Justified belief is a core concept in epistemology and there has been an increasing interest in its logic over the last years. While many logical investigations consider justified belief as an operator, in this paper, we propose a logic for justified belief in which the relevant notion is treated as a predicate instead. Although this gives rise to the possibility of liar-like paradoxes, a predicate treatment allows for a rich and highly expressive framework, which lives up (...) to the universal ambitions of investigating epistemological concepts. We start with a base theory for justified belief, and then systematically present putative additional axioms for justified belief. We provide an overview of consistency results when the additional principles are added to the base theory, and discuss their philosophical plausibility. (shrink)

We present a complete, decidable logic for reasoning about a notion of completely trustworthy evidence and its relations to justifiable belief and knowledge, as well as to their explicit justifications. This logic makes use of a number of evidence-related notions such as availability, admissibility, and “goodness” of a piece of evidence, and is based on an innovative modification of the Fitting semantics for Artemovʼs Justification Logic designed to preempt Gettier-type counterexamples. We combine this with ideas from belief revision (...) and awareness logics to provide an account for explicitly justified knowledge based on conclusive evidence that addresses the problem of omniscience. (shrink)

Accuracy in the philosophical theory of rationality demands that we recognize particular beliefs as arising within the context of larger units, the cultural or conceptual schemes, patterns, or practices, involvement in which itself provides standards and grounds for their rational evaluation. At the same time, though, a satisfactory account of rationality cannot hold the standards, values, or commitments of one particular culture, practice, or conceptual scheme, even one’s own, immune from rational criticism. In order to accurately and responsibly picture the (...) shape of our commitments and the dynamics of their revision over time, in other words, the theory of rationality must reconcile the immanence of reason to particular cultural and conceptual units with its transcendence of them. This raises a deep and far-ranging problem of perspective. In his perspicuous presentation of it, Hilary Putnam put the problem this way: There are two points that must be balanced, both points that have been made by philosophers of many different kinds: (1) talk of what is ‘right’ and ‘wrong’ in any area only makes sense against the background of an inherited tradition; but (2) traditions themselves can be criticized … On the one hand, there is no notion of reasonableness at all without cultures, practices, procedures; on the other hand, the cultures, practices, procedures we inherit are not an algorithm to be slavishly followed. As Mill said, commenting on his own inductive logic, there is no rule book which will not lead to terrible results ‘if supposed to be conjoined with universal idiocy.’ Reason is, in this sense, both immanent (not to be found outside of concrete language games and institutions) and transcendent (a regulative idea that we use to criticize the conduct of all activities and institutions). (p. 431). As Putnam argues, it is difficult to find a standpoint of theory from which the contrasting claims of immanence and transcendence can be reconciled.. (shrink)

This essay presents a philosophical and computational theory of the representation of de re, de dicto, nested, and quasi-indexical belief reports expressed in natural language. The propositional Semantic Network Processing System (SNePS) is used for representing and reasoning about these reports. In particular, quasi-indicators (indexical expressions occurring in intentional contexts and representing uses of indicators by another speaker) pose problems for natural-language representation and reasoning systems, because--unlike pure indicators--they cannot be replaced by coreferential NPs without changing the meaning of (...) the embedding sentence. Therefore, the referent of the quasi-indicator must be represented in such a way that no invalid coreferential claims are entailed. The importance of quasi-indicators is discussed, and it is shown that all four of the above categories of belief reports can be handled by a single representational technique using belief spaces containing intensional entities. Inference rules and belief-revision techniques for the system are also examined. (shrink)

The aim of this paper is to show the unity and consistency of Kant’s reflections throughout all three sections of the Canon of Pure Reason. More specifically, I argue that Section 3, which is devoted to the issue of Fürwahrhalten, or taking-to-be-true, is crucial to achieving the methodological goal of the Canon, which is to justify the legitimacy of the speculative assumptions of pure reason. After examining the historical roots of Kant’s notion of a transcendental doctrine of method, I focus (...) on the methodological role that the practical element plays in the first two sections of the Canon. I then show how the limitations of Kant’s argument necessitate the introduction of a third crucial section, which serves both an analytic and an orientative function. (shrink)

This essay presents a philosophical and computationol theory of the representation of de re, de dlcto, nested, and quasi-indexical belief reports expressed in natural language. The propositional Semantic Network Processing System (SNePS) is used for representing and reasoning about these reports. In particular, quasi-indicators (indexical expressions occurring in intentional contexts and representing uses of indicators by another speaker) pose problems for natural language representation and reasoning systems, because--unlike pure indicators --they cannot be replaced by coreferential NPs without changing the (...) meaning of the embedding sentence. Therefore, the referent of the quasi-indicator must be represented in such a way that no invalid coreferential claims are entailed. The importance of quasi-indicators is discussed, and it is shown that all four of the above categories of belief reports can be handled by a single representational technique using belief spaces containing intensional entities. Inference rules and belief-revision techniques for the system are also examined. (shrink)

In Pure Inductive Logic, the rational principle of Predicate Exchangeability states that permuting the predicates in a given language L and replacing each occurrence of a predicate in an L-sentence phi according to this permutation should not change our belief in the truth of phi. In this paper we study when a prior probability function w on a purely unary language L satisfying Predicate Exchangeability also satisfies the principle of Unary Language Invariance.

Coherentism in epistemology has long suffered from lack of formal and quantitative explication of the notion of coherence. One might hope that probabilistic accounts of coherence such as those proposed by Lewis, Shogenji, Olsson, Fitelson, and Bovens and Hartmann will finally help solve this problem. This paper shows, however, that those accounts have a serious common problem: the problem of belief individuation. The coherence degree that each of the accounts assigns to an information set (or the verdict it gives (...) as to whether the set is coherent tout court) depends on how beliefs (or propositions) that represent the set are individuated. Indeed, logically equivalent belief sets that represent the same information set can be given drastically different degrees of coherence. This feature clashes with our natural and reasonable expectation that the coherence degree of a belief set does not change unless the believer adds essentially new information to the set or drops old information from it; or, to put it simply, that the believer cannot raise or lower the degree of coherence by purely logical reasoning. None of the accounts in question can adequately deal with coherence once logical inferences get into the picture. Toward the end of the paper, another notion of coherence that takes into account not only the contents but also the origins (or sources) of the relevant beliefs is considered. It is argued that this notion of coherence is of dubious significance, and that it does not help solve the problem of belief individuation. (shrink)

Logicians treat assertions as true, believed or merely hypothesized sentences. The reasoner who uses them, however, is the sole referee who can validate their truth, their aptness to describe an actual situation, their strength (as beliefs) or the relevance of their use in the current logical context. Moreover, the reasoner actively counts on these factors, as part of the reasoning process itself, and should normally be capable, when asked to do so, to assign consistently relative strengths to the assertions (...) used. The paper assumes, first, that assertions have -each- an associated, measurable strength, and that, second, this strength has significant -and measurable- effects on the truth of the sentences, the validity of the conclusion and the soundness of the reasoning. The concepts and formulas required for this are explored, and a semantics and proof theory for a sentential calculus of assertions are proposed as a natural extension of ordinary two-valued reasoning. The resulting theory, though reminiscent of Probability,is autonomous, self-contained and of a purely logical nature. (shrink)

Modal logics, originally conceived in philosophy, have recently found many applications in computer science, artificial intelligence, the foundations of mathematics, linguistics and other disciplines. Celebrated for their good computational behaviour, modal logics are used as effective formalisms for talking about time, space, knowledge, beliefs, actions, obligations, provability, etc. However, the nice computational properties can drastically change if we combine some of these formalisms into a many-dimensional system, say, to reason about knowledge bases developing in time or moving objects. To study (...) the computational behaviour of many-dimensional modal logics is the main aim of this book. On the one hand, it is concerned with providing a solid mathematical foundation for this discipline, while on the other hand, it shows that many seemingly different applied many-dimensional systems (e.g., multi-agent systems, description logics with epistemic, temporal and dynamic operators, spatio-temporal logics, etc.) fit in perfectly with this theoretical framework, and so their computational behaviour can be analyzed using the developed machinery. We start with concrete examples of applied one- and many-dimensional modal logics such as temporal, epistemic, dynamic, description, spatial logics, and various combinations of these. Then we develop a mathematical theory for handling a spectrum of 'abstract' combinations of modal logics - fusions and products of modal logics, fragments of first-order modal and temporal logics - focusing on three major problems: decidability, axiomatizability, and computational complexity. Besides the standard methods of modal logic, the technical toolkit includes the method of quasimodels, mosaics, tilings, reductions to monadic second-order logic, algebraic logic techniques. Finally, we apply the developed machinery and obtained results to three case studies from the field of knowledge representation and reasoning: temporal epistemic logics for reasoning about multi-agent systems, modalized description logics for dynamic ontologies, and spatio-temporal logics. The genre of the book can be defined as a research monograph. It brings the reader to the front line of current research in the field by showing both recent achievements and directions of future investigations (in particular, multiple open problems). On the other hand, well-known results from modal and first-order logic are formulated without proofs and supplied with references to accessible sources. The intended audience of this book is logicians as well as those researchers who use logic in computer science and artificial intelligence. More specific application areas are, e.g., knowledge representation and reasoning, in particular, terminological, temporal and spatial reasoning, or reasoning about agents. And we also believe that researchers from certain other disciplines, say, temporal and spatial databases or geographical information systems, will benefit from this book as well. Key Features: Integrated approach to modern modal and temporal logics and their applications in artificial intelligence and computer science Written by internationally leading researchers in the field of pure and applied logic Combines mathematical theory of modal logic and applications in artificial intelligence and computer science Numerous open problems for further research Well illustrated with pictures and tables. (shrink)

Until recently, it seemed like no theory about the relationship between rational credence and rational outright belief could reconcile three independently plausible assumptions: that our beliefs should be logically consistent, that our degrees of belief should be probabilistic, and that a rational agent believes something just in case she is sufficiently confident in it. Recently a new formal framework has been proposed that can accommodate these three assumptions, which is known as “the stability theory of belief” or (...) “high probability cores.” In this paper, I examine whether the stability theory of belief can meet two further constraints that have been proposed in the literature: that it is irrational to outright believe lottery propositions, and that it is irrational to hold outright beliefs based on purely statistical evidence. I argue that these two further constraints create a dilemma for a proponent of the stability theory: she must either deny that her theory is meant to give an account of the common epistemic notion of outright belief, or supplement the theory with further constraints on rational belief that render the stability theory explanatorily idle. This result sheds light on the general prospects for a purely formal theory of the relationship between rational credence and belief, i.e. a theory that does not take into account belief content. I argue that it is doubtful that any such theory could properly account for these two constraints, and hence play an important role in characterizing our common epistemic notion of outright belief. (shrink)

The logic of ‘being informed’ gives a formal analysis of a cognitive state that does not coincide with either belief, or knowledge. To Floridi, who first proposed the formal analysis, the latter is supported by the fact that unlike knowledge or belief, being informed is a factive, but not a reflective state. This paper takes a closer look at the formal analysis itself, provides a pure and an applied semantics for the logic of being informed, and tries to (...) find out to what extent the formal analysis can contribute to an information-based epistemology. (shrink)

We examine a contribution L. Susan Stebbing made to the understanding of critical thinking and its relation to formal logic. Stebbing took expertise in formal logic to authorise logical intervention in public debate, specifically in assessing of the validity of everyday reasoning. She held, however, that formal logic is purely the study of logical form. Given the problems of ascertaining logical form in any particular instance, and that logical form does not always track informal validity, (...) it is difficult to see how she could justify her belief in logical interventionism. Her answer to this problem is the contribution we explore here. It involves the view that although the logician’s expertise is not sufficient to assess arguments made in everyday contexts on its own, it nevertheless plays a unique role in giving systematicity and direction to the critique of such arguments, in particular, in public debate. (shrink)

Is it possible to give an explicit definition of belief in terms of subjective probability, such that believed propositions are guaranteed to have a sufficiently high probability, and yet it is neither the case that belief is stripped of any of its usual logical properties, nor is it the case that believed propositions are bound to have probability 1? We prove the answer is ‘yes’, and that given some plausible logical postulates on belief that involve (...) a contextual “cautiousness” threshold, there is but one way of determining the extension of the concept of belief that does the job. The qualitative concept of belief is not to be eliminated from scientific or philosophical discourse, rather, by reducing qualitative belief to assignments of resiliently high degrees of belief and a “cautiousness” threshold, qualitative and quantitative belief turn out to be governed by one unified theory that offers the prospects of a huge range of applications. Within that theory, logic and probability theory are not opposed to each other but go hand in hand. (shrink)

Theories of belief and meaning have long occupied philosophers. Typically, there is a correlation between the meaning of a sentence that is uttered and the content of the attitude that the speaker thereby conveys. This is also why a sentence can be used to specify content in an attribution of the attitude to the speaker. From the perspective of a theory of semantic content, there is a level of description where mental states and sentences can be said to share (...) a content or meaning. But there is a contrary view gaining currency, claiming that belief and meaning have to be kept apart conceptually, theoretically, and methodologically. Thus it could be that meaning is an internal or private notion that can be accounted for purely linguistically (or even non-intentionally altogether), while the same may not be true of belief. The volume brings together researchers from various areas in philosophy, psychology, and linguistics to address these questions. The tradition of logical positivism, sometimes thought of as having been a passing phase in twentieth-century philosophy, has as a matter of record remained a vibrant force. But it has shifted from broadside critiques of other systems of thought into a deeper study of how the structure of logic and language impact human behavior and psychological conditioning. Among the contributors to this international symposium are Michael Esfeld, Wolfram Hisses, Max Kolbel, Isaac Levi, Diego Marconi, James McGilvary, Olaf Muller, Paul Peitroski and Norbert Hornstein, Sebastian Rodl, and Alberto Voltolini. (shrink)

Gravitation is interpreted to be an “ontomathematical” force or interaction rather than an only physical one. That approach restores Newton’s original design of universal gravitation in the framework of “The Mathematical Principles of Natural Philosophy”, which allows for Einstein’s special and general relativity to be also reinterpreted ontomathematically. The entanglement theory of quantum gravitation is inherently involved also ontomathematically by virtue of the consideration of the qubit Hilbert space after entanglement as the Fourier counterpart of pseudo-Riemannian space. Gravitation can be (...) also interpreted as purely mathematical or logical “force” or “interaction” as a corollary from its ontomathematical (rather than physical) realization. The ontomathematical approach to gravitation is implicit in general relativity equating it to operators in pseudo-Riemannian space obeying the Einstein field equation and also well-known by the “geometrization of physics”. Quantum mechanics shares the same by the separable complex Hilbert space and defining “physical quantity” by the Hermitian operators on it. One can interpret special Minkowski space involved by special relativity and the qubit Hilbert space of quantum information as Fourier counterparts immediately noticing that general relativity means gravitation as the Fourier counterpart of non-Hermitian operators implying non-unitarity and the violation of energy conservation and thus destroying Pauli’s particle paradigm. Since the Standard model obeys it, this explains the impossibility of “quantum gravitation” in any framework conservatively generalizing the Standard model so that it would include gravitation along with electromagnetic, weak, and strong interactions. Einstein’s geometrization of gravitation can be continued into a purely mathematical theory of it following Euclid’s realization for geometry to be exhaustively built in a deductive and axiomatic way as well as Riemann’s parametrization of all the class of Euclidean and non-Euclidean geometries by “space curvature”, then being generalized to Minkowski space as the operators on pseudo-Riemannian space as the Einstein field equation means gravitation. The transition from mathematical gravitation to logical one can rely on the historical lesson of the pair of Lobachevski’s and Riemann’s approaches now “reversely”, i.e., from the latter to the former. Logical gravitation is linkable to Hegel’s dialectical logic and ontological dialectics abandoning their interpretations as a new zero logic substituting classical propionyl logic. The approach of ontomathematics generalizing that of ontology, traceable even to Aristotle’s reformation of Plato’s doctrine, needs Hegel’s doctrine to be formalized as a first-order logic naturally containing Boolean algebra, isomorphic to both classical propositional logic and set theory being the class of all first-order logics, as a sub-logic along with Peano arithmetic as another sub-logic. The first-order logic at issue is called Hilbert arithmetic and elaborated in detail in other papers. It allows for both self-foundation of mathematics to be internally proved as complete and furthermore, quantum mechanics reinterpreted as quantum information to be included by the qubit Hilbert space interpretable in turn as a dual and physical counterpart of Hilbert arithmetic in a narrow sense, that is, both counterparts constitute Hilbert arithmetic in a wide sense, being mathematical and physical simultaneously and thus overcoming the Cartesian dualism of “body” gapped from “mind” by an abyss. Then, the proper philosophical interpretation of gravitation to be the fundamental ontomathematical force or interaction overcomes the ridiculous belief of the Big Bang wrongly alleged to be a scientific theory. Ontomathematical gravitation suggests an omnipresent and omnitemporal medium of “God’s” creation “ex nihilo” following only the natural necessity of quantum-information conservation particularly and locally manifested as energy conservation. (shrink)

We explore ways in which purely qualitative belief change in the AGM tradition throws light on options in the treatment of conditional probability. First, by helping see why it can be useful to go beyond the ratio rule defining conditional from one-place probability. Second, by clarifying what is at stake in different ways of doing that. Third, by suggesting novel forms of conditional probability corresponding to familiar variants of qualitative belief change, and conversely. Likewise, we explain how (...) recent work on the qualitative part of probabilistic inference leads to a very broad class of 'proto-probability' functions. (shrink)

Kant identifies knowledge [Wissen], belief [Glaube], and opinion [Meinung] as our three primary modes of “holding-to-be-true” [Fürwahrhalten]. He also identifies opinion as making up the greatest part of our cognition. After a preliminary sketch of Kant’s system of propositional attitudes, this paper will explore what he says about the norms governing opinion and empirical hypotheses. The final section will turn to what, in the Critique of Pure Reason and elsewhere, Kant refers to as “General Applied Logic”. It concerns the (...) “contingent conditions of the subject, which can hinder or promote” good inquiry; and, though rarely mentioned in the secondary literature, it offers Kant’s methodological alternative to the traditional epistemological goal of finding “a sufficient and at the same time general criterion of truth”. (shrink)

In recent literature in the philosophy of mind and language, one finds a variety of examples that raise serious problems for the traditional analysis of belief as a two-term relation between a believer and a proposition. My main purpose in this essay is to provide a critical test case for any theory of the propositional attitudes, and to demonstrate that this case really does present an unsolved puzzle. Chapter I defines the traditional, propositional analysis of belief, and then (...) introduces a distinction, motivated by the intuitions that underlie Kripke's arguments for direct reference, between purely qualitative and individual propositions. Beliefs typically expressed using proper names, indexicals or demonstratives appear to relate the believer to individual propositions with the entity that may be referred to as subject constituent. Chapter II presents the critical test case . In this and Chapters III-VI it is used to show that the latter sorts of beliefs are not analyzable as dyadically relating the believer to individual propositions. The case constitutes a genuine counterexample to the traditional analysis only if it is possible for a believer to believe an individual proposition with a contingent thing other than herself as a constituent; and the believer in the case is in optimum conditions for believing an individual proposition. In Chapters III, IV, and VI, I criticize views prompted by rejection of , and in Chapter V, I criticize Stalnaker's view, which rejects . Chapter VI also considers the non-traditional, triadic analyses of belief proposed by Kaplan and Richard; they fall prey to the main criticisms of Chapter V. In the Postscript, I give a comparative assessment of approaches to resolving the Two Tubes Puzzle, and I place it in historical context by pointing out the puzzle's similarities to the 'problem of sense data' . Correlatively, I indicate the bearing of Methodological Solipsism on future attempts to solve the puzzle. My conclusion is that although the puzzle remains a puzzle, it gives us reason to supplement, rather than completely abandon, the use of propositions in the analysis of thought; and I say what a supplementing solution must do to remain faithful to the intuitions of Chapter I. (shrink)

This book is a specialized monograph on interpolation and definability, a notion central in pure logic and with significant meaning and applicability in all areas where logic is applied, especially computer science, artificial intelligence, logic programming, philosophy of science and natural language. Suitable for researchers and graduate students in mathematics, computer science and philosophy, this is the latest in the prestigous world-renowned Oxford Logic Guides, which contains Michael Dummet's Elements of intuitionism, J. M. Dunn and G. Hardegree's Algebraic Methods in (...) Philosophical Logic, H. Rott's Change, Choice and Inference: A Study of Belief Revision and Nonmonotonic Reasoning, P. T. Johnstone's Sketches of an Elephant: A Topos Theory Compendium: Volumes 1 and 2, and David J. Pym and Eike Ritter's Reductive Logic and Proof Search: Proof theory, semantics and control. (shrink)

In this paper I address the question 'How is knowledge of logical truths possible'. The sought-after explanation should be independent of what the true story about logical truth is. In particular, I try to account for the epistemic warrant that is conferred upon logical beliefs when they are neither inferred from other beliefs nor grounded on empirical evidence or testimony. The need for such an account is motivated by the apparent failure of the notions ofanalyticity on the (...) one hand and intuition on the other in addressing the relevant question. I end up defending an account according to which warranted logical beliefs can be grounded on pure reasoning: they can be inferentially formed on the basis of pieces of suppositional reasoning. (shrink)

Paradoxes have played an important role both in philosophy and in mathematics and paradox resolution is an important topic in both fields. Paradox resolution is deeply important because if such resolution cannot be achieved, we are threatened with the charge of debilitating irrationality. This is supposed to be the case for the following reason. Paradoxes consist of jointly contradictory sets of statements that are individually plausible or believable. These facts about paradoxes then give rise to a deeply troubling epistemic problem. (...) Specifically, if one believes all of the constitutive propositions that make up a paradox, then one is apparently committed to belief in every proposition. This is the result of the principle of classical logical known as ex contradictione (sequitur) quodlibetthat anything and everything follows from a contradiction, and the plausible idea that belief is closed under logical or material implication (i.e. the epistemic closure principle). But, it is manifestly and profoundly irrational to believe every proposition and so the presence of even one contradiction in one’s doxa appears to result in what seems to be total irrationality. This problem is the problem of paradox-induced explosion. In this paper it will be argued that in many cases this problem can plausibly be avoided in a purely epistemic manner, without having either to resort to non-classical logics for belief (e.g. paraconsistent logics) or to the denial of the standard closure principle for beliefs. The manner in which this result can be achieved depends on drawing an important distinction between the propositional attitude of belief and the weaker attitude of acceptance such that paradox constituting propositions are accepted but not believed. Paradox-induced explosion is then avoided by noting that while belief may well be closed under material implication or even under logical implication, these sorts of weaker commitments are not subject to closure principles of those sorts. So, this possibility provides us with a less radical way to deal with the existence of paradoxes and it preserves the idea that intelligent agents can actually entertain paradoxes. (shrink)

Pessimists about moral deference argue that there is something special about moral beliefs which make it impermissible for agents to defer on moral matters. In this paper, I argue that, even if pessimists are right that there is something special about moral beliefs, that is not enough to render moral deference impermissible. A stronger requirement—the rationality requirement—makes deferring to experts not only permissible but also rationally required. When one does not defer to one’s perceived moral expert, one either violates (...) class='Hi'>Belief Consistency or violates Belief Closure. The moral considerations, such as moral understanding or virtue, for not deferring to experts either fail to show that not deferring is a better option than deferring or fail to show that those moral considerations outweigh rationality requirements. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Michael Wreen THE LOGIC OF IONESCO'S THE LESSON As men abound in copiousness of language, so they become more wise, or more mad than ordinary. Hobbes, Leviathan, chap. 4 (L a RiTHMETic leads to philology, and philology leads to crime."1 This is both XXthe plot and die pessimism of Ionesco's The Lesson. As the drama unfolds, the spectator watches the world of progress-through-education crumble and a world oflust and (...) murder rise in its ruins. What has gone wrong? In a word, the life oflogic has become the logic oflife. To understand Ionesco's lesson, we must examine the (largely implicit) logic and philosophy of language of his Lesson. Logic, whether die classical syllogistic logic of Aristode, the modern symbolic logic of Russell and Whitehead, or die dialectical logic of Hegel, has two essentia ] components: a syntax, which distinguishes permissible from impermissible combinations and inferences, and a semantics, which allows interpretation and thus fills out the purely formal shell provided by the former. Ionesco's strategy is to show how each of these components as diey have come to be developed philosophically is inadequate to its real content — life, and how, together, they lead, at least metaphorically, to life's devastation. These diree conceptual moments correspond to the three dramatic divisions of the play, marked out by the interruptions of die maid. Ionesco begins with the methodology of logic, syntax, and focuses on arithmetic, which, we are told, "is more a method than a science" (p. 50). Since the time of Descartes, arithmetic, or more generally mathematics, has been the academic discipline par excellence, the study diat all of the empirical sciences have aspired to. So completely has the idea of the mathematical nature of reality impressed itself upon us diat for many people it has acquired the status of an 229 230Philosophy and Literature unquestioned, and even unquestionable, assumption. And for many in this group, including the Professor, it is more dianjust an assumption; it is a way of life. "Let us arithmetize a little," he says to his pupil (p. 51), and his neologism refers not just to a subject matter, arithmetic, but to a way of dealing with subject matters and, ultimately, to a way of dealing with the whole of reality. The noun "arithmetic" has become a verb, and the ascendancy of abstract method has begun. Formal logic, in adi diree of its classic Western forms, is now subjected to sustained and specific criticism. Generally speaking, the Pupil represents Aristotelian and Russellian humanism, a view based on an optimistic belief in man's capacity for direct knowledge, in understanding through analysis by fine distinctions between terms, and in the elimination of paradoxes, both in logic and life. The Professor, again roughly speadcing, represents Hegeliainism, a view based on an optimistic belief in die capacity of reason to unify all oppositions and to overcome, through a higher syndiesis, the fundamentally paradoxical nature of all phenomena, including life itself. Thus, at die level of formal logic and ontology, the Professor amd the Pupil aire diametrically opposed, united only in their uncritical reliatnce upon a method of reason. This philosophical opposition is in turn correlated with a psycho-physical opposition: the Professor is male, old, retiring, and initially lifeless; the Pupil is female, young, forwaurd, amd initiadly vivacious. The confrontation of the two embodied philosophical/ psychological principles over die matter of arithmetic makes dieir opposition manifest and demonstrates, for the first time in the play, die utter inability of bodi philosophical traditions to maintain a grip on reality. This confrontation is also a struggle, one which the fresh, straightforward, vital Pupil begins with great success. She is "magnificent" in addition, and claims she can "count to infinity" — an ability which would vindicate her confident, optimistic belief in man's mental capacities, but an ability, nevertheless, which is logically impossible to possess, since "infinity" is not the name of a particulatrly large number, ais she seems to think. Her claim to understand reveals her as limited and ignorant of the deeper and paradoxical nature of her subject, and thus as in need of further, more abstract lessons. "One must also be able to subtract," die Professor... (shrink)

My goal here is to explore the relationship between pure and applied mathematics and then, eventually, to draw a few morals for both. In particular, I hope to show that this relationship has not been static, that the historical rise of pure mathematics has coincided with a gradual shift in our understanding of how mathematics works in application to the world. In some circles today, it is held that historical developments of this sort simply represent changes in fashion, or in (...) social arrangements, governments, power structures, or some such thing, but I resist the full force of this way of thinking, clinging to the old school notion that we have gradually learned more about the world over time, that our opinions on these matters have improved, and that seeing how we reached the point we now occupy may help us avoid falling back into old philosophies that are now no longer viable. In that spirit, it seems to me that once we focus on the general question of how mathematics relates to science, one observation is immediate: the march of the centuries has produced an amusing reversal of philosophical fortunes. Let me begin there. In the beginning, that is, in Plato, mathematical knowledge was sharply distinguished from ordinary perceptual belief about the world. According to Plato’s metaphysics, mathematics is the study of eternal and unchanging abstract Forms,1 while science is uncertain and changeable opinion about the world of mere becoming. Indeed, in Plato’s lights, of the two, only mathematics deserves to be called ‘knowledge’ at all! Of course if sense perception cannot give us knowledge, if mathematics is not about perceivable things, then Plato owes us an account of how we ordinary humans achieve this wonderful insight into the properties of the abstract world of Forms. Plato’s answer is that we do not actually acquire mathematical knowledge at all; rather, we recollect it from a time before birth, when our souls, unencumbered by physical bodies, were free to commune with the Forms, and not just the mathematical ones, either – also Truth, Beauty, Justice, the Good, and so on.2 Whatever appeal this position may have held for the ancient Greeks, it will not begin to satisfy a contemporary, scientifically minded philosopher.. (shrink)

This paper derives a mathematical expression giving the development of the probability of a scientific hypothesis with the number of confirming tests, as determined by Bayes's theorem, in a special case in which all the tests are "independent" of one another. The simple expression obtained shows clearly how the various factors influence the growth of the probability. The result is used to set a numerical lower bound on the probabilities representing the a priori beliefs of humans in generalizations that become (...) accepted. By making a comparison with the predictions of a "logical atomic" model in the case of physical laws, it is argued that humans have significant a priori "knowledge" in a weak sense. (shrink)

This paper continues the recent tradition of investigating iterated AGM revision by reasoning directly about the dynamics for total pre-order (“implausibility ordering”) representations of AGM revision functions. We reorient discussion, however, by proving that symmetry considerations, almost by themselves, suffice to determine a particular, AGM-friendly implausibility ordering dynamics due to Spohn 1988, which we call “J-revision”. After exploring the connections between implausibility ordering dynamics and the social choice theory of Arrow 1963, we provide symmetry arguments in the social choice-theoretic framework (...) for an interesting generalization of J-revision due to Nayak 1994. We conclude by arguing that the symmetry principles that uniquely favor J-revision and its generalizations are importantly expressive of the purely qualitative framework for representing beliefs that distinguishes the AGM program. Our results therefore comprehensively vindicate Spohn's 1988 conjecture that essentially J-revision is the best that can be done by way of a purely qualitative model of belief revision. (shrink)

We propose an extension of answer sets, that we call safe beliefs, that can be used to study several properties and notions of answer sets and logic programming from a more general point of view. Our definition, based on intuitionistic logic and following ideas from D. Pearce [Stable inference as intuitionistic validity, Logic Programming 38 79–91], also provides a general approach to define several semantics based on different logics or inference systems. We prove that, in particular, intuitionistic logic can be (...) replaced with any other proper intermediate logic without modifying the resulting semantics. We also show that the answer set semantics satisfies an important property, the “extension by definition”, that can be used to construct program translations. As a result we are able to provide a polynomial translation from propositional theories into the class of disjunctive programs. (shrink)

This book illustrates the program of Logical-Informational Dynamics. Rational agents exploit the information available in the world in delicate ways, adopt a wide range of epistemic attitudes, and in that process, constantly change the world itself. Logical-Informational Dynamics is about logical systems putting such activities at center stage, focusing on the events by which we acquire information and change attitudes. Its contributions show many current logics of information and change at work, often in multi-agent settings where social (...) behavior is essential, and often stressing Johan van Benthem's pioneering work in establishing this program. However, this is not a Festschrift, but a rich tapestry for a field with a wealth of strands of its own. The reader will see the state of the art in such topics as information update, belief change, preference, learning over time, and strategic interaction in games. Moreover, no tight boundary has been enforced, and some chapters add more general mathematical or philosophical foundations or links to current trends in computer science. The theme of this book lies at the interface of many disciplines. Logic is the main methodology, but the various chapters cross easily between mathematics, computer science, philosophy, linguistics, cognitive and social sciences, while also ranging from pure theory to empirical work. Accordingly, the authors of this book represent a wide variety of original thinkers from different research communities. And their interconnected themes challenge at the same time how we think of logic, philosophy and computation. Thus, very much in line with van Benthem's work over many decades, the volume shows how all these disciplines form a natural unity in the perspective of dynamic logicians (broadly conceived) exploring their new themes today. And at the same time, in doing so, it offers a broader conception of logic with a certain grandeur, moving its horizons beyond the traditional study of consequence relations. (shrink)

Foundations of Bayesianism is an authoritative collection of papers addressing the key challenges that face the Bayesian interpretation of probability today. Some of these papers seek to clarify the relationships between Bayesian, causal and logical reasoning. Others consider the application of Bayesianism to artificial intelligence, decision theory, statistics and the philosophy of science and mathematics. The volume includes important criticisms of Bayesian reasoning and also gives an insight into some of the points of disagreement amongst advocates of the Bayesian (...) approach. The upshot is a plethora of new problems and directions for Bayesians to pursue.The book will be of interest to graduate students or researchers who wish to learn more about Bayesianism than can be provided by introductory textbooks to the subject. Those involved with the applications of Bayesian reasoning will find essential discussion on the validity of Bayesianism and its limits, while philosophers and others interested in pure reasoning will find new ideas on normativity and the logic of belief. (shrink)

It is now well known that, on pain of triviality, the probability of a conditional cannot be identified with the corresponding conditional probability [25]. This surprising impossibility result has a qualitative counterpart. In fact, Peter Gärdenfors showed in [13] that believing ‘If A then B’ cannot be equated with the act of believing B on the supposition that A — as long as supposing obeys minimal Bayesian constraints. Recent work has shown that in spite of these negative results, the question (...) ‘how to accept a conditional?’ has a clear answer. Even if conditionals are not truth-carriers, they do have precise acceptability conditions. Nevertheless most epistemic models of conditionals do not provide acceptance conditions for iterated conditionals. One of the main goals of this essay is to provide a comprehensive account of the notion of epistemic conditionality covering all forms of iteration. First we propose an account of the basic idea of epistemic conditionality, by studying the conditionals validated by epistemic models where iteration is permitted but not constrained by special axioms. Our modeling does not presuppose that epistemic states should be represented by belief sets (we only assume that to each epistemic state corresponds an associated belief state). A full encoding of the basic epistemic conditionals (encompassing all forms of iteration) is presented and a representation result is proved. In the second part of the essay we argue that the notion of change involved in the evaluation of conditionals is suppositional, and that such notion should be distinguished from the notion of updating (modelled by AGM and other methods). We conclude by considering how some of the recent modellings of iterated change fare as methods for iterated supposing. (shrink)

We discuss two-layered logics formalising reasoning with paraconsistent probabilities that combine the Łukasiewicz [0, 1]-valued logic with Baaz ▵\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\triangle $$\end{document} operator and the Belnap–Dunn logic. The first logic (introduced in [7]) formalises a ‘two-valued’ approach where each event ϕ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\phi $$\end{document} has independent positive and negative measures that stand for, respectively, the likelihoods of ϕ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\phi (...) $$\end{document} and ¬ϕ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\lnot \phi $$\end{document}. The second logic that we introduce here corresponds to ‘four-valued’ probabilities. There, ϕ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\phi $$\end{document} is equipped with four measures standing for pure belief, pure disbelief, conflict and uncertainty of an agent in ϕ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\phi $$\end{document}.We construct faithful embeddings of and into one another and axiomatise using a Hilbert-style calculus. We also establish the decidability of both logics and provide complexity evaluations for them using an expansion of the constraint tableaux calculus for. (shrink)

Dynamic doxastic logic (DDL) is the modal logic of belief change. In basic DDL a modal operator [* ϕ ] carries the informal meaning "after the agent has revised his beliefs by ϕ " or "after the agent has accepted the information that ϕ "; it is assumed that the arguments of the star operator * are pure Boolean formulae. That assumption is discarded in full DDL where any pure doxastic formula may be an argument. As noted by other (...) authors, a straight-forward extension of the theory from basic DDL to full DDL invites problems of the kind first discussed by G. E. Moore. In this paper it is argued that a way to escape those problems is to redefine revision in a way that seems appropriate for this semantically richer context. The paper deals only with the one-agent case, but the approach can be extended to the case of multiple agents. (shrink)

Euclid in the Rainforest combines the literary with the mathematical to explore logic--the one indispensable tool in man's quest to understand the world. Mazur argues that logical reasoning is not purely robotic. At its most basic level, it is a creative process guided by our intuitions and beliefs about the world.

Several of William James' finest essays are brought together in this collection, including his spiritual masterwork The Will to Believe, and his famous lecture concerning immortality. The Will to Believe was first delivered as a lengthy lecture by William James in 1896. Following a strong reception, it was later published as a distinct book in its own right. Setting out to defend the right of individuals to be religious irrespective of pure logic and reason, the lecture highlights many of the (...) proven advantages conferred by the belief in a guiding divine force. The benefits of belief to the believer are thus noted. James deftly cites many real life examples to prove his points - noting that many tasks or duties require confidence, he notes how individuals can perform and surmount difficulties if they believe in the divine. For such persons to abandon faith would therefore be irrational, as their religious beliefs have helped them in life. This argument is closely aligned with James' personal philosophical alignment with pragmatism. The Will to Believe also contains arguments in favor of persons having their own free will. James contested simply that as he believed in his own free will, he had it. As well as this, we hear several philosophical arguments in which James discusses the merits of empiricism versus absolutism. Other essays in this compendium include 'Is Life Worth Living?' and 'The Dilemma of Determinism'. In these and other writings, James demonstrates a superb command of philosophical principles and theoretical daring, at various times explaining and refuting established discussions on the subjects. The final essay in this edition, Human Immortality, sees James object to the notion that humans cannot be immortal if their bodies and minds are separated due to death. He objects to the assertion that human thought is concluded if the brain ceases to function, noting that human consciousness exists with the world and may philosophically have a life of its own. Notable for both his psychological and philosophical ideas, William James would author numerous lectures and books surrounding both subjects. The importance of spiritualism to the human being, the permanence of the spirit, and its effects on the thought processes, is but one area in which James distinguished himself. (shrink)

We often have to draw conclusions about states of machines in computer science and about states of knowledge and belief in artificial intelligence based on partial information. Nerode suggested using constructive logic as the language to express such deductions and also suggested designing appropriate intuitionistic Kripke frames to express the partial information. Following this program, Nerode and Wijesekera developed syntax, semantics and completeness for a system of intuitionistic dynamic logic for proving properties of concurrent programs. Like all dynamics logics, (...) this was a logic of many modalities, each expressing a program, but in intuitionistic rather than in classical logic. In that logic, both box and diamond are needed, but these two are not intuitionistically interdefinable and, worse, diamond does not distribute over ‘or’, except for sequential programs. This also happens in other contemplated computer science and AI applications, and leads outside the class of constructive logics investigated in the literature. The present paper fills this gap. We provide intuitionistic logics with independent box and diamond without assuming distribution of diamond over ‘or’. The completeness theorem is based on intuitionistic Kripke frames , but equipped with an additional, quite separate accessibility relation between worlds. In the interpretation of Nerode and Wijesekera , worlds under the partial order represent states of partial knowledge, the accessibility represents change in state of partial knowledge resulting from executing a specific program. But there are many other computer science interpretations. This formalism covers all computer science applications of which we are aware. We also give a cut elimination theorem and algebraic and topological formulations, since these present some new difficulties. Finally, these results were obtained prior to those in Nerode and Wijesekera. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:Philosophers of Nothingness: An Essay on the Kyoto School, and: A Buddhist-Christian Logic of the Heart: Nishida's Kyoto School and Lonergan's "Spiritual Genome" as World BridgeAmos YongPhilosophers of Nothingness: An Essay on the Kyoto School. By James W. Heisig. Honolulu: University of Hawai'i Press, 2001. xi + 380 pp.A Buddhist-Christian Logic of the Heart: Nishida's Kyoto School and Lonergan's "Spiritual Genome" as World Bridge. By John Raymaker. Lanham, (...) MD: University Press of America, 2002. x + 214 pp.These are two very different types of books. Heisig, research fellow (since 1978) and former director (1999-2001) of the Nanzan Institute for Religion and Culture and well known to readers of this journal as author, book editor, and translator extraordinaire, [End Page 271] has produced the definitive exposition of the Kyoto School in the English language with Philosophers of Nothingness. Raymaker, a longtime Roman Catholic missionary to Japan and student of Lonergan's work, attempts in A Buddhist-Christian Logic of the Heart to establish points of contact between Lonergan's transcendental method and Nishida's pure experience. Let me briefly summarize the two volumes before making some comparative observations.Philosophers of Nothingness is divided into five sections: an "Orientation" (introduction) and a "Prospectus" (transitional epilogue) flanking the three sections on Nishida, Tanabe, and Nishitani, each constituting approximately twenty short chapters. In each case, Heisig combines intellectual biography and history of ideas approaches, thus both setting forth the wider social, political, and intellectual contexts of the Kyoto School thinkers and elaborating on their distinctive ideas. Those interested in the latter will not be disappointed. Nishida's "pure experience," "active intuition," "absolutely contradictory self-identity," "logic of locus" (or basho, topos, place), and "historical world," among other themes, are all given special attention within the broader framework of his philosophical project. In the case of Tanabe, unique concepts such as "absolute mediation," "logic of species," and "metanoetic philosophy" (or philosophy of repentance) are illuminated. And, of course, the contributions of Nishitani are fully represented: "nihilism," "the standpoint of emptiness," and the sunyata of time and history.At the same time, those looking for background discussion will also find Heisig's exposition helpful, and that along (at least) the following three lines. First, an attempt is made to take seriously the self-understanding of Kyoto School thinkers of doing philosophy in the world context. This is, of course, a bold undertaking which some in our time might summarily dismiss either as hubris or as ignorance. Yet beginning with Nishida and continuing through Tanabe, Nishitani and others (such as Tanabe's student, Abe Masao), the task was to engage as Japanese philosophers with Western thinkers and ideas. Here, of course, the tension between particularity and universality is most intense, and the Kyoto philosophers proceeded with full awareness of the issues at stake. Now while their endeavors can be criticized from either direction, what cannot be criticized without self-refutation is their motivating belief that they could understand the West and vice versa.Second, and connected with the first, is the social and political twentieth-century context of Japan and its relationship with modernity and with the Western world. Here, Heisig brilliantly negotiates between laying out the facts and locating the passions and failures of the Kyoto philosophers. This requires that he correctly identify their contributions as Japanese thinkers engaging modernity without ignoring their blind spots. As such, longstanding questions concerning Kyoto School philosophy as an ideology for Japanese nationalism are confronted head-on. Heisig shows how political naīvete resulted in political entanglements. At the same time, his discussion illuminates the sociopolitical backdrop that informs and shapes all philosophizing. The result is a balanced presentation that is neither apologetic on the one side nor condemnatory on the other.Finally, the question of religion and its relationship to Kyoto School philosophy [End Page 272] is also taken up. Nishida's practice of zazen is thus shown to inform his philosophizing, if only implicitly (on Nishida's own account), even while Tanabe's experience of metanoia (conversion) as mediated through the "Other-power" matrix of Shinran's religious thought is shown to impact his philosophy explicitly... (shrink)

This is an excellent book for philosophers, and others concerned with natural language and cognition, who have not kept up with post-Aspects work in syntax, in particular with the Extended Standard Theory work on government and binding that relates to anaphora and quantification. It is a direct challenge to those who think that there must be a reasonably clearcut semantic level of description for sentences in natural language, one which is crucial for explaining how we learn, understand, and use natural (...) language. Hornstein argues that the properties of quantification such as relative quantifier scope and pronoun binding in natural language are best explained in purely syntactic terms. "Not only are the explanations best construed syntactically but, more important, the distinctions and concepts needed to articulate them cut against the semantic distinctions one would naturally make". This syntactic theory will, of course, be supplemented in a full theory of language use by pragmatic theories that will assign meaning, force, reference, etc., in particular contexts, given all sorts of real world knowledge. But what we won't have will be a compositional, context insensitive level of semantic description in which true, denotation, object, model, etc., loom large. Though Hornstein is a philosopher, his arguments derive from a linguist's familiarity with recent syntactical work; however, the general line is consonant with Stich's From Folk Psychology to Cognitive Science: The Case Against Belief, in which Stich argues beliefs are so context and intrepretive-stance relative that they cannot be grist for a scientific psychology, which must rather limit itself to syntactical characterizations of sentences in cognition. (shrink)

In _The Philosophy of Logical Atomism_, Russell defends a version of semantic empiricism according to which direct acquaintance with logical atoms is the source of our semantic capacities. Previous commentators have construed Russellian acquaintance in one of two ways: either as an act of _de re_ designation involving neither conceptualization nor propositional content, or as a species of belief _de re_, which does involve conceptualization or classification. I argue that two further, interim possibilities have been overlooked: that (...) direct acquaintance involves purely phenomenal content or that direct acquaintance involves protoconceptual content. I conclude, however, that on none of the four interpretations considered, can direct acquaintance with logical atoms be the source of our semantic capacities. (shrink)

This dissertation alleges to successfully defend the argument from evil and thereby show that belief in an omnipotent, omniscient and omnibenevolent god is implausible. The three basic premises of the argument juxtapose the perfect attributes of the traditional Western notion of god to the existence of evil in an attempt to lead to the conclusion that god lacks one or more of the aforementioned attributes. Though some argue that the conclusion is not necessitated by the premises since there is (...) no logical inconsistency in asserting both that god possesses these attributes and that evil exists, it is argued here that a suppressed premise needs to be made explicit for the argument to function properly such that evil can be taken as evidence against the existence of a perfect deity. ;The theist proposes a variety of solutions to the apparent discord engendered by the coexistence of evil and a perfect deity. J. L. Mackie, in criticizing these various theistic proposals, claims that they all are either adequate or fallacious. Adequate solutions are comprised, essentially, of a denial of one of the three original premises of the argument, i.e., that either omnipotence, omniscience, omnibenevolence or evil is not real. The fallacious solutions, of which there are four types generally thought to be exhaustive, are shown to be inadequate for salvaging the traditional Western concept of deity. Familiar themes discussed among the fallacious solutions are: that the world is better with some evil than without; evil is necessary as a contrast to good; evil is necessary to bring about a greater good; evil is necessary for soul-making; evil is the result of free-will. ;Finally, a solution proposed by Clement Dore which does not properly fit into Mackie's schema, the "pollution" solution, so nicknamed because evil is viewed as a waste by-product of the natural functioning of causal laws upon the matter of the universe, is discussed. Four possible interpretations of this solution are offered and each interpretation, in turn, is found to be invalid. In conclusion, evil is shown to be powerful evidence against the existence of an omnipotent, omniscient and omnibenevolent god. (shrink)

The notions of common knowledge or common belief play an important role in several areas of computer science , in philosophy, game theory, artificial intelligence, psychology and many other fields which deal with the interaction within a group of “agents”, agreement or coordinated actions. In the following we will present several deductive systems for common knowledge above epistemic logics –such as K, T, S4 and S5 –with a fixed number of agents. We focus on structural and proof-theoretic properties of (...) these calculi. (shrink)

Deflationists about truth generally regard the contribution that ‘true’ makes to utterances to be purely logical or expressive: it exists to facilitate communication, and remedy our expressive deficiencies that are due to ignorance or finitude. This paper presents a challenge to that view by considering alethic desires. Alethic desires are desires for one’s beliefs to be true. Such desires, I argue, do not admit of any deflationarily acceptable analysis, and so challenge the deflationist’s austere view about the semantic (...) role of ‘true’. I consider a number of deflationist proposals for analyzing alethic desires, and find them all problematic. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:BOOK REVIEWS 719 An Apology for Apologetics: A Study in the Logic of lnterreligious Dialogue. By PAUL J. GRIFFITHS. New York: Orbis, 1991. ISBN: 0 88344 761 4. pp. 113. Jesus Christ at the Encounter of World Religions. By J. DUPUIS. New York: Orbis, 1991 (ET: Robert R. Barr, from French, 1989). ISBN: 0 88344 723 1. pp. 301. Griffiths presents a rigorous argument for the possibility of con· (...) tradictory claims between different religious communities. His inspira· tion, as he acknowledges, is William Christian Snr. His basic argu· ment is: " If representative intellectuals belonging to some specific religious community come to judge at a particular time that some or all of their own doctrine-expressing sentences are incompatible with some alien religious claim(s), then they should feel obliged to engage in both positive and negative apologetics vis-a-vis these alien religious claim(s) and their promulgators" (3). He takes negative apologetics to be a critique of arguments made against one's own religious claims, showing that such arguments fail or are inconsistent or incoherent. Positive apologetics shows how a particular religious community's doctrines are cognitively superior, in some respect(s), to another religious community 's doctrines. It is essential for this enterprise that only methods of argumentation and criteria of knowledge acceptable to the adversary are employed. This requires the acceptance of natural theology. Griffiths is well aware of the lion's den he is entering, as his proposals run counter to much scholarship in the area of interreligious dialogue, so he spends three chapters apologetically tackling the lions. The objectors (who mainly remain in notes) include Derrida, Barthes, Winch, Lindbeck, Hick, Huxley, Nasr, Plantinga and others, although Mac· Intyre is curiously missing. This technique has the advantage of isolating and presenting arguments, without falling into problems of cor· rect exegesis of opponents. And this is also its weakness, as objectors will sometimes feel caricatured or misunderstood-as is surely the case with Plantinga and in one instance, Hick. First, he tackles objections that sentences from one tradition are either incomprehensible or incommensurable with those of another, convincingly showing that the strong versions of both claims are self· defeating and unsustainable. Weaker versions still allow for his proj· ect-or so he thinks. This is where Maclntyre's work should have been considered. Then he tackles various theories of religious language (following Lindbeck's typology). He argues against non-cognitive accounts that reduce beliefs to the credibility of causes for holding beliefs, a position incapable of asserting its truth over other views because of its 720 BOOK REVIEWS own presuppositions. He follows Lindbeck in criticizing experiental expressivism, and then turns upon Lindbeck's own form of rule theory (which is ambivalent regarding cognitive claims), arguing convincingly that to suggest that only sentences uttered confessionally and with performative function can possess ontological truth is confused (42). In a brief review it is not possible to rehearse Griffiths's careful argumentation. Griffiths then sets about tackling two types of universalists: Hick and Huxley. Of Hick, he argues that some criteria are required to discern true from false religions (e.g. Jim Jones) and in so doing such a position needs to support and develop such criteria, thereby effectively introducing apologetics. He neglects to deal with Hick's pragmatic criteria of beneficial ' fruits ' evident in adherents, but the logic of his argument can be applied to Hick's proposals. Using Katz and Zaehner, he argues against the esoteric universalism of the philosophia perennis. (The arguments of Robert Forman's recent book, The Problems of Pure Consciousness, are strangely neglected, despite Griffiths's being a contributor to that collection.) Finally, he tackles objections against positive apologetics-first, on the grounds that it has a negative effect on interreligious relations. Logically, this need not be the case, although Griffiths is well aware that the political context of apologetics can obscure its proper goal: deeper critical understanding, learning and problem solving. Then, in sustained dialogue with Plantinga, he argues against the objection that success is impossible. It is impossible only if " knockdown drag-out" (64) argumentative victory is expected. Griffiths suggests the cumulative -case argument and gives instances of such successful apologetics (medieval... (shrink)

The concept of relevance between classical propositional formulae, defined in terms of letter-sharing, has been around for a long time. But it began to take on a fresh life in the late 1990s when it was reconsidered in the context of the logic of belief change. Two new ideas appeared in independent work of Odinaldo Rodrigues and Rohit Parikh: the relation of relevance was considered modulo the choice of a background belief set, and the belief set was (...) put into a canonical form, called its finest splitting. In the first part of this paper, we recall the ideas of Rodrigues and Parikh, and show that they yield equivalent definitions of what may be called canonical cell/path relevance. The second part presents the main new result of the paper: while the relation of canonical relevance is syntax-independent in the usual sense of the term, it nevertheless remains language-dependent in a deeper sense, as is shown with an example. The final part of the paper turns to questions of application, where we present a new concept of parameter-sensitive relevance that relaxes the Rodrigues/Parikh definition, allowing it to take into account extra-logical sources as well as purely logical ones. (shrink)

W. V. Quine famously defended two theses that have fallen rather dramatically out of fashion. The first is that intensions are “creatures of darkness” that ultimately have no place in respectable philosophical circles, owing primarily to their lack of rigorous identity conditions. However, although he was thoroughly familiar with Carnap’s foundational studies in what would become known as possible world semantics, it likely wouldn’t yet have been apparent to Quine that he was fighting a losing battle against intensions, due in (...) large measure to developments stemming from Carnap’s studies and culminating in the work of Kripke, Hintikka, and Bayart. These developments undermined Quine’s crusade against intensions on two fronts. First, in the context of possible world semantics, intensions could after all be given rigorous identity conditions by defining them (in the simplest case) as functions from worlds to appropriate extensions, a fact exploited to powerful and influential effect in logic and linguistics by the likes of Kaplan, Montague, Lewis, and Cresswell. Second, the rise of possible world semantics fueled a strong resurgence of metaphysics in contemporary analytic philosophy that saw properties and propositions widely, fruitfully, and unabashedly adopted as ontological primitives in their own right. This resurgence — happily, in my view — continues into the present day. -/- For a time, at any rate, Quine experienced somewhat better success with his second thesis: that higher-order logic is, at worst, confused and, at best, a quirky notational alternative to standard first-order logic. However, Quine notwithstanding, a great deal of recent work in formal metaphysics transpires in a higher-order logical framework in which properties and propositions fall into an infinite hierarchy of types of (at least) every finite order. Initially, the most philosophically compelling reason for embracing such a framework since Russell first proposed his simple theory of types was simply that it provides a relatively natural explanation of the paradoxes. However, since the seminal work of Prior there has been a growing trend to consider higher-order logic to be the most philosophically natural framework for metaphysical inquiry, many of the contributors to this volume being among the most important and influential advocates of this view. Indeed, this is now quite arguably the dominant view among formal metaphysicians. -/- In this paper, and against the current tide, I will argue in §1 that there are still good reasons to think that Quine’s second battle is not yet lost and that the correct framework for logic is first-order and type-free — properties and propositions, logically speaking, are just individuals among others in a single domain of quantification — and that it arises naturally out of our most basic logical and semantical intuitions. The data I will draw upon are not new and are well-known to contemporary higher-order metaphysicians. However, I will try to defend my thesis in what I believe is a novel way by suggesting that these basic intuitions ground a reasonable distinction between “pure” logic and non-logical theory, and that Russell-style semantic paradoxes of truth and exemplification arise only when we move beyond the purely logical and, hence, do not of themselves provide any strong objection to a type-free conception of properties and propositions. -/- Most of my arguments in §1 are largely independent of any specific account of the nature of properties and propositions beyond their type-freedom. However, I will in addition argue that there are good reasons to take propositions, at least, to be very fine-grained. My arguments are thus bolstered significantly if it can be shown that there are in fact well-defined examples of logics that are not only type-free but which comport with such a conception of propositions. It is the purpose of §2 to lay out a logic of this sort in some detail, drawing especially upon work by George Bealer and related work of my own. With the logic in place, it will be possible to generalize the line of argument noted above regarding Russell-style paradoxes and, in §3, apply it to two propositional paradoxes — the Prior-Kaplan paradox and the Russell-Myhill paradox — that are often taken to threaten the sort of account developed here. (shrink)

On a common view of scenario-based sceptical arguments sceptical scenarios are error-possibilities, i.e. their point is to introduce the possibility of having only false beliefs. However, global error is impossible for purely logical/conceptual reasons: Even if one’s beliefs are consistent, the negations of one’s beliefs need not be consistent as well. My paper deals with the question of what the consequences of this result are. Two attempts at repairing scenario-based sceptical arguments within the framework of understanding sceptical scenarios (...) as error-possibilities are found wanting. Instead, what should be given up is the assumption that sceptical scenarios are error-possibilities. What is thought-provoking about the scenario of the brain in a vat is not that none of its empirical beliefs are true, but that all of its empirical beliefs fall short of knowledge at the same time. Hence, sceptical scenarios are not error-possibilities, but ignorance possibilities. If this is so, both the closure argument and the underdetermination argument commit a subtle mistake and should be replaced by slightly different arguments. The principle of excluded ignorance-possibilities turns out to be an epistemological principle that is faithful to scepticism’s tenets without misinterpreting sceptical scenarios as error-possibilities. (shrink)

A logic of grounding where what is grounded can be a collection of truths is a “many-many” logic of ground. The idea that grounding might be irreducibly many-many has recently been suggested by Dasgupta. In this paper I present a range of novel philosophical and logical reasons for being interested in many-many logics of ground. I then show how Fine’s State-Space semantics for the Pure Logic of Ground can be extended to the many-many case, giving rise to the Pure (...) Logic of Many-Many Ground. In the second, more technical, part of the paper, I do two things. First, I present an alternative formalization of plg; this allows us to simplify Fine’s completeness proof for plg. Second, I formalize plmmg using an infinitary sequent calculus and prove that this formalization is sound and complete. (shrink)

Experiences are interpreted as conscious mental occurrences that are of phenomenal character. There is already a kind of (weak) intentionality involved with this phenomenal interpretation. A stricter conception of experiences distinguishes between purely phenomenal experiences and intentional experiences in a narrow sense. Wittgenstein’s account of psychological (experiential) verbs is taken over: Usually, expressing mental states verbally is not describing them. According to this, I believe can be seen as an expression of one’s own belief, but not as an (...) expression of a belief about one’s belief. Hence, the utterance I believe it is raining shows that I believe that it is raining, although it is not said by these words that I believe that it is raining. Thinking thoughts such as I believe it is raining, but it is not raining (a variant of Moore’s paradox) is an absurdity between what is already said by silently uttering It is not raining and what is shown by silently uttering I believe it is raining. The paper agrees with a main result of Wittgenstein’s considerations of Moore’s paradox, namely the view that logical structure, deducibility, and consistency cannot be reduced solely to propositions—besides a logic of propositions, there is, for example, a logic of assertions and of imperatives, respectively. (shrink)