A basic aim of E. Beth's work in philosophy of science was to explore the use of formal semantic methods in the analysis of physical theories. We hope to show that a general framework for Beth's semantic analysis is provided by the theory of semi-interpreted languages, introduced in a previous paper. After developing Beth's analysis of nonrelativistic physical theories in a more general form, we turn to the notion of the 'logic' of a physical theory. Here we (...) prove a result concerning the conditions under which semantic entailment in such a theory is finitary. We argue, finally, that Beth's approach provides a characterization of physical theory which is more faithful to current practice in foundational research in the sciences than the familiar picture of a partly interpreted axiomatic theory. (shrink)

This collection examines an aspect of Gilles Deleuze’s thought that has largely been neglected; whether or not Deleuze was a metaphysician. Answering this question may reveal the problematic nature of so-called postmodernism and the critique it leveled at the first philosophy, and it may help readers to better understand philosophy’s fate.

In 1969, De Jongh proved the “maximality” of a fragment of intuitionistic predicate calculus forHA. Leivant strengthened the theorem in 1975, using proof-theoretical tools (normalisation of infinitary sequent calculi). By a refinement of De Jongh's original method (using Beth models instead of Kripke models and sheafs of partial combinatory algebras), a semantical proof is given of a result that is almost as good as Leivant's. Furthermore, it is shown thatHA can be extended to Higher Order Heyting Arithmetic+all trueΠ 2 (...) 0 -sentences + transfinite induction over primitive recursive well-orderings. As a corollary of the proof, maximality of intuitionistic predicate calculus is established wrt. an abstract realisability notion defined over a suitable expansion ofHA. (shrink)

We critically evaluate arguments in a recent Journal of Law, Medicine & Ethics article by Svoboda, Adler, and Van Howe disputing the 2012 affirmative infant male circumcision policy recommendations of the American Academy of Pediatrics. We provide detailed evidence in explaining why the extensive claims by these opponents are not supported by the current strong scientific evidence. We furthermore show why their legal and ethical arguments are contradicted by a reasonable interpretation of current U.S. and international law and ethics. After (...) all considerations are taken into account it would be logical to conclude that failure to recommend male circumcision early in infancy may be viewed as akin to failure to recommend childhood vaccination to parents. In each case, parental consent is required and the intervention is not compulsory. Our evaluation leads us to dismiss the arguments by Svoboda et al. Instead, based on the evidence, infant male circumcision is both ethical and lawful. (shrink)

Formulating how biomimicry relates to nature has been crucial to ‘deepening’ its theory. Currently, an autopoietic model of nature dominates the literature. However, advances in the natural and human sciences have demonstrated that autopoiesis does not adequately explain complex, dynamic, responsive, and situated systems. This article draws on Beth Dempster’s (1998) characterisation of ecosystems as sympoietic, that is as homeorhetic, evolutionary, distributively controlled, unpredictable, and adaptive, and on Donna Jeanne Haraway’s (2016) critique that entities do not pre-exist their relationships. (...) We argue that using sympoietic processes of becoming as our model, measure, and mentor impacts biomimicry’s practice and relation to sustainability. Taking John Todd’s Living Machines as a case study, we explicate how sympoiesis unfurls autopoiesis. By integrating advances in the natural and human sciences into the philosophy of biomimicry, we address the limitations of the autopoietic model and provide a more comprehensive and adequate model of ‘nature.’. (shrink)

Beth models of analysis are used in model theoretic proofs of the disjunction and existence property. By glueing strings of models one obtains a model that combines the properties of the given models. The method asks for a common generalization of Kripke and Beth models. The proof is carried out in intuitionistic analysis plus Markov's Principle. The main new feature is the external use of intuitionistic principles to prove their own preservation under glueing.

During a conference entitled “_Un logicien consciencieux. La philosophie de Evert Willem Beth_,” held in Nancy in 1998 and published in this journal, volume 3, cahier 4 [Barth, Heinzmann _et al._ 1998-1999], the participants regretted that a reasoned biography of Beth was not available. In view of the efforts made since then in this direction, in particular by Paul van Ulsen in his PhD thesis in Dutch [2000], this article attempts to provide an overview of Beth’s work for (...) a broader community of philosophers of science. However, my focus is not so much on Beth’s widely discussed and important contributions to mathematical logic, where his most creative merits reside. My aim is to emphasize Beth’s philosophical and cultural background. Both are also discussed in the first two chapters of Ulsen’s thesis, which globally focuses on Beth’s work in logic. Of course, philosophical and scientific aspects cannot be systematically separated, but Beth’s influence on the philosophy of mathematics be... (shrink)

In this article I give an overview of some recent work in philosophy of science dedicated to analysing the scientific process in terms of (conceptual) mathematical models of theories and the various semantic relations between such models, scientific theories, and aspects of reality. In current philosophy of science, the most interesting questions centre around the ways in which writers distinguish between theories and the mathematical structures that interpret them and in which they are true, i.e. between scientific theories as linguistic (...) systems and their non-linguistic models. In philosophy of science literature there are two main approaches to the structure of scientific theories, the statement or syntactic approach -- advocated by Carnap, Hempel and Nagel -- and the non- statement or semantic approach --advocated, among others, by Suppes, the structuralists, Beth, Van Fraassen, Giere, Wojcicki. In conclusion, I briefly review some of the usual realist inspired questions about the possibility and character of relations between scientific theories and reality as implied by the various approaches I discuss in the course of the article. The models of a scientific theory should indeed be adequate to the phenomena, but if the theory is 'adequate' to (true in) its conceptual (mathematical) models as well, we have a model-theoretic realism that addresses the possible meaning and reference of 'theoretical entities' without relapsing into the metaphysics typical of the usual scientific realist approaches. (shrink)

Conceived by Johan van Benthem and Yde Venema, arrow logic started as an attempt to give a general account of the logic of transitions. The generality of the approach provided a wide application area ranging from philosophy to computer science. The book gives a comprehensive survey of logical research within and around arrow logic. Since the natural operations on transitions include composition, inverse and identity, their logic, arrow logic can be studied from two different perspectives, and by two (complementary) methodologies: (...) modal logic and the algebra of relations. Some of the results in this volume can be interpreted as price tags. They show what the prices of desirable properties, such as decidability, (finite) axiomatisability, Craig interpolation property, Beth definability etc. are in terms of semantic properties of the logic. The research program of arrow logic has considerably broadened in the last couple of years and recently also covers the enterprise to explore the border between decidable and undecidable versions of other applied logics. The content of this volume reflects this broadening. The editors included a number of papers which are in the spirit of this generalised research program. (shrink)