The Curry-Howard isomorphism states an amazing correspondence between systems of formal logic as encountered in proof theory and computational calculi as found in type theory. For instance, minimal propositional logic corresponds to simply typed lambda-calculus, first-order logic corresponds to dependent types, second-order logic corresponds to polymorphic types, sequent calculus is related to explicit substitution, etc. The isomorphism has many aspects, even at the syntactic level: formulas correspond to types, proofs correspond to terms, provability corresponds to inhabitation, proof normalization corresponds to (...) term reduction, etc. But there is more to the isomorphism than this. For instance, it is an old idea---due to Brouwer, Kolmogorov, and Heyting---that a constructive proof of an implication is a procedure that transforms proofs of the antecedent into proofs of the succedent; the Curry-Howard isomorphism gives syntactic representations of such procedures. The Curry-Howard isomorphism also provides theoretical foundations for many modern proof-assistant systems (e.g. Coq). This book give an introduction to parts of proof theory and related aspects of type theory relevant for the Curry-Howard isomorphism. It can serve as an introduction to any or both of typed lambda-calculus and intuitionistic logic. Key features - The Curry-Howard Isomorphism treated as common theme - Reader-friendly introduction to two complementary subjects: Lambda-calculus and constructive logics - Thorough study of the connection between calculi and logics - Elaborate study of classical logics and control operators - Account of dialogue games for classical and intuitionistic logic - Theoretical foundations of computer-assisted reasoning · The Curry-Howard Isomorphism treated as the common theme. · Reader-friendly introduction to two complementary subjects: lambda-calculus and constructive logics · Thorough study of the connection between calculi and logics. · Elaborate study of classical logics and control operators. · Account of dialogue games for classical and intuitionistic logic. · Theoretical foundations of computer-assisted reasoning. (shrink)

In Capitalism, Alienation and Critique Asger Sørensen offers a wide-ranging argument for the classical Critical Theory of the Frankfurt School, thus endorsing the dialectical approach of the original founders (Horkheimer, Adorno, Marcuse) and criticizing suggested revisions of later generations (Habermas, Honneth). Being situated within the horizon of the late 20th century Cultural Marxism, the main issue is the critique of capitalism, emphasizing experiences of injustice, ideology and alienation, and in particular exploring two fundamental subject matters within this horizon, namely economy (...) and dialectics. Apart from in-depth discussions of classical political economy and Hegelian dialectics, the explorative and inclusive argument also takes issues with Émile Durkheim’s theory of value, the general economy of Georges Bataille and the dialectics of Mao Zedong. -/- - See below External Links to the book's homepage at the publisher Brill and to the Introduction. - See also External Links to a Youtubevideo from a seminar on the book in Belgrade, November 2019 and two Author Meet Critics sections from 2020 and 2021. (shrink)

This paper explores the gray area of questionable research practices (QRPs) between responsible conduct of research and severe research misconduct in the form of fabrication, falsification, and plagiarism (Steneck in SEE 12(1): 53–57, 2006). Up until now, we have had very little knowledge of disciplinary similarities and differences in QRPs. The paper is the first systematic account of variances and similarities. It reports on the findings of a comprehensive study comprising 22 focus groups on practices and perceptions of QRPs across (...) main areas of research. The paper supports the relevance of the idea of epistemic cultures (Knorr Cetina in: Epistemic cultures: how the sciences make knowledge, Harvard University Press, Cambridge, 1999), also when it comes to QRPs. It shows which QRPs researchers from different areas of research (humanities, social sciences, medical sciences, natural sciences, and technical sciences) report as the most severe and prevalent within their fields. Furthermore, it shows where in the research process these self-reported QRPs can be found. This is done by using a five-phase analytical model of the research process (idea generation, research design, data collection, data analysis, scientific publication and reporting). The paper shows that QRPs are closely connected to the distinct research practices within the different areas of research. Many QRPs can therefore only be found within one area of research, and QRPs that cut across main areas often cover relatively different practices. In a few cases, QRPs in one area are considered good research practice in another. (shrink)

Videnskabsteori handler om krav til videnskabelig viden, og disse krav hviler på forudsætninger, der kan ekspliciteres yderligere. -/- Specielt i dag er der dog brug for en bog, der ikke blot analyserer den klassiske videnskabsteori, men i samme diskurs også forholder sig til de meget forskellige tankegange, der i dag giver sig ud for at være videnskabsteori. -/- Om videnskabelig viden til dem, der ønsker et bedre videnskabsteoretisk overblik, og til dem som ønsker at gå mere i dybden med den (...) egentlige filosofiske videnskabsteori. Bogen henvender sig til studerende og færdige kandidater inden for især samfundsvidenskab og humaniora. -/- Asger Sørensens ambition med bogen er at bidrage til klarhed og fornuft i en verden, hvor ideologisk forblændelse ikke blot sker gennem massemedier og underholdningsindustri, men også gennem en akademisk teoriproduktion, der udvikler og anerkender alle mulige programmer for videnskab. (shrink)

Today the idea of cosmopolitanism has become widely accepted as an appropriate answer to what we now call globalization. A key reference is Kant who argues for a Recht of the world citizen, and this is normally understood as a cosmopolitan law. Apparently Kant lets the law of the world citizen be limited to a right to visit, but somehow his peace project must imply something more than just this very modest claim. Following a hint from Kant himself I take (...) a closer look at the material aspect of cosmopolitanism, i.e. the economy of travelling, and it appears that cosmopolitanism can function as an ideology for letting possible investors look for business cases, that is, for promising places for capitalist exploitation. As an answer to such strong material processes cosmopolitanism is insufficient, both as a moral imperative and as a stipulated right. What we need is a more comprehensive political and legal perspective and the solutions this indicates. To get inspiration for this, however, we can turn to Kant again, since it turns out that he does not argue for cosmopolitanism at all, neither as a programme nor as an ideology. For Kant the overall goal is perpetual peace, and the law of the world citizen represents only one subordinate element. As an answer to globalization we should thus drop the limited ideal of cosmopolitanism and follow Kant in his ambition of a threefold political constitution comprising state law, law of the people and law of the world citizen. (shrink)

Considering citizenship education specifically in relation to deliberative politics, first, I focus on the role that Habermas in Between Facts and Norms allots to opinion and will formation as a kind of Bildung, emphasizing the collective aspect of discursive formation in the state as well as in civil society. Secondly, even though I have stressed the crucial role of deliberation in the formation to virtue, I recognize that Habermas attempts to combine the republican call for civic virtue with the liberal (...) claims to have rights. Thirdly, I emphasize that also for Habermas Bildung in some sense constitutes the truth of human being, although it is not specified in detail. Fourthly, I argue that democratic citizenship education would benefit from a substantial notion of Bildung, but that Habermas does not support such an argument. Recognizing that Habermas’s idea of collective formation is restricted to providing justice in terms of politics and law, and bearing in mind the alienation in fact produced within the multitudes of modern capitalist and militarist society, I conclude by expressing the fear that Habermas’s account of democratic formation will not be sufficiently attractive to contemporary democratic citizens and thus unable to function as a normative ideal. (shrink)

Value is a basic concept in economics, ethics and sociology. Locke made labour the source of value, whereas Smith referred to an ideal exchange and Kant specified that commodities only have a market price, no intrinsic value. One can distinguish two modern concepts of value, an economic one trying to explain value in terms of utility, interest or preferences, and an ideal one considering values as ends in themselves. On this basis, Durkheim constructed his theory of value, which was developed (...) by his followers Mauss and Bouglé and further by Bataille. Their line of thought makes it possible to develop a conceptual framework, which can be used to criticise neo-liberalism, big business and the effects of globalisation, while at the same time defending the moral value of business and giving an interpretation of the anti-globalisation protests. (shrink)

Fortunately, the challenge of alienation is now again taken seriously in intellectual discussions. Already years ago, Axel Honneth made the reflection on alienation a defining issue for social philosophy per se, and as the prime example of social philosophy, he brought forth Critical Theory. Within this horizon, recently two conceptions of alienation have been proposedby Rahel Jeaggi and Hartmut Rosa, and the present article takes issue with both of these proposals, criticizing in particular their anti-essentialism. Hence, questioning the post-metaphysical agenda (...) that Jaeggi has inherited from Honneth, I criticize her juxtaposition of the existentialist and the Marxist critique of alienation, her understanding of the good life as autonomy, and finally her acceptance of post-modern and liberal criticism of metaphysics and ontology. Turning to Rosa, I appreciate his societal approach to the critique of alienation, emphasizing the significance of capitalist modernity, but also he accepts the post-metaphysical agenda, and his aesthetic idea of the good life as resonance remains strongly individualistic. Both of these conceptions of alienation thus have ideological implications that threatens to turn upside down the original intentions and implications of Critical Theory in relation to social and political justice. To conclude, the criticism of capitalism, political economy and real life politics is still relevant for understanding alienation, and therefore it is worth returning to the classics of the discussion. (shrink)

I sin udmærkede kommentar til vores artikel «En etisk diskussion af screening for kræftsygdomme» beskriver Geir Hoff den udtalte mangel på evidens vedrørende nytteværdien af screeningsprogrammer for kræftsygdomme baseret på randomiserede studier. Ydermere fremhæver Geir Hoff misforholdet mellem den manglende evidens ved screening og de strenge krav, der er til evidensen i den farmaceutiske industri. Dette er en velkommen kritik, pga. en udtalt ukritisk og uvidenskabelig tilgang til anvendelse af screening for denne eller hin sygdom eller risikofaktor.

The dialectical aspect in the work of Georges Bataille is often neglected. At the suggestion of Foucault and Derrida, Bataille is most often even taken to be a non-dialectical thinker. But Bataille worked intensely with Hegel's ideas, his thought was expressed in Hegelian terms, and both his epistemology and his ontology can be considered a determinate negation of Hegel's position in the Phenomenology. This is shown, first, by analysing Bataille's notions of `inner experience', and, second, by showing how Bataille extends (...) dialectics to the natural, non-human realm, and even conceives the link between the human and non-human as itself dialectical. However, once we see the dialectical nature of his theoretical stance, we are struck by a great vagueness in his practical conception of where society ought to be going. (shrink)

At Danish universities, the governance structure is regulated by law. This structure was radically changed in 2003, abolishing the republican rule of the senate consisting of academics, students, and staff in favour of an authoritarian system assigning all executive power to the vice-chancellor, or as we say in Denmark, the rector. To introduce the current situation at Danish universities, in the first two sections of this article, I will compare them with more well-known counterparts in other countries. This situation is (...) reflected in exemplary cases, and in the third section, I focus on the most dramatic controversy ever encountered at a Danish university, the Koldau case, which reached national newspaper headlines and broadcasting in two rounds in 2011 and 2012. In the fourth section, I will interpret the case as an educational controversy in light of two conflicting ideas of the modern university, which may be attributed to two leading Enlightenment figures, Wilhelm von Humboldt and Denis Diderot. The conclusion is that to some extent, the failure to resist the neo-liberal university reforms in Denmark and the UK, and the drama of the Koldau case, may be explained with reference to the conflicting ideologies of those involved in these controversies. (shrink)

In the present paper, I go beyond these examples by bringing into play an example that I nd more experimental in nature, namely that of the use of the so-called PSLQ algorithm in researching integer relations between numerical constants. It is the purpose of this paper to combine a historical presentation with a preliminary exploration of some philosophical aspects of the notion of experiment in experimental mathematics. This dual goal will be sought by analysing these aspects as they are presented (...) by some of the protagonists of the eld and discussing them using notions from contemporary philosophy of science. (shrink)

Filosoffen og etikeren, lektor ved DPU, Asger Sørensen har samlet og nyskrevet artikler om den franske filosof, sociolog og forfatter Georges Bataille (10. september 1897 - 8. juli 1962), som vi udgiver i 50 året for hans død. En omfattende monografi med både filosofiske og sociologiske aspekter af den kontroversielle forfatter. Desuden en 2. del om forfatterens personlige møde med Batailles univers.

In my response, I initially defend my preference for classical Critical Theory, emphasizing its continued relevance in capitalist modernity, stressing that the epistemological approach does not imply dogmatism with regards to scientific theory or Historical Materialism, just as it does not imply closure with regards to political democracy. When it comes to the dialectics of the classics, I also defend an epistemological approach, arguing that the dialectics aiming for truth implies critique and negativity. However, confronted with the duality of transcendental (...) ideas and historical relativity, I express my confidence in human intuition. Following Hegel, determinate negation must sublate the intuitively conceived universality to a new conception that contains the result of the negation. Finally, I do not see how the conceptual aporias of general economy can be solved by the current political degrowth project. Still, politics is what we need more of, namely social democracy. (shrink)

This article reintroduces a phenomenological experiment designed in the early 1960’s, The Alien-Hand Experiment (TAHE), and it illustrates how phenomena denoted by theoretical concepts like body image, body schema and agency can be studied via the experiment. An analysis of the verbal reports from 26 subjects who participated in TAHE is presented in this article. Subjects were divided into three groups: A group of non-bulimic men, a group of non-bulimic women and a group of female bulimics. The group of (female) (...) bulimics was studied due to the widely spread notion that subjects suffering from eating disorders have a distorted body image. TAHE can be thought of as both a qualitative and quantitative way to study the phenomena arising when the normal relationship between motor behaviour and body experience is disrupted. The present investigation is not an operational definition of body schema and body image, but the two concepts offer a useful interpretive framework. (shrink)

Although Charles S. Peirce, strictly speaking, never formulated a ‘full-blown’ normative theory—a single over-all architectonic system—we believe that there lies within his work a valuable sketch of the ideal for feeling, action, and thought, and how this ideal should be followed, and in connection to this, Peirce offered a model for rational behaviour, including self-control. In the following essay we will try, modestly, to draw a rough outline of this sketch. Firstly, we will focus on the three normative sciences, their (...) relationship and their task of finding out how feeling, action and thought ought to be controlled. Then, we will take a look at the sign-universe. The very universe is a sign-universe and within this evolutionary universe feeling, matter and thought incessantly melt together into ‘concrete reasonableness’; according to Peirce, rendering the world more reasonable. This is the Summum Bonum that man can and indeed should pursue. Hence it makes absolutely no sense to speak of the three normative sciences out of this metaphysical or cosmological context. Finally, we will try to see in what way rationality can be said to fall within the spheres of self-control, bearing in mind that self-control is directly related to conditional purpose. (shrink)

Understanding political philosophy as practical implies reflecting on principles as well as on material matters, on justice as well as on government. Liberalism is the main challenge to political philosophy, since its optimistic laissez faire attitude denies the legitimacy of political government. Even the modern political liberalism reflects these basic traits of liberalism. However, liberalism returns again and again, since it makes sense for human beings, who need to trust and have a capacity to imagine, but find themselves deceived by (...) political authority. The conclusion is that we must overcome liberalism to be able to practice politics and political philosophy in the way presented here. (shrink)

This is a comment to Graham Harman’s 2019 response to an article by Þóra Pétursdóttir and Bjørnar Olsen (2018) in which they propose that a materially grounded, archaeological perspective might complement Harman’s historical approach in Immaterialism (2016). Harman responds that his book is indeed already more archaeological than historical, stipulating that history is the study of media with a high density of information, whereas archaeology studies media with a low density of information. History, Harman holds, ends up in too much (...) detail, while archaeology has the advantage of lending itself to the imagination. Hence, his reading of history had the aim of tempering the historical information overload, in effect making the book a work of archaeology. In this comment, I want to do three things: (1) critique the idea that archaeological and historical media are inherently different with regard to their densities of information, (2) discuss how archaeology and history approach their media, and (3) reflect on conceptualisations of “archaeology” outside the discipline itself. (shrink)

The idea of the university is habitually discussed in relation to German or English language classics. Instead, I will focus on the Spanish language periphery arguing that the discussions there merit attention for distinguishing between three central Old World models of the university, namely, apart from the English and the German, also a French one. Moreover, the marginal perspective stresses the social and political importance of the university. In this perspective, José Ortega y Gasset deserves attention for arguing for a (...) university in the service of a modern republican state. Ortega stresses the importance of a cultural formation that includes the sciences to make enlightened decisions, the distinction between teaching a discipline and doing research within it, and that between a scientist doing research and a highly educated professional practitioner. Unfortunately, the role of knowledge and truth is neglected. The argument from the periphery is therefore necessary albeit not sufficient. (shrink)

From a purely formalist viewpoint on the philosophy of mathematics, experiments cannot (and should not) play a role in warranting mathematical statements but must be confined to heuristics. Yet, due to the incorporation of new mathematical methods such as computer-assisted experimentation in mathematical practice, experiments are now conducted and used in a much broader range of epistemic practices such as concept formation, validation, and communication. In this article, we combine corpus studies and qualitative analyses to assess and categorize the epistemic (...) roles experiments are seen—by mathematicians—to have in actual mathematical practice. We do so by text-mining a corpus of reviews from the _Mathematical Reviews_, which include the indicator word “experiment”. Our qualitative, grounded classification of samples from this corpus allows us to explore the various roles played by experiments. We thus identify instances where experiments function as references to established knowledge, as tools for heuristics or exploration, as epistemic warrants, as communication or pedagogy, and instances simply proposing experiments. Focusing on the role of experiments as epistemic warrants, we show through additional sampling that in some fields of mathematics, experiments can warrant theorems as well as methods. We also show that the expressed lack of experiments by reviewers suggests concordant views that experiments could have provided epistemic warrants. Thus, our combination of corpus studies and qualitative analyses has added a typology of roles of experiments in mathematical practice and shown that experiments can and do play roles as epistemic warrants depending on the mathematical field. (shrink)

Tong Shijun holds a concept of dialectics which can also be found in Mao’s writings and in classical Chinese philosophy. Tong, however, is ambivalent in his attitude to dialectics in this sense, and for this reason he recommends Chinese philosophy to focus more on formal logic. My point will be that with another concept of dialectics Tong can have dialectics without giving up on logic and epistemology. This argument is given substance by an analysis of texts by Mao, Tong and (...) Hegel. (shrink)

In this paper, I describe some aspects of the phenomenon of "experimental mathematics" in order to discuss whether it constitutes a subdiscipline or a particular style of mathematics. My conclusion is that neither of these notions accurately capture the complex culture of experimental mathematics.

Although the use of mathematical models is ubiquitous in modern science, the involvement of mathematical modeling in the sciences is rarely seen as cases of interdisciplinary research. Often, mathematics is “applied” in the sciences, but mathematics also features in open-ended, truly interdisciplinary collaborations. The present paper addresses the role of mathematical models in the open-ended process of conceptualizing new phenomena. It does so by suggesting a notion of cultures of mathematization, stressing the potential role of the mathematical model as a (...) boundary object around which negotiations of different desiderata can take place. This framework is then illustrated by a case study of the early efforts to produce a mathematical model for quasi-crystals in the first two decades after Dan Shechtman’s discovery of this new phenomenon in 1984. (shrink)

The first part of the article demonstrates how the concept of mental resilience has developed from the 1970s to the 2010s, spreading from the field of developmental psychopathology to a wide range of psychological and psychotherapeutic disciplines. Today, there are many varied definitions of mental resilience, ranging from a relation to the concept of mental vulnerability to a related concept of mental strength. The second part of the article demonstrates how the current popularisation of the idea of individual resilience is (...) associated with a social and cultural problematisation of the vulnerable life as well as with a psychopolitical and governmental focus on enhancing the mental capacity of citizens. (shrink)

This article analyses the general economy of Georges Bataille (1897–1962) in relation to political economy. In the first section I present a critical perspective on economy that is necessary in order to appreciate Bataille’s conception of general economy, which is presented in the second section. The general economy is first considered in a macro-perspective, which comprises the whole of the universe, second in a micro-perspective, where the subjective aspect of economy is maintained as non-objectified desire and inner experience. In the (...) third section I turn to the general economy as it was explicitly intended, namely as a political economy. First I argue that the suggestions that Bataille himself presents are apolitical in an ordinary sense of politics, and that this can be shown to be due to some conceptual slides between nature and society and between history and ontology. I then sketch some postmodern attempts to legitimize respectively capitalism and communism, which refer to the general economy, but argue finally that Bataille can escape both, since he maintains the important distinction between need and desire. Although Bataille’s conception of economy thus reminds us of aspects often overlooked by economy in an ordinary sense, it also contains some serious aporias, which means that it cannot constitute the theoretical basis of a new general political economy, as Bataille had hoped. (shrink)

: C. S. Peirce had no theory of metaphor and provided only few remarks concerning the trope. Yet, some of these remarks seem to suggest that Peirce saw metaphor as fundamental to consciousness and thought. In this article we sketch a possible connection between metaphor and cognition; we understand Peircean metaphor as rooted in abduction; it is part of an intricate relation between experience, body, sign and guessing instinct as a semeiotic mechanism which can convey new insights.

Name der Zeitschrift: Semiotica Jahrgang: 2015 Heft: 207 Seiten: 529-538.

Journal Name: Semiotica Issue: Ahead of print.

200 years ago, on August 5, 1802, Niels Henrik Abel was born on Finnøy near Stavanger on the Norwegian west coast. During a short life span, Abel contributed to a deep transition in mathematics in which concepts replaced formulae as the basic objects of mathematics. The transformation of mathematics in the 1820s and its manifestation in Abel’s works are the themes of the author’s PhD thesis. After sketching the formative instances in Abel’s well-known biography, this article illustrates two aspects of (...) the transformation which concern the introduction of concept based mathematics and the related shift in standards of mathematical rigor. Furthermore, the article outlines some of the many bicentennial celebrations in Norway and gives a short, thematic introduction to the literature on Abel and his work. (shrink)

This article describes the transformation of the agricultural economy that took place as a result of the disintegration of the state provision of marketing in Uganda in the 1970s and 1980s. In this context, the article examines how the commercialization of food crops is constructing new relations of gender within agricultural production. In the transformation caused by the commercialization of food crops, men appeared to have gained total control over food production, causing the gender relations to move from a complementary (...) to a patriarchal system. Closer examination, however, reveals an increased significance of marital bargaining and a movement from established gender roles to more negotiable relationships. The evidence underscores the continued significance of differentiated socioeconomic status to women's bargaining potential in gender relations. (shrink)

Intelligence augmentation was one of the original goals of computing. Artificial Intelligence (AI) inherits this project and is at the leading edge of computing today. Computing can be considered an extension of brain and body, with mathematical prowess and logic fundamental to the infrastructure of computing. Multimedia computing—sensing, analyzing, and translating data to and from visual images, animation, sound and music, touch and haptics, as well as smell—is based on our human senses and is now commonplace. We use data visualization (...) and sonification, as well as data mining and analysis, to sort through the complexity and vast volume of data coming from the world inside and around us. It helps us ‘see’ in new ways. We can think of this capacity as a new kind of “digital glasses”. The Internet of Living Things (IOLT) is potentially an even more profound extension of ourselves to the world: a network of electronic devices embedded into objects, but now with subcutaneous, ingestible devices, and embedded sensors that include people and other living things. Like the Internet of Things (IOT), living things are connected; we call those connections “ecology”. As the IOT becomes increasingly synonymous with the IOLT, the question of ethics that is at the centre of aesthetics and the arts will move to the forefront of our experience of and regard for the world in and around us. (shrink)

This chapter is devoted to discussions about the nature of experiments in mathematics during the formative period of experimental mathematics and to a quantitative and qualitative analysis of the journal Experimental Mathematics founded in 1992. Particular attention is paid to interpret the roles of experiment and observation in the mathematical practices surrounding Experimental Mathematics.