Allard Tamminga

We present a method that generates two-sided sequent calculi for four-valued logics like "first degree entailment" (FDE). (We say that a logic is FDE-like if it has finitely many operators of finite arity, including negation, and if all of its operators are truth-functional over the four truth-values 'none', 'false', 'true', and 'both', where 'true' and 'both' are designated.) First, we show that for every n-ary operator * every truth table entry f*(x1,...,xn) = y can be characterized in terms of a pair of sequent rules. Secondly, we use these sequent rules to build sequent calculi and prove their completeness. With the help of two simplification procedures we then show that the 2⋅4^n sequent rules that characterize an n-ary operator can be systematically reduced to at most four sequent rules. Thirdly, we use our method to investigate the proof-theoretical consequences of including intuitive truth-functional implications in FDE-like logics.

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 (at least two) 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.

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.

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.

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 [2002] argument that we should think of empiricism as a stance, rather than as a doctrine.

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.

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.

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.

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.

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’.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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