing, 1977: 142-149. Galloway, Alexander R. The Interface Effect. Cambridge and Malden: Polity, 2012. Harvey, David. The Condition of Postmodernity: An Enquiry into the Origins of Cultural Change. Cambridge and Oxford: Blackwell, 1989. Laruelle, François. From Decision to Heresy: Experiments in Non-Standard Thought. Ed. Robin Mackay. Falmouth: Urbanomic, 2012. Leary, Timothy. “Foreword.” Counterculture through the Ages: From Abraham to Acid House. Ken Goffman and Dan Joy. New York City: Villard Books, 2004: ix-xiv. Marcuse, Herbert. One Dimensional Man. London and New York: Routledge, 1991. ---. Eros and Civilization: A Philosophical Inquiry into Freud. London: Routledge, 1998. Marx, Karl. Capital, Volume One. London: Penguin, 1976. Nietzsche, Friedrich. The Will to Power. Ed. Walter Kaufmann. New York: Vintage Books, 1967. Roszak, Theodore. The Makings of a Counter Culture. Garden City, New York: Anchor Books, 1969. Williams, Raymond. Marxism and Literature. Oxford and New York: Oxford University Press, 1977.
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Marquis, Nicolas. "“What Can I Do to Get Out of It?”: How Self-Help Readers Make Use of the Language Game of Resilience". M/C Journal 16, nr 5 (20.08.2013). http://dx.doi.org/10.5204/mcj.693.

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Introduction Resilience is, as a concept and as a discourse, a cultural resource that has experienced a growing importance over the last two decades, especially in the field of psychology. In September 2013, the most important database for scientific productions in psychology (www.psycinfo.org) contained more than 14,000 references concerning resilience. In French-speaking countries, for example, each new book by Boris Cyrulnik, the famous neuropsychiatrist who imported the notion of resilience into the psychological field, sells like hotcakes, with total sales of several million copies (see Marquis). Generally considered as the individual’s tendency to cope with stress and adversity, resilience is not only a successful but also a much-debated concept. Is every human potentially resilient, as Masten puts it, or should this notion only apply, in a Darwinian perspective, to the strongest of us? Should resilience be understood as a process in which culture and environment play important roles, as Ungar shows, or as an individual ability? Should we make a distinction between resilient and non-resilient? Does resilience automatically imply having been deeply traumatised, as Cyrulnik puts it? The main reason why these debates have taken such an important place in psychology is that using the concept of resilience is likely to take on, except for its scientific use, a normative or an evaluative dimension. To avoid this shortcoming, most recent works on resilience clearly insist upon the fact that being resilient is not a character trait or an indicator of the power of a person's will (Rutter). It is a multidimensional ecological process. However, nowadays resilience has become a common sense notion, a cultural resource mobilised by the layman or by self-help (SH) books. Accordingly, “resilience” will not be considered here as a scientific concept but rather as a common sense category. Drawing on an analysis of the success of such books, this article intends to show why a description of the common sense uses of this cultural resource is of prime importance when it comes to understanding some salient characteristics of liberal-individualistic societies, especially by comparison with traditional societies. In fact the success of the discursive category of resilience tells something about ourselves, as people living in societies where personal autonomy is highly valued. Therefore, the description of these common sense uses will show how the “resilience” category also constitutes a resource to evaluate both oneself and others as well as an tool to measure one’s own will or the others’, which is exactly what most psychologists try to avoid doing in their theorisation of resilience. Confidence and Breach in Everyday Life Risk management is part of human life. Actually, we spend most of our time minimising the risks we are running when engaging with the world. This attitude is neither a rational action nor a conscious one. It is, in fact, quite the reverse. In everyday life, we simply trust the world. As Luhmann says, confidence is a sine qua non condition of our existence. Our everyday life turns into a close-meshed fabric that makes us feel secure as it ensures consistency over time. This security enables us to avoid the issue of the relevance of our expectations or of the success of our acts. The common sense attitude we are describing here refers to what the American pragmatists call the “practice regime”, in which our main concern is to make sure that life goes on. But a breach might arise (in the form of a more or less tragic event, a change in one’s routine, a vague unease, etc.). What used to be obvious (and above all unquestioned) now becomes uncertain. Such a breach may seriously lead us to question our involvement with a world that has suddenly become strange, threatening, or complete nonsense. The Reading of Self-Help Books: Mobilising Resilience as a Cultural Reaction to Breaches It may be interesting to observe what people do, in the moments when disquiet has invaded their existence, in order to overcome misfortune, both at a symbolic and operative level. My hypothesis is that our attitude towards misfortune is in line with a specific cultural context. Like Illouz, I understand culture as the way we make sense of who we are through actions shaped by values, key images and scenarios, ideals, and habits of thought; through the stories we use to frame our own and others’ experience; through the accounts we use to explain our own and others’ failures and successes; through what we feel entitled to; through the moral categories we use to hierarchize our social world. (8) In other words: in order to allow life to come back to normal after a breach, people resort to the resources their own culture makes available to them. Nowadays resilience has become one such cultural resource that we use to construct our attitude towards misfortune. The question put here is not whether people are really resilient or not, but why this category experiences such traction in liberal-individualistic societies. Therefore, I have made a sociological study of a well-know social phenomenon: in particular, the reading of SH books, in which the discursive tropes of trauma and resilience are indeed very present. Sociologists too often refer to SH books as having hypothetical effects, or consequences. However, unlike what one might find in a literature review, I haven’t tried to make the success of these books a sign or a cause of the decline of society or of the individual, or of a more reflexive society with happier citizens. As numerous authors shown (including Barker and Petley), it is extremely difficult to assess the impact of cultural resources (for example cinema, books, and all forms of media) on individuals and a fortiori on groups of human through scientific procedures. Needless to say, these books have a bad reputation in academic circles, and this negative reputation is maintained because we actually know very little about how they are used by their readers. To overcome this shortcoming, I have tried to provide an answer to the apparently naïve question as to how reading SH literature can make sense to people who praise the virtues of these books, and the claim that they “have changed their life”, readily resorting to the tropes of resilience and trauma. To put it another way, I tried to understand how readers could know “how to go about” these books and have the expertise “to perform these texts” (Alexander) so they can bring them a degree of help, relief and satisfaction. With this objective in mind, I have explored an empirical field of about a hundred SH books, conducted 50 in-depth conversations with readers of SH books, and examined around 300 letters to three well-known authors of such texts. So why do people that read SH books containing such specific content have no trouble finding a meaning, as well as a symbolic and operative effectiveness, in them? My hypothesis is that these books make use of what Wittgenstein calls a “language game”. A “language game” is constituted by a set of (common sense) words and concepts that we mobilise when confronted with specific situations. In contemporary societies, people experiencing a breach in the fabric of their life will probably summon up a particular “language game” influenced by a psychological vision of the world to express and explain what has happened, what the consequences of this breach are, and what possibilities there are to get out of this situation. “Resilience” is one of the most prominent notions of this “language game”. It is not only to be found in the SH books, but also in the discourse of the readers of such books. What does this particular “language game” look like? What role does resilience play in it ? Two characteristics can be observed. First, this “language game” seems to give an extremely important signal of "interiority", an entity that pervades SH readers’ discourse. More precisely SH readers experience (and explain) that they are being inhabited by a “true self” that is the guardian of the “truth” about themselves, but is also the source of an unsuspected power of action. In a supposedly democratic anthropology, people making use of this “language game” consider that all human beings have such interiority, and can therefore harness the hidden resources it contains. In such narratives the pursuit of and engagement with this “true self” are endowed with important qualities. In short, these actions are considered to be the solution to most of our problems. The second characteristic, leading from the first, is that when faced with misfortune, be it big or small, the readers of SH books place great value on "working on the self”. Generally speaking, only efficient action in dealing with our problems finds favour in their eyes. To be precise, in such people’s discourses, having been traumatized is endowed with the power of revealing who we really are and what we are really capable of. Furthermore, such people come to believe that having suffered makes you a survivor, from now on entitled to become a reference for other people on their road to their “true self”. Let us look at a letter to a famous French-speaking SH book author: I want to thank you for your book “Being Genuine: Stop Being Nice, Start Being Real”, which allowed me to identify two problems that stop me from being who I really am: my lack of self-esteem and of self-confidence. Your book was a revelation to me. At the age of 39, I have at last understood how the 26 years spent with my parents created an attitude of submission and passivity in myself, which caused my lack of self-esteem and self-confidence. I have now decided to tackle these problems and to begin a therapy, in order to get rid of all these limiting issues. I feel that it will offer me a rebirth. Thank you so much. (my translation) This letter illustrates clearly how the “language game” is mobilised. It is used first to translate (or to put words on) a vague unease that relies on interiority (“who I really am”, “lack of self-esteem”, “in myself”, etc.) and secondly to create possibilities action to deal with the unease that has now been defined (“tackle the problem”, “begin a therapy”, “get rid of”, etc.). To sum it up, there is no doubt that, contrary to the stance often observed in the scientific literature on resilience, in the SH readers’ eyes, resilience is first a personal capacity, and even more precisely a question of will, and only second a process depending on contextual elements. The Discourse around Sorcery in Azande’s Society as a Point of Comparison I would like now to give an indication of the way reading such books and drawing on this “language game” constitute a practical attitude towards everyday risks, and how this is particularly adapted to our liberal-individualistic culture, in which the question of personal autonomy and individual responsibility is of unprecedented importance (Ehrenberg): in such cultural contexts each individual is expected to be the entrepreneur of his own life. To make this point clearer, I will briefly sketch a comparison with another practical attitude that has been well-documented in anthropological work: the “language game” of sorcery, which is practiced in many traditional societies but also in some parts of the western societies (Favret-Saada). The first anthropologist to have gone beyond the issue of the reality of magic was Evans-Pritchard. During the first half of the 20th century, he studied the use of sorcery in a tribe of South Sudan: the Azande. Evans-Pritchard thought that such a phenomenon could only be understood if the social institutions making a form of magical thinking plausible were taken into account. On the basis of his fieldwork, he considered the types of situations in which the Azande resorted to magic. His answer was that magic (which is notably present in accusations of sorcery) only intervenes in difficult times and more precisely when two things coincide. The first is the fact that an event (even a totally explicable one) arises, the second is the fact that it happens to the person in question, at that precise moment. For example the Azande understand that it was lightning that made the tree fall down, but they wondered why lightning struck in that place, at that time, above the head of that person in particular. For them, such phenomenon could not remain unexplained. They understood what caused their misfortune, but they needed to find a reason for it all the same. When faced with adversity, the Azande will always wonder: "who is holding a grudge against me”, and “who has got reasons to cast a spell on me?" The discourse around sorcery is what Winch later called an "attitude towards contingencies", which he defines as the “way of dealing (symbolically) with misfortunes and their disruptive effect on a man’s relations with his fellows, with ways in which life can go on despite such disruptions” (321). In this sense, reading SH books and mobilizing the category of resilience both have a similar function, just as praying does: this practice and the corresponding “language game” also testify of an attitude towards contingencies. As is the case with magical practices, both are socially instituted systems of interpretations that enable the people in question to find some meaning to misfortune and to go on living after it (in this matter, Masten’s consideration of resilience as “ordinary magic” is interesting). Nevertheless, the ways these two attitudes towards contingencies enable people to make sense and to set up possible actions are very different. The two systems of accountability are not alike. The Azande’s attitude is fundamentally projective (the responsibility or blame for a misfortune is shifted to somebody else, most of the time to a sorcerer). On the other hand, the attitude of the readers of SH books is introspective: the question that is socially valued is not “who is holding a grudge against me?”, but “what can I do to get out of it?”. In SH readers’ eyes, this is the very question to be answered in order to be considered as a resilient person. The sorcery system makes it possible to consider that the responsibility for the misfortune and the responsibility for the end of it go to the same entity: the sorcerer. In the SH readers’ attitude towards contingencies, these two responsibilities are uncoupled: while “another” is often held responsible for the misfortune, the person that experienced the misfortune is always considered responsible for getting over it: they are supposed to pick themselves up and improve themselves. Likewise, the projective attitude (which is characteristic of the discussions on sorcery) is highly discredited in the “language game” of resilience used by the SH readers. It is considered as the sign of a fake resilience. This is obvious from the distrust that is present in their discourse towards the character of the "victim", as well as towards the figure of the “complaint”, as the following excerpts from interviews with readers clearly show:Woman, 64 years old: People reading SH books are people who want to feel good, find their place in the world and solve the problems arising from their past. They are people who try to get over victimisation and to responsibilise themselves. Woman, 35 years old: I find it a good thing that more and more people read SH books. But a lot of other people continue to consider themselves as the genuine victims of their parents or of their education, and they need a lot of time to get through it. As for me, I believe that we have what we need in ourselves: we choose what we want, and we have what we want. Man, 40 years old: We need to get out of the vicious circle that makes us consider that “the others” are always responsible for our problems. For example: “Oh if I am unemployed, it is because society does not provide me with a job”. Well, maybe, but the good question is “why don’t you have a job while other people do?” It is useless to accuse society. The question is: “which actions do you take to get a job? (my translation for the three quotes) This “language game”, which so enhances both interiority as the resource of meaning and power, and efficient work on one’s own self, allows us to consider others or the environment as responsible for our own misfortune. Yet, it certainly doesn’t allow us to wait passively for things to improve on their own. In the common sense use of resilience, improvement must be caused in a proactive way by exploring our inner resources. In the end, this “language game” is indeed what people try to put into practice when they read SH books: these books build up their conviction that, whatever the situation they find themselves in (and whoever is responsible for it), they can always do something to it, they can always make use of this event to improve themselves. SH books and the “language game”, which resilience is a part of, enable the readers to consider all their problems as finding a solution in a more efficient practice of their interiority. Conclusion: The Evaluative Dimension of Resilience The “language game” of SH books is not only employed by readers as a means to make problems manageable. It is also experienced as a powerful resource for assessing oneself and others. The main finding of this article is the hiatus that exists between the scientific interpretations of resilience as an analytic (thus not normative) resource and the way this notion is mobilized in the common sense by laypeople in their everyday lives order to evaluate responsibilities. It is exactly as if people could not help asking the question: “if this person is not resilient and can’t cope with adversity, isn’t it, at least partly, their own fault?” The reason of this hiatus is that resilience is used in a cultural context where autonomy has taken an unprecedented importance. The key message of SH books, which is endorsed by most readers, is that happiness, well-being and resilience are a matter of personal choice. Behind the democratic proposition of SH books: “everybody has the ability to manage, everybody might be resilient,” lurks a much more meritocratic attitude: namely, “if you cannot come to terms with a problem, it is because you don’t really want to”. In the world of SH books, people who do not “put on a brave face”, or who do not work at being consistent with themselves, who content themselves with the secondary benefits of a life that does not really suit them, who expect solutions to drop down from heaven, – in a word people who do not show what SH readers consider as a genuinely resilient behaviour – only have themselves to blame. This phrase (“only have themselves to blame”), has negative connotations in French-speaking sociological discourses, but is not attached to such negativity in the mind of SH readers that get the most out of such books. “Blaming oneself as the only one responsible”, not for what happened but for what we do/don’t do to get through it, is exactly what the “language game” mobilising resilience and its emphasis on interiority and efficient activity allow. This is what readers are seeking when reading SH books. Indeed, people seeking a solution to their problems would ask: what is the use of reading books saying there is nothing to do to improve our situation? Thus, when using the “language game” of resilience, the SH book readers willingly accept the consequence that their problems have now been brought out into the open: the consequence being that people should take the responsibility for the fact that their problems persist (due to their own failure to act) or disappear (due to their actions). This theory of the consequence of one’s actions is today criticised by sociologists, notably French-speaking ones. References Alexander, Jeffrey. “Cultural Pragmatics: Social Performance between Ritual and Strategy.” Sociological Theory 22 (2004): 527–573. Barker, Martin, and Julian Petley, eds. Ill Effects: The Media/Violence Debate: London: Routledge, 2001. Cyrulnik, Boris. Parler d’Amour au Bord du Gouffre. Paris: Odile Jacob, 2004. Ehrenberg, Alain. La Société du Malaise. Paris: Odile Jacob, 2010. Evans-Pritchard, Edward E. Sorcellerie, Oracles et Magie chez les Azandé. Paris: Gallimard, 1972. Favret-Saada, Jeanne. Les Mots, la Mort, les Sorts. La Sorcellerie dans le Bocage. Paris: Gallimard, 1977. Hazleden, Rebecca. “Promises of Peace and Passion: Enthusing the Readers of Self-Help.” M/C Journal 12.2 (2009). 1 Aug. 2013 ‹http://journal.media-culture.org.au/index.php/mcjournal/article/viewArticle/124>. Illouz, Eva. Saving the Modern Soul: Therapy, Emotions, and the Culture of Self-Help. Berkeley: U of California P, 2008. Luhmann Niklas. La Confiance: Un Mécanisme de Réduction de la Complexité Sociale. Paris: Economica, 2006. Marquis, Nicolas. “Se Remettre en Jeu quand Rien ne va Plus: Une Réflexion Sociologique sur la Catégorie de la Résilience. ” Recherches Sociologiques et Anthropologiques 40.1 (2009): 93–110. Masten Ann S., “Ordinary Magic: Resilience Processes in Development.” American Psychologist 56.3 (2001): 227–238. McGee Micki. Self-Help, Inc.: Makeover Culture in American Life. New York: Oxford UP, 2005. Rutter, Michael. “Resilience Reconsidered: Conceptual Considerations, Empirical Findings, and Policy Implications.” Handbook of Early Childhood Intervention. Eds. Jack P. Shonkoff and Samuel J. Meisels. New York: Cambridge UP, 2000. 651–682. Ungar, Michael. “Resilience across Cultures.” British Journal of Social Work 38.2 (2008): 218–235. Winch, Peter. “Understanding a Primitive Society.” American Philosophical Quarterly 1 (1964): 307–324. Wittgenstein, Ludwig. Recherches Philosophiques. Paris: Gallimard, 2005.
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Rozprawy doktorskie na temat "Totally primitive elements"

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Mlodecki, Hugo. "Décompositions des mots tassés et auto-dualité de l'algèbre des fonctions quasi-symétriques en mots". Electronic Thesis or Diss., université Paris-Saclay, 2022. http://www.theses.fr/2022UPASG088.

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Ce travail est fondé sur la théorie des bigèbres bidendriformes, développée par Foissy, qui sont des algèbres de Hopf particulières où le produit et le coproduit peuvent être scindés en deux. Son théorème principal est: Une bigèbre bidendriforme est générée librement par ``l'espace des éléments totalement primitifs'' en tant qu'algèbre dendriforme. Une conséquence est l'auto-dualité des bigèbres bidendriformes.Parmi les nombreuses algèbres de Hopf, Hivert a défini l'algèbre des fonctions quasi-symétriques en mots, notée WQSym. En prouvant que WQSym est une bigèbre bidendriforme, Novelli-Thibon résolvent la conjecture de Duchamp-Hivert-Thibon sur l'auto-dualité de WQSym. Cependant, comme aucune construction générale de l'ensemble des totalement primitifs n'est formulée, nous n'avons pas d'auto-morphisme explicite pour le passage de la primale à la duale.La question centrale de cette thèse est donc de construire un isomorphisme bidendriforme entre WQSym et sa duale. Cette construction passe par la décomposition des mots tassés à l'aide de deux nouvelles opérations que nous avons définies. En outre, pour illustrer ces décompositions, nous avons créé une nouvelle famille d'objets combinatoires: les forêts d'arbres biplans. Certains sous-ensembles de mots tassés ne peuvent être décomposés par ces opérations. Nous avons prouvé que leurs séries génératrices sont égales aux dimensions de l'espace des éléments totalement primitifs. L'intérêt des forêts biplanes est de faire apparaître visuellement les sous-ensembles de mots tassés indécomposables.Ces forêts biplanes sont donc la forme idéale pour indexer des nouvelles bases, que nous avons créées, de l'algèbre WQSym et sa duale. En effet, il est aisé d'en extraire un sous-ensemble qui définit deux bases des espaces totalement primitifs de WQSym et sa duale. Enfin, des arbres biplans bicolores permettent d'obtenir un isomorphisme bidendriforme par un simple échange de couleurs, ce qui répond à notre question initiale et constitue le résultat principal de cette thèse.Après l'obtention de ce résultat, nous nous intéressons aux relations entre les opérations évoquées. Nous remarquons alors fortuitement que ces opérations vérifient des relations semblables à des opérades bien connues (dupliciale déformée, L-algèbre, bigraft) mais qui sont a priori sans lien avec l'opérade dendriforme. Nous prouvons que l'ensemble des mots tassés munis de ces opérations décrit une algèbre sur ces opérades et en donnons des sous-ensembles de générateurs.L'algèbre PQSym, indexée par les fonctions de parking, est très similaire à WQSym, mais aussi plus complexe et serait un premier pas vers la généralisation de notre résultat principal. La question de généraliser ce résultat aux fonctions de parking relève à la fois de la combinatoire et de l'algèbre. Nous présentons ce qui est sans doute le premier ingrédient de cette généralisation. Il s'agit du calcul d'un changement de base où le produit de mélange des valeurs est sans chevauchement.Nous terminons cette thèse par une partie expliquant notre démarche expérimentale de recherche utilisant SageMath. Nous décrivons les tutoriels que nous avons conçus sous la forme de notebooks et mis en ligne à disposition des autres chercheurs. Nous y présentons le code qui permet de vérifier tous nos résultats sur des exemples calculés par des algorithmes
This work is founded on the theory of bidendriform bialgebras, developped by Foissy, which are particular Hopf algebras where the product and the coproduct can be split into two parts. His main theorem is: A bidendriform bialgebra is freely generated by ``the space of totally primitive elements'' as a dendriform algebra. A consequence of this is the self-duality of bidendriform bialgebras.Among the many Hopf algebras, Hivert defined the algebra of word quasi-symmetric functions, denoted WQSym. By proving that WQSym is a bidendriform bialgebra, Novelli-Thibon solved the Duchamp-Hivert-Thibon conjecture on the self-duality of WQSym. However, since no general construction of the set of totally primitive was formulated, we do not have an explicit isomorphism between the primal and the dual.The central question of this thesis is the construction of a bidendriform isomorphism between WQSym and its dual. This construction goes through a decomposition of packed words using two new operations that we havedefined. Furthermore, to illustrate these decompositions, we have created a new family of combinatorial objects: forests of biplane trees. Some subsets of packed words cannot be decomposed by these operations. We proved that their generating series are equal to the dimensions of the space of the totally primitive elements. The interest of biplane forests is to visually reveal the subsets of indecomposable packed words.These biplane forests are therefore the ideal form for indexing the new bases, that we have created, of the algebra WQSym and its dual. In fact, it is easy to extract from them a subset which defines two bases of totally primitives spaces of WQSym and its dual. Finally, bicolored biplane trees allow us to obtain a bidendriform isomorphism by a simple exchange of colors, which answers our initial question and constitutes the main result of this thesis.After obtaining this result, we study the relationships between the aforementioned operations. We then remark fortuitously that these operations verify relations similar to well-known operads (skew-duplicial, L-algebra,bigraft) but which are unrelated to the dendriform operad. We prove that the set of packed words endowed with these operations describes an algebra over these operads and give subsets of generators.The PQSym algebra, indexed by parking functions, is very similar to WQSym, but also more complex and would be a first step towards a generalization of our main result. The question of generalizing this result to parking functions is both combinatorics and algebra. We present what is undoubtedly the first ingredient of this generalization. This is the calculation of a change of bases where the shuffle product on values is not overlapped.We end this thesis with a part explaining our experimental approach of research using SageMath. We describe the tutorials that we have designed in the form of notebooks and made available online for other researchers. We present the code that allows to check all our results on examples calculated by algorithms
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Części książek na temat "Totally primitive elements"

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Bloch, Maurice m. "The Presence of Violence 1n Religion". W Why We Watch, 163–78. Oxford University PressNew York, NY, 1998. http://dx.doi.org/10.1093/oso/9780195118209.003.0009.

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Abstract This chapter concerns the place of violence in religion and more particularly in religious rituals. Although much of the discussion will refer to peoples living outside the industrial world, in societies that would often be qualified as simple, peasant, or even primitive, the conclusions apply to religious practices in general. To talk of violence in religion may at first seem surprising, especially to North American or European audiences, which often have a some what sentimental view of religion and a totally negative view of violence, in the abstract at least. That being so, the question for them seems to be how the two things can be mixed together. In fact, violence and religion are intimately linked all over the world. For example, a moment’s reflection about the familiar Semitic religions-Judaism, Christianity, and Islam-reveals the great role that violence has always played for them. The Old Testament is full of the celebrations of wars and killings, of maledictions and blood-curdling threats. The same is true of the Koran and the New Testament, in which we are told, for example, how, in the Acts of the Apostles, a couple who had not disclosed the full profit they had made on a property transaction to Saint Peter and to an early Christian congregation were immediately struck dead by God in an episode that seems to make matters worse by adding an element of grim humor. The presence of violence, or the evocation of it, is also very clear in rituals, such as the Muslim celebration of Abraham’s sacrifice or the Christian evocation of the crucifixion.
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Sambin, Giovanni, i Silvio Valentini. "Building up a toolbox for Martin-Löf’s type theory: subset theory". W Twenty Five Years of Constructive Type Theory. Oxford University Press, 1998. http://dx.doi.org/10.1093/oso/9780198501275.003.0014.

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Beginning in 1970, Per Martin-Löf has developed an intuitionistic type theory (hence-forth type theory for short) as a constructive alternative to the usual foundation of mathematics based on classical set theory. We assume the reader is aware at least of the main peculiarities of type theory, as formulated in Martin-Löf 1984 or Nordström et al. 1990; here we recall some of them to be able to introduce our point of view. The form of type theory is that of a logical calculus, where inference rules to derive judgements are at the same time set-theoretic constructions, because of the “propositions-as-sets” interpretation. The spirit of type theory—expressing our interpretation in a single sentence-—is to adopt those notions and rules which keep total control of the amount of information contained in the different forms of judgement. We now briefly justify this claim. First of all, the judgement asserting the truth of a proposition A, which from an intuitionistic point of view means the existence of a verification of A, in type theory is replaced by the judgement a ∈ A which explicitly exhibits a verification a of A. In fact, it would be unwise, for a constructivist, to throw away the specific verification of A which must be known to be able to assert the existence of a verification! The judgement that A is a set, which from an intuitionistic point of view means that there exists an inductive presentation of A, is treated in type theory in a quite similar way (even if in this case no notation analogous to a ∈ A is used) since the judgement A set in type theory becomes explicit knowledge of the specific inductive presentation of A. In fact, the rules for primitive types and for type constructors are so devised that whenever a judgement A set is proved, it means that one also has complete information on the rules which describe how canonical elements of A are formed. Such a property, which might look like a peculiarity of type theory, is as a matter of fact necessary in order to give a coherent constructive treatment of quantifiers.
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Tait, William. "Remarks on Finitism". W The Provenance of Pure Reason, 43–60. Oxford University PressNew York, NY, 2005. http://dx.doi.org/10.1093/oso/9780195141924.003.0003.

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Abstract The background of these remarks is that in “Constructive reasoning” (Tait, 1968), I sketched an argument that finitist arithmetic coincides with primitive recursive arithmetic (PRA) and in “Finitism” (Tait, 1981), reprinted here as chapter 1, I expanded on the argument. But some recent discus­ sions and some of the more recent literature on the subject lead me to think that a few further remarks would be useful. The question “What is finitism?” is really two questions, which I did separate in Tait (1981), but perhaps not sufficiently clearly. First, and, in truth, for me most important, there is the conceptual problem of making sense of the idea of a ‘finitist’ function or ‘finitist’ proof of a finitist arithmetic proposition such as Vxy[x + y = y + x], which seems to refer to the infinite totality of numbers. And second, there is the historical question of what Hilbert-or perhaps better, Hilbert and Bernays1-meant by “finitism.” The two questions are not entirely independent, of course, since it was Hilbert and Bernays who originally marked out the conception of finitist mathematics. But, if we take as the central issue the question of the ‘finite’ in finitism, we may be led to reject some aspects of the Hilbert-Bernays account. Indeed, my analysis rejects the Kantian element in their discussions. Their account of finitist mathematics begins with the restriction to objects representable in intuition or obtained by ‘intu­ itive abstraction’-’formal objects’ as Bernays calls them (Hilbert, 1926; Bernays, 1930-31). For Bernays the finiteness of mathematical objects is a consequence of their representability in intuition. (See Bernays, 1976, p. 40.) But our problem is, of course, not the finiteness of a number, but the infinity of numbers. There is, I think, a difficulty with Bernays’s notion of formal object, where this is intended to extend to numbers so large as not only to be beyond processing by the human mind, but possibly to be beyond representability in the physical world (Bernays, 1976, p. 39). This difficulty ought to be discussed more adequately than I have so far done, but I won’t take it up here.
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