A meadow is a commutative ring with an inverse operator satisfying 0⁻¹ = 0. We determine the initial algebra of the meadows of characteristic 0 and prove a normal form theorem for it. As an immediate consequence we obtain the decidability of the closed term problem for meadows and the computability of their initial object.

What do mathematicians mean when they use terms such as ‘deep’, ‘elegant’, and ‘beautiful’? By applying empirical methods developed by social psychologists, we demonstrate that mathematicians' appraisals of proofs vary on four dimensions: aesthetics, intricacy, utility, and precision. We pay particular attention to mathematical beauty and show that, contrary to the classical view, beauty and simplicity are almost entirely unrelated in mathematics.

Inside a combinatory algebra, there are ‘internal’ versions of the finite type structure over ω, which form models of various systems of finite type arithmetic. This paper compares internal representations of the intensional and extensional functionals. If these classes coincide, the algebra is called ft-extensional. Some criteria for ft-extensionality are given and a number of well-known ca's are shown to be ft-extensional, regardless of the particular choice of representation for ω. In particular, DA, Pω, Tω, Hω and certain D∞-models all (...) share the property of ft-extensionality. It is also shown that ft-extensionality is by no means an intrinsic property of ca's i.e., that there exists a very concrete class of ca's—the class of reflexive coherence spaces—no member of which has this property. This leads to a comparison of ft-extensionality with the well-studied notions of extensionality and weak extensionality. Ft-extensionality turns out to be completely independent. (shrink)

Adapting a claim of Kracht (Theor Comput Sci 354:131–141, 2006), we establish a characterization of the typable partial applicative structures.

(1996). Feminism as a traveling theory: The dynamic process of cross‐cultural representation. The European Legacy: Vol. 1, Fourth International Conference of the International Society for the Study of European Ideas, pp. 1465-1470.

On several levels, there is now a debate whether the concept of God can be made compatible with modern science. In an attempt to elucidate this debate, I give an account of my own experiences from writing a book on the foundation of quantum mechanics. In my opinion, one can give two independent arguments for the existence of God by taking as departure an epistemic (knowledge-based) interpretation of quantum theory. However, I also argue that any religious belief should be the (...) result of an existential choice governed by each person’s own context (history and culture). In particular, I give my account of Christianity as a religion connected to our western culture, how one as a scientist can relate to the relevant dogmas. (shrink)

The well known Bell experiment with two actors Alice and Bob is considered. First the simple deduction leading to the CHSH inequality under local realism is reviewed, and some arguments from the literature are recapitulated. Then I take up certain background themes before I enter a discussion of Alice’s analysis of the situation. An important point is that her mind is limited by the fact that her Hilbert space in this context is two-dimensional. General statements about a mind’s limitation during (...) a decision process are derived from recent results on the reconstruction of quantum theory from conceptual variables. These results apply to any decision situation. Let all the data from the Bell experiment be handed over to a new actor Charlie, who performs a data analysis. But his mind is also limited: He has a four-dimensional Hilbert space in the context determined by the experiment. I show that this implies that neither Alice nor Charlie can have the argument leading to the CHSH inequality as a background for making decisions related to the experiment. Charlie may be any data analyst, and he may communicate with any person. It is argued that no rational person can be convinced by the CHSH argument when making empirical decisions on the Bell situation. (shrink)

The inner ear of mammals uses neurosensory cells derived from the embryonic ear for mechanoelectric transduction of vestibular and auditory stimuli (the hair cells) and conducts this information to the brain via sensory neurons. As with most other neurons of mammals, lost hair cells and sensory neurons are not spontaneously replaced and result instead in age‐dependent progressive hearing loss. We review the molecular basis of neurosensory development in the mouse ear to provide a blueprint for possible enhancement of therapeutically useful (...) transformation of stem cells into lost neurosensory cells. We identify several readily available adult sources of stem cells that express, like the ectoderm‐derived ear, genes known to be essential for ear development. Use of these stem cells combined with molecular insights into neurosensory cell specification and proliferation regulation of the ear, might allow for neurosensory regeneration of mammalian ears in the near future. BioEssays 28: 1181–1193, 2006. © 2006 Wiley Periodicals, Inc. (shrink)

In this article, we report a study in which 109 research-active mathematicians were asked to judge the validity of a purported proof in undergraduate calculus. Significant results from our study were as follows: (a) there was substantial disagreement among mathematicians regarding whether the argument was a valid proof, (b) applied mathematicians were more likely than pure mathematicians to judge the argument valid, (c) participants who judged the argument invalid were more confident in their judgments than those who judged it valid, (...) and (d) participants who judged the argument valid usually did not change their judgment when presented with a reason raised by other mathematicians for why the proof should be judged invalid. These findings suggest that, contrary to some claims in the literature, there is not a single standard of validity among contemporary mathematicians. (shrink)

This article may be seen as a summary and a final discussion of the work that the author has done in recent years on the foundation of quantum theory. It is shown that quantum mechanics as a model follows under certain specific conditions from a quite different, much simpler model. This model is connected to the mind of an observer, or to the joint minds of a group of communicating observers. The model is based upon conceptual variables, and an important (...) aspect is that an observer (a group of observers) must decide on which variable to measure. The model is then linked more generally to a theory of decisions. The results are discussed from several angles. (shrink)

Nonsymbolic comparison tasks are commonly used to index the acuity of an individual's Approximate Number System (ANS), a cognitive mechanism believed to be involved in the development of number skills. Here we asked whether the time that an individual spends observing numerical stimuli influences the precision of the resultant ANS representations. Contrary to standard computational models of the ANS, we found that the longer the stimulus was displayed, the more precise was the resultant representation. We propose an adaptation of the (...) standard model, and suggest that this finding has significant methodological implications for numerical cognition research. (shrink)

The objective was to test the Theory of Planned Behavior and the proposition that relative measures should be used in travel mode choice situations. Data from a survey in Norway was analyzed using regression analysis. The results indicated that factors of the Theory of Planned Behavior and past behavior predicted intentions to travel by car, public, transport, bicycle, and on foot. The results supported the idea that there is a split in perceived behavioral control in controllability and self-efficacy, as controllability (...) was a significant predictor only for intention to travel by car. The use of relative measures added to the predictive strength of all predictors and increased prediction of behavioral intention for all travel modes. The results supported the Theory of Planned Behavior and the proposition regarding choice situations. Previous tests of the theory may have underestimated its predictive power. Attitudes, subjective norms, and perceived behavioral control predict travel intentions and may be targeted in interventions aimed at promoting travel mode choice. (shrink)

_The Worship and Love of God_ is one of the most unusual writings of Swedish scientist and theologian Emanuel Swedenborg. A "poetical novel," it dramatizes the Creation and examines the life of Adam and Eve as the first truly united couple. Considered Swedenborg's last work before he embarked on his visionary period, the manuscript was left unfinished by its author and published only after his death. Inge Jonsson, one of the world's leading scholars on Swedenborg's works, offers a scholarly (...) look into a neglected literary achievement. He examines this unique work from the perspective of sources and influences. The literary genre f hexaemeron, ancient and modern philosophy, and scientific discoveries in the seventeenth and eighteenth centuries come into play in Swedenborg's richly imagined and beautifully articulated world. Yet _The Worship and Love of God _also offers an intriguing glimpse into Swedenborg's future as a biblical exegete and revelator. (shrink)

Ce texte est tiré de I. Baxmann et al., Arbeit und Rhythmus – Lebensformen im Wandel, Paderborn, Wilhelm Fink Verlag, 2009, p. 15-36. La traduction en a été assurée par Anthony Liébault et déjà mise en ligne par la revue Agôn. Nous remercions Inge Baxman de nous avoir autorisé à le reproduire ici. L'époque moderne et la critique de la conception séculaire du travail « Travailler, c'est danser ». Voilà ce que prétend Karl Bücher, économiste allemand originaire de Leipzig, (...) dans son ouvrage de 1896 intitulé - 1er XXe siècle – Nouvel article. (shrink)

To build a front against neoliberalism, those in the alter-globalisation movement work across perceived divides. Such transversal openness, however, has not been embraced fully within the academic sphere, even though theoretical coalitions are also important for developing a life-affirming societal ethos. Meaningful opportunities for theoretical bridging do exist, particularly where alternative value systems, hitherto isolated, can be drawn into the wider global dialogue on societal futures. In this spirit, this article offers some transversal reflections on materialist ecofeminism, and one such (...) marginalised value system: the African ethic of ubuntu. (shrink)

In this paper we present a logic that determines when implications in a classical logic context express a relevant connection between antecedent and consequent. In contrast with logics in the relevance logic literature, we leave classical negation intact—in the sense that the law of non-contradiction can be used to obtain relevant implications, as long as there is a connection between antecedent and consequent. On the other hand, we give up the requirement that our theory of relevance should be able to (...) define a new standard of deduction. We present and argue for a list of requirements such a logical theory of classical relevance needs to meet and go on to formulate a system that respects each of these requirements. The presented system is a Tarski logic that extends the relevance logic R with a new relevant implication which allows for Disjunctive Syllogism and similar rules. This is achieved by interpreting the logical symbols in the antecedents in a stronger way than the logical symbols in consequents. A proof theory and an algebraic semantics are formulated and interesting metatheorems are proven. Finally we give a philosophical motivation for our non-standard relevant implication and the asymmetric interpretation of antecedents and consequents. (shrink)

Two experiments are reported which investigate the factors that influence how persuaded mathematicians are by visual arguments. We demonstrate that if a visual argument is accompanied by a passage of text which describes the image, both research-active mathematicians and successful undergraduate mathematics students perceive it to be significantly more persuasive than if no text is given. We suggest that mathematicians’ epistemological concerns about supporting a claim using visual images are less prominent when the image is described in words. Finally we (...) suggest that empirical studies can make a useful contribution to our understanding of mathematical practice. (shrink)

In vitro meat is presented by innovators as the most realistic and sustainable solution to the problems of current meat production and consumption. The innovators argue that in vitro meat could be more environmentally friendly, animal friendly, healthier, and safer than conventional meat. The paper elaborates different reactions of experts and stakeholders from science, civil society, economy, and politics to the innovators’ reasoning. The semi-structured interviews were conducted for the project “Visions of in vitro meat. Analysis of technical and societal (...) aspects and visions of in vitro meat” funded by the German Ministry of Education and Research. In this paper we will show how our interview partners positioned themselves in relation to the innovators’ vision on IVM and which other visions they brought into the discussion about IVM and the future of meat. The project was based on a concept of visions as socio-epistemic practices that are increasingly recognised as important elements in innovation and transformation processes. The analysis of these visions conducted in interviews with experts and stakeholders provided new knowledge for the conceptualisation and appraisal of in vitro meat beyond the innovators’ rhetoric. (shrink)

The ancient Greek historian and political scientist Polybius is not as well known in the present day as figures such as Herodotus, Thucydides, Plato and Aristotle. This is in part due to his having lived in the Hellenistic period, an epoch often thought to be characteristic of Greek cultural and political decline, rather than in the earlier ‘golden age’ of Greek intellectual life in the 5th and 4th centuries BCE. Yet Polybius’s ideas have been of profound importance in modern western (...) thought, in areas as diverse as historiography, philosophy of history and the theorization of political institutions. This article illustrates the main contours of how subsequent thinkers have received and made use of Polybian ideas and themes, and argues for regarding Polybius as an important precursor of contemporary social scientific analyses of ‘globalization’. The article first excavates and identifies some of the main forms of appropriation of Polybius’s ideas that have occurred in the West over the last 500 years. Secondly, it delineates the most important appropriation of Polybius in the human sciences that has been effected in recent times, namely the use made of Polybian themes by Michael Hardt and Antonio Negri in Empire, their influential diagnosis of the contemporary state of world affairs. Thirdly, the article proffers a critique of these authors’ use of Polybius, and in its stead offers an alternative mode of appropriation of his work for the purposes of analytically reorienting the human sciences in light of present-day concerns with globalization and conditions of globality. It is argued that, far from being a figure of only antiquarian interest, Polybius continues to be of much relevance for human scientists today, for he may be seen as a foundational figure in efforts to think about the ‘global’ level in human affairs. (shrink)

A new approach to quantum theory is proposed in this paper. The basis is taken to be theoretical variables, variables that may be accessible or inaccessible, i.e., it may be possible or impossible for an observer to assign arbitrarily sharp numerical values to them. In an epistemic process, the accessible variables are just ideal observations connected to an observer or to some communicating observers. Group actions are defined on these variables, and group representation theory is the basis for developing the (...) Hilbert space formalism here. Operators corresponding to accessible theoretical variables are derived, and in the discrete case, it is proved that the possible physical values are the eigenvalues of these operators. The focus of the paper is some mathematical theorems paving the ground for the proposed foundation of quantum theory. It is shown here that the groups and transformations needed in this approach can be constructed explicitly in the case where the accessible variables are finite-dimensional. This simplifies the theory considerably: To reproduce the Hilbert space formulation, it is enough to assume the existence of two complementary variables. The interpretation inferred from the proposed foundation here may be called a general epistemic interpretation of quantum theory. A special case of this interpretation is QBism; it also has a relationship to several other interpretations. (shrink)

Students’ educational engagement is both an important predictor of study success and a key preventive factor for dropout. Vocational tracks in secondary education show high dropout rates. There is strong evidence that the solution to educational disengagement lies in student‐centred, powerful learning environments. This study investigates characteristics of PLEs from the perspective of students in vocational secondary education. Students’ perspectives on a learning environment are crucial for their satisfaction and learning engagement. Therefore, we investigated whether the perceived learning environment meets (...) the requirements of PLEs, and to what extent it meets students’ preferences. Additionally, it was investigated whether students who perceive their learning environment as more powerful, are also more engaged for school. Survey data of 532 students showed that student perceptions of their current learning environment were largely discrepant from the characteristics of PLEs. Students strongly asked for more challenging learning pathways, in combination with adaptive learning support. Students who perceived the characteristics of PLEs as being present, reported higher satisfaction and stronger engagement than students who perceived their education to be a less powerful environment. There is a need to redesign curricula in vocational education in such a way that these more intensely implement characteristics of PLEs. (shrink)