Proof Theory of Modal Logic is devoted to a thorough study of proof systems for modal logics, that is, logics of necessity, possibility, knowledge, belief, time, computations etc. It contains many new technical results and presentations of novel proof procedures. The volume is of immense importance for the interdisciplinary fields of logic, knowledge representation, and automated deduction.

In the exceptional book _Divine Holiness and Divine Action_, Mark Murphy defends what he calls the _holiness framework _for divine action. The purpose of our essay-response to Murphy’s book is to consider an alternative framework for divine action, what we call the _agapist framework_. We argue that the latter framework is more probable than Murphy’s holiness framework with respect to_ select _theological desiderata.

We develop and knit together several theodicies in order to find a more complete picture of why certain forms of animal suffering might be permitted by a perfect being. We focus on an especially potent form of the problem of evil, which arises from considering why a perfectly good, wise, and powerful God might use evolutionary mechanisms that predictably result in so much animal suffering and loss of life. There are many existing theodicies on the market, and although they offer (...) helpful resources, we combine and further develop several proposals to produce a composite theodicy that avoids certain shortcomings of the individual theodicies. An important element of our project is locating a role for randomness in cosmic and biological evolution. In particular, we show how randomness might enhance or enable certain goods, including everlasting goods, at the risk of temporary evils. (shrink)

In a number of recent works, Nicholas Wolterstorff defends the claim that human rights inhere in the dignity of every human. He further contends that the explanation of this dignity cannot be found in the intrinsic features of humans; rather, the only plausible explanation for human dignity is that it is bestowed upon humans by God’s love. In this paper, I argue that Wolterstorff’s theory concerning the ground of human dignity falls prey to something quite similar to the classic Euthyphro (...) dilemma: either God must love every existing human in a dignity-bestowing manner or he need not, and either option is problematic. If the former, then whatever it is about humans that ensures God’s love can reasonably be thought to be the independent source of human dignity and/or rights, thereby leaving us without cause to appeal to God’s love for the explanation of this dignity. If the latter, the implication is that moral statements which appear to be necessarily true are only contingently so. Wolterstorff’s theory will thus require substantial modification, or else abandonment. (shrink)

A number of philosophers and theologians have recently challenged the common assumption that it would be impossible for God to cause humans actions which are free in the libertarian or incompatibilist sense. Perhaps the most sophisticated version of this challenge is due to W. Matthews Grant. By offering a detailed account of divine causation, Grant argues that divine universal causation does not preclude humans from being ultimately responsible for their actions, nor free according to typical libertarian accounts. Here, we argue (...) that the kind of divine universal causation that Grant proposes is incompatible with a plausible interpretation of Robert Kane’s influential conception of ultimate responsibility. This conclusion is significant since Grant seeks to harmonize his divine causal account with Kane’s articulation of ultimate responsibility. (shrink)

I here respond to my interlocutors in the symposium on my book, Love Divine: A Systematic Account of God’s Love for Humanity. Addressing each of them in the order in which their essays appear within this symposium, I reply to the comments by R. T. Mullins, Keith Hess, and Ty Kieser.

To set the stage for the symposium on my monograph, Love Divine: A Systematic Account of God’s Love for Humanity, I present the purpose of this manuscript and summarize its main themes and chapters. Additionally, to orient readers to the wider literature in which Love Divine is situated, I respond to recent reviews of Love Divine and mention some of the most significant challenges to the book raised so far by those not represented within the symposium.

Many Christian theorists notice that love should contain, in additional to benevolence, some kind of interpersonal or unitive component. The difficulty comes in trying to provide an account of this unitive component that is sufficiently interpersonal in other-love and yet is also compatible with self-love. Eleonore Stump is one of the few Christian theorists who directly addresses this issue. Building upon the work of Thomas Aquinas, Stump argues that love is constituted by two desires: the desire for an individual’s good (...) and the desire to be united to that individual. Stump further develops the desire for union within this Thomistic understanding of love, and she maintains that her developed account not only captures the robustly interpersonal nature of one’s love of another but is also compatible with the love of oneself. Unfortunately, Stump’s way of making sense of this latter claim introduces a significant inconsistency in her analyses of the desire for union in self-love and other-love. Nevertheless, the most important features of Stump’s Neo-Thomistic account are salvageable. For there is a way of understanding love’s desire for union that emerges out of Thomas’s views on love and is compatible with the desiderata suggested by Stump, only does not have the same difficulties that beset Stump’s account. What is offered, then, is a modification of Stump’s account that might better serve her purposes. The resulting view of love, however, is one not only relevant to Stump. Rather, the view that emerges is a broadly Thomistic conception of love that is plausible in its own right and captures a certain biblical emphasis on the relational or interpersonal nature of love. (shrink)

Some Christian theologians and philosophers maintain that God’s punishments are always (at least partly) motivated by redemptive love for those punished, even when these punishments are considerably severe (e.g., killings or damnations). However, advocates of such a conception of divine punishment face significant challenges. Perhaps most fundamentally, it is not entirely apparent how severe and loving features of divine punishment might be understood to fit together within a viable theological model. In this article this foundational issue is addressed. By culling (...) resources from St. Gregory of Nyssa, the present aim is to proffer a contemporary model of divine punishment that naturally combines redemptive love for those punished with apparently harsh treatment. (shrink)

SummaryChristians often presume that immediate and universally extensive divine governance of human behavior is incompatible with human agency and responsibility. Against this presumption, Kathryn Tanner argues for a distinctive metalinguistic paradigm whereby Christians can coherently speak of God’s transcendence in such a way that divine action could never in principle ‘compete’ with human action. Thus, it is said, God can comprehensively will each human action without thereby compromising significant human freedom and corresponding moral responsibility. In this article, it is argued (...) that Tanner’s non-competitivist paradigm fails to circumvent a theological version of the ‘direct argument’ for the incompatibility between human moral responsibility and causal determinism. (shrink)

Heinrich Rickert (1863-1936) war einer der bedeutendsten deutschen Philosophen vor dem Zweiten Weltkrieg und gilt neben Wilhelm Windelband als einer der Hauptvertreter der südwestdeutschen Schule des Neukantianismus. Seine auch heute noch anregende Philosophie hatte großen, interdisziplinären wie internationalen Einfluss. Die philologisch-kritische Ausgabe macht die Schriften endlich wieder verfügbar.

Some Christian theorists define love in terms of benevolence, or benevolence plus some minor addition. Here I rely on a thought experiment involving a fully benevolent human, dubbed “Benevolent Billy,” to show that benevolence accounts of this kind are insufficient as a distinctly Christian account of love. This is because those who exemplify ideal Christian love for another must be intrinsically motivated to form or maintain caring, reciprocal relationships with those loved ; yet there is nothing about Billy’s perfect benevolence (...) that so motivates. (shrink)

In Analyzing Doctrine: Toward a Systematic eology, Oliver Crisp infers from a general principle concerning God’s providential care for the church that it is implausible that God would allow substantial error on the central theological promulgations of an ecumenical council. is conclusion is then used specifically against contemporary neo-monothelites, who consciously contravene the dyothelite teachings of the third Council of Constantinople. In this paper, I raise several doubts about the inference utilized by Crisp against these neo-monothelites, and I seek to (...) point to a more promising manner of upholding the deliverances of the ecumenical councils. (shrink)

Name der Zeitschrift: Neue Zeitschrift für Systematische Theologie und Religionsphilosophie Jahrgang: 58 Heft: 4 Seiten: 505-524.

In the course of defending the doctrine of universalism (the teaching that God will eventually reconcile all created persons to Himself ), the philosopher of religion Thomas Talbott has defended the logically independent claim that God loves every created person with what might be termed “supreme love”: the love that makes it so that God, without internal conflict and cessation, truly desires and seeks a created person’s supreme or highest good. Talbott’s arguments concerning God’s supreme love for all have received (...) considerably less attention than his arguments for universalism, a regrettable fact given the relative paucity of philosopher literature dealing with the nature and scope of divine love. Therefore, in this paper, I defend not universalism, but develop and defend one of Talbott’s arguments for the universal scope of God’s supreme love. (shrink)

In recent work, W. Matthews Grant challenges the common assumption that if humans have libertarian free will, and the moral responsibility it affords, then it is impossible for God to cause what humans freely do. He does this by offering a “non-competitivist” model that he calls the “Dual Sources” account of divine and human causation. Although we find Grant’s Dual Sources model to be the most compelling of models on offer for non-competitivism, we argue that it fails to circumvent a (...) theological version of Peter van Inwagen’s direct argument for incompatibilism. In the paper, we motivate and deploy a theological take on the direct argument, and we contend that this theological rendition of the direct argument effectively dismantles Grant’s Dual Sources account of non-competitivism. (shrink)

Imagination has recently attracted considerable attention from epistemologists and is recognized as a source of belief and even knowledge. One remarkable feature of imagination is that it is often and typically agentive: agents decide to imagine. In cases in which imagination results in a belief, the agentiveness of imagination may be taken to give rise to indirect doxastic control and epistemic responsibility. This observation calls for a proper understanding of agentive imagination. In particular, it calls for the development of a (...) semantics of imagination ascriptions. In the present paper an earlier suggestion by Ilkka Niiniluoto for a logic of imagination is considered. This proposal does not capture the agentive nature of imagination, and an alternative semantics is suggested. The new semantics combines the modal logic of agency with the neighbourhood semantics from alethic modal logic. (shrink)

The present monograph is a slightly revised version of my Habilitations schrift Proof-theoretic Aspects of Intensional and Non-Classical Logics, successfully defended at Leipzig University, November 1997. It collects work on proof systems for modal and constructive logics I have done over the last few years. The main concern is display logic, a certain refinement of Gentzen's sequent calculus developed by Nuel D. Belnap. This book is far from offering a comprehensive presentation of generalized sequent systems for modal logics broadly conceived. (...) The proof-theory of non-classical logics is a rapidly developing field, and even the generalizations of the ordinary notion of sequent listed in Chapter 1 can hardly be presented in great detail within a single volume. In addition to further investigating the various approaches toward generalized Gentzen systems, it is important to compare them and to discuss their relative advantages and disadvantages. An initial attempt at bringing together work on different kinds of proof systems for modal logics has been made in [188]. Another step in the same direction is [196]. Since Chapter 1 contains introductory considerations and, moreover, every remaining chapter begins with some surveying or summarizing remarks, in this preface I shall only emphasize a relation to philosophy that is important to me, register the sources of papers that have entered this book in some form or another, and acknowledge advice and support. (shrink)

Pars 1. Contemplativa -- Pars 2. Activa.

In a recent article, Mario Günther presented a conditional that is claimed to be connexive. The aim of this short discussion note is to show that Günther’s claim is not without problems.

In this paper, a family of paraconsistent propositional logics with constructive negation, constructive implication, and constructive co-implication is introduced. Although some fragments of these logics are known from the literature and although these logics emerge quite naturally, it seems that none of them has been considered so far. A relational possible worlds semantics as well as sound and complete display sequent calculi for the logics under consideration are presented.

In this paper, Graham Priest’s understanding of dialetheism, the view that there exist true contradictions, is discussed, and various kinds of metaphysical dialetheism are distinguished between. An alternative to dialetheism is presented, namely a thesis called ‘dimathematism’. It is pointed out that dimathematism enables one to escape a slippery slope argument for dialetheism that has been put forward by Priest. Moreover, dimathematism is presented as a thesis that is helpful in rejecting the claim that logic is a normative discipline.

In this paper non-normal worlds semantics is presented as a basic, general, and unifying approach to epistemic logic. The semantical framework of non-normal worlds is compared to the model theories of several logics for knowledge and belief that were recently developed in Artificial Intelligence (AI). It is shown that every model for implicit and explicit belief (Levesque), for awareness, general awareness, and local reasoning (Fagin and Halpern), and for awareness and principles (van der Hoek and Meyer) induces a non-normal worlds (...) model validating precisely the same formulas (of the language in question). (shrink)

In this paper, we shall consider the so-called cancellation view of negation and the inferential role of contradictions. We will discuss some of the problematic aspects of negation as cancellation, such as its original presentation by Richard and Valery Routley and its role in motivating connexive logic. Furthermore, we will show that the idea of inferential ineffectiveness of contradictions can be conceptually separated from the cancellation model of negation by developing a system we call qLPm, a combination of Graham Priest’s (...) minimally inconsistent Logic of Paradox with q-entailment as introduced by Grzegorz Malinowski. (shrink)

The topic of identity of proofs was put on the agenda of general (or structural) proof theory at an early stage. The relevant question is: When are the differences between two distinct proofs (understood as linguistic entities, proof figures) of one and the same formula so inessential that it is justified to identify the two proofs? The paper addresses another question: When are the differences between two distinct formulas so inessential that these formulas admit of identical proofs? The question appears (...) to be especially natural if the idea of working with more than one kind of derivations is taken seriously. If a distinction is drawn between proofs and disproofs (or refutations) as primitive entities, it is quite conceivable that a proof of one formula amounts to a disproof of another formula, and vice versa. A notion of inherited identity of derivations is introduced for derivations in a cut-free sequent system for Almukdad and Nelson’s constructive paraconsistent logic N4 with strong negation. The notion is obtained by identifying sequent rules the application of which has no effect on the identity of derivations. Then the notion of inherited identity is used to define a bilateralist notion of synonymy between formulas, which is a relation drawing more fine-grained distinctions between formulas than strong equivalence. (shrink)

In this paper we will consider the existing notions of bilateralism in the context of proof-theoretic semantics and propose, based on our understanding of bilateralism, an extension to logical multilateralism. This approach differs from what has been proposed under this name before in that we do not consider multiple speech acts as the core of such a theory but rather multiple consequence relations. We will argue that for this aim the most beneficial proof-theoretical realization is to use sequent calculi with (...) multiple sequent arrows satisfying some specific conditions, which we will lay out in this paper. We will unfold our ideas with the help of a case study in logical tetralateralism and present an extension of Almukdad and Nelson’s propositional constructive four-valued logic by unary operations of meaningfulness and nonsensicality. We will argue that in sequent calculi with multiple sequent arrows it is possible to maintain certain features that are desirable if we assume an understanding of the meaning of connectives in the spirit of proof-theoretic semantics. The use of multiple sequent arrows will be justified by the presence of congruentiality-breaking unary connectives. (shrink)

In Phenomena of Power, one of the leading figures of postwar German sociology reflects on the nature, and many forms of, power. For Heinrich Popitz, power is rooted in the human condition and is therefore part of all social relations. Drawing on philosophical anthropology, he identifies the elementary forms of power to provide detailed insight into how individuals gain and perpetuate control over others. Instead of striving for a power-free society, Popitz argues, humanity should try to impose limits on (...) power where possible and establish counterpower where necessary. Phenomena of Power delves into the sociohistorical manifestations of power and breaks through to its general structures. Popitz distinguishes the forms of the enforcement of power as well as of its stabilization and institutionalization, clearly articulating how the mechanisms of power work and how to track them in the social world. Philosophically trained, historically informed, and endowed with keen observation, Popitz uses examples ranging from the way passengers on a ship organize deck chairs to how prisoners of war share property to illustrate his theory. Long influential in German sociology, Phenomena of Power offers a challenging reworking of one of the essential concepts of the social sciences. (shrink)

This is a purely conceptual paper. It aims at presenting and putting into perspective the idea of a proof-theoretic semantics of the logical operations. The first section briefly surveys various semantic paradigms, and Section 2 focuses on one particular paradigm, namely the proof-theoretic semantics of the logical operations.

According to Suszko’s Thesis, there are but two logical values, true and false. In this paper, R. Suszko’s, G. Malinowski’s, and M. Tsuji’s analyses of logical twovaluedness are critically discussed. Another analysis is presented, which favors a notion of a logical system as encompassing possibly more than one consequence relation. [A] fundamental problem concerning many-valuedness is to know what it really is. [13, p. 281].

1. Probleme und Positionen der Wissenschaftstheorie.

This chapter is concerned with logical aspects of negation, i.e. with the role of negation in valid inferences and hence with the contribution negation makes to the truth and falsity conditions of declarative expressions. Negation is an important philosophical and logical concept. Often differences between logical systems can ‐ at least partially ‐ be described as differences between the notions of negation used in these logics.