Pure Type Systems, PTSs, introduced as a generalisation of the type systems of Barendregt's lambda-cube, provide a foundation for actual proof assistants, aiming at the mechanic verification of formal proofs. In this paper we consider simplifications of some of the rules of PTSs. This is of independent interest for PTSs as this produces more flexible PTS-like systems, but it will also help, in a later paper, to bridge the gap between PTSs and systems of Illative Combinatory Logic. First we consider (...) a simplification of the start and weakening rules of PTSs, which allows contexts to be sets of statements, and a generalisation of the conversion rule. The resulting Set-modified PTSs or SPTSs, though essentially equivalent to PTSs, are closer to standard logical systems. A simplification of the abstraction rule results in Abstraction-modified PTSs or APTSs. These turn out to be equivalent to standard PTSs if and only if a condition (*) holds. Finally we consider SAPTSs which have both modifications. (shrink)

It is well known that the simple types of closed lambda terms or combinators can be interpreted as the theorems of intuitionistic implicational logic . Venneri, using an equivalence between the intersection type system for lambda calculus, without the universal type ω, TA∧λ, and a similar system for combinators, TA∧, shows that the types of TA∧λ are the theorems of a Hilbert-style sublogic of the → ∧ fragment of H→.In this paper we fill a gap in the equivalence proof and (...) introduce a new system of intersection types for lambda calculus that is weaker than TA∧λ, but has the same set of types. The new system has the advantage that the logic of types can be obtained directly from the rules - just as H→ can be obtained from simple type theory. (shrink)

Illative combinatory logic consists of the theory of combinators or lambda calculus extended by extra constants (and corresponding axioms and rules) intended to capture inference. The paper considers 4 systems of illative combinatory logic that are sound for first-order propositional and predicate calculus. The interpretation from ordinary logic into the illative systems can be done in two ways: following the propositions-as-types paradigm, in which derivations become combinators, or in a more direct way, in which derivations are not translated. Both translations (...) are closely related in a canonical way. In a preceding paper, Barendregt, Bunder and Dekkers, 1993, we proved completeness of the two direct translations. In the present paper we prove completeness of the two indirect translations by showing that the corresponding illative systems are conservative over the two systems for the direct translations. In another version, DBB (1997), we shall give a more direct completeness proof. These papers fulfill the program of Church and Curry to base logic on a consistent system of $\lambda$ -terms or combinators. Hitherto this program had failed because systems of ICL were either too weak (to provide a sound interpretation) or too strong (sometimes even inconsistent). (shrink)

Chakraborty and Banerjee have introduced a rough consequence logic based on the modal logic S5. This paper shows that rough consequence logics, with many of the same properties, can be based on modal logics as weak as K, with a simpler formulation than that of Chakraborty and Banerjee. Also provided are decision procedures for the rough consequence logics and equivalences and independence relations between various systems S and the rough consequence logics, based on them. It also shows that each logic, (...) based on such an S, is theorem equivalent, but not necessarily equivalent, to the modal logic M-S. The paper also shows that rough consequence logic, which was designed to handle rough equality, is somewhat limited for that purpose. (shrink)

Illative combinatory logic consists of the theory of combinators or lambda calculus extended by extra constants (and corresponding axioms and rules) intended to capture inference. The paper considers systems of illative combinatory logic that are sound for first-order propositional and predicate calculus. The interpretation from ordinary logic into the illative systems can be done in two ways: following the propositions-as-types paradigm, in which derivations become combinators or, in a more direct way, in which derivations are not translated. Both translations are (...) closely related in a canonical way. The two direct translations turn out to be complete. The paper fulfills the program of Church [1932], [1933] and Curry [1930] to base logic on a consistent system of λ-terms or combinators. Hitherto this program had failed because systems of ICL were either too weak (to provide a sound interpretation) or too strong (sometimes even inconsistent). (shrink)

Because the main difference between combinatory weak equality and λβ-equality is that the rule \begin{equation*}\tag{\xi} X = Y \vdash \lambda x.X = \lambda x.Y\end{equation*} is valid for the latter but not the former, it is easy to assume that another way of defining combinatory β-equality is to add rule (ξ) to the postulates for weak equality. However, to make this true, one must choose the definition of combinatory abstraction in (ξ) very carefully. If one tries to use one of the (...) more common abstraction algorithms, the result will be an equality, = ξ , that is either equivalent to βη-equality (and so strictly stronger than β-equality) or else strictly weaker than β-equality. This paper will study the relations = ξ for several commonly used abstraction algorithms, distinguish between them, and axiomatize them. (shrink)

Chakraborty and Banerjee have introduced a rough consequence logic based on the modal logic S5. This paper shows that rough consequence logics, with many of the same properties, can be based on modal logics as weak as K, with a simpler formulation than that of Chakraborty and Banerjee. Also provided are decision procedures for the rough consequence logics and equivalences and independence relations between various systems S and the rough consequence logics, based on them. It also shows that each logic, (...) based on such an S, is theorem equivalent, but not necessarily equivalent, to the modal logic M-S. The paper also shows that rough consequence logic, which was designed to handle rough equality, is somewhat limited for that purpose. (shrink)

Illative combinatory logic consists of the theory of combinators or lambda calculus extended by extra constants (and corresponding axioms and rules) intended to capture inference. In a preceding paper, [2], we considered 4 systems of illative combinatory logic that are sound for first order intuitionistic propositional and predicate logic. The interpretation from ordinary logic into the illative systems can be done in two ways: following the propositions-as-types paradigm, in which derivations become combinators, or in a more direct way, in which (...) derivations are not translated. Both translations are closely related in a canonical way. In the cited paper we proved completeness of the two direct translations. In the present paper we prove that also the two indirect translations are complete. These proofs are direct whereas in another version, [3], we proved completeness by showing that the two corresponding illative systems are conservative over the two systems for the direct translations. Moreover we shall prove that one of the systems is also complete for predicate calculus with higher type functions. (shrink)

Illative combinatory logic consists of the theory of combinators or lambda calculus extended by extra constants intended to capture inference. In a preceding paper, [2], we considered 4 systems of illative combinatory logic that are sound for first order intuitionistic propositional and predicate logic. The interpretation from ordinary logic into the illative systems can be done in two ways: following the propositions-as-types paradigm, in which derivations become combinators, or in a more direct way, in which derivations are not translated. Both (...) translations are closely related in a canonical way. In the cited paper we proved completeness of the two direct translations. In the present paper we prove that also the two indirect translations are complete. These proofs are direct whereas in another version, [3], we proved completeness by showing that the two corresponding illative systems are conservative over the two systems for the direct translations. Moreover we shall prove that one of the systems is also complete for predicate calculus with higher type functions. (shrink)

First published in 1995. Routledge is an imprint of Taylor & Francis, an informa company.

Contents Preface General Introduction 1 | Science and Pseudoscience Introduction Karl Popper, Science: Conjectures and Refutations Thomas S. Kuhn, Logic of Discovery or Psychology of Research? Imre Lakatos, Science and Pseudoscience Paul R. Thagard, Why Astrology Is a Pseudoscience Michael Ruse, Creation-Science Is Not Science Larry Laudan, Commentary: Science at the Bar---Causes for Concern Commentary 2 | Rationality, Objectivity, and Values in Science Introduction Thomas S. Kuhn, The Nature and Necessity of Scientific Revolutions Thomas S. Kuhn, Objectivity, Value Judgment, and (...) Theory Choice Ernan McMullin, Rationality and Paradigm Change in Science Larry Laudan, Kuhn’s Critique of Methodology Helen E. Longino, Values and Objectivity Kathleen Okruhlik, Gender and the Biological Sciences Commentary 3 | The Duhem-Quine Thesis and Underdetermination Introduction Pierre Duhem, Physical Theory and Experiment W. V. Quine, Two Dogmas of Empiricism Donald Gillies, The Duhem Thesis and the Quine Thesis Larry Laudan, Demystifying Underdetermination *Colin Howson and Peter Urbach, The Duhem Problem Commentary 4 | Induction, Prediction, and Evidence Introduction Peter Lipton, Induction Karl Popper, The Problem of Induction Wesley C. Salmon, Rational Prediction Carl G. Hempel, Criteria of Confirmation and Acceptability Peter Achinstein, Explanation v. Prediction: Which Carries More Weight? *Nelson Goodman, The New Riddle of Induction Commentary 5 | Confirmation and Relevance: Bayesian Approaches Introduction Wesley C. Salmon, Rationality and Objectivity in Science *Deborah G. Mayo, A Critique of Salmon’s Bayesian Way *Alan Chalmers, The Bayesian Approach Paul Horwich, Therapeutic Bayesianism Commentary 6 | Models of Explanation Introduction Rudolf Carnap, The Value of Laws: Explanation and Prediction Carl G. Hempel, Two Basic Types of Scientific Explanation Carl G. Hempel, The Thesis of Structural Identity Carl G. Hempel, Inductive-Statistical Explanation Peter Railton, A Deductive-Nomological Model of Probabilistic Explanation *Philip Kitcher, Explanatory Unification *James Woodward, The Manipulability Conception of Causal Explanation Commentary 7 | Laws of Nature Introduction A. J. Ayer, What Is a Law of Nature? Fred I. Dretske, Laws of Nature D. H. Mellor, Necessities and Universals in Natural Laws Nancy Cartwright, Do the Laws of Physics State the Facts? Commentary 8 | Intertheoretic Reduction Introduction Ernest Nagel, Issues in the Logic of Reductive Explanations Paul K. Feyerabend, How to Be a Good Empiricist *Jerry A. Fodor, Special Sciences Philip Kitcher, 1953 and All That: A Tale of Two Sciences Commentary 9 | Empiricism and Scientific Realism Introduction Grover Maxwell, The Ontological Status of Theoretical Entities Bas C. van Fraassen, Arguments Concerning Scientific Realism Alan Musgrave, Realism versus Constructive Empiricism Larry Laudan, A Confutation of Convergent Realism *Juha T. Saatsi, On the Pessimistic Induction and Two Fallacies Ian Hacking, Experimentation and Scientific Realism David B. Resnik, Hacking’s Experimental Realism *Martin Carrier, What Is Right with the Miracle Argument Arthur Fine, The Natural Ontological Attitude Alan Musgrave, NOA’s Ark---Fine for Realism Commentary Glossary Bibliography Name Index Subject Index. (shrink)

Wie kein anderer Philosoph vor oder nach ihm thematisierte Heidegger die metaphysischen Denkschemata, die der abendländisch-neuzeitlichen Technikentwicklung zugrunde liegen. Auf verständliche Weise rekonstruiert dieses Buch Heideggers radikal metaphysikkritischen Ansatz vor dem Hintergrund seiner frühen und mittleren Schriften. Dabei wird nicht nur deutlich, wie sehr sein spätes Denken der Technik in Kontinuität zu seinem frühen fundamentalontologischen Projekt (und dessen Scheitern) steht, sondern es werden auch die Alternativen zum rechnenden Denken und Handeln in Kunst und Dichtung aufgezeigt. (Quelle: www.buchhandel.de).

Die Abhandlung "Sein und Zeit" erschien zuerst im Frühjahr 1927 in dem von Edmund Husserl herausgegebenen "Jahrbuch für Philosophie und phänomenologische Forschung", Band VIII, und gleichzeitig als Sonderdruck. Als eines der berühmtesten und wirkungsmächtigsten philosophischen Bücher des 20. Jahrhunderts ist es ein unverzichtbarer Quellentext für die Philosophie, übersetzt in über 25 Sprachen der Welt. Dreißig Jahre nach dem Tod Martin Heideggers (1889-1976) wird sein epochemachendes Hauptwerk über den Sinn des Seins nun neu gesetzt aufgelegt, um das Werk seinen zahlreichen (...) Leserinnen und Lesern in aller Welt wieder in einem ansprechenden Druck zu präsentieren. Diese 19. Auflage ist textidentisch, zeilen- und seitengleich mit den zuletzt unveränderten Nachdrucken der 15. anhand der Gesamtausgabe durchgesehenen Auflage mit den Randbemerkungen aus dem Handexemplar des Autors im Anhang. (shrink)

A century ago, John Dewey remarked that when home changes radically, school must change as well. With home, family, and gender roles dramatically altered in recent years, we are faced with a difficult problem: in the lives of more and more American children, no one is home. The Schoolhome proposes a solution. Drawing selectively from reform movements of the past and relating them to the unique needs of today's parents and children, Jane Martin presents a philosophy of education that (...) is responsive to America's changed and changing realities. As more and more parents enter the workforce, the historic role of the domestic sphere in the education and development of children is drastically reduced. Consequently, Martin advocates removing the barriers between the school and the home--making school a metaphorical "home," a safe and nuturant environment that provides children with the experience of affection and connection otherwise missing or inconsistent in their lives. In this proposition, the traditional schoolhouse where children are drilled in the three Rs is transformed into a "schoolhome" where learning is animated by an ethic of social awareness. At a time when many school reformers are calling for a return to basics and lobbying for skills education and quick-fix initiatives, Martin urges us to reconsider the distinctive legacies of Dewey and Montessori and to conceive of a school that integrates the values of the home with those of social responsibility. With cultural diversity and gender equality among its explicit goals, the schoolhome expands upon Dewey's edict to educate the "whole child," seeking instead to educate all children in the culture's whole heritage. Martin eloquently challenges reformers to reclaim the founding fathers' vision of the nation as a domestic realm, and to imagine a learning environment whose curriculum and classroom practice reflect not merely an economic but a moral investment in the future of our children. More than a summons to action, this remarkable book is a call to rethink the assumptions we bring to the educational enterprise, and so, to act wisely. (shrink)

A moral requirement R1 is said to be lexically prior to a moral requirement R2 just in case we are morally obliged to uphold R1 at the expense of R2 – no matter how many times R2 must be violated thereby. While lexical priority is a feature of many ethical theories, and arguably a part of common sense morality, attempts to model it within the framework of decision theory have led to a series of problems – a fact which is (...) sometimes spun as a ‘decision theoretic critique’ of lexical priority. In this paper, I develop an enriched decision theoretic framework that is capable of modelling lexical priority while avoiding all extant problems. This will involve introducing several new ingredients into the standard decision theoretic framework, including multidimensional utilities, de minimis risks, and the means to represent two different conceptions of risk. (shrink)

I consider the question of how literally one can construe the “gauge argument,” which is the canonical means of understanding the putatively central import of local gauge symmetry principles for fundamental physics. As I argue, the gauge argument must be afforded a heuristic reading. Claims to the effect that the argument reflects a deep “logic of nature” must, for numerous reasons I discuss, be taken with a grain of salt.

This article develops an ecological framework for understanding collective action. This is contrasted with approaches familiar from the collective intentionality debate, which treat individuals as fundamental units of collective action. Instead, we turn to social ecological psychology and dynamical systems theory and argue that they provide a promising framework for understanding collectives as the central unit in collective action. However, we submit that these approaches do not yet appreciate enough the relevance of social identities for collective action. To analyze this (...) aspect, we build on key insights from social identity theory and synthesize it with embodied and ecological accounts of perception and action. This results in the proposal of two new types of affordances. For an individual who enacts her "embodied social identity" of being a member of a particular collective, there can be what we call embodied social identity affordances. Moreover, when several individuals dynamically interact with each other against the background of their embodied social identities, this might lead to the emergence of a collective, which we understand as a dynamically constituted and ecologically situated perception-action system consisting of several individuals enacting relevant embodied social identity affordances. Building on previous work in social ecological psychology, we suggest that there can be genuine collective affordances, that is, affordances whose subject is not an individual, but a collective. (shrink)

Recent empirical findings from social psychology, ecological psychology, and embodied cognitive science indicate that situational factors crucially shape the course of human behavior. For instance, it has been shown that finding a dime, being under the influence of an authority figure, or just being presented with food in easy reach often influences behavior tremendously. These findings raise important new questions for the philosophy of action: Are these findings a threat to classical conceptions of human agency? Are humans passively pushed around (...) by situational factors, or are there agential aspects in the way we spontaneously experience and react to situations? How can one conceptualize the pervasive influence of situational factors on human action? What are situations in the first place, and how should the influence of these situations on action be thought of? This paper sets out to develop a new conceptual repertoire for thinking about the influence of situations on action, drawing on research from ecological psychology as well as from embodied and enactive cognitive science. The key proposal is the development of a philosophical sensorimotor account of agency: Action, it is proposed, should be conceived of as constant dynamical interaction of agential and environmental factors – factors which should all be conceptualized in new ways. (shrink)

This book is a philosophers' attempt to bring together ideas put forward by economists, sociologists and political theorists. The author begins by exploring the economist's assumption that action is rational if it helps to achieve the agent's goals as efficiently as possible. The assumption is explored with the aid of rational-choice theory and game-theory, but it is rejected in the end for failing to account for the elements of trust and morality which rational social life requires. A discussion of 'Rational (...) Expectations' and of 'maximising' and 'satisficing' leads to a portrait of social actors as rational role-players. Rationality is, finally, the expression of the self in a social world. The book intervenes in intense current debates within and among several disciplines. Its concern is with the true nature of social actors and the proper character of social science. Its arguments are the more challenging for being presented in a simple, incisive and lucid prose. It will be of particular interest to philosophers, social theorists and social scientists interested in the philosophical aspects of their discipline. (shrink)

This is the lightly revised text of my commentary/response to David Carr’s keynote address, “Phenomenology of Crisis,” at the 2024 meeting of the Husserl Circle.

There is broad agreement that humans can be wronged independently of their incurring any harm, that is, when their welfare is not affected. Examples include unnoticed infringements of privacy, ridiculing unaware individuals, or disregarding individuals’ autonomous decision-making in their best interest. However, it is less clear whether the same is true of animals—that is, whether moral agents can wrong animals in situations that do not involve any harm to the animals concerned. In order to answer this question, I concentrate on (...) the illustrative case of treating animals in a demeaning yet harmless way that would be disrespectful if humans were concerned. I discuss whether such actions are permissible or unjustifiably discriminatory from a moral point of view. I conclude that moral agents cannot directly wrong animals without harming them and thus do not owe it to a particular animal to refrain from such actions. However, if the actions increase the likelihood that animal abuse will occur, this presents a strong indirect reason against performing them. Thus, the reasons for refraining from such actions are merely indirect rather than direct. (shrink)

There are two perspectives from which formal theories can be viewed. On the one hand, one can take a theory to be about some privileged models. On the other hand, one can take all models of a theory to be on a par. In contrast with what is usually done in philosophical debates, we adopt the latter viewpoint. Suppose that from this perspective we want to add an adequate truth predicate to a background theory. Then on the one hand the (...) truth theory ought to be semantically conservative over the background theory. At the same time, it is generally recognised that the central function of a truth predicate is an expressive one. A truth predicate ought to allow us to express propositions that we could not express before. In this article we argue that there are indeed natural truth theories which satisfy both the demand of semantical conservativeness and the demand of adequately extending the expressive power of our language. (shrink)

Name der Zeitschrift: Kant-Studien Jahrgang: 110 Heft: 1 Seiten: 49-73.

In their invocations of the Muses the early epic poets use indifferently verbs meaning ‘tell’, ‘speak of’ and the verb which we normally translate as ‘sing’ When they refer directly to their own performance they may use the non-committalμνήσομαι, or ἐρέω, ἐνισπεῖνbut more often it isάείδω, ἄρχομ ἀείδεινor something of the sort; and they will pray for goodἀοιδήor hope for reward from it. We cannot make a distinction between two styles of performance, one characterized asἀείδειν the other as ἐνέπεινthe Iliad (...) beginsμῆνιν ἄειδε θεάbut later hasἔσπετε νῦν μοι Μοῦσαι;Hesiod moves straight fromχαίρετε τέκνα Διός, δότε δ᾿ ἱμερόεσσαν ἀοιδήνtoεἴπατε δ᾿ ὡς... ταῦτά μοι ἔσπετε Μοῦσαι... καὶ εἴπατε; the author of the Hymn to Pan beginsἔννεπε Μοῦσαand endsἴλαμαι δέ σ᾿ ἀοιδῇ... καὶ σεῖο καὶ ἄλλης μνήσομ᾿ ἀοιδῆς. (shrink)