In this paper we prove that three of the main propositional logics of dependence, none of which is structural, are structurally complete with respect to a class of substitutions under which the logics are closed. We obtain an analogous result with respect to stable substitutions, for the negative variants of some well-known intermediate logics, which are intermediate theories that are closely related to inquisitive logic.

This paper presents a simple decidable logic of functional dependence LFD, based on an extension of classical propositional logic with dependence atoms plus dependence quantifiers treated as modalities, within the setting of generalized assignment semantics for first order logic. The expressive strength, complete proof calculus and meta-properties of LFD are explored. Various language extensions are presented as well, up to undecidable modal-style logics for independence and dynamic logics of changing dependence models. Finally, more (...) concrete settings for dependence are discussed: continuous dependence in topological models, linear dependence in vector spaces, and temporal dependence in dynamical systems and games. (shrink)

In this paper, we axiomatize the negatable consequences in dependence and independence logic by extending the systems of natural deduction of the logics given in [22] and [11]. We prove a characterization theorem for negatable formulas in independence logic and negatable sentences in dependence logic, and identify an interesting class of formulas that are negatable in independence logic. Dependence and independence atoms, first-order formulas belong to this class. We also demonstrate our extended system (...) of independence logic by giving explicit derivations for Armstrong's Axioms and the Geiger-Paz-Pearl axioms of dependence and independence atoms. (shrink)

We characterize the expressive power of extensions of Dependence Logic and Independence Logic by monotone generalized quanti ers in terms of quanti er extensions of existential second-order logic.

We examine the relationship between dependence logic and game logics. A variant of dynamic game logic, called Transition Logic, is developed, and we show that its relationship with dependence logic is comparable to the one between first-order logic and dynamic game logic discussed by van Benthem. This suggests a new perspective on the interpretation of dependence logic formulas, in terms of assertions about reachability in games of imperfect information against Nature. (...) We then capitalize on this intuition by developing expressively equivalent variants of dependence logic in which this interpretation is taken to the foreground. (shrink)

Starting from cardinals κ κ is measurable, we construct a model for the theory “ZF + n < ω[DCn] + ω + 1 is a measurable cardinal”. This is the maximum amount of dependent choice consistent with the measurability of ω + 1, and by a theorem of Shelah using p.c.f. theory, is the best result of this sort possible.

The four main essays in this volume investigate new sectors of the theory of decision, preference, act-characteristics, and action analysis. Herbert A. Simon applies tools developed in the theory of decision-making to the logic of action, and thereby develops a novel concept of heuristic power. Adapting ideas from utility and decision theory, Nicholas Rescher proposes a logic of preference by which conflicting theories proposed by G. H. von Wright, R. M. Chisholm, and others can be systematized. Donald Davidson (...) discusses difficulties in specifying the structure of action sentences to elucidate how their meaning depends on that structure. G. H. von Wright devises a method for describing each “state of the world” that results from an action, in a revision of his own earlier work. Additionally, a study of the logic of norms by Alan Ross Anderson is presented as an appendix, along with an appendix by Rescher outlining the aspects of action. (shrink)

This book revives the study of conventional implicatures in natural language semantics. H. Paul Grice first defined the concept. Since then his definition has seen much use and many redefinitions, but it has never enjoyed a stable place in linguistic theory. Christopher Potts returns to the original and uses it as a key into two presently under-studied areas of natural language: supplements and expressives. The account of both depends on a theory in which sentence meanings can be multidimensional. The theory (...) is logically and intuitively compositional, and it minimally extends a familiar kind of intensional logic, thereby providing an adaptable, highly useful tool for semantic analysis. The result is a linguistic theory that is accessible not only to linguists of all stripes, but also philosophers of language, logicians, and computer scientists who have linguistic applications in mind. (shrink)

Humans, unlike other animals, are equipped with a powerful brain that permits conscious awareness and reflection. A growing trend in psychological science has questioned the benefits of consciousness, however. Testing a hypothesis advanced by [Lieberman, M. D., Gaunt, R., Gilbert, D. T., & Trope, Y. . Reflection and reflexion: A social cognitive neuroscience approach to attributional inference. Advances in Experimental Social Psychology, 34, 199–249], four studies suggested that the conscious, reflective processing system is vital for logical reasoning. Substantial decrements in (...) logical reasoning were found when a cognitive load manipulation preoccupied conscious processing, while hampering the nonconscious system with consciously suppressed thoughts failed to impair reasoning . Nonconscious activation of the idea of logical reasoning increased the activation of logic-relevant concepts, but failed to improve logical reasoning performance unless the logical conclusions were largely intuitive and thus not reliant on logical reasoning . Meanwhile, stimulating the conscious goal of reasoning well led to improvements in reasoning performance . These findings offer evidence that logical reasoning is aided by the conscious, reflective processing system. (shrink)

There are three distinct questions associated with Simpson's paradox, (i) Why or in what sense is Simpson's paradox a paradox? (ii) What is the proper analysis of the paradox? (iii) How one should proceed when confronted with a typical case of the paradox? We propose a "formar" answer to the first two questions which, among other things, includes deductive proofs for important theorems regarding Simpson's paradox. Our account contrasts sharply with Pearl's causal (and questionable) account of the first two questions. (...) We argue that the "how to proceed question?" does not have a unique response, and that it depends on the context of the problem. We evaluate an objection to our account by comparing ours with Blyth's account of the paradox. Our research on the paradox suggests that the "how to proceed question" needs to be divorced from what makes Simpson's paradox "paradoxical.". (shrink)

Deontic Logic goes back to Ernst Mally’s 1926 work, Grundgesetze des Sollens: Elemente der Logik des Willens [Mally. E.: 1926, Grundgesetze des Sollens: Elemente der Logik des Willens, Leuschner & Lubensky, Graz], where he presented axioms for the notion ‘p ought to be the case’. Some difficulties were found in Mally’s axioms, and the field has much developed. Logic of Knowledge goes back to Hintikka’s work Knowledge and Belief [Hintikka, J.: 1962, Knowledge and Belief: An Introduction to the (...) Logic of the Two Notions, Cornell University Press] in which he proposed formal logics of knowledge and belief. This field has also developed quite a great deal and is now the subject of the TARK conferences. However, there has been relatively little work combining the two notions of knowledge (belief) with the notion of obligation. (See, however, [Lomuscio, A. and Sergot, M.: 2003, Studia Logica 75 63–92; Moore, R. C.: 1990, In J. F. Allen, J. Hendler and A. Tate (eds.), Readings in Planning, Morgan Kaufmann Publishers, San Mateo, CA]) In this paper we point out that an agent’s obligations are often dependent on what the agent knows, and indeed one cannot reasonably be expected to respond to a problem if one is not aware of its existence. For instance, a doctor cannot be expected to treat a patient unless she is aware of the fact that he is sick, and this creates a secondary obligation on the patient or someone else to inform the doctor of his situation. In other words, many obligations are situation dependent, and only apply in the presence of the relevant information. Thus a case for combining Deontic Logic with the Logic of Knowledge is clear. We introduce the notion of knowledge based obligation and offer an S5, history based Kripke semantics to express this notion, as this semantics enables us to represent how information is transmitted among agents and how knowledge changes over time as a result of communications. We consider both the case of an absolute obligation (although dependent on information) as well as the (defeasible) notion of an obligation which may be over-ridden by more relevant information. For instance a physician who is about to inject a patient with drug d may find out that the patient is allergic to d and that she should use d′ instead. Dealing with the second kind of case requires a resort to non-monotonic reasoning and the notion of justified belief which is stronger than plain belief, but weaker than absolute knowledge in that it can be over-ridden. This notion of justified belief also creates a derived notion of default obligation where an agent has, as far as the agent knows, an obligation to do some action a. A dramatic application of this notion is our analysis of the Kitty Genovese case where, in 1964, a young woman was stabbed to death while 38 neighbours watched from their windows but did nothing. The reason was not indifference, but none of the neighbours had even a default obligation to act, even though, as a group, they did have an obligation to take some action to protect Kitty. (shrink)

There are three distinct questions associated with Simpson’s paradox. Why or in what sense is Simpson’s paradox a paradox? What is the proper analysis of the paradox? How one should proceed when confronted with a typical case of the paradox? We propose a “formal” answer to the first two questions which, among other things, includes deductive proofs for important theorems regarding Simpson’s paradox. Our account contrasts sharply with Pearl’s causal account of the first two questions. We argue that the “how (...) to proceed question?” does not have a unique response, and that it depends on the context of the problem. We evaluate an objection to our account by comparing ours with Blyth’s account of the paradox. Our research on the paradox suggests that the “how to proceed question” needs to be divorced from what makes Simpson’s paradox “paradoxical.”. (shrink)

Since Kaplan : 81–98, 1979) first provided a logic for context-sensitive expressions, it has been thought that the only way to construct a logic for indexicals is to restrict it to arguments which take place in a single context— that is, instantaneous arguments, uttered by a single speaker, in a single place, etc. In this paper, I propose a logic which does away with these restrictions, and thus places arguments where they belong, in real world conversations. The (...) central innovation is that validity depends not just on the sentences in the argument, but also on certain abstract relations between contexts. This enrichment of the notion of logical form leads to some seemingly counter-intuitive results: a sequence of sentences may make up a valid argument in one sequence of contexts, and an invalid one in another such sequence. I argue that this is an unavoidable result of context sensitivity in general, and of the nature of indexicals in particular, and that reflection on such examples will lead us to a better understanding of the idea of applying logic to context sensitive expressions, and thus to natural language in general. (shrink)

Time, space, causality, communicating and acting together set limits on our freedom. Starting from the position of Wittgenstein, who advocates neither a position of pure subjectivity nor of pure objectivity, and taking into account what is implied by initiation into the symbolic order of language and culture, it is argued that the limitations on our freedom are not to be deplored. The problems of conservatism, relativism and scepticismwhich confront us often in the context of education and child rearingare inadequately dealt (...) with if attention is primarily focused on ways to resist or act differently. Following Cavell and his insistence that we should not try to escape from the existential conditions we find ourselves in and look for false certainties, the relevance of embracing a particular stance is elaborated. A commitment to giving substance to an ideal of the good life is neither an injustice towards the other nor an ignorance of her freedom. On the contrary, here responsibility is accepted, and at the same time it is acknowledged that we always have only the particular points of departure that we contingently start from. Coming to terms with this kind of dependency constitutes living out the scepticism that is implied by our being human: the logic of this is given along with our human condition. (shrink)

This paper is the sequel to Part 1, which appeared in this Journal, Vol. 46 No. 2, 2012. Following Cavell and his insistence that we should not try to escape from the existential conditions we find ourselves in and look for false certainties, the relevance of embracing a particular stance is elaborated. A commitment to giving substance to an ideal of the good life is neither an injustice towards the other nor an ignorance of her freedom. On the contrary, here (...) responsibility is accepted and at the same time it is acknowledged that we always have only the particular points of departure that we contingently start from. Coming to terms with this kind of dependency constitutes living out the scepticism that is implied by our being human: the logic of this is given along with our human condition. (shrink)

A definition is given for formulae $A_1,\ldots,A_n$ in some theory $T$ which is formalized in a propositional calculus $S$ to be (in)dependent with respect to $S$. It is shown that, for intuitionistic propositional logic $\mathbf{IPC}$, dependency (with respect to $\mathbf{IPC}$ itself) is decidable. This is an almost immediate consequence of Pitts' uniform interpolation theorem for $\mathbf{IPC}$. A reasonably simple infinite sequence of $\mathbf{IPC}$-formulae $F_n(p, q)$ is given such that $\mathbf{IPC}$-formulae $A$ and $B$ are dependent if and only if at (...) least on the $F_n(A, B)$ is provable. (shrink)

We present a logic for reasoning about attribute dependencies in data involving degrees such as a degree to which an object is red or a degree to which two objects are similar. The dependencies are of the form A ⇒ B and can be interpreted in two ways: first, in data tables with entries representing degrees to which objects have attributes ; second, in database tables where each domain is equipped with a similarity relation. We assume that the degrees (...) form a scale equipped with operations representing many-valued logical connectives. If 0 and 1 are the only degrees, the algebra of degrees becomes the two-element Boolean algebra and the two interpretations become well-known dependencies in Boolean data and functional dependencies of relational databases. In a setting with general scales, we obtain a new kind of dependencies with naturally arising degrees of validity, degrees of entailment, and related logical concepts. The deduction rules of the proposed logic are inspired by Armstrong rules and make it possible to infer dependencies to degrees—the degrees of provability. We provide a soundness and completeness theorem for such a setting asserting that degrees of entailment coincide with degrees of provability, prove the independence of deduction rules, and present further observations. (shrink)

We show in this paper that the AGM postulates are too weak to ensure the rational preservation of conditional beliefs during belief revision, thus permitting improper responses to sequences of observations. We remedy this weakness by proposing four additional postulates, which are sound relative to a qualitative version of probabilistic conditioning. Contrary to the AGM framework, the proposed postulates characterize belief revision as a process which may depend on elements of an epistemic state that are not necessarily captured by a (...) belief set. We also show that a simple modification to the AGM framework can allow belief revision to be a function of epistemic states. We establish a model-based representation theorem which characterizes the proposed postulates and constrains, in turn, the way in which entrenchment orderings may be transformed under iterated belief revision. (shrink)

When we say “I know why he was late”, we know not only the fact that he was late, but also an explanation of this fact. We propose a logical framework of “knowing why” inspired by the existing formal studies on why-questions, scientific explanation, and justification logic. We introduce the Kyi\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\mathcal {K}}{}\textit{y}}_i$$\end{document} operator into the language of epistemic logic to express “agent i knows why φ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} (...) \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varphi $$\end{document}” and propose a Kripke-style semantics of such expressions in terms of knowing an explanation of φ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varphi $$\end{document}. We obtain two sound and complete axiomatizations w.r.t. two different model classes depending on different assumptions about introspection. Finally we connect our logic with justification logic technically by providing an alternative semantics and an in-depth comparison on various design choices. (shrink)

This paper considers the question of whether Mill's account of the nature and justificatory foundations of deductive logic is psychologistic. Logical psychologism asserts the dependency of logic on psychology. Frequently, this dependency arises as a result of a metaphysical thesis asserting the psychological nature of the subject matter of logic. A study of Mill's System of Logic and his Examination reveals that Mill held an equivocal view of the subject matter of logic, sometimes treating it (...) as a set of psychological processes and at other times as the objects of those processes. The consequences of each of these views upon the justificatory foundations of logic are explored. The paper concludes that, despite his providing logic with a prescriptive function, and despite his avoidance of conceptualism, Mill's theory fails to provide deductive logic with a justificatory foundation that is independent of psychology. (shrink)

Is methodological theory a priori or a posteriori knowledge? It is perhaps a posteriori improvable, somehow. For example, Duhem discovered that since scientists disagree on methods, they do not always know what they are doing. How is methodological innovation possible? If it is inapplicable in retrospect, then it is not universal and so seems defective; if it is, then there is a miracle here. Even so, the new explicit awareness of rules previously implicitly known is in itself beneficial. And so, (...) improved methodology may make for improved methods. Hence, methodology is in part descriptive, in part prescriptive. Knowing this, a methodologist might improve his own studies. For example, Popper would then not hasten to conclude from the fact that past scientists depended on positive evidence that they had better do so in future as well; perhaps a lesser concern with confirmation may increase the productivity of scientific inquiry. (shrink)

In this study, Worsley argues that it is rational to believe in a loving God in the face of evil. Beginning with a critique of Alvin Plantinga, he shows that human freedom is highly complex, and so depends upon complex structures in nature. These are both necessary for freedom but also sufficient for natural evil. He offers close analysis of the evolution of the human brain. The book develops a parallel argument that human evil stems from the evolution of personality.

We study, in an abstract and general framework, formal representations of dependence and groundedness which occur in semantic theories of truth. Our goals are: (a) to relate the different ways in which groundedness is defined according to the way dependence is represented; and (b) to represent different notions of dependence as instances of a suitable generalisation of the mathematical notion of functional dependence.

This paper proposes an analytical taxonomy of ‘mystery’ based upon what makes a mystery mysterious. I begin by distinguishing mysteries that depend on what we do not know (e.g. detective fiction) from mysteries that depend on what we do know (e.g. religious mysteries). Then I distinguish three possible grounds for the latter type. The third and most provocative ground offers a mathematical analogy for how rational reflection can be appropriate to mystery without compromising its intrinsically mysterious character. I conclude with (...) reflections on the metaphysical presuppositions that this understanding of mystery requires. (Published Online January 15 2007). (shrink)

Traditional logical theories are concerned with the characterization of valid reasoning. For such logical theories, the main object of investigation is the notion of entailment, a notion that is construed as a relation between two or more declarative statements, dictating when one of them can be legitimately inferred from the others. In the course of the previous century, however, and especially since the 1970s, the scope of logical theories has become much broader. In particular, logic is no longer only (...) concerned with declarative statements, but also with questions. Accordingly, the field is no longer focusing exclusively on the entailment relation that may hold between two or more statements, but also aims to characterize fundamental relations that may hold between questions, or between questions and statements. For instance, when does a statement resolve a given question? When does a statement evoke a certain question? And when does the resolution of one question depend on the resolu .. (shrink)

The paper introduces a semantics for the language of classical first order logic supplemented with the additional operators and . This semantics understands formulas as tasks. An agent , working as a slave for its master , can carry out the task αβ if it can carry out any one of the two tasks α, β, depending on which of them was requested by the master; similarly, it can carry out xα if it can carry out α for any (...) particular value for x selected by the master; an agent can carry out α→β if it can carry out β as long as it has, as a slave , an agent who carries out α; finally, carrying out P, where P is an atomic formula, simply means making P true; in particular, is a task that no agent can carry out. When restricted to the language of classical logic, the meaning of formulas is isomorphic to their classical meaning, which makes our semantics a conservative extension of classical semantics.This semantics can claim to be a formalization of the resource philosophy associated with linear logic, if resources are understood as agents carrying out tasks. The classical operators of our language correspond to the multiplicative operators of linear logic, while and correspond to the additive conjunction and universal quantifier, respectively.Our formalism may also have a potential to be used in AI as an alternative logic of planning and action. Its main appeal is that it is immune to the frame problem and the knowledge preconditions problem.The paper axiomatically defines a logic L in the above language and proves its soundness and completeness with respect to the task semantics in the following intuitive sense: L α iff α can be carried out by an agent who has nothing but its intelligence for carrying out tasks. This logic is shown to be semidecidable in the full language and decidable when the classical quantifier is forbidden in it. (shrink)

Aim of the paper is to present a new logic of technical malfunction. The need for this logic is motivated by a simple-sounding philosophical question: Is a malfunctioning corkscrew, which fails to uncork bottles, nonetheless a corkscrew? Or in general terms, is a malfunctioning F, which fails to do what Fs do, nonetheless an F? We argue that ‘malfunctioning’ denotes the modifier Malfunctioning rather than a property, and that the answer depends on whether Malfunctioning is subsective or privative. (...) If subsective, a malfunctioning F is an F; if privative, a malfunctioning F is not an F. An intensional logic is required to raise and answer the question, because modifiers operate directly on properties and not on sets or individuals. This new logic provides the formal tools to reason about technical malfunction by means of a logical analysis of the sentence “a is a malfunctioning F”. (shrink)

Sometimes emotions excuse. Fear and anger, for example, sometimes excuse under the headings of (respectively) duress and provocation. Although most legal systems draw the line at this point, the list of potentially excusatory emotions outside the law seems to be longer. One can readily imagine cases in which, for example, grief or despair could be cited as part of a case for relaxing or even eliminating our negative verdicts on those who performed admittedly unjustified wrongs. To be sure, the availability (...) of such excuses depends on what wrong one is trying to excuse. No excuse is available in respect of all wrongs. Some wrongs, indeed, are inexcusable. This throws up the interesting question of what makes a particular emotion apt to excuse a particular wrong. Why is fear, for example, more apt to excuse more serious wrongs than, say, pride or shame? This question leads naturally to another. Why are some emotions, such as lust, greed, and envy, apparently not apt to furnish any excuses at all? Can one not be overcome by them? Can they not drive one to wrongdoing as readily as fear and grief? Or is that not the point? (shrink)

I consider the idea of a propositional logic of location based on the following semantic framework, derived from ideas of Prior. We have a collection L of locations and a collection S of statements such that a statement may be evaluated for truth at each location. Typically one and the same statement may be true at one location and false at another. Given this semantic framework we may proceed in two ways: introducing names for locations, predicates for the relations (...) among them and an “at” preposition to express the value of statements at locations; or introduce statement operators which do not name locations but whose truth-conditional effect depends on the truth or falsity of embedded statements at various locations. The latter is akin to Prior’s approach to tense logic. In any logic of location there will be some basic operators which we can define. By ringing the changes on the topology of locations, different logical systems may be generated, and the challenge for the logician is then in each case to find operators, axioms and rules yielding a proof theory adequate to the semantics. The generality of the approach is illustrated with familiar and not so familiar examples from modal, tense and place logic, mathematics, and even the logic of games. To the memory of Ted Dawson, who introduced me to philosophy and the writings of Arthur Prior. (shrink)

A reactive graph generalizes the concept of a graph by making it dynamic, in the sense that the arrows coming out from a point depend on how we got there. This idea was first applied to Kripke semantics of modal logic in [2]. In this paper we strengthen that unimodal language by adding a second operator. One operator corresponds to the dynamics relation and the other one relates paths with the same endpoint. We explore the expressivity of this interpretation (...) by axiomatizing some natural subclasses of reactive frames. The main objective of this paper is to present a methodology to study reactive logics using the existent classic techniques. (shrink)

The verb ‘to know’ can be used both in ascriptions of propositional knowledge and ascriptions of knowledge of acquaintance. In the formal epistemology literature, the former use of ‘know’ has attracted considerable attention, while the latter is typically regarded as derivative. This attitude may be unsatisfactory for those philosophers who, like Russell, are not willing to think of knowledge of acquaintance as a subsidiary or dependent kind of knowledge. In this paper we outline a logic of knowledge of acquaintance (...) in which ascriptions like ‘Mary knows Smith’ are regarded as formally interesting in their own right, remaining neutral on their relation to ascriptions of propositional knowledge. The resulting logical framework, which is based on Hintikka’s modal approach to epistemic logic, provides a fresh perspective on various issues and notions at play in the philosophical debate on acquaintance. (shrink)

Autonomy is the central idea of modern practical philosophy. Understood as self-legislation, autonomy seems to require that the validity of norms depends on recognition, namely, that their addressees, being autonomous agents, recognise these norms to be valid. But how can one be bound by norms whose validity depends on their being recognised as valid by their addressees? The questions of how autonomous morality and, on this basis, the authoritative character of law can be understood, present persistent puzzles that have been (...) widely discussed, but still await a satisfactory solution. This book presents an analysis of the idea of autonomy as self-legislation and its consequences for law and morality. It links the idea of autonomy with the idea of the balancing of normative arguments, develops a notion of normative arguments as distinct from normative judgements and statements and explains claims to correctness and objectivity that are found in normative discourse. Thus, a 'logic of autonomy' emerges, and it is pervasive in normative reasoning. It connects theses regarding the logic of norms, the structure of balancing, human and fundamental rights, legal validity, legal interpretation, and the relations among legal systems, offering a theory of central elements of normative argumentation, a theory that is undergirded by the mutual relations that exist between and among its parts as well as through the relations that it bears to other theories. Moreover, it offers an alternative to Kantian notions of autonomy and provides solutions to problems that other theories have failed to master. (shrink)

In the paper we define a class of languages for representation o knowledge in those application areas when a complete information about a domain is not available. In the languages we introduce modal operators determined by accessibility relations depending on parameters.

A central argument for the view that God's necessary omniscience [( Bgf p )] precludes freewill is unsound, because the necessity of the consequence is not the necessity of the consequent, and nor is Bgf true. God's belief in some particular proposition f about what I will do is not necessary, as I might do something that makes ~ f true. Fischer and Tognazzini claim that this counterargument argument assumes that I must freely do the something that makes f true. (...) But plainly it doesn't. All that it assumes is that I will do the something that makes f true. It makes no difference whether I do that thing unfreely, or "deterministicall". The argument does not assume the existence of a case of freewill in the face of divine foreknowledge, but instead considers the necessity of God's belief in some particular designated proposition f. The argument does not depend, as Fischer and Tognazzini suppose, on whether God's knowledge is a function of the facts (omniscience) or vice versa (infallibility). (shrink)

The problem of induction reminds us that science cannot wait for empirical hypotheses to be verified and Duhem’s problem reminds us that we cannot expect full refutations either. We must settle for something less. The shape of this something less depends on which features of full verification and refutation we choose to emphasize. If we conceive of verification and refutation as arguments in which evidence entails the hypothesis or its negation, then the central problem of the philosophy of science is (...) to explicate a relation of confirmation or support that is weaker than full entailment but which serves, nonetheless, to justify empirical conclusions. (shrink)

Despite the tendency to think that the justification of revealed truths depends on a verifiable contact with divine reality, this essay argues that the authoritative status of revelations is due to their role in defining a distinctively religious order of judgment. Rather than being immediately apparent to everyone, this kind of authority is local to particular forms of judgment that depend on the principles that frame these ways of thinking. Revelatory claims are logically exempted from the normal demands of justification (...) because of this role they have as definitive judgments, and they share their immunity from ordinary forms of justification with other axiomatic principles. Yet their authority can in certain cases be challenged, and it is a secondary purpose of this essay to bring the various ways of challenging their truth to light. (shrink)

The four main essays in this volume investigate new sectors of the theory of decision, preference, act-characteristics, and action analysis. Herbert A. Simon applies tools developed in the theory of decision-making to the logic of action, and thereby develops a novel concept of heuristic power. Adapting ideas from utility and decision theory, Nicholas Rescher proposes a logic of preference by which conflicting theories proposed by G. H. von Wright, R. M. Chisholm, and others can be systematized. Donald Davidson (...) discusses difficulties in specifying the structure of action sentences to elucidate how their meaning depends on that structure. G. H. von Wright devises a method for describing each “state of the world” that results from an action, in a revision of his own earlier work. Additionally, a study of the logic of norms by Alan Ross Anderson is presented as an appendix, along with an appendix by Rescher outlining the aspects of action. (shrink)

In our paper, "Omniscience, Freedom, and Dependence" (Philosophy and Phenomenological Research 88: 346-367), we argued that recent attempts (by Merricks, McCall, and Westphal) to resolve the dilemma of freedom and foreknowledge fail because they are question-begging. Westphal replied to our paper in an earlier issue of Analysis, and this article is our rejoinder to his reply.

Imagine that you and a duplicate of yourself are lying unconscious, next to each other, about to undergo a complete step-by-step exchange of bits of your bodies. It certainly seems that at no stage in this exchange of bits will you have thereby switched places with your duplicate. Yet it also seems that the end-result, with all the bits exchanged, will be essentially that of the two of you having switched places. Where will you awaken? I claim that one and (...) the same person possesses both bodies, occupies both places and will experience both awakenings, just as a person whose brain has been bisected must at once experience both of the unconnected fields of awareness, even though each of these will falsely appear to him as the entirety of his experience. I also claim that the more usual apparent boundaries of persons are as illusory as those in brain bisection; personal identity remains unchanged through any variation or multiplication of body or mind. In all conscious life there is only one person - I - whose existence depends merely on the presence of a quality that is inherent in all experience - its quality of being mine, the simple immediacy of it for whatever is having experience. One powerful argument for this is statistical: on the ordinary view of personhood it is an incredible coincidence for you (though not for others) that out of 200,000,000 sperm cells the very one required on each occasion for your future existence was first to the egg in each of the begettings of yourself and all your ancestors. The only view that does not make your existence incredible, and that is not therefore (from your perspective) an incredible view, is that any conscious being would necessarily have been you anyway. It is a consequence that self-interest should extend to all conscious organisms. (shrink)

The proper treatment of correlation in evolutionary game theory has unexpected connections with recent philosophical discussions of the theory of rational decision. The Logic of Decision (Jeffrey 1983) provides the correct framework for correlated evolutionary game theory and a variant of "ratifiability" is the appropriate generalization of "evolutionarily stable strategy". The resulting theory unifies the treatment of correlation due to kin, population viscosity, detection, signaling, reciprocal altruism, and behavior-dependent contexts. It is shown that (1) a strictly dominated strategy may (...) be selected, and (2) under conditions of perfect correlation a strictly efficient strategy must be selected. (shrink)

In the paper, we examine tableau systems for R. Epstein’s logics of content relationship: D (Dependence Logic), DD (Dual Dependence Logic), Eq (Logic of Equality of Content), S (Symmetric Relatedness Logic) and R (Nonsymmetric Relatedness Logic) (cf. Epstein in Philos Stud 36:137–173, 1979, Epstein in Rep. Math. Logic 21:19–34, 1987, Klonowski in Logic Log Philos 30(4):579–629, 2021, Krajewski in J Non Class Logic 8:7–33, 1991). The first tableau systems for those (...) logics were defined by Carnielli. However, his approach has some limitations, for example, it requires a proof of functional completeness and axiomatization. Notwithstanding the first two constraints, it does not include all Epstein logics, e.g., logic Eq. Unlike Carnielli’s approach, here we use set-assignment semantics to determine those logics. Since syntax and semantics of a given logic usually determine a minimal syntax and structure of a tableau system for the logic along with other properties, we propose a uniform tableau framework for the logics determined by set-assignment semantics. What distinguishes our tableau systems is that they combine the features of tableaux for propositional logics and syllogistic logics when the problem of content of propositions is analysed in tableau proofs. To denote the content of propositions in the proofs, we use generalised labels (see Jarmużek and Goré in Landscapes in Logic, College Publications, London, 2021). (shrink)

First-order logic with dependent sorts, such as Makkai's first-order logic with dependent sorts (FOLDS), or Aczel's and Belo's dependently typed (intuitionistic) first-order logic (DFOL), may be regarded as logic enriched dependent type theories. Categories with families (cwfs) is an established semantical structure for dependent type theories, such as Martin-Löf type theory. We introduce in this article a notion of hyperdoctrine over a cwf, and show how FOLDS and DFOL fit in this semantical framework. A soundness and (...) completeness theorem is proved for DFOL. The semantics is functorial in the sense of Lawvere, and uses a dependent version of the Lindenbaum-Tarski algebra for a DFOL theory. Agreement with standard first-order semantics is established. Applications of DFOL to constructive mathematics and categorical foundations are given. A key feature is a local propositions-as-types principle. (shrink)

One may formulate the dependent product types of Martin-Löf type theory either in terms of abstraction and application operators like those for the lambda-calculus; or in terms of introduction and elimination rules like those for the other constructors of type theory. It is known that the latter rules are at least as strong as the former: we show that they are in fact strictly stronger. We also show, in the presence of the identity types, that the elimination rule for dependent (...) products–which is a “higher-order” inference rule in the sense of Schroeder-Heister–can be reformulated in a first-order manner. Finally, we consider the principle of function extensionality in type theory, which asserts that two elements of a dependent product type which are pointwise propositionally equal, are themselves propositionally equal. We demonstrate that the usual formulation of this principle fails to verify a number of very natural propositional equalities; and suggest an alternative formulation which rectifies this deficiency. (shrink)