This paper develops in certain directions the work of Meyer in [3], [4], [5] and [6]. In those works, Peano’s axioms for arithmetic were formulated with a logical base of the relevant logic R, and it was proved finitistically that the resulting arithmetic, called R♯, was absolutely consistent. It was pointed out that such a result escapes incau- tious formulations of Goedel’s second incompleteness theorem, and provides a basis for a revived Hilbert programme. The absolute consistency result used as a (...) model arithmetic modulo two. Modulo arithmetics are not or- dinarily thought of as an extension of Peano arithmetic, since some of the propositions of the latter, such as that zero is the successor of no number, fail in the former. Consequently a logical base which, unlike classical logic, tolerates contradictory theories was used for the model. The logical base for the model was the three-valued logic RM3, which has the advantage that while it is an extension of R, it is finite valued and so easier to handle. The resulting model-theoretic structure is interesting in its own right in that the set of sentences true therein consti- tutes a negation inconsistent but absolutely consistent arithmetic which is an extension of R♯. In fact, in the light of the result of [6], it is an extension of Peano arithmetic with a base of a classical logic, P♯. A generalisation of the structure is to modulo arithmetics with the same logical base RM3, but with varying moduli. We first study the properties of these arithmetics in this paper. The study is then generalised by vary- ing the logical base, to give the arithmetics RMni, of logical base RMn and modulus i. Not all of these exist, however, as arithmetical properties and logical properties interact, as we will show. The arithmetics RMni give rise, on intersection, to an inconsistent arithmetic RMω which is not of modulo i for any i. We also study its properties, and, among other results, we show by finitistic means that the more natural relevant arithmetics R♯ and R♯♯ are incomplete. In the rest of the paper we apply these techniques to several topics, particularly relevant quantum arithmetic in which we are able to show that the law of distribution remains unprovable. Aside from its intrinsic interest, we regard the present exercise as a demonstration that inconsistent theories and models are of mathematical worth and interest. (shrink)

This paper develops in certain directions the work of Meyer in [3], [4], [5] and [6] (see also Routley [10] and Asenjo [11]). In those works, Peano’s axioms for arithmetic were formulated with a logical base of the relevant logic R, and it was proved finitistically that the resulting arithmetic, called R♯, was absolutely consistent. It was pointed out that such a result escapes incau- tious formulations of Goedel’s second incompleteness theorem, and provides a basis for a revived Hilbert programme. (...) The absolute consistency result used as a model arithmetic modulo two. Modulo arithmetics are not or- dinarily thought of as an extension of Peano arithmetic, since some of the propositions of the latter, such as that zero is the successor of no number, fail in the former. Consequently a logical base which, unlike classical logic, tolerates contradictory theories was used for the model. The logical base for the model was the three-valued logic RM3 (see e.g. [1] or [8]), which has the advantage that while it is an extension of R, it is finite valued and so easier to handle. The resulting model-theoretic structure (called in this paper RM32) is interesting in its own right in that the set of sentences true therein consti- tutes a negation inconsistent but absolutely consistent arithmetic which is an extension of R♯. In fact, in the light of the result of [6], it is an extension of Peano arithmetic with a base of a classical logic, P♯. A generalisation of the structure is to modulo arithmetics with the same logical base RM3, but with varying moduli (called RM3i here). We first study the properties of these arithmetics in this paper. The study is then generalised by vary- ing the logical base, to give the arithmetics RMni, of logical base RMn and modulus i. Not all of these exist, however, as arithmetical properties and logical properties interact, as we will show. The arithmetics RMni give rise, on intersection, to an inconsistent arithmetic RMω which is not of modulo i for any i. We also study its properties, and, among other results, we show by finitistic means that the more natural relevant arithmetics R♯ and R♯♯ are incomplete (whether or not consistent and recursively enumerable). In the rest of the paper we apply these techniques to several topics, particularly relevant quantum arithmetic in which we are able to show (unlike classical quantum arithmetic) that the law of distribution remains unprovable. Aside from its intrinsic interest, we regard the present exercise as a demonstration that inconsistent theories and models are of mathematical worth and interest. (shrink)

Klaus Peter Mortensen; The Double Call: on Bildung in a Literary and Reflective Perspective, Journal of Philosophy of Education, Volume 36, Issue 3, 16 December.

Our traditional ways of thinking about politics and society are becoming obsolete. We need some new points of reference in order to re-imagine the possible character, growth, and functioning of our private and common life. Such re-imagination would imply doing away with every-man-for-himself individualism as well as consumption-makes-me-happy materialism and the-state-will-take-care-of-it passivity. There is an alternative: Personalism is a forgotten, yet golden perspective on humanity that seeks to describe what a human being is and to then draw the social consequences. (...) Personalism builds upon the thinking of Martin Buber and Emmanuel Levinas, among others, and has been a source of inspiration for Martin Luther King, Desmond Tutu, and other important personalities in recent history. According to personalism, humans are relational and engaged and possess dignity. The person and the relationship amongst persons are the universal point of departure: Human beings have inherent dignity, and good relationships amongst humans are crucial for the good, engaged life and for a good society. Personalism has been greatly neglected in Western political thought. In this book, Jonas Norgaard Mortensen attempts to introduce personalism while simultaneously demonstrating its historical origins, acquainting the reader with its thinkers and those who have practiced it, and showing that personalism has a highly relevant contribution to make in the debate about today's social and political developments. (shrink)

Once symbolized by a burning armchair, experimental philosophy has in recent years shifted away from its original hostility to traditional methods. Starting with a brief historical review of the experimentalist challenge to traditional philosophical practice, this chapter looks at research undercutting that challenge, and at ways in which experimental work has evolved to complement and strengthen traditional approaches to philosophical questions.

Paraconsistent logic, logic in which inconsistent information does not deliver arbitrary conclusions, is one of the fastest growing areas of logic, with roots in profound philosophical issues, and applications in information processing and philosophy of science. This book contains selected papers presented at the First World Congress on Paraconsistency, held in Ghent in 1997. It contains papers on various aspects of the subject. As such, it should be of interest to all who want to learn what the subject is, and (...) where it is going. (shrink)

Sociological studies into alcohol use seem to find it difficult to deal with the substance itself. Alcohol tends to be reduced to a symbol of a social process and in this way the sociological research loses sight of effects beyond the social. This article suggests a new theoretical approach to the study of alcohol and teenagers' (romantic) relationships, inspired by actor-network theory (ANT). The central feature of ANT is to search for relationships, or rather networks, between all things relevant to (...) the phenomenon. All material and semantic structures, things, persons, discourses, etc. that influence a given situation are described as actants and are entered into the analysis. The aim of this article is to propose a way of including materiality in sociological analyses of alcohol and to explore ways of using focus group interview material in ANT-inspired analysis. By analysing a girl's development from being a non-drinker at the age of 14, to a heavy drinker at 16, the article investigates how the actants brought out by young people in the focus groups themselves constitute different forms of agency. The analysis is based on a qualitative study consisting of 37 focus groups conducted with teenagers in Denmark over a three-year period. (shrink)

First, we consider an argument due to Popper for maximal strength in choice of logic. We dispute this argument, taking a lead from some remarks by Susan Haack; but we defend a set of contrary considerations for minimal strength in logic. Finally, we consider the objection that Popper presupposes the distinctness of logic from science. We conclude from this that all claims to logical truth may be in equal epistemological trouble.

Dirac’s treatment of his well known Delta function was apparently inconsistent. We show how to reconstruct his reasoning using the inconsistency-tolerant technique of Chunk and Permeate. In passing we take note of limitations and developments of that technique.

Sven Erik Nordenbo; Bildung and the Thinking of Bildung, Journal of Philosophy of Education, Volume 36, Issue 3, 16 December 2002, Pages 341–352, https://doi.or.

Our view is that the folk concept of knowing how is more complicated than many epistemologists assume. We present four studies that go some way towards supporting our view—that the folk concept of knowledge-how is a philosophical hybrid, comprising both intellectualist and anti-intellectualist features. One upshot is, if we are going to award a presumptive status to philosophical theories of know-how that best accord with the folk concept, it ought to go to those that combine intellectualist and anti-intellectualist elements.

One of Arthur Prior’s constructions of the relational calculus for times within tense logic plus propositional quantifiers is considered using Malcolm Rennie’s multimodal semantics and found wantin...

The article addresses the emerging framework of ‘positioning theory’, which has become influential in educational theory. We will present the central concepts and ideas of ‘positioning theory’ and subsequently how they are being used to contribute to educational theory. We will focus on an article by Svend Brinkmann where he uses ‘positioning theory’ as the foundation for moral education. Seemingly, Brinkmann uses ‘positioning theory’ rather uncritically in an attempt to ‘strengthen’ the educational process by introducing fixed categorisations and concepts to (...) it. Contrary to this approach, we will use the educational theories of Knud Grue-Sørensen and Gert Biesta to emphasise how we instead should recognise what is here defi ned as the ‘weakness’ of educational theory, and how we have to consider both the adaptive element of education as well as the emancipatory element of it. (shrink)

The paper examines connections between ontology and finance. The ontological debates concerning the role of finance are examined between two opposing schools of thought that can be labelled, very broadly, ‘instrumentalist’ and ‘realist’. These two schools of thought have had momentous repercussions in understanding what is a good society. Each school defines Nature in particular ways which can be explored using ontology and philosophical insight. Our theoretical investigation aims to accommodate Nature in community financial deliberations. A positive role for government (...) is advocated to finance environmental infrastructure initiatives. For example, precautionary strategies to address climate change must be funded. New roles for finance and government are proposed to align human relationships with Nature. Environmental precautionary principles must be developed in conjunction with finance theory to maintain decent standards of living for all. Reliance on impersonal market forces will not be enough to save the planet given the power of some over the many in the neoliberal arena. (shrink)

We present experimental results that support the claim that the folk concept of knowledge how is an epistemological hybrid, encompassing both intellectualist and praxist elements.

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)

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)

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.

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 distinction between rules and principles is highly controversial. This is due to its significant impact on almost every fundamental philosophy of law and legal theory issue, for instance, the application of legal norms, the concept of the legal system, the relation between law and morality, or the structure of basic rights. The actual debate is based on three main theses: the “strong separation” thesis, the “weak separation” thesis and the “conformity” thesis. The author concentrates on the development of the (...) “strong separation” thesis, first elaborated by Josef Esser, then developed by Ronald Dworkin and lately worked out by Robert Alexy. The several objections raised to Alexy´s thesis on principles as optimization commands will be discussed in detail. The author comes finally to his own formal description of principles as norms, with both an abstract and a concrete validity. (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)