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)

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.

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 study investigates the prevalence of ‘Seeking God's Help’, its relation to time since diagnosis, and its association with Life Satisfaction for all cancer types. This study also investigates Disease-Specific Quality of Life for patients with breast, prostate, and colorectal cancers. Data were obtained from the third wave of the Nord-Trøndelag Health Study of Norway, with 2,086 cancer patients identified by the Cancer Registry of Norway and 6,258 cancer-free controls. Our results indicate a higher prevalence of ‘Seeking God's Help’ after (...) a shorter time since diagnosis among men. No association was observed in multivariate analyses between ‘Seeking God's Help’ and ‘Life Satisfaction’ or ‘Disease-Specific QoL’ in long-term cancer survivors. Longitudinal investigations are needed to elucidate the relationship between the ‘Seeking God's Help’ variable and Life Satisfaction and Disease-Specific QoL among cancer patients in a Norwegian context. (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)

There is a simple technique, due to Dragalin, for proving strong cut-elimination for intuitionistic sequent calculus, but the technique is constrained to certain choices of reduction rules, preventing equally natural alternatives. We consider such a natural, alternative set of reduction rules and show that the classical technique is inapplicable. Instead we develop another approach combining two of our favorite tools—Klop's l-translation and perpetual reductions. These tools are of independent interest and have proved useful in a variety of settings; it is (...) therefore natural to investigate, as we do here, what they have to offer the field of sequent calculus. (shrink)

The article discusses the relation between political office and the rule of law in Plato’s dialogue Statesman. Taking its starting-point from an observation about the Statesman’s peculiar approach to constitutional analysis, the article argues that what Plato is concerned to show is how the reconceptualisation of the role of law in government proposed in that dialogue has important implications for what we take the role of the institution of office-holding to be. While Greek political tradition held the main aim of (...) archē to be the formal circumscription and control of official power within a constitutional order, Plato insists that it should primarily be understood as ensuring that the exercise of political power approximates, by means of law, the ideal rule by a political expert. The article ends by pointing out how this reading complements another recent discussion of office-holding in the Statesman. (shrink)

Taking up the controversial issue of the value of the laws of non-ideal cities in Plato’s Statesman, the paper argues for a modified version of the traditional interpretation, as defended against Christopher Rowe’s influential criticism. The paper agrees with the traditional view that the established laws of non-ideal cities are assumed to be good laws and that the Eleatic Stranger’s justification for this assumption can be found in 300b. But it also argues that this defence of the traditional interpretation must (...) be based on a revised understanding of the role of legislation in the Stranger’s conception of ideal rule. The unique contribution of the expert to good government consists in his distinctive ability to judge what is appropriate in each case, not in his work as legislator, which, on closer inspection, turns out to be based on the very same ancestral traditions that the second best city must resort to. (shrink)

Fortunately, alienation has returned to the agenda of critical thought. Discussing the idea that alienation is implied by capitalism rather than human existence, it is argued Marx’s original idea of alienation still has critical as well as educational and political potential.

The basis of perception is the processing and categorization of perceptual stimuli from the environment. Much progress has been made in the science of perceptual categorization. Yet there is still no consensus on how the brain generates sensory individuals, from sensory input and perceptual categories in memory. This chapter argues that perceptual categorization is highly variable across perceivers due to their use of different perceptual strategies for solving perceptual problems they encounter, and that the perceptual system structurally adjusts to the (...) strategies that are most successful. Despite this variability, the different sensory individuals that result when different perceivers rely on different strategies nonetheless correspond to actual external world objects/features. This view is called 'perceptual pluralism'. (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.

There is a simple technique, due to Dragalin, for proving strong cut-elimination for intuitionistic sequent calculus, but the technique is constrained to certain choices of reduction rules, preventing equally natural alternatives. We consider such a natural, alternative set of reduction rules and show that the classical technique is inapplicable. Instead we develop another approach combining two of our favorite tools—Klop’s ι-translation and perpetual reductions. These tools are of independent interest and have proved useful in a variety of settings; it is (...) therefore natural to investigate, as we do here, what they have to offer the field of sequent calculus. (shrink)

Whether visual perceptual consciousness is gradable or dichotomous has been the subject of fierce debate in recent years. If perceptual consciousness is gradable, perceivers may have less than full access to—and thus be less than fully phenomenally aware of—perceptual information that is represented in working memory. This raises the question: In virtue of what can a subject be less than fully perceptually conscious? In this chapter, we provide an answer to this question, according to which inexact categorizations of visual input (...) may result in a representation of the visual information in working memory that is less than fully available to the perceiver, and of which the perceiver is therefore less than fully phenomenally aware. The latter proposal is a natural extension of a theory of perception we have proposed in previous works, namely, the template tuning theory (TTT). We argue that although TTT is compatible with both gradable and dichotomous conceptions of perceptual consciousness, the available empirical evidence favours a gradable conception of perceptual consciousness. (shrink)

Predictive processing models of perception take issue with standard models of perception as hierarchical bottom-up processing modulated by memory and attention. The predictive framework posits that the brain generates predictions about stimuli, which are matched to the incoming signal. Mismatches between predictions and the incoming signal – so-called prediction errors – are then used to generate new and better predictions until the prediction errors have been minimized, at which point a perception arises. Predictive models hold that all bottom-up processes are (...) signals conveying prediction errors to higher areas, which respond by updating their predictions. We take issue with this claim and argue that object recognition requires bottom-up processing that cannot be understood in terms of prediction errors. Along the way, we expand on previous work casting doubt on the framework's ability to account for attention. Specifically, we argue that the type of attention that allows us to rapidly extract the gist of an object or scene presents an additional challenge to the predictive approach. We conclude by considering how the framework may be augmented to avoid these problems. (shrink)

To study whether the distinction between introspective and non-introspective states of mind is an empirical reality or merely a conceptual distinction, we measured event-related potentials elicited in introspective and non-introspective instruction conditions while the observers were trying to detect the presence of a masked stimulus. The ERPs indicated measurable differences related to introspection in both preconscious and conscious processes. Our data support the hypothesis that introspective states empirically differ from non-introspective states.

A discussion of the historical development of the relationship between moral philosophy and political economy and economics qua disciplines, followed by a treatment of questions of justice in the contemporary discussion and then by an overview of the subdiscipline of busness ethics.

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)

Aim:The purpose of this study was to explore how adolescent patients displaying developmental trauma experience and describe meaning in life. Schnell’s model of meaning in life is applied to explore meaningfulness, crises of meaning and sources of meaning. Method: The study has a qualitative design based on individual interviews with eight adolescents aged 14–18 years in treatment in an outpatient clinic for mental health care for children and adolescents. The interviews were transcribed and analyzed using systematic text condensation. Results: The (...) adolescents related meaning in life to the experience of coherence, intrinsic values, progress and belonging, or the absence of these. Examples of sources of meaning among the informants were positive relations with meaningful others, structure and routines, moments of well-being, achieving goals related to education, work and family, and seeking something else outside oneself such as playing computer games, being engaged in politics, being with animals, having a belief in a god or being outdoors in natural surroundings. Conclusion: Although the topic of meaning in life was unknown to this group, they used sources of meaning intuitively. This group seems to have similar preferences to the general population. More knowledge is needed on how the topic of meaning in life can be useful in therapy for adolescents with development trauma. (shrink)

How do historians understand the minds, motivations and intentions of historical agents? What might evolutionary and cognitive theorizing contribute to this work? What is the relation between natural and cultural history? Historians have been intrigued by such questions ever since publication in 1859 of Darwin's The Origin of Species, itself the historicization of biology. This interest reemerged in the latter part of the twentieth century among a number of biologists, philosophers and historians, reinforced by the new interdisciplinary finding of cognitive (...) scientists about the universal capacities of and constraints upon human minds. The studies in this volume, primarily by historians of religion, continue this discussion by focusing on historical examples of ancient religions as well as on the theoretical promises and problems relevant to that study. (shrink)

After years of neglect, alienation has again reached the agenda of critical thought. In my case, I recognize alienation as a challenge for education in contemporary societies. To obtain conceptual resources to overcome this challenge, I have revisited the comprehensive 20 th century discussion of alienation. Today, alienation is naturally discussed as an existential condition of human being, but still in the 1980s, there was a strong Marxist current that claimed alienation to be implied by capitalism, in particular by the (...) institution of private property and the social division of labor, and that alienation therefore should be criticized as part of the critique of capitalism and political economy and possibly overcome. Today, under the hegemony of neo-liberal capitalism, this critical and processual concept of alienation is more relevant than ever. Hence, in the present work I argue that the basic logic of Marx's idea of alienation still has critical potential. The argument forms a long engagement with mainly 20 th century literature, departing from the very idea of capitalism, considering the ideas of history, education and democracy, discussing how to distinguish and translate key terms, considering why alienation became an object of controversy among Marxists, offering an interpretation of Marx's critique relevant for contemporary society, thus considering alienation a consequence of working under conditions of private property, i.e. being a human being in a capitalist society, and finally presenting Marx's idea of communism as relevant to the contemporary educational agenda. (shrink)

Cognitive Science, Volume 46, Issue 4, April 2022.

Ethnic minority patients have been discussed and problematised in Western health literature. Drawing on an interpretation of central parts of the French philosopher Michel Foucault's authorship, we analysed a broad selection of materials to identify mechanisms through which the truth about ethnic minority patients is constructed. We identified a single, yet consistent discursive strategy that we termed ‘figure of inconvenience’ in which ethnic minority patients were classified and assigned a specific subjection illustrating them as ‘inconvenient’ to the nurse's practice. Concurrently, (...) their relatives were afforded the position of substitutes. The discourse exemplifies how the behaviour or appearances of ethnic minority patients cannot be reconciled with the traits of ethnic Danish patients. Finally, we discussed implications that such a strategy may have for the provision of healthcare services for ethnic minority patients in Denmark. (shrink)