This volume examines the notion of an analytic proof as a natural deduction, suggesting that the proof's value may be understood as its normal form--a concept with significant implications to proof-theoretic semantics.

The main question addressed in this chapter is how to analyze the modal ingredient in the concept of logical consequence or logical validity of an inference, here expressed by saying that the truth of the conclusion of a logically valid inference should follow by necessity of thought from the truth of the premisses. It is claimed that this modal ingredient is not taken care of by Tarski’s requirement, later developed in model theory, that for all interpretations of the non-logical terms (...) of the sentences, the conclusion is true if the premisses are. Instead we must bring in reasoning or the notion of proof in the analysis, and it is shown how one may develop a notion of proof or validity of an argument based on the constructive meaning of the logical constants. It is proposed that from a constructive point of view, a sentence is a consequence of a set of premisses if and only if there is a proof in the sense explained of the sentence from the set of premisses. Knowledge of such a proof compels us to hold the conclusion true given that we hold the premisses true. (shrink)

"Das Ringen ums Seyn" entwickelt eine Destruktion der Schriften Martin Heideggers von "Das Ende der Philosophie und die Aufgabe des Denkens" bis zu "Sein und Zeit". Dabei wird zunächst untersucht, ob die Annahme einer Kehre in diesem Denkprozess berechtigt ist. Im zweiten Teil wird vor diesem Hintergrund das "Denken des Selben" als zentrales Besinnungsmoment herausgestellt, um Rückschlüsse auf den Umgang Heideggers mit den Topoi Existenz, Eigentlichkeit und Apperzeption ziehen zu können.

Ziel dieser Untersuchung ist es, den Zusammenhang der kantischen Kritiken unter Wahrung einer transzendental-kritischen Perspektive nachzuweisen. Dazu wird zunächst eine Paraphrasierung der einzelnen Kritiken entwickelt und aus einem gemeinsamen erkenntnistheoretischen Horizont heraus interpretiert, der anschließend jeweils mit einschlägigen Positionen der Forschungsliteratur diskutiert wird. Der inhaltliche Schwerpunkt der Arbeit zielt auf eine besondere Einordnung der Leistung Kants: Eine Differenzierung der Bereiche "Metaphysik", "Transzendentalphilosophie" und "transzendentale Kritik" lässt Kants Standpunkt einheitlich bestimmen und zeigt unter der Berücksichtigung der Notwendigkeit für das menschliche Denken (...) die grundlegenden allgemeingültigen Strukturen des menschlichen Erkenntnisvermögens. Diese Akzentuierung der Betrachtung hat einige Verschiebungen des heute gelehrten Kant-Bildes zur Folge, die bes. den Kategorischen Imperativ und die sogenannte "Ästhetik" der Kritik der Urteilskraft betreffen. (shrink)

In der jüngeren Philosophie entbrannte eine Debatte über den Geltungsanspruch ethischer Aussagen. Wie sich zeigen lässt, treten im Spektrum der metaethischen Positionen dialektische Begründungsmuster im Stile der vorkantischen Metaphysik auf. Die vorliegende Studie untersucht, ob sich die Metaethik auf ähnliche Weise „therapieren“ lässt wie die Metaphysik zu Kants Zeiten. Sie entwickelt dazu eine transzendentale Architektonik der Moralphilosophie und übergibt die Aufgabe der Moralforschung an empirische Wissenschaften, wobei eine pragmatistische Methodologie gewährleistet, dass diese unterschiedlichen Perspektiven nahtlos ineinander übergehenden.

We study the logical and computational properties of basic theorems of uncountable mathematics, in particular Pincherle's theorem, published in 1882. This theorem states that a locally bounded function is bounded on certain domains, i.e. one of the first ‘local-to-global’ principles. It is well-known that such principles in analysis are intimately connected to (open-cover) compactness, but we nonetheless exhibit fundamental differences between compactness and Pincherle's theorem. For instance, the main question of Reverse Mathematics, namely which set existence axioms are necessary to (...) prove Pincherle's theorem, does not have an unique or unambiguous answer, in contrast to compactness. We establish similar differences for the computational properties of compactness and Pincherle's theorem. We establish the same differences for other local-to-global principles, even going back to Weierstrass. We also greatly sharpen the known computational power of compactness, for the most shared with Pincherle's theorem however. Finally, countable choice plays an important role in the previous, we therefore study this axiom together with the intimately related Lindelöf lemma. (shrink)

All of metaethical positions today can be replaced by a universal architecture of moral philosophy, all but one: moral realism. Here, I use the term “metaethics” to refer to any theory of ethics concerning the groundwork of ethics, on the one hand, and the inquiry of the use of philosophical words, concepts or methods on the other. In this article, I will present my hypothesis that in moral philosophy, we do not need any specialized metaethics at all. Metaethics as a (...) discipline of philosophy is only required by the work of moral realists, who try to show us a realm of values and norms that exist (per se) naturally, non-naturally or supernaturally. How can they know? The effort of metaethical realists cannot be proven either in ontology or in the philosophy of language or in cognitive science or in any meta-science that works en plus to ethics, because even in every additional discipline, we have to accept the presupposition of a validity of judgments. So, let us try it the other way around; we have to find a way to found ethics by following its structures, and that means, based on David Velleman’s concepts: a) We have to search for a ubiquitous point of ethical theory in its foundation – here, no kind of value or norm can be found that is not based on a universal formal structure of normativity. b) We have to start an empirical inquiry to collect norms and values in actual use. MFT, moral psychology and moral sociology are in charge here. The combination of such an abstract groundwork with mere empirical study has to be legitimized again. Hence, I am going to try to sum up the main ideas of such a project to show the relevance of a new architecture of moral philosophy today. There is a line of reasoning that addresses the possibility of a transcendental critique in practical philosophy; therefore, it has to look into the different notions of “intuition” in moral methods like it was used by Sidgwick (Rashdall, Green, Ross, Brentano, McTaggart) and Moore on the one hand and Brentano and Bergson on the other. In my view, there is a way to combine these perspectives using the two-level-model of Hare, Singer, Greene, where “intuition” is used to categorize habits and customs of the common sense morality in general while a critical reflection uses act-utilitarian calculus to provide a universal decision – in the sense of “concrete reason” – for any possible actor in a singular situation (Hegel, Peirce, Bloch etc.). The change between these levels may be explained by means of a pragmatistic kind of continuum of research with an ideal summum bonum in the long run and a concept of common sense morality as can be found in every group or society. (shrink)

The category of heroic action is important in both everyday life and the wider social context. This article argues that interest in the notion of heroic actions and heroic defeats also brings out an important set of sociological problems, such as disagreements on identity, norms, and rational choice explanations. Illustrations are provided from recent analyses of union militancy in Britain and Italy, and of the student movement in Beijing. Different versions of the critique of rational choice theory often take norm-guided (...) action as a point of departure. Another version of this critique is represented by theories of new social movements and identity maintenance. The article suggests that rational choice theory is more useful than some of its opponents would have it; yet the general argument favors a mixed motivation approach. The discussion points out some of the strengths and limitations of different explanatory perspectives, and some of the links between them. (shrink)

According to a main idea of Gentzen the meanings of the logical constants are reflected by the introduction rules in his system of natural deduction. This idea is here understood as saying roughly that a closed argument ending with an introduction is valid provided that its immediate subarguments are valid and that other closed arguments are justified to the extent that they can be brought to introduction form. One main part of the paper is devoted to the exact development of (...) this notion. Another main part of the paper is concerned with a modification of this notion as it occurs in Michael Dummett’s book The Logical Basis of Metaphysics. The two notions are compared and there is a discussion of how they fare as a foundation for a theory of meaning. It is noted that Dummett’s notion has a simpler structure, but it is argued that it is less appropriate for the foundation of a theory of meaning, because the possession of a valid argument for a sentence in Dummett’s sense is not enough to be warranted to assert the sentence. (shrink)

I attempt an explication of what it means for an operation across domains to be the same on all domains, an issue that ) took to be central for a successful delimitation of the logical operations. Some properties that seem strongly related to sameness are examined, notably isomorphism invariance, and sameness under extensions of the domain. The conclusion is that although no precise criterion can satisfy all intuitions about sameness, combining the two properties just mentioned yields a reasonably robust and (...) useful explication of sameness across domains. (shrink)

Levinas did not present any new ethical theories; he did not even give any normative recommendations. But his phenomenological investigations help us to understand how the idea of ethics emerges and how we try to cope with it. The purpose of this paper is to suggest some implications from a reading of Levinas on how ethical challenges are handled within a management perspective. The paper claims that management, both in theory and in practice, is necessarily egocentric and thus ethically biased. (...) Therefore, ethics, defined as the idea that it is possible to do otherwise than pursue one's own interest, must have its source outside the scope of management. Levinas identifies this source as the call for responsibility from the Other, beyond the reach of managerial control. He also suggests how this idea of ethics is put into practice, especially in economic life: the existence of money makes it both possible and necessary to compare unique and incomparable others. Management tools may be used in the service of always more justice, as it also may be used for the opposite purpose. Instead of trying to draw a normative conclusion from Levinas, we may distinguish between two ways of experiencing reality: one through language and knowledge, covering both descriptive and normative knowledge, including business ethics, and the other through the particular events of encounters, from where this knowledge is continuously questioned through the call for responsibility, and thereby may provide possibilities for continuous improvements towards always more justice. (shrink)

This is a reply to H. Ben-Yami, 'Generalized quantifiers, and beyond' (this journal, 2009), where he argues that standard GQ theory does not explain why natural language quantifiers have a restricted domain of quantification. I argue, on the other hand, that although GQ theory gives no deep explanation of this fact, it does give a sort of explanation, whereas Ben-Yami's suggested alternative is no improvement.

We show that to every recursive total continuous functional $\Phi$ there is a PCF-definable representative $\Psi$ of $\Phi$ in the hierarchy of partial continuous functionals, where PCF is Plotkin's programming language for computable functionals. PCF-definable is equivalent to Kleene's S1-S9-computable over the partial continuous functionals.

Ethics in business and economics is often attacked for being too superficial. By elaborating the conclusions of two such critics of business ethics and welfare economics respectively, this article will draw the attention to the ethics behind these apparently well-intended, but not always convincing constructions, by help of the fundamental ethics of Emmanuel Levinas. To Levinas, responsibility is more basic than language, and thus also more basic than all social constructions. Co-operation relations in organizations, markets and value networks are generated (...) from personal relations and personal responsibilities. It is not sufficient to integrate ethics in an impersonal, rational system, neither in business organizations nor in the world economy. Ethics has its source not in rationality, but in the personal. (shrink)

This article examines the metaphysical and moral foundations of Spinoza’s account of suicide. Spinoza’s treatment of suicide is brought into question by his conatus doctrine, which posits the striving to preserve one’s own being as the very essence of existence. Accordingly, suicide, or the termination of life, as the destruction of one’s own being, represents the exhaustion of this striving. The analysis of the causes that lead to self-destruction has sparked significant debate in Spinoza’s literature, raising the question of whether (...) suicide is a passive and irrational decision or a free and rational choice. This article, which engages with prominent scholars of this literature, notably Matson, Bennett, LeBuffe and Nadler, aims to alleviate this controversy by offering alternative readings and arguments. It concludes that free and rational suicide does not exist in Spinoza’s thought; instead, the “suicide of reason or rationality” forms the basis for bodily suicide. (shrink)

We prove that the hierarchy of hereditarily effective typestreams, that are effective models of inductivly defined types, has the length of the first recursivly inaccessible ordinal.

WeingartnerPaul and LeebHans-Peter, eds, Kreisel’s Interests: On the Foundations of Logic and Mathematics. Tributes; 41. London: College Publications, 2020. Pp. viii + 171. ISBN: 978-1-84890-330-2.

The traditional picture of logic takes it for granted that "valid arguments have a fundamental epistemic significance", but neither model theory nor traditional proof theory dealing with formal system has been able to give an account of this significance. Since valid arguments as usually understood do not in general have any epistemic significance, the problem is to explain how and why we can nevertheless use them sometimes to acquire knowledge. It is suggested that we should distinguish between arguments and acts (...) of inferences and that we have to reconsider the latter notion to arrive at the desired explanation. More precisely, the notions should be developed so that the following relationship holds: one gets in possession of a ground for a conclusion by inferring it from premisses for which one already has grounds, provided that the inference in question is valid. The paper proposes explications of the concepts of ground and deductively valid inference so that this relationship holds as a conceptual truth. Logical validity of inference is seen as a special case of deductive validity, but does not add anything as far as epistemic significance is concerned—it resides already in the deductively valid inferences. (shrink)