In the mathematics education research literature, there is a growing body of scholarship on how mathematicians practice their craft. The purpose of this chapter is to survey some of this literature and explain how it can contribute to the philosophy of mathematical practice. We first describe how mathematics educators use empirical methodologies to investigate the behaviors of mathematicians and argue that findings from these studies can inform the philosophy of mathematical practice. We then illustrate this by summarizing research on mathematicians’ (...) understandings and mathematicians’ proof reading. (shrink)

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)

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)

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)

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)

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)

I. Egner, “The role of topos in the use of a Wobe particle”.In the paper I am trying to show how a speaker using the particle {ie271-1} in his utterance calls upon a contextual assumption that can be formulated as a topos.After formulating a working hypothesis according to which the particle {ie271-2} signals to the hearer that the speaker's utterance is justified, I use English and Wobe paraphrases of the examples quoted in order to make explicit that justification.Wobe paraphrases given (...) by the informant suggest that in using {ie271-3} the speaker calls upon t contextual assumption that he feels is relevant in the speech situation. To the extent that this assumption is based on common sense knowledge, it seemed appropriate to use Ducrot's notion of topos to formulate it, e.g. (T) [The deeper one gets into the bush, the fewer white people he meets].One of the examples quoted calls attention to the fact that the topos called upon by way of {ie271-4} may or may not be validated, i.e. confirmed in the speech situation.Finally, the validation or non-validation of a topos seems to determine the illocutionary value of a wh-question containing {ie271-5} as request for information or request for explanation respectively. (192 words). (shrink)

In der Reihe werden herausragende monographische Untersuchungen und Sammelbände zu allen Aspekten der Philosophie Kants veröffentlicht, ebenso zum systematischen Verhältnis seiner Philosophie zu anderen philosophischen Ansätzen in Geschichte und Gegenwart. Veröffentlicht werden Studien, die einen innovativen Charakter haben und ausdrückliche Desiderate der Forschung erfüllen. Die Publikationen repräsentieren damit den aktuellsten Stand der Forschung.

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.

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)

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)

Aquinas is often presented as following Aristotle's "Nicomachean Ethics" when treating moral virtue. Less often do philosophers consider that Aquinas's conception of the highest good and its relation to the functional character of human activity led him to break with Aristotle by replicating each of the acquired moral virtues on an infused level. The author suggests that we can discern reasons for this move by examining Aquinas's commentary on the "Sententiae" of Peter the Lombard and the "Summa theologiae" within their (...) historical context. The author's thesis is that Dominican pastoral and intellectual concerns led Aquinas to argue that moral virtue must necessarily be ordered toward the highest good. Understanding this purpose helps to explain his presentation of moral virtue and its implications for standard philosophical interpretations of his work. (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)

_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)

To give the necessary affirmation to the historical role played by the Legalists and to study and analyze the Legalists' writings from the Marxist point of view is a major task on the ideological front called for by the deepening of the Campaign to Criticize Lin Piao and Confucius. Han Fei was an outstanding representative of the Legalists of the late Warring States period. He summed up the experience, both positive and negative, of the newly emerging landlord class in the (...) process of instituting reform, and he criticized the reactionary Confucianism. He thus fully and theoretically formed a comprehensive system of Legalist thought which served as a direct theoretical preparation for the establishment of a unified feudal state under a centralized authority. The "Wu Tu" is representative of the more than one hundred thousand words of Han Fei's writings. This important political essay made a revolutionary criticism of the reactionary ideology hindering the progress of the newly emerging landlord class and outlined a theoretical program by which the landlord class could exercise an all-round dictatorship over the slave-owning class. Acquiring a clear understanding about this will help us see further through the ultra-Right essence of Lin Piao's practice of honoring Confucius and opposing Legalism. (shrink)

In this article, ecosexuality – as popularized by activist-artists Beth Stephens and Annie Sprinkle – is explored through archaeological and genealogical means. Through an archaeological le...

The book attempts to build a bridge across three cultures: mathematical statistics, quantum theory and chemometrical methods.

The results of artistic experimentation with data sets from the natural sciences differ considerably with respect to quality and consistency. The British artist duo Semiconductor (Ruth Jarman and Joe Gerhardt) counts among those setting the standard. In its animations and videos, it explores, in an equally multifaceted and concise manner, how scientists affect our world-view with their respective pictorial languages and visualization strategies. Especially in domains that elude our natural sense of space and time, the researchers’ representations are inevitably creative. (...) Semiconductor combines everyday experiences and complex imaging techniques in manifold ways. Thus, they offer unseen and sometimes unorthodox interpretations of a world in constant flux while retaining a high degree of complexity in their subtly crafted works. Semiconductor’s works provide opportunities for reflection on the extensive procedures in the sciences on various levels and in doing so they create poetic pieces that shift and recombine in various ways. With these means, sensualized data – like sounds and images – take on a strong role in their time-based works. As operative entities they not only represent but they seem to act. (shrink)

Berkeley’s ‘esse is percipi’ has been criticized for implying epistemological solipsism, the main argument being that different minds cannot harbor numerically one and the same idea. Similarly, C. J. Boström, the dominating Swedish philosopher in the nineteenth century, was early scorned because his principle of esse est percipi allegedly contradicts the simultaneous claim that two spirits can perceive the same thing under qualitatively different appearances. Whereas the criticism against Berkeley is here regarded as valid, it is argued that Boström successfully (...) defended himself by employing a dual concept of meaning, resembling Frege’s Sinn and Bedeutung some thirty years later, and by postulating an ontology that permits human minds to share in the divine ideas that constitute reality. (shrink)

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