A general class of labeled sequent calculi is investigated, and necessary and sufficient conditions are given for when such a calculus is sound and complete for a finite -valued logic if the labels are interpreted as sets of truth values. Furthermore, it is shown that any finite -valued logic can be given an axiomatization by such a labeled calculus using arbitrary "systems of signs," i.e., of sets of truth values, as labels. The number of labels needed is logarithmic in the (...) number of truth values, and it is shown that this bound is tight. (shrink)

Any intermediate propositional logic can be extended to a calculus with epsilon- and tau-operators and critical formulas. For classical logic, this results in Hilbert’s $\varepsilon $ -calculus. The first and second $\varepsilon $ -theorems for classical logic establish conservativity of the $\varepsilon $ -calculus over its classical base logic. It is well known that the second $\varepsilon $ -theorem fails for the intuitionistic $\varepsilon $ -calculus, as prenexation is impossible. The paper investigates the effect of adding critical $\varepsilon $ - (...) and $\tau $ -formulas and using the translation of quantifiers into $\varepsilon $ - and $\tau $ -terms to intermediate logics. It is shown that conservativity over the propositional base logic also holds for such intermediate ${\varepsilon \tau }$ -calculi. The “extended” first $\varepsilon $ -theorem holds if the base logic is finite-valued Gödel–Dummett logic, and fails otherwise, but holds for certain provable formulas in infinite-valued Gödel logic. The second $\varepsilon $ -theorem also holds for finite-valued first-order Gödel logics. The methods used to prove the extended first $\varepsilon $ -theorem for infinite-valued Gödel logic suggest applications to theories of arithmetic. (shrink)

Mathias Frisch provides the first sustained philosophical discussion of conceptual problems in classical particle-field theories. Part of the book focuses on the problem of a satisfactory equation of motion for charged particles interacting with electromagnetic fields. As Frisch shows, the standard equation of motion results in a mathematically inconsistent theory, yet there is no fully consistent and conceptually unproblematic alternative theory. Frisch describes in detail how the search for a fundamental equation of motion is partly driven by pragmatic considerations (...) (like simplicity and mathematical tractability) that can override the aim for full consistency. The book also offers a comprehensive review and criticism of both the physical and philosophical literature on the temporal asymmetry exhibited by electromagnetic radiation fields, including Einstein's discussion of the asymmetry and Wheeler and Feynman's influential absorber theory of radiation. Frisch argues that attempts to derive the asymmetry from thermodynamic or cosmological considerations fail and proposes that we should understand the asymmetry as due to a fundamental causal constraint. The book's overarching philosophical thesis is that standard philosophical accounts that strictly identify scientific theories with a mathematical formalism and a mapping function specifying the theory's ontology are inadequate, since they permit neither inconsistent yet genuinely successful theories nor thick causal notions to be part of fundamental physics. (shrink)

Jan Krajíček posed the following problem: Is there is a generalization result in the theory of real closed fields of the form: If A is provable in length k for all n ϵ ω , then A is provable? It is argued that the answer to this question depends on the particular formulation of the “theory of real closed fields.” Four distinct formulations are investigated with respect to their generalization behavior. It is shown that there is a positive answer to (...) Krajíček's question for 1. the axiom system RCF of Artin-Schreier with Gentzen's LK as underlying logical calculus, 2. RCF with the variant LK B of LK allowing introduction of several quantifiers of the same type in one step, 3. LK B and the first-order schemata corresponding to Dedekind cuts and the supremum principle. A negative answer is given for 4. any system containing the schema of extensionality. (shrink)

The aim of this paper is to emphasize the fact that for all finitely-many-valued logics there is a completely systematic relation between sequent calculi and tableau systems. More importantly, we show that for both of these systems there are al- ways two dual proof sytems (not just only two ways to interpret the calculi). This phenomenon may easily escape one’s attention since in the classical (two-valued) case the two systems coincide. (In two-valued logic the assignment of a truth value and (...) the exclusion of the opposite truth value describe the same situation.). (shrink)

Deepfakes are a new form of synthetic media that broke upon the world in 2017. Bringing photoshopping to video, deepfakes replace people in existing videos with someone else’s likeness. Currently most of their reach is limited to pornography, and they are also used to discredit people. However, deepfake technology has many epistemic promises and perils, which concern how we fare as knowers. Our goal is to help set an agenda around these matters, to make sure this technology can help realize (...) epistemic rights and epistemic justice and unleash human creativity, rather than inflict epistemic wrongs of any sort. Our project is exploratory in nature, and we do not aim to offer conclusive answers at this early stage. There is a need to remain vigilant to make sure the downsides do not outweigh the upsides, and that will be a tall order. (shrink)

Statman and Orevkov independently proved that cut-elimination is of nonelementary complexity. Although their worst-case sequences are mathematically different the syntax of the corresponding cut formulas is of striking similarity. This leads to the main question of this paper: to what extent is it possible to restrict the syntax of formulas and — at the same time—keep their power as cut formulas in a proof? We give a detailed analysis of this problem for negation normal form , prenex normal form and (...) monotone formulas. We show that proof reduction to NNF is quadratic, while PNF behaves differently: although there exists a quadratic transformation into a proof in PNF too, additional cuts are needed; the elimination of these cuts requires nonelementary expense in general. By restricting the logical operators to {,,,}, we obtain the type of monotone formulas. We prove that the elimination of monotone cuts can be of nonelementary complexity . On the other hand, we define a large class of problems where cut-elimination of monotone cuts is only exponential and show that this bound is tight. This implies that the elimination of monotone cuts in equational theories is at most exponential. Particularly, there are no short proofs of Statman's sequence with monotone cuts. (shrink)

In this paper an alternative Skolemization method is introduced that, for a large class of formulas, is sound and complete with respect to intuitionistic logic. This class extends the class of formulas for which standard Skolemization is sound and complete and includes all formulas in which all strong quantifiers are existential. The method makes use of an existence predicate first introduced by Dana Scott.

This volume commemorates the life, work, and foundational views of Kurt Gödel (1906-1978), most famous for his hallmark works on the completeness of first-order logic, the incompleteness of number theory, and the consistency - with the other widely accepted axioms of set theory - of the axiom of choice and of the generalized continuum hypothesis. It explores current research, advances, and ideas for future directions not only in the foundations of mathematics and logic, but also in the fields of computer (...) science, artificial intelligence, physics, cosmology, philosophy, theology, and the history of science. The discussion is supplemented by personal reflections from several scholars who knew Gödel personally, providing some interesting insights into his life. By putting his ideas and life's work into the context of current thinking and perceptions, this book will extend the impact of Gödel's fundamental work in mathematics, logic, philosophy, and other disciplines for future generations of researchers. (shrink)

We study the formal first order system TIND in the standard language of Gentzen's LK . TIND extends LK by the purely logical rule of term-induction, that is a restricted induction principle, deriving numerals instead of arbitrary terms. This rule may be conceived as the logical image of full induction.

This paper provides a survey of several philosophical issues arising in classical electrodynamics arguing that there is a philosophically rich set of problems in theories of classical physics that have not yet received the attention by philosophers that they deserve. One issue, which is connected to the philosophy of causation, concerns the temporal asymmetry exhibited by radiation fields in the presence of wave sources. Physicists and philosophers disagree on whether this asymmetry reflects a fundamental causal asymmetry or is due to (...) statistical or thermodynamic considerations. I suggest that an explanation appealing to the asymmetry of causation is more promising. Another issue concerns the conceptual structure of the theory. Despite its empirical success, classical electrodynamics faces serious foundational problems. Models of charged particles involve what by the theory's own lights are idealizations, I maintain, and this is a feature that is not readily captured by traditional philosophical accounts of scientific theories. Other issues I discuss concern (i) the relation between Lorentz's theory of the electron and Einstein's Theory of Special Relativity; (ii) the notion of the domain of a theory, the question of theory reduction, and the relation between classical and more fundamental quantum theories; and (iii) the role of locality constraints, their relation to the concept of causation; and the status of locality conditions in the semi-classical theory of the Aharanov-Bohm effect. (shrink)

The grounds of justice -- "Un pouvoir ordinaire": shared membership in a state as a ground of -- Justice -- Internationalism versus statism and globalism: contemporary debates -- What follows from our common humanity? : the institutional stance, human rights, and nonrelationism -- Hugo Grotius revisited : collective ownership of the Earth and global public reason -- "Our sole habitation" : a contemporary approach to collective ownership of the earth -- Toward a contingent derivation of human rights -- Proportionate use (...) : immigration and original ownership of the Earth -- "But the earth abideth for ever" : obligations to future generations -- Climate change and ownership of the atmosphere -- Human rights as membership rights in the global order -- Arguing for human rights : essential pharmaceuticals -- Arguing for human rights : labor rights as human rights -- Justice and trade -- The way we live now -- "Imagine there's no countries" : a reply to John Lennon -- Justice and accountability : the state -- Justice and accountability : the World Trade Organization. (shrink)

We study cut-elimination in first-order classical logic. We construct a sequence of polynomial-length proofs having a non-elementary number of different cut-free normal forms. These normal forms are different in a strong sense: they not only represent different Herbrand-disjunctions but also differ in their propositional structure. This result illustrates that the constructive content of a proof in classical logic is not uniquely determined but rather depends on the chosen method for extracting it.

Much has been written on the role of causal notions and causal reasoning in the so-called 'special sciences' and in common sense. But does causal reasoning also play a role in physics? Mathias Frisch argues that, contrary to what influential philosophical arguments purport to show, the answer is yes. Time-asymmetric causal structures are as integral a part of the representational toolkit of physics as a theory's dynamical equations. Frisch develops his argument partly through a critique of anti-causal arguments and (...) partly through a detailed examination of actual examples of causal notions in physics, including causal principles invoked in linear response theory and in representations of radiation phenomena. Offering a new perspective on the nature of scientific theories and causal reasoning, this book will be of interest to professional philosophers, graduate students, and anyone interested in the role of causal thinking in science. (shrink)

In this paper a method for the replacement, in formulas, of strong quantifiers by functions is introduced that can be considered as an alternative to Skolemization in the setting of constructive theories. A constructive extension of intuitionistic predicate logic that captures the notions of preorder and existence is introduced and the method, orderization, is shown to be sound and complete with respect to this logic. This implies an analogue of Herbrand's theorem for intuitionistic logic. The orderization method is applied to (...) the constructive theories of equality and groups. (shrink)

ALTHOUGH majority rule finds ready acceptance whenever groups make decisions, there are surprisingly few philosophically interesting arguments in support of it.1 Jeremy Waldron’s The Dignity of Legislation contains the most interesting recent defense of majority rule. Waldron combines his own argument from respect with May’s influential characterization of majority rule, tying both to a reinterpretation of a well-known passage from Locke’s Second Treatise (“the body moves into the direction determined by the majority of forces”). Despite its impressive resourcefulness, Waldron’s defense (...) is deficient, and one goal of this essay is to show how. Yet our main concern is not to criticize Waldron, but to demonstrate general deficiencies of arguments for majority rule and to suggest a strategy for a more adequate and more complete defense. Such arguments tend to have one of two weaknesses: Either they assume that collective decisionmaking is done in terms of ranking options and thus neglect both aggregation methods using more information than the relative standing of options in rankings (such as so-called positional methods) and rules that are not aggregation methods at all (such as fair-division procedures); or they also constitute arguments for other decision rules. In the first case, the argument is too narrow, in the second it is too broad. The narrowness problem is bigger than stated so far because arguments for majority rule tend to assume not only that decisions are made by ranking options, but also that only two options are to be ranked. Both problems arise for Waldron’s defense and leave it incomplete. Yet such incompleteness also characterizes the state of the art in arguing for majority rule. So in addition to.. (shrink)

Working in Z + KP, we give a new proof that the class of hereditarily finite sets cannot be proved to be a set in Zermelo set theory, extend the method to establish other failures of replacement, and exhibit a formula Φ(λ, a) such that for any sequence $\langle A_{\lambda} \mid \lambda \text{a limit ordinal} \rangle$ where for each $\lambda, A_{\lambda} \subseteq ^{\lambda}2$ , there is a supertransitive inner model of Zermelo containing all ordinals in which for every λ A (...) λ = {α ∣Φ(λ, a)}. (shrink)

All first-order Gödel logics G_V with globalization operator based on truth value sets V C [0,1] where 0 and 1 lie in the perfect kernel of V are axiomatized by Ciabattoni’s hypersequent calculus HGIF.

The problem of approximating a propositional calculus is to find many-valued logics which are sound for the calculus (i.e., all theorems of the calculus are tautologies) with as few tautologies as possible. This has potential applications for representing (computationally complex) logics used in AI by (computationally easy) many-valued logics. It is investigated how far this method can be carried using (1) one or (2) an infinite sequence of many-valued logics. It is shown that the optimal candidate matrices for (1) can (...) be computed from the calculus. (shrink)

von Lothar Brock Wer dieses Buch zur Hand nimmt, sollte sich einen Autor vorstellen, der einer Gruppe hartgesottener Geschäftsleute aus der Wüste von New Mexico morgens um sieben mit charmanter Leichtigkeit und spärlichen, aber Verbindung stiftenden Gesten einen Vortrag über die EU als einer vorgestellten Gemeinschaft hält und dafür überschwenglich gefeiert wird. Oder einen Theoretiker mit verblüffend praktischen Kenntnissen über Höhenmedizin und der unter bestimmten Umständen lebensrettenden Fähigkeit, panischen Berggefährten den Anblick der Tiefe erträglich zu machen. Oder den lead-Sänger einer (...) ziemlich professionellen Musikgruppe, die sich die öffentliche Pflege des Liedgutes der Rolling Stones zur Aufgabe gemacht hat und als Meister der Reproduktion die Bewunderer des Originals in Taumel versetzt - von Stockholm bis OfIenbach. Auf keinen Fall aber sollte man sich einen Autor vorstellen wie man ihn sich vorstellt, wenn man dieses Buch zur Hand nimmt. Oder doch? Doch! Es könnte ja sein, daß jemand dieses Buch nicht nur als lohnende Strapaze erlebt, sondern auch als Vergnügen, wenn er erst einmal über den Untertitel hinweggekommen ist. Zur Sache:,,Fallen der Welt-Ordnung" - die Fallen oder das Fallen? Das Thema verrät es nicht; denn zwischen Moderne und Postmoderne ist ein weites Feld, auf dem alles mögliche passieren kann. Worum also geht es? Mathias Albert versteht das Arbeitsgebiet der Internationalen Beziehungen (also der Lehre und Forschung über diesen Gegenstandsbereich) als jenen Teilbereich der Sozialwissenschaften, der sich mit der Weltordnung befaßt. (shrink)

In Frisch 2004 and 2005 I showed that the standard ways of modeling particle-field interactions in classical electrodynamics, which exclude the interactions of a particle with its own field, results in a formal inconsistency, and I argued that attempts to include the self-field lead to numerous conceptual problems. In this paper I respond to criticism of my account in Belot 2007 and Muller 2007. I concede that this inconsistency in itself is less telling than I suggested earlier but argue that (...) existing solutions to the theory's foundational problems do not support the kind of traditional philosophical conception of scientific theorizing defended by Muller and Belot. *Received January 2007; revised October 2007. †To contact the author, please write to: Department of Philosophy, University of Maryland, Skinner Building, College Park, MD 20742; e-mail: [email protected]. (shrink)

We introduce Gentzen calculi for intuitionistic logic extended with an existence predicate. Such a logic was first introduced by Dana Scott, who provided a proof system for it in Hilbert style. We prove that the Gentzen calculus has cut elimination in so far that all cuts can be restricted to very simple ones. Applications of this logic to Skolemization, truth value logics and linear frames are also discussed.

Though much attention has been paid to different principles of justice, far less has been done reflecting on what the larger concern behind the notion is. In this work, Mathias Risse proposes that the perennial quest for justice is about ensuring that each individual has an appropriate place in what our uniquely human capacities permit us to build, produce, and maintain, and is appropriately respected for the capacity to hold such a place to begin with. Risse begins by investigating (...) the role of political philosophers and exploring how to think about the global context where philosophical inquiry occurs. Next, he offers a quasi-historical narrative about how the notion of distributive justice identifies a genuinely human concern that arises independently of cultural context and has developed into the one we should adopt now. Finally, he investigates the core terms of this view, including stringency, moral value, ground and duties of justice. (shrink)

The length of resolution proofs is investigated, relative to the model-theoretic measure of Herband complexity. A concept of resolution deduction is introduced which is somewhat more general than the classical concepts. It is shown that proof complexity is exponential in terms of Herband complexity and that this bound is tight. The concept of R-deduction is extended to FR-deduction, where, besides resolution, a function introduction rule is allowed. As an example, consider the clause P Q: conclude P) Q, where a, f (...) are new function symbols extending Herbrand's universe. P ()Q from Q) and Skolemization). By modification of a construction of Statman it is shown that FR-deductions may be nonelementarily shorter than R-deductions . Finally it is proved that FR-deduction has weaker effects only if clausal logic is restricted to Horn logic. (shrink)

Many climate scientists have made claims that may suggest that evidence used in tuning or calibrating a climate model cannot be used to evaluate the model. By contrast, the philosophers Katie Steele and Charlotte Werndl have argued that, at least within the context of Bayesian confirmation theory, tuning is simply an instance of hypothesis testing. In this paper I argue for a weak predictivism and in support of a nuanced reading of climate scientists’ concerns about tuning: there are cases, model-tuning (...) among them, in which predictive successes are more highly confirmatory of a model than accommodation of evidence. (shrink)

in Dirac's classical theory of the electron—is causally non-local. I distinguish two distinct causal locality principles and argue, using Dirac's theory as my main case study, that neither can be reduced to a non-causal principle of local determinism.

Biographical note: Mathias Denecke is a PhD student at the University of Konstanz, Germany.Anne Ganzert is a PhD student at the University of Konstanz, Germany.Isabell Otto (PhD) is junior professor for Media Studies at the University of Konstanz, Germany.Robert Stock (MA) coordinates the research initiative ”Media and Participation“ at the University of Konstanz, Germany.

We have benefited from conversations with Archon Fung, Brian Jacob, Todd Pittinsky, Peter Schuck, Ani Satz, Andrew Williams, and students in a joint class on statistics and ethics at the John F. Kennedy School of Government in October 2002. We are also grateful to our audience at the conference “The Priority of Practice,” organized by Jonathan Wolff at University College London in September 2003, and to Arthur Applbaum, Miriam Avins, Frances Kamm, Simon Keller, Frederick Schauer, Alan Wertheimer, and the Editors (...) of Phi- losophy & Public Affairs for insightful comments. We have benefited from prepublication reading of Schauer’s work on profiling, Profiles, Probabilities, and Stereotypes (Cambridge, Mass: Harvard University Press, 2003). We thank Avedis Koutoujian for research assistance. (shrink)

Provides a robust theoretical and methodological framework for researching of resistance and social change.

Evolution seems tobe a perfect example of a historical process: It began with the earliest “living” units, progressed to massive diversity and disparity, and resulted in our recent lifeworld, the subject-matter of the evolutionary biologist. Yet some irritation remains considering the logical grammar of “history”, as it seems to introduce non-functional aspects into evolutionary theory – which is often addressed as contingency in evolutionary biology. But even reducing the “historical” aspect of evolutionary biology to a functional understanding of lifeworld, we (...) have to consider the specific historicity of the epistemic situation of the evolutionary biologist. This paper argues for the relevance of the explication of this peculiar epistemic situation, taking into account the recent systemic transformations of evolutionary theory.The argument is developed in three steps: first, a revision of the use of temporal expressions in (bio-)sciences, revealing the prevalence of a non-modal understanding of time, which leads to “thin” temporal characterizations of biological processes. Second, based upon biology’s shift toward system paradigms, the formal structure of recent evolutionary approaches is shown to result in a “loss of historicity”. Finally, the consequences for the self-understanding of humans as evolutionary lifeforms are explicated.This reconstruction of the difference between historical and evolutionary judgment emphasizes the relevance of the modal aspects of temporality, which is demonstrated by considering a significant shift of the underlying temporal frames. Accordingly to human beings as historical entities, the differences between natural history, prehistory and history proper are relocated within the concept of history itself. (shrink)

Religionen unterbreiten Sinnstiftungsangebote und beeinflussen nicht unwesentlich den Umgang der Menschen miteinander. SIe konnen zu Fortschritt und Freiheit der Menschen beitragen, aber auch zu Fanatismus und Intoleranz fuhren. DEshalb ist ihr Stellenwert in einer sakularen Gesellschaft umstritten. WElcher Umgang mit Religionen empfiehlt sich? Ist es fur eine soziomoralische Fundierung der Gesellschaft nicht besser, allein auf eine vernunftbasierte Ethik zu setzen? Und lassen sich Glauben und Wissen uberhaupt miteinander versohnen? Mit Beitragen von Konrad Paul Liessmann, Volker Gerhardt, Nadia Baghdadi und Jan (...) Assmann. (shrink)

Political philosophy is mostly what I do, and in one way or another, it’s organized around ideas about justice. Often, my work focuses on problems that are present in public political discourse, which then I try to approach by offering a solution to them that is tied to philosophically acceptable foundations. For a few years now, my work has been concerned with building a constructive theory of the “grounds of justice” at the global level. The book that is in the (...) process of emerging is called "The Grounds of Justice: An Inquiry about the State in Global Perspective," and is under contract with Princeton University Press. Since I've been working on this project for a while, and since I have been presenting bits and pieces of it at numerous conferences and colloquia, I'm putting the first thirteen chapters up here, so that people who are interested in this work can see how it all fits together. The remaining four chapters and the epilogue and currently in progress. (shrink)

Cet essai à teneur philosophique s'intéresse à la force d'évocation et d'invocation de la musique. à son charme magique dirait Nietzsche. Comment la musique me parle-t-elle '? Que suggère-t-elle? Pourquoi parle-t-elle de moi? Quelle fonction a-t-elle dans l'humanité '? L'argumentation de l'auteur utilise la philosophie et la psychologie musicales afin d'expliquer la scandaleuse disproportion entre la puissance à dire de la musique et l'inévidence foncière de ce qu'elle dit (pour reprendre les mots de Jankelé?itch). disproportion en laquelle réside selon l'auteur (...) tout son mystère, en laquelle réside tout son sens. Ce texte court mais dense s'adresse aux musicologues ainsi qu'à tout lecteur ou musicien éclairé voulant densifier son horizon de compréhension de la musique et de ses effets. Il puise ses exemples dans de nombreux corpus : musiques classique et romantique, avant-gardes, jazz, musiques de film."--Page 4 of cover. (shrink)

This essay proposes that What Is Philosophy? (1991), written in collaboration with Félix Guattari, not only presents a summary of Gilles Deleuze’s late creative period and, to some extent, a recapitulation of his entire oeuvre but also constitutes his third masterwork. The essay begins by tracing Deleuze’s three periods, especially the development of his thought during the last period, and the process of writing his final book. Then it explores the inextricable connection between the method of creation that results from (...) What Is Philosophy? and its stylistic devices. Through its refined composition and succinct prose, the book puts itself at the service of the approach that leads to bringing forth philosophical concepts, and it attunes the reader to the creative activity. Thus, like The Logic of Sense (1969) and A Thousand Plateaus (1980), it forms a masterwork in which Deleuze’s philosophical efforts that spanned a whole period are condensed and mobilized such that while reading one finds oneself exposed to these efforts and is forced to continue them. (shrink)

Wie lassen sich die globalen Ökosysteme und damit auch die Lebensgrundlage zukünftiger Generationen dauerhaft vor ihrer Zerstörung bewahren? Weder bessere Technologien noch Effizienzsteigerungen reichen aus, es bedarf vielmehr der Hinwendung zu suffizienten Lebensstilen. Die Studie, die an der Schnittstelle von Naturphilosophie, angewandter Ethik und empirisch-ökologischer Forschung anzusiedeln ist, thematisiert eine der dringendsten Fragen der Zeitgeschichte: das Naturverständnis des Menschen angesichts einer "ökologischen Krise". Dabei geht es auch um die Frage, warum Natur als raumzeitliche Verflechtung aller Lebewesen einen Eigenwert besitzt, der (...) menschlichen Interessen Grenzen setzt. (shrink)