This paper is concerned with a natural deduction system for First Degree Entailment (FDE). First, we exhibit a brief history of FDE and of combined systems whose underlying idea is used in developing the natural deduction system. Then, after presenting the language and a semantics of FDE, we develop a natural deduction system for FDE. We then prove soundness and completeness of the system with respect to the semantics. The system neatly represents the four-valued semantics for FDE.
Individualists claim that collective obligations are reducible to the individual obligations of the collective’s members. Collectivists deny this. We set out to discover who is right by way of a deontic logic of collective action that models collective actions, abilities, obligations, and their interrelations. On the basis of our formal analysis, we argue that when assessing the obligations of an individual agent, we need to distinguish individual obligations from member obligations. If a collective has a collective obligation to bring about (...) a particular state of affairs, then it might be that no individual in the collective has an individual obligation to bring about that state of affairs. What follows from a collective obligation is that each member of the collective has a member obligation to help ensure that the collective fulfills its collective obligation. In conclusion, we argue that our formal analysis supports collectivism. (shrink)
I apply Kooi and Tamminga's (2012) idea of correspondence analysis for many-valued logics to strong three-valued logic (K3). First, I characterize each possible single entry in the truth-table of a unary or a binary truth-functional operator that could be added to K3 by a basic inference scheme. Second, I define a class of natural deduction systems on the basis of these characterizing basic inference schemes and a natural deduction system for K3. Third, I show that each of the resulting (...) natural deduction systems is sound and complete with respect to its particular semantics. Among other things, I thus obtain a new proof system for Lukasiewicz's three-valued logic. (shrink)
If group members aim to fulfill a collective obligation, they must act in such a way that the composition of their individual actions amounts to a group action that fulfills the collective obligation. We study a strong sense of joint action in which the members of a group design and then publicly adopt a group plan that coordinates the individual actions of the group members. We characterize the conditions under which a group plan successfully coordinates the group members' individual actions, (...) and study how the public adoption of a plan changes the context in which individual agents make a decision about what to do. (shrink)
We use a deontic logic of collective agency to study reducibility questions about collective agency and collective obligations. The logic that is at the basis of our study is a multi-modal logic in the tradition of *stit* logics of agency. Our full formal language has constants for collective and individual deontic admissibility, modalities for collective and individual agency, and modalities for collective and individual obligations. We classify its twenty-seven sublanguages in terms of their expressive power. This classification enables us to (...) investigate reducibility relations between collective deontic admissibility, collective agency, and collective obligations, on the one hand, and individual deontic admissibility, individual agency, and individual obligations, on the other. (shrink)
We develop a multi-agent deontic action logic to study the logical behaviour of two types of deontic conditionals: (1) conditional obligations, having the form "If group H were to perform action aH, then, in group F's interest, group G ought to perform action aG" and (2) conditional permissions, having the form "If group H were to perform action aH, then, in group F's interest, group G may perform action aG". First, we define a formal language for multi-agent deontic action logic (...) and a class of consequentialist models to interpret the formulas of the language. Second, we define a transformation that converts any strategic game into a consequentialist model. Third, we show that an outcome a* is a Nash equilibrium of a strategic game if and only if a conjunction of certain conditional permissions is true in the consequentialist model that results from the transformation of that strategic game. (shrink)
Quine's holistic empiricist account of scientific inquiry can be characterized by three constitutive principles: *noncontradiction*, *universal revisability* and *pragmatic ordering*. We show that these constitutive principles cannot be regarded as statements within a holistic empiricist's scientific theory of the world. This claim is a corollary of our refutation of Katz's [1998, 2002] argument that holistic empiricism suffers from what he calls the Revisability Paradox. According to Katz, Quine's empiricism is incoherent because its constitutive principles cannot themselves be rationally revised. Using (...) Gärdenfors and Makinson's logic of belief revision based on epistemic entrenchment, we argue that Katz wrongly assumes that the constitutive principles are *statements* within a holistic empiricist's theory of the world. Instead, we show that constitutive principles are best seen as *properties* of a holistic empiricist's theory of scientific inquiry and we submit that, without Katz's mistaken assumption, the paradox cannot be formulated. We argue that our perspective on the status of constitutive principles is perfectly in line with Quinean orthodoxy. In conclusion, we compare our findings with van Fraassen's  argument that we should think of empiricism as a stance, rather than as a doctrine. (shrink)
We present a theory that copes with the dynamics of inconsistent information. A method is set forth to represent possibly inconsistent information by a finite state. Next, finite operations for expansion and contraction of finite states are given. No extra-logical element — a choice function or an ordering over (sets of) sentences — is presupposed in the definition of contraction. Moreover, expansion and contraction are each other's duals. AGM-style characterizations of these operations follow.
Taking our inspiration from modal correspondence theory, we present the idea of correspondence analysis for many-valued logics. As a benchmark case, we study truth-functional extensions of the Logic of Paradox (LP). First, we characterize each of the possible truth table entries for unary and binary operators that could be added to LP by an inference scheme. Second, we define a class of natural deduction systems on the basis of these characterizing inference schemes and a natural deduction system for LP. Third, (...) we show that each of the resulting natural deduction systems is sound and complete with respect to its particular semantics. (shrink)
This paper presents two systems of natural deduction for the rejection of non-tautologies of classical propositional logic. The first system is sound and complete with respect to the body of all non-tautologies, the second system is sound and complete with respect to the body of all contradictions. The second system is a subsystem of the first. Starting with Jan Łukasiewicz's work, we describe the historical development of theories of rejection for classical propositional logic. Subsequently, we present the two systems of (...) natural deduction and prove them to be sound and complete. We conclude with a ‘Theorem of Inversion’. (shrink)
Two groups of agents, G1 and G2, face a *moral conflict* if G1 has a moral obligation and G2 has a moral obligation, such that these obligations cannot both be fulfilled. We study moral conflicts using a multi-agent deontic logic devised to represent reasoning about sentences like "In the interest of group F of agents, group G of agents ought to see to it that phi". We provide a formal language and a consequentialist semantics. An illustration of our semantics with (...) an analysis of the Prisoner’s Dilemma follows. Next, necessary and sufficient conditions are given for (1) the possibility that a single group of agents faces a moral conflict, for (2) the possibility that two groups of agents face a moral conflict within a single moral code, and for (3) the possibility that two groups of agents face a moral conflict. (shrink)
Every truth-functional three-valued propositional logic can be conservatively translated into the modal logic S5. We prove this claim constructively in two steps. First, we define a Translation Manual that converts any propositional formula of any three-valued logic into a modal formula. Second, we show that for every S5-model there is an equivalent three-valued valuation and vice versa. In general, our Translation Manual gives rise to translations that are exponentially longer than their originals. This fact raises the question whether there are (...) three-valued logics for which there is a shorter translation into S5. The answer is affirmative: we present an elegant linear translation of the Logic of Paradox and of Strong Three-valued Logic into S5. (shrink)
In the 1930s, Carnap set out to incorporate psychology into the unity of science, by showing that all cognitively meaningful sentences of psychology can be translated into the language of physics. I will argue that Carnap, relying on his notion of protocol languages, defends a physicalistic philosophy of psychology that shows due appreciation to 'introspection' as a strictly subjective, but reliable way to verify sentences about one’s own mind. Second, I will point out that Carnap’s philosophy of psychology not only (...) takes into account overt behaviour, but must comprise neurophysiological processes as well. Last, I will show that Carnap aims to develop a philosophy of psychology that does justice to the ongoing changeability of scientific knowledge. (shrink)
C.S. Peirce's and Isaac Levi's accounts of the belief-doubt-belief model are discussed and evaluated. It is argued that the contemporary study of belief change has metamorphosed into a branch of philosophical logic where empirical considerations have become obsolete. A case is made for reformulations of belief change systems that do allow for empirical tests. Last, a belief change system is presented that (1) uses finite representations of information, (2) can adequately deal with inconsistencies, (3) has finite operations of change, (4) (...) can do without extra-logical elements, and (5) only licenses consistent beliefs. (shrink)
The branch of philosophical logic which has become known as “belief change” has, in the course of its development, become alienated from its epistemological origins. However, as formal criteria do not suffice to defend a principled choice between competing systems for belief change, we do need to take their epistemological embedding into account. Here, on the basis of a detailed examination of Isaac Levi's epistemology, we argue for a new direction of belief change research and propose to construct systems for (...) belief change that can do without, but do not rule out, selection functions, in order to enable an *empirical* assessment of the relative merits of competing belief change systems. (shrink)
In the 1930s, several members of the Vienna Circle set out to incorporate psychology in the unity of science, by showing that all cognitively significant sentences of psychology can be translated into the language of physics. This epistemological analysis of psychology has become known as logical behaviourism. Carnap was the first logical empiricist to expound this programme in considerable detail. Relying on his particular notion of protocol languages, Carnap develops a view on the philosophy of psychology that not only is (...) thoroughly physicalistic, but also shows due appreciation to 'introspection' as a purely subjective, but reliable way to verify sentences about one's own mind. Second, contrary to the received view on logical behaviourism, Carnap's philosophy of psychology not only takes into account overt behaviour, but micro-physiological processes as well. Last, Carnap's physicalistic philosophy of mind couples full awareness of the changeability of scientific knowledge with the aspiration to develop a philosophy of psychology that really does justice to this changeability. (shrink)
We investigate the genesis of metaphysical physicalism and its influence on the development of Place's, Smart's, and Armstrong's ideas on the relation between the mental and the physical. We first reconstruct the considerations that led Armstrong and Smart to a 'scientific' world view. We call 'metaphysical physicalism' the comprehensive theory on reality, truth, and meaning which ensued from this world view. Against the background of this metaphysical physicalism we study Armstrong's and Smart's analyses of secondary properties and the genesis of (...) their identity theories of mind and matter. We argue that fundamental revisions in Smart's theories on colour and consciousness were driven by his aspiration to fully work out the philosophical consequences of metaphysical physicalism. Finally, we briefly consider the role metaphysical physicalism has played in twentieth-century philosophy of mind. (shrink)
Levi, setting out to formalize Peirce's and Dewey's *belief-doubt-belief*-model, took the lead in defining the field of philosophical logic that has become known as *belief change*. First, Levi's theory of knowledge is placed within the context of American pragmatism. A discussion follows of Levi's criteria under which a change of belief must be judged an improvement. In the final section, a critical evaluation of Levi's logical epistemology opens new venues for logical and epistemological inquiry.
In order to come to grips with Peirce's definition of truth as the ideal limit of inquiry, I give a succinct exposition of Peirce's theory of inquiry and his philosophical logic, paying attention to several types of reasoning and their interrelations. Subsequently, the arguments of a contemporary apologist of Peirce's notion of truth, C.J. Misak, are subjected to a scrutiny and found to be insufficient, as the principle of bivalence is defended improperly and, as a Peircean definition of truth, turns (...) out to be incompatible with a pragmatist epistemology. (shrink)
Methodological individualists often claim that any social phenomenon can ultimately be explained in terms of the actions and interactions of individuals. Any Nagelian version of methodological individualism requires that there be bridge laws that translate social statements into individualistic ones. We show that Nagelian individualism can be put to logical scrutiny by making the relevant social and individualistic languages fully explicit and mathematically precise. In particular, we prove that the social statement that a group of agents performs a deontically admissible (...) group action cannot be expressed in a well-established deontic logic of agency that models every combination of actions, omissions, abilities, and obligations of finitely many individual agents. (shrink)
The biennial DEON conferences are designed to promote interdisciplinary cooperation amongst scholars interested in linking the formal-logical study of normative concepts and normative systems with computer science, artificial intelligence, linguistics, philosophy, organization theory and law. In addition to these general themes, DEON 2016 encouraged a special focus on the topic "Reasons, Argumentation and Justification.".
Investigations into inter-level relations in computer science, biology and psychology call for an *empirical* turn in the philosophy of mind. Rather than concentrate on *a priori* discussions of inter-level relations between 'completed' sciences, a case is made for the actual study of the way inter-level relations grow out of the developing sciences. Thus, philosophical inquiries will be made more relevant to the sciences, and, more importantly, philosophical accounts of inter-level relations will be testable by confronting them with what really happens (...) in science. Hence, close observation of the ever-changing reduction relations in the developing sciences, and revision of philosophical positions based on these empirical observations, may, in the long run, be more conducive to an adequate understanding of inter-level relations than a traditional *a priori* approach. (shrink)
In this article, we consider similarities and differences in emotion research on older adults and individuals with bipolar disorder (BD). Recent research and theory within both areas has focused on the importance of positive emotion, but the case of older adults is generally considered a case of “adaptive” positivity whereas BD is usually considered maladaptive positivity. We explore the paradox of the same phenomenon being labeled as adaptive in one group and yet maladaptive in another, with attention to commonalities and (...) distinctions between these two groups. We identify only limited areas of overlap, and suggest a refinement of models of positive emotionality in the two populations. (shrink)
ABSTRACTIn this paper, we present a generalisation of proof simulation procedures for Frege systems by Bonet and Buss to some logics for which the deduction theorem does not hold. In particular, we study the case of finite-valued Łukasiewicz logics. To this end, we provide proof systems and which augment Avron's Frege system HŁuk with nested and general versions of the disjunction elimination rule, respectively. For these systems, we provide upper bounds on speed-ups w.r.t. both the number of steps in proofs (...) and the length of proofs. We also consider Tamminga's natural deduction and Avron's hypersequent calculus GŁuk for 3-valued Łukasiewicz logic and generalise our results considering the disjunction elimination rule to all finite-valued Łukasiewicz logics. (shrink)
The papers which constitute this volume, and which were first presented at a Conference in 1978 at the Catholic University of America, are arranged chronologically according to the five periods in which Neoplatonism confronted Christianity: Patristic, Later Greek and Byzantine, Medieval Latin, Renaissance, and Modern. Its editor suggests, in his valuable "Introduction", that the papers fall also into three groups in line with their contents. The first group concerns Christian thinkers who knew and used specific Neoplatonic texts and includes the (...) following: H. D. Saffrey, "New Objective Links Between the Pseudo-Dionysius and Proclus"; J. Dillon, "Origen's Doctrine of the Trinity and Some Later Neoplatonic Theories"; J. Pépin, "The Platonic and Christian Ulysses"; M. T. Clark, "A Neoplatonic Commentary on the Christian Trinity: Marius Victorinus"; J. O'Meara, "The Neoplatonism of Saint Augustine"; G. H. Allard, "The Primacy of Existence in the Thought of Eriugena"; C. Fabro, "The Overcoming of the Neoplatonic Triad of Being, Life and Intellect by Thomas Aquinas"; B. McGinn, "Meister Echkart on God as Absolute Unity"; E. Bieman, "Triads and Trinity in the Poetry of Robert Browning"; M. Rose, "The Christian Platonism of C. S. Lewis, J. R. R. Tolkien and Charles Williams.". (shrink)
A key argument of Dixon et al. in the target article is that prejudice reduction through intergroup contact and collective action work in opposite ways. We argue for a complementary approach focusing on extreme emotions to understand why people turn to non-normative collective action and to understand when and under what conditions extreme emotions may influence positive effects of contact on reconciliation.
This book is a major contribution to the study of the philosopher F. H. Bradley, the most influential member of the nineteenth-century school of British Idealists. It offers a sustained interpretation of Bradley's Principles of Logic, explaining the problem of how it is possible for inferences to be both valid and yet have conclusions that contain new information. The author then describes how this solution provides a basis for Bradley's metaphysical view that reality is one interconnected experience and how this (...) gives rise to a new problem of truth. (shrink)
Using as a springboard a three-way debate between theoretical physicist Lee Smolin, philosopher of science Nancy Cartwright and myself, I address in layman’s terms the issues of why we need a unified theory of the fundamental interactions and why, in my opinion, string and M-theory currently offer the best hope. The focus will be on responding more generally to the various criticisms. I also describe the diverse application of string/M-theory techniques to other branches of physics and mathematics which render the (...) whole enterprise worthwhile whether or not “a theory of everything” is forthcoming. (shrink)