In this paper, I will develop a set of boulesic-doxastic tableau systems and prove that they are sound and complete. Boulesic-doxastic logic consists of two main parts: a boulesic part and a doxastic part. By ‘boulesic logic’ I mean ‘the logic of the will’, and by ‘doxastic logic’ I mean ‘the logic of belief’. The first part deals with ‘boulesic’ concepts, expressions, sentences, arguments and theorems. I will concentrate on two types of boulesic expression: ‘individual x wants it to be (...) the case that’ and ‘individual x accepts that it is the case that’. The second part deals with ‘doxastic’ concepts, expressions, sentences, arguments and theorems. I will concentrate on two types of doxastic expression: ‘individual x believes that’ and ‘it is imaginable to individual x that’. Boulesic-doxastic logic investigates how these concepts are related to each other. Boulesic logic is a new kind of logic. Doxastic logic has been around for a while, but the approach to this branch of logic in this paper is new. Each system is combined with modal logic with two kinds of modal operators for historical and absolute necessity and predicate logic with necessary identity and ‘possibilist’ quantifiers. I use a kind of possible world semantics to describe the systems semantically. I also sketch out how our basic language can be extended with propositional quantifiers. All the systems developed in this paper are new. (shrink)

In this paper, I develop a new set of doxastic logical systems and I show how they can be used to solve several well-known problems in doxastic logic, for example the so-called problem of logical omniscience. According to this puzzle, the notions of knowledge and belief that are used in ordinary epistemic and doxastic symbolic systems are too idealised. Hence, those systems cannot be used to model ordinary human or human-like agents' beliefs. At best, they can describe idealised individuals. The (...) systems in this paper can be used to symbolise not only the doxastic states of perfectly rational individuals, but also the beliefs of finite humans. Proof-theoretically, I will use a tableau technique. Every system is combined with predicate logic with necessary identity and ‘possibilist’ quantifiers and modal logic with two kinds of modal operators for relative and absolute necessity. The semantics is a possible world semantics. Finally, I prove that every tableau system in the paper is sound and complete with respect to its semantics. (shrink)

The principal aim of this essay is to discuss some logical features of the so-called Classical model of cognitive architecture as it is advocated by J. Fodor and Z. Pylyshyn in their much discussed article 'Connectionism and Cognitive Architecture: A Critical Analysis'. It is pointed out that their structural assumptions have consequences of a logical kind which call into question the view that the Classical architecture (in their sense) can be employed to model human cognition. It seems that the consequences (...) have escaped Fodor and Pylyshyn's notice, or else they have failed to appreciate them, since some of their claims evidently conflict with them. It is also investigated whether the human mind can be characterized as being logical in some weaker sense of logic. Furthermore, it is argued that J. H. Fetzer's view that it is a semiotic system is more realistic than the Classical model, but the distinction he suggests between human cognition and other kinds may be problematic. (shrink)

The canonical version of possible worlds semantics for story prefixes is due to David Lewis. This paper reassesses Lewis's theory and draws attention to some novel problems for his account.

Many people hold that there is a distinctive notion of metaphysical necessity. In this paper I explain why I am skeptical about the view. I examine the sorts of considerations that are adduced for it, and argue that they meet equal and opposite considerations.

The essay introduces a non-Diodorean, non-Kantian temporal modal semantics based on part-whole, rather than class, theory. Formalizing Edmund Husserl’s theory of inner time consciousness, §3 uses his protention and retention concepts to define a relation of self-awareness on intentional events. §4 introduces a syntax and two-valued semantics for modal first-order predicate object-languages, defines semantic assignments for variables and predicates, and truth for formulae in terms of the axiomatic version of Edmund Husserl’s dependence ontology (viz. the Calculus [CU] of Urelements) introduced (...) by The Ontology of Intentionality I & II. It then uses the §3 results to define the modalities of truth, and §5 extends the semantics to identity claims. §6 defines and contrasts synthetic a priori truths to analytic a priori truths, and §7 compares Brentano School noetic semantic and Leibnizian possible-world semantic perspectives on modality. The essay argues that the modal logics it defines semantically are two-valued, first-order versions of the type of language which Husserl viewed as the language of any ontology of experience (i.e. of any science), and conceived as the logic of intentionality. (shrink)

This essay examines some of the arguments in David Deutsch's book The Fabric of Reality , chief among them its case for the so-called many-universe interpretation of quantum mechanics (QM), presented as the only physically and logically consistent solution to the QM paradoxes of wave/particle dualism, remote simultaneous interaction, the observer-induced 'collapse of the wave-packet', etc. The hypothesis assumes that all possible outcomes are realized in every such momentary 'collapse', since the observer splits off into so many parallel, coexisting, but (...) epistemically non-interaccessible 'worlds' whose subsequent branchings constitute the lifeline-or experiential world-series- for each of those proliferating centres of consciousness. Although Deutsch concedes that his 'multiverse' theory is counter-intuitive, he none the less takes it to be borne out beyond question by the sheer observational/predictive success of QM and the conceptual dilemmas that supposedly arise with alternative (single-universe) accounts. Moreover, he claims the theory resolves a range of longstanding philosophical problems, notably those of mind/body dualism, the various traditional paradoxes of time, and the freewill/determinism issue. The essay suggests on the contrary, that Deutsch unwittingly transposes into the framework of presentday quantum debate speculative themes from the history of rationalist metaphysics, often with bizarre or philosophically dubious results, and that he rules out at least one promising rival account, namely Bohm's 'hidden variables' theory. It goes on to consider reasons for resistance to that theory among proponents of the 'orthodox' (Copenhagen) doctrine, and for the strong anti-realist, at times even irrationalist bias that has characterized much of this discussion since Bohr's debates with Einstein about quantum non-locality, observer-intervention, and the limits of precise measurement. Finally, the contrast is pointed out between Deutsch's ontologically extravagant use of the many-worlds hypothesis (akin to certain ideas advanced by speculative metaphysicians from Leibniz down) and those realist modes of counterfactual reasoning- e.g. in Kripke and the early Putnam- which deploy similar arguments to very different causal-explanatory ends. (shrink)

We give complete sequent-like tableau systems for the modal logics KB, KDB, K5, and KD5. Analytic cut rules are used to obtain the completeness. Our systems have the analytic superformula property and can thus give a decision procedure. Using the systems, we prove the Craig interpolation lemma for the mentioned logics.

The concept of God is studied using the ontological argument of Anselm of Canterbury that proves God’s existence using a syllogism based on ontology. Unlike metaphysical arguments that demonstrate the existence of God through the study of being and its attributes, the ontological argument aims to reach this same goal based on a concept of God by means of the idea of an entity “greater than anything that can be conceived”. Descartes’ influence highlighted some of the philosophical difficulties with the (...) inherent dualism implicit in ontology. Logic does not say whether ideas are true or false, as Logic is concerned with right or wrong inference. We take a non-dualist approach in contrast to some of the approaches reviewed. To investigate belief and faith, a modal logical formalization is used, especially modal logic S5, which we find appropriate for presenting arguments. While mathematics and logic can convince, they do not help one to believe in God. This can make us think that reason is not enough to accept God, one must have faith to have access to Him. The relation between reason and faith needs clarification, and the ontological argument requires an unsustainable dualism. (shrink)

The axiomatic presentation of modal systems and the standard formulations of natural deduction and sequent calculus for modal logic are reviewed, together with the difficulties that emerge with these approaches. Generalizations of standard proof systems are then presented. These include, among others, display calculi, hypersequents, and labelled systems, with the latter surveyed from a closer perspective.

This is a thorough treatment of first-order modal logic. The book covers such issues as quantification, equality (including a treatment of Frege's morning star/evening star puzzle), the notion of existence, non-rigid constants and function symbols, predicate abstraction, the distinction between nonexistence and nondesignation, and definite descriptions, borrowing from both Fregean and Russellian paradigms.

The claim that truth is mind dependent has some initial plausibility only if truth bearers are taken to be mind dependent entities such as beliefs or statements. Even on that assumption, however, the claim is not uncontroversial. If it is spelled out as the thesis that “in a world devoid of mind nothing would be true”, then everything depends on how the phrase ‘true in world w’ is interpreted. If ‘A is true in w’ is interpreted as ‘A is true (...) of w’ (i.e. ‘w satisfies A’s truth conditions’, the claim need not be true. If on the other hand it is interpreted as ‘A is true of w and exists in w’ then the claim is trivially true, though devoid of any antirealistic efficacy. Philosophers like Heidegger and Rorty, who hold that truth is mind dependent but reality is not, must regard such principles as “A if and only if it is true that A” as only contingently true, which may be a good reason to reject the mind dependence of truth anyway. (shrink)

The paper presents a formal explication of the early Wittgenstein's views on ontology, the syntax and semantics of an ideal logical language, and the propositional attitudes. It will be shown that Wittgenstein gave a language of thought analysis of propositional attitude ascriptions, and that his ontological views imply that such ascriptions are truth-functions of (and supervenient upon) elementary sentences. Finally, an axiomatization of a quantified doxastic modal logic corresponding to Tractarian semantics will be given.

The aim of this paper is to present the method of Socratic proofs for seven modal propositional logics: K5, S4.2, S4.3, S4M, S4F, S4R and G. This work is an extension of [10] where the method was presented for the most common modal propositional logics: K, D, T, KB, K4, S4 and S5.

The aim of this paper is to present a loop-free decision procedure for modal propositional logics K4, S4 and S5. We prove that the procedure terminates and that it is sound and complete. The procedure is based on the method of Socratic proofs for modal logics, which is grounded in the logic of questions IEL.

The aim of this paper is to present a loop-free decision procedure for modal propositional logics K4, S4 and S5. We prove that the procedure terminates and that it is sound and complete. The procedure is based on the method of Socratic proofs for modal logics, which is grounded in the logic of questions IEL.

I argue that common nouns should be analyzed as variables, rather than as predicates which take variables as arguments. This necessitates several unusual features to the analysis, such as allowing variables to be modally non-rigid, and assigning their values compositionally. However, treating common nouns as variables offers a variety of theoretical and empirical advantages over a more traditional analysis: It predicts the conservativity of nominal quantification, simplifies the analysis of articleless languages, derives the weak reading of sentences with donkey anaphora, (...) solves the proportion problem presented by quantifiers like ‘most’, improves the analysis of the temperature paradox, allows a more unified analysis of bare plurals, and regularizes the correspondence between syntactic categories and semantic types. (shrink)

The situation calculus is one of the most established formalisms for reasoning about action and change. In this paper we will review the basics of Reiter’s version of the situation calculus, show how knowledge and time have been addressed in this framework, and point to some of the weaknesses of the situation calculus with respect to time. We then present a modal version of the situation calculus where these problems can be overcome with relative ease and without sacrificing the advantages (...) of the original. (shrink)

This paper contributes to the principled construction of tableau-based decision procedures for hybrid logic with global, difference, and converse modalities. We also consider reflexive and transitive relations. For converse-free formulas we present a terminating control that does not rely on the usual chain-based blocking scheme. Our tableau systems are based on a new model existence theorem.

We give a reading of binary necessity statements of the form “ϕ is necessary for ψ” in terms of proofs. This reading is based on the idea of interpreting such statements as “Every proof of ψ uses ϕ”.

This essay contains material which will hopefully be of interest not only to philosophers, but also to those social scientists whose research concerns the analysis of communication, verbal or non-verbal. Although most of the topics taken up here are central to issues in the philosophy of language, they are, in my opinion, indistinguishable from topics in descriptive social psychology. The essay aims to provide a conceptual framework within which various key aspects of communication can be described, and it presents a (...) formal language, using techniques from modern modal logic, in which such descriptions can themselves be formulated. It is my hope that this framework, or parts of it, might also turn out to be of value in future empirical work. There are, therefore, essentially two sides to this essay: the development of a framework of concepts, and the construction of a formal language rich enough to express the elements of which that framework is composed. The first of these two takes its point of departure in the statement quoted from Lewis (1972) on the page preceding this introduction. The distinction drawn there by Lewis is accepted as a working hypothesis, and in one sense this essay may be seen as an attempt to explore some of the consequences of that hypothesis. (shrink)

Biological modalities (e.g., biological possibility, necessity and counterfactuality) play an important explanatory role in biological practice. However, biological modalities lack truth conditions and the inferential relationship between biological and other modalities is unclear. This thesis addresses these problems, first, by improving upon Daniel Dennett's Library of Mendel. Second, a family of modal logics is introduced. In the simplest model, states are interpreted as codons, the binary relation is interpreted as single substitution mutation and the valuation induces a partition of blocks (...) of codons that code for some amino acid. In addition, the proposed framework allows for a grading of biological possibility and captures various competing notions of biological possibility. Applications include a model checker and a lawless Lewis-style semantics for biological counterfactuals. In short, this thesis lays the groundwork for a theory of biological modalities. (shrink)

Gentzen’s and Jaśkowski’s formulations of natural deduction are logically equivalent in the normal sense of those words. However, Gentzen’s formulation more straightforwardly lends itself both to a normalization theorem and to a theory of “meaning” for connectives . The present paper investigates cases where Jaskowski’s formulation seems better suited. These cases range from the phenomenology and epistemology of proof construction to the ways to incorporate novel logical connectives into the language. We close with a demonstration of this latter aspect by (...) considering a Sheffer function for intuitionistic logic. (shrink)

In 1880, when Oliver Wendell Holmes (later to be a Justice of the U.S. Supreme Court) criticized the logical theology of law articulated by Christopher Columbus Langdell (the first Dean of Harvard Law School), neither Holmes nor Langdell was aware of the revolution in logic that had begun, the year before, with Frege's Begriffsschrift. But there is an important element of truth in Holmes's insistence that a legal system cannot be adequately understood as a system of axioms and corollaries; and (...) this element of truth is not obviated by the more powerful logical techniques that are now available. (shrink)

The Hooded Man Paradox of Eubulides concerns the apparent failure of the substitutivity of identicals in epistemic (and other intentional) contexts. This paper formulates a number of different versions of the paradox and shows how these may be solved using semantics for quantified epistemic logic. In particular, two semantics are given which invalidate substitution, even when rigid designators are involved.

We show that if an agent reasons according to standard inference rules, the truth and introspection axioms extend from the set of non-epistemic propositions to the whole set of propositions. This implies that the usual axiomatization of partitional possibility correspondences is redundant, and provides a justification for truth and introspection that is partly based on reasoning.

Of late, evidentiality has received great attention in formal semantics. In this paper I develop ‘evidentiality-informed’ truth conditions for modal operators such as must and may . With language data drawn from Luoping Nase (a Tibeto-Burman language spoken in the P.R. of China and belonging to the Yi Nationality), I illustrate that epistemic modals clash with clauses articulating first-hand information. I then demonstrate that existing models such as Kratzer’s graded possible-worlds semantics fail to provide accurate truth conditions for modals tagging (...) clauses with first-hand information. As a remedy I propose a fuzzy version of possible-worlds semantics with various grades of belief and knowledge. In addition to preserving the expressive power of graded possible-worlds semantics, the fuzzy model will be shown to supply appropriate truth conditions for epistemic modals appended to evidential clauses (i.e. clauses expressing first-hand information). (shrink)

ukasiewicz''s four-valued modal logic is surveyed and analyzed, together with ukasiewicz''s motivations to develop it. A faithful interpretation of it in classical (non-modal) two-valued logic is presented, and some consequences are drawn concerning its classification and its algebraic behaviour. Some counter-intuitive aspects of this logic are discussed in the light of the presented results, ukasiewicz''s own texts, and related literature.

In [8] it is proved that all the intermediate logics axiomatizable by formulas in one variable, except four of them, are not strongly complete. We considerably improve this result by showing that all the intermediate logics axiomatizable by formulas in one variable, except eight of them, are not strongly ω-complete. Thus, a definitive classification of such logics with respect to the notions of canonicity, strong completeness, ω-canonicity and strong ω-completeness is given.

We introduce a methodology whereby an arbitrary logic system L can be enriched with temporal features to create a new system T(L). The new system is constructed by combining L with a pure propositional temporal logic T (such as linear temporal logic with Since and Until) in a special way. We refer to this method as adding a temporal dimension to L or just temporalising L. We show that the logic system T(L) preserves several properties of the original temporal logic (...) like soundness, completeness, decidability, conservativeness and separation over linear flows of time. We then focus on the temporalisation of first-order logic, and a comparison is make with other first-order approaches to the handling of time. (shrink)

In the first two sections I present and motivate a formal semantics program that is modeled after the application of numbers in measurement (e.g., of length). Then, in the main part of the paper, I use the suggested framework to give an account of the semantics of necessity and possibility: (i) I show thatthe measurement theoretic framework is consistent with a robust (non-Quinean) view of modal logic, (ii) I give an account of the semantics of the modal notions within this (...) framework, and (iii) I defend the suggested account against various objections. (shrink)

This book is both an introduction to and a research work on Meinongianism. “Meinongianism” is taken here, in accordance with the common philosophical jargon, as a general label for a set of theories of existence – probably the most basic notion of ontology. As an introduction, the book provides the first comprehensive survey and guide to Meinongianism and non-standard theories of existence in all their main forms. As a research work, the book exposes and develops the most up-to-date Meinongian theory (...) (called modal Meinongianism), applies it to specific fields, and discusses its open problems. Part I of the book provides a historical introduction to, and critical discussion of, the dominant philosophical view of existence: the “Kantian-Fregean-Quinean” perspective. Part II is the full-fledged introduction to the Meinongian theories of existence as a real property of individuals: after starting with the so-called naïve Meinongian conception and its problems, it provides a self-contained presentation of the main neo-Meinongian proposals, and a detailed discussion of their strengths and weaknesses. Part III develops a specific neo-Meinongian theory of existence employing a model-theoretic semantic framework. It discusses its application to the ontology and semantics of fictional objects, and its open problems. The methodology of the book follows the most recent trends in analytic ontology. In particular, the meta-ontological point of view is largely privileged. (shrink)

When the original Dutch version of this book was presented in 1971 to the University of Leiden as a thesis for the Doctorate in philosophy, I was prevented by the academic mores of that university from expressing my sincere thanks to three members of the Philosophical Faculty for their support of and interest in my pursuits. I take the liberty of doing so now, two and a half years later. First and foremost I want to thank Professor G. Nuchelmans warmly (...) for his expert guidance of my research. A number of my most im portant sources were brought to my attention by him. During the whole process of composing this book his criticism and encouragement were carried out in a truly academic spirit. He thereby provided working conditions that are a sine qua non for every author who is attempting to approach controversial matters in a scientific manner, conditions which, however, were not easily available at that time. In a later phase I also came into contact with Professors L. M. de Rijk and J. B. Ubbink, with both of whom I had highly stimulating discussions and exchanges of ideas. The present edition contains some entirely new sections, viz. 1-9, IV-29, V-9, V-20, VII-14 (iii), (iv), VII-17 (i), VIII-22, IX-17, IX-19, X-9 and XI-8. Section X-9 was inspired by a remark made by Professor A. (shrink)

Planlama --- bir amaca ulaşmak üzere bir aksiyonlar bütünü tasarlamak --- yapay zekadaki en temel problemlerden biridir. Bu yazıda, robotikte planlama konusuna mantıkçı (logicist) yaklaşım ele alınmaktadır. [Planning --- devising a plan of action to reach a given goal --- is a fundamental problem in AI. This paper reviews the logicist approach to planning in robotics.].

Tras una breve presentación / explicación de la noción de similaridad intermundana que se utiliza en lógica condicional, se explican cuatro nociones intuitivas, pre-teóricas, de similaridad, así como las implicaciones formales que posee su adopción como correlato informal para la noción técnica de similaridad entre mundos: parecido entre objetos, magnitud del cambio, semejanza estructural, y probabilidad / posibilidad de eventos. Por ultimo, se retoman dos problemas tradicionales de la lógica condicional a la luz de los conceptos recién definidos: la asunción (...) de unicidad (vinculada al tercio excluso condicional), y el principio de comparabilidad (vinculada al principio de monotonía racional). (shrink)

This paper explores early Australasian philosophy in some detail. Two approaches have dominated Western philosophy in Australia: idealism and materialism. Idealism was prevalent between the 1880s and the 1930s, but dissipated thereafter. Idealism in Australia often reflected Kantian themes, but it also reflected the revival of interest in Hegel through the work of ‘absolute idealists’ such as T. H. Green, F. H. Bradley, and Henry Jones. A number of the early New Zealand philosophers were also educated in the idealist tradition (...) and were influential in their communities, but produced relatively little. In Australia, materialism gained prominence through the work of John Anderson, who arrived in Australia in 1927, and continues to be influential. John Anderson had been a student of Henry Jones, who might therefore be said to have influenced both main strands of Australian philosophical thought. (shrink)