A unified and modular falsification-aware single-succedent Gentzen-style framework is introduced for classical, paradefinite, paraconsistent, and paracomplete logics. This framework is composed of two special inference rules, referred to as the rules of explosion and excluded middle, which correspond to the principle of explosion and the law of excluded middle, respectively. Similar to the cut rule in Gentzen’s LK for classical logic, these rules are admissible in cut-free LK. A falsification-aware single-succedent Gentzen-style sequent calculus fsCL for classical logic (...) is formalized based on the proposed framework. The calculus fsCL is obtained from the existing falsification-aware single-succedent Gentzen-style sequent calculus GN4 for Nelson’s paradefinite (or paraconsistent) four-valued logic N4 by adding the rules of explosion and excluded middle. A falsification-aware single-succedent Gentzen-style sequent calculus GN3 for Nelson’s paracomplete three-valued logic N3 is also obtained from GN4 by adding the rule of explosion. The cut-elimination theorems for fsCL, GN3, and some of their neighbors as well as the Glivenko theorem for fsCL are proved. (shrink)

This paper employs (and defends where needed) a familiar four-part methodology for assessing moral theories. This methodology makes the most popular kind of moral pluralism--here called Ross-style pluralism--look extremely attractive. The paper contends, however, that, if rule-consequentialism's implications match our considered moral convictions as well as Ross-style pluralism's implications do, the methodology makes rule-consequentialism look even more attractive than Ross-style pluralism. The paper then attacks two arguments recently put forward in defence of Ross-style pluralism. (...) One of these arguments is that no moral theory containing some single normative principle to justify general pro tanto duties can do justice to the ineliminable role of judgment in moral thinking. The other argument is that no such theory is plausible in light of the fact that our moral ideas come from disparate historical sources. (shrink)

We discuss a `negative' way of defining frame classes in (multi)modal logic, and address the question of whether these classes can be axiomatized by derivation rules, the `non-ξ rules', styled after Gabbay's Irreflexivity Rule. The main result of this paper is a metatheorem on completeness, of the following kind: If Λ is a derivation system having a set of axioms that are special Sahlqvist formulas and Λ+ is the extension of Λ with a set of non-ξ rules, then Λ+ (...) is strongly sound and complete with respect to the class of frames determined by the axioms and the rules. (shrink)

We know we have thoughts, but are we aware that we have styles of thought? This book, written by one of the most gifted and celebrated social thinkers of our time, is a contribution to understanding the rules of the different styles of thinking. Author Mary Douglas takes us through a range of thought styles from the vulgar to the refined. Throughout this fascinating journey, Thought Styles shows us how the different styles work and how outsiders can learn the styles (...) of insiders. The discussion ranges from the style of folklore to the styles of therapy, shopping, religion, and animal rights. The result is a book full of insight. Readers will find themselves thinking in new ways about the mechanics of communication in everyday life. Professionals and researchers in sociology, communication, and anthropology will especially appreciate this auspicious new book. (shrink)

This study presents the results of an empirical analysis of the relationship between managerial thinking style and ethical decision-making. Data from 200 managers across multiple organizations and industries demonstrated that managers predominantly adopt a utilitarian perspective when forming ethical intent across a series of business ethics vignettes. Consistent with expectations, managers utilizing a balanced linear/nonlinear thinking style demonstrated a greater overall willingness to provide ethical decisions across ethics vignettes compared to managers with a predominantly linear thinking style. (...) However, results comparing the ethical decision-making of balanced thinking managers and nonlinear thinking managers were generally inconsistent across the ethics vignettes. Unexpectedly, managers utilizing a balanced linear/nonlinear thinking style were least likely to adopt an act utilitarian rationale for ethical decision-making across the vignettes, suggesting that balanced thinkers may be more likely to produce ethical decisions by considering a wider range of alternatives and ruling out those that are justified solely on the basis of their outcomes. Implications are discussed for future research and practice related to management education and development, and ethical decision-making theory. (shrink)

In this article, I attempt to restore the philosophical significance of that nonformalizable, noniterable, “singular’ element of natural language that I call “style.” I begin by critically addressing the exclusion of such instances of natural language by both semantics‐oriented logical analysis and a restricted variation of structuralist linguistics. Despite the obvious advantages – with regard to style – of ”pragmatic“approaches to language, such pragmatism merely returns to rule‐determination in the guise of “normativity.” Although style by definition (...) resists any kind of rule‐determination – whether posed in terms of semantics or intersubjective regulations of speech‐acts – there can be no consideration of language that ignores the persistence of style in natural language. In terms of cognition, any discursive agent understands more than allowed by either semantics or speech‐act theory. I ascribe this element of excessive signification to the role of style. My principal thesis is twofold: (1) a hermeneutic approach (exemplified by Schleiermacher) to literature should reveal the heuristically decisive role played by style in philosophy; and, more radically still, (2) style, in fact, may be crucially determinative of philosophical discourse in general. I suggest that a closer scrutiny of the lesser‐known works of Ludwig Wittgenstein, conventionally regarded as having dreamt of a “philosophy without style,” may consolidate the restoration of style's philosophical import. (shrink)

According to the Dilemma Defense, it is question-begging against the incompatibilist defender of the principle of alternative possibilities (PAP) to assume that the agent in a deterministic Frankfurt-style case (FSC) cannot do otherwise in light of causal determinism, but is nevertheless morally responsible. As a result, Fischer (Philos Rev 119:315–336, 2010; Analysis 73:489–496, 2013) attempts to undermine PAP in a different manner via a deterministic FSC. More specifically, Fischer attempts to show that if causal determinism rules out an agent’s (...) moral responsibility, it is not in virtue of its eliminating the agent’s alternative possibilities. I contend that, once we focus upon the distinction between entailment and explanation, the incompatibilist defender of PAP can successfully rebut Fischer’s argument. I argue for this claim while granting Fischer a number of assumptions that only render a defense of PAP more difficult. Additionally, I cast doubt upon Palmer’s (Synthese 191:3847–3864, 2014) critique of Fischer’s argument, which in turn renders my defense of PAP all the more critical. (shrink)

We introduce two Gentzen-style sequent calculus axiomatizations for conservative extensions of basic propositional logic. Our first axiomatization is an ipmrovement of, in the sense that it has a kind of the subformula property and is a slight modification of. In this system the cut rule is eliminated. The second axiomatization is a classical conservative extension of basic propositional logic. Using these axiomatizations, we prove interpolation theorems for basic propositional logic.

We introduce a cyclic proof system for the two-way alternation-free modal μ-calculus. The system manipulates one-sided Gentzen sequents and locally deals with the backwards modalities by allowing analytic applications of the cut rule. The global effect of backwards modalities on traces is handled by making the semantics relative to a specific strategy of the opponent in the evaluation game. This allows us to augment sequents by so-called trace atoms, describing traces that the proponent can construct against the opponent’s strategy. (...) The idea for trace atoms comes from Vardi’s reduction of alternating two-way automata to deterministic one-way automata. Using the multi-focus annotations introduced earlier by Marti and Venema, we turn this trace-based system into a path-based system. We prove that our system is sound for all sequents and complete for sequents not containing trace atoms. (shrink)

Natural deduction with alternatives extends Gentzen–Prawitz-style natural deduction with a single structural addition: negatively signed assumptions, called alternatives. It is a mildly bilateralist, single-conclusion natural deduction proof system in which the connective rules are unmodi_ed from the usual Prawitz introduction and elimination rules — the extension is purely structural. This framework is general: it can be used for (1) classical logic, (2) relevant logic without distribution, (3) affine logic, and (4) linear logic, keeping the connective rules fixed, and varying (...) purely structural rules. The key result of this paper is that the two principles that introduce kinds of irrelevance to natural deduction proofs: (a) the rule of explosion (from a contradiction, anything follows); and (b) the structural rule of vacuous discharge; are shown to be two sides of a single coin, in the same way that they correspond to the structural rule of weakening in the sequent calculus. The paper also includes a discussion of assumption classes, and how they can play a role in treating additive connectives in substructural natural deduction. (shrink)

If we consider Wittgenstein's career as a whole, it appears that he wrote more on the philosophy of logic and mathematics than any other subject. Yet his writings on these subjects have exerted little influence. Indeed, the tide of response to Remarks on the Foundations of Mathematics, which contains the bulk of his latest views of mathematics, has been for the most part overwhelmingly negative. Given his later emphasis on the context-bound character of language, mathematics and logic--where language apparently operates (...) in an maximally precise, clear and general way--represent two of the most difficult cases for Wittgenstein to confront. My thesis aims to defend Wittgenstein from the charges of benighted arrogance traditionally levelled against him. I argue that Wittgenstein's later discussions of mathematics form a central part of a larger philosophical project, internally related to Philosophical Investigations and shaping in specific ways Wittgenstein's reaction to both scepticism and accounts of the nature of logical and mathematical truth. I see Wittgenstein criticizing the unreflective use of mathematical tools in philosophy, not offering a competing philosophy of mathematics. ;Too few of Wittgenstein's readers have been willing to offer detailed exegesis of his writing . This has made it difficult to understand how the aphoristic style of his late writing bears on the philosophical problems being discussed. On my view, the quality of Wittgenstein's writing is intrinsic to his later conception of the nature of logic, mathematics and philosophy. Line by line engagement with his texts is thus imperative in order to achieve an understanding of his philosophical objectives and criticisms. My dissertation offers as a paradigm of such reading a detailed exegesis and criticism of the opening five sections of Remarks on the Foundations of Mathematics. ;I briefly explore in some detail the origin and genesis of Wittgenstein's interest in rule-following, from its roots in the Tractatus's conception of logical syntax. This background illuminates Wittgenstein's later conception of logical truth and his criticisms of Frege's and Russell's arguments for logicism. To explore these criticisms, I focus on Wittgenstein' s discussions of the Frege-Russell definition of "Number" in "logical" terms. Placed in their appropriate philosophical and historical context, Wittgenstein's seemingly outrageous remarks about the nature of proof, mathematical logic and the foundations of mathematics do not simply betray his ignorance. Nor do they commit him to a revisionist attitude toward mathematical practice. Rather, they raise fundamental questions about the philosophical presuppositions lying behind attempts to bring particular mathematical results to bear in philosophy. (shrink)

It has been argued that a successful counterexample to the principle of alternative possibilities must rule out any possibility of the agent making an alternative decision right up to the moment of choice. This paper challenges that assumption. Distinguishing between an ability and an opportunity, this paper presents a Frankfurt-style case in which there is an alternative possibility, but one it is highly improbable that the agent will access. In such a case the agent has only the opportunity, (...) not the ability to do otherwise. (shrink)

This paper presents a recent formalization of a Henkin-style completeness proof for the propositional modal logic S5 using the Lean theorem prover. The proof formalized is close to that of Hughes and Cresswell, but the system, based on a different choice of axioms, is better described as a Mendelson system augmented with axiom schemes for K, T, S4, and B, and the necessitation rule as a rule of inference. The language has the false and implication as the (...) only primitive logical connectives and necessity as the only primitive modal operator. The full source code is available online and has been typechecked with Lean 3.4.2. (shrink)

Admissible rules of a logic are those rules under which the set of theorems of the logic is closed. In this paper, a Gentzen-style framework is introduced for analytic proof systems that derive admissible rules of non-classical logics. While Gentzen systems for derivability treat sequents as basic objects, for admissibility, the basic objects are sequent rules. Proof systems are defined here for admissible rules of classes of modal logics, including K4, S4, and GL, and also Intuitionistic Logic IPC. With (...) minor restrictions, proof search in these systems terminates, giving decision procedures for admissibility in the logics. (shrink)

According to this chapter's arguments, rule‐consequentialism need not be guilty of either collapse into extensional equivalence with act‐consequentialism or incoherence. The chapter also explains how rule‐consequentialism and contractualism differ over what is the best account of impartially justified rules. The final two sections consider rule‐consequentialism's relation to intuitionism and Ross‐style pluralism and whether rule‐consequentialism fails to be a form of consequentialism.

The semantical structures called T×W frames were introduced in (Thomason, 1984) for the Ockhamist temporal-modal language, ℒO, which consists of the usual propositional language augmented with the Priorean operators P and F and with a possibility operator ⋄. However, these structures are also suitable for interpreting an extended language, ℒSO, containing a further possibility operator ⋄s which expresses synchronism among possibly incompatible histories and which can thus be thought of as a cross-history ‘simultaneity’ operator. In the present paper we provide (...) an infinite set of axioms in ℒSO, which is shown to be strongly complete forT ×W-validity. Von Kutschera (1997) contains a finite axiomatization of T×W-validity which however makes use of the Gabbay Irreflexivity Rule (Gabbay, 1981). In order to avoid using this rule, the proof presented here develops a new technique to deal with reflexive maximal consistent sets in Henkin-style constructions. (shrink)

Bergmann’s rule and Allen’s rule played important roles in mid-twentieth century discussions of adaptation, variation, and geographical distribution. Although inherited from the nineteenth-century natural history tradition these rules gained significance during the consolidation of the modern synthesis as evolutionary theorists focused attention on populations as units of evolution. For systematists, the rules provided a compelling rationale for identifying geographical races or subspecies, a function that was also picked up by some physical anthropologists. More generally, the rules provided strong (...) evidence for adaptation by natural selection. Supporters of the rules tacitly, or often explicitly, assumed that the clines described by the rules reflected adaptations for thermoregulation. This assumption was challenged by the physiologists Laurence Irving and Per Scholander based on their arctic research conducted after World War II. Their critique spurred a controversy played out in a series of articles in Evolution, in Ernst Mayr’s Animal Species and Evolution, and in the writings of other prominent evolutionary biologists and physical anthropologists. Considering this episode highlights the complexity and ambiguity of important biological concepts such as adaptation, homeostasis, and self-regulation. It also demonstrates how different disciplinary orientations and styles of scientific research influenced evolutionary explanations, and the consequent difficulties of constructing a truly synthetic evolutionary biology in the decades immediately following World War II. (shrink)

If the mental is subject to indeterminacy, does this rule out the possibility of psychophysical laws? One might think so. However, Jaegwon Kim has argued for the existence of a kind of psychophysical law that is not obviously susceptible to problems posed by indeterminacy. I begin by introducing a weak and relatively uncontroversial indeterminacy thesis. Then, by appealing to constraints on theories of strong supervenience and to general considerations about the nature of indeterminacy, I argue that even Kim’s laws (...) cannot accommodate indeterminacy. The result is an argument against the possibility of Kim‐Style psychophysical laws. (shrink)

This study provides a comparison of thinking style and ethical decision-making patterns between 386 U.S. students and 506 students from the People’s Republic of China enrolled in undergraduate business education in their respective countries. Contrary to our expectations, the Chinese students demonstrated a significantly greater linear thinking style compared to American students. As hypothesized, both Chinese and U.S. students possessing a balanced linear and nonlinear thinking style profile demonstrated greater ethical intent across a series of ethics vignettes. (...) Chinese students also were more likely to adopt an act utilitarian rationale, an ethical philosophy that in practice may violate government regulations or social rules to benefit one’s family instead of society for explaining their decisions across the vignettes. We conclude with a discussion of important theoretical as well as practical and potential future implications based on this comparative study. (shrink)

The third author gave a natural deduction style proof system called the \-calculus for implicational fragment of classical logic in. In -calculus, 2015, Post-proceedings of the RIMS Workshop “Proof Theory, Computability Theory and Related Issues”, to appear), the fourth author gave a natural subsystem “intuitionistic \-calculus” of the \-calculus, and showed the system corresponds to intuitionistic logic. The proof is given with tree sequent calculus, but is complicated. In this paper, we introduce some reduction rules for the \-calculus, and (...) give a simple and purely syntactical proof to the theorem by use of the reduction. In addition, we show that we can give a computation model with rich expressive power with our system. (shrink)

We provide five semantic preservation properties which apply to the various rules -- primitive, derived and admissible -- of Hilbert-style axiomatizations of relevant logics. These preservation properties are with respect to the Routley-Meyer semantics, and consist of various truth- preservations and validity-preservations from the premises to the conclusions of these rules. We establish some deduction theorems, some persistence theorems and some soundness and completeness theorems, for these preservation properties. We then apply the above ideas, as best we can, to (...) the classical sentential and predicate calculi, to normal and non- normal modal logics, and to many- valued logics. (shrink)

If the mental is subject to indeterminacy, does this rule out the possibility of psychophysical laws? One might think so. However, Jaegwon Kim has argued for the existence of a kind of psychophysical law that is not obviously susceptible to problems posed by indeterminacy. I begin by introducing a weak and relatively uncontroversial indeterminacy thesis. Then, by appealing to constraints on theories of strong supervenience and to general considerations about the nature of indeterminacy, I argue that even Kim’s laws (...) cannot accommodate indeterminacy. The result is an argument against the possibility of Kim‐Style psychophysical laws. (shrink)

A distinctive feature of Merleau-Ponty’s thought is the central role he assigns style in generally characterizing embodied agents’ perceptual and cognitive functioning. Despite this, he says little to explain how he conceives style itself. This article therefore aims to clarify Merleau-Ponty’s notion of style and its significance within and beyond his work. It begins by surveying his broad application of the term and using his discussions of painting to reconstruct his conception of style, identifying two major (...) roles Merleau-Ponty attributes it in unifying intentional structures and founding conceptual meaning. His view is related to several competing philosophical conceptions of style to highlight its distinctiveness and some conceptual difficulties in adequately defining style. I then argue that Merleau-Ponty succeeds in coherently distinguishing style from rules by recognizing that style conceives pattern formation, especially the relation of general and particular, in a way contrasting with the identity-based thinking inherent in the functioning of rules. With this distinction I conclude that, although Merleau-Ponty overgeneralizes its role, his conception of style has broader philosophical significance in accurately capturing the nonmechanical cohesion of certain embodied intelligent activities (such as painting) and enabling better understanding of the variety of forms such activities can take. (shrink)

In this paper, we consider multiplicative-additive fragments of affine propositional classical linear logic extended with n-contraction. To be specific, n-contraction (n 2) is a version of the contraction rule where (n+ 1) occurrences of a formula may be contracted to n occurrences. We show that expansions of the linear models for (n + 1)- valued ukasiewicz logic are models for the multiplicative-additive classical linear logic, its affine version and their extensions with n-contraction. We prove the finite axiomatizability for the (...) classes of finite models, as well as for the class of infinite linear models based on the set of rational numbers in the interval [0, 1]. The axiomatizations obtained in a Gentzen-style formulation are equivalent to finite and infinite-valued ukasiewicz logics. (shrink)

Difficulty of distinguishing rules and similarity in categorization comes from reliance on relatively simple manipulation-response designs and a style of modeling with abstract parameters, rather than assessment of intervening and controlling mental states. This commentary proposes a strategy in which rules and similarity would be distinguished by their different roles in a theory interrelating reportable conscious contents in deliberative categorization.

Philosophers employing Frankfurt-style cases to challenge the principle of alternative possibilities have mostly sought to construct scenarios that eliminate as many of an agent’s alternatives as possible—and all alternatives at the moment of action, within the agent’s control—without causally determining the agent’s actions. One of the chief difficulties for this traditional approach is that the closer one gets to ruling out absolutely all alternative possibilities the more it appears that agents’ actions in these cases are causally determined. “Limited-blockage” versions (...) of these cases are meant to sidestep this worry by blocking all and only those alternatives that are intrinsically relevant to moral responsibility (“robust alternatives”) while leaving open all other alternatives, including a significant range of alternatives that are within the agent’s voluntary control at the moment of action. I argue that, owing to the fact that omissions (and not just actions) are capable of constituting robust alternative possibilities, limited-blockage cases cannot avoid collapsing into the more traditional sort of Frankfurt-style case to which they are meant to be an alternative and so are vulnerable to the very same concerns they are meant to avoid. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Gerald Prince WORLDS WITH STYLE Whether it is taken to be a laudable characteristic of verbal artifacts (as in, "This essay is really well written"), a distinctive feature of an individual manner of speaking or writing (as in, "Jane definitely has a style of her own"), an ornamental supplement to that which is expressed (style as elocutio), or an appropriate way of using language in different (...) contexts (there is — or was — a style for tragedy, another one for comedy, and still another one for pastoral; there is a style for speaking at business meetings and other styles better suited to everyday conversations, political rallies, or Ph.D. exams), whether it is taken to be any of these four things (or many other things as well), the style of an utterance is traditionally viewed as a secondary phenomenon different from and added to some primary base. It is the mode of expressing a given matter, the way of "saying" some thing, the how of a what. The same is true when the notion style is used in connection with nonverbal artifacts — we talk about musical styles and about pictorial ones — but also in connection with any number of activities or states of affairs: walking down the street, dancing the tango, being pleasant, or playing ping-pong. Ping-pong players use rackets, a net, and a ball, in accordance with certain rules, when they engage in a casual game; but they are thought to be doing somediing more than merely playing: they are performing an activity (the what) in a particular way. They do it stylishly, idiosyncratically, with a lot of showboating, or in a manner appropriate to the informal context.1 It is somewhat surprising, therefore, that, when it comes to verbal (and nonverbal) representations, style is often thought to be irrelevant to the signified (what is represented) as opposed to the signifier (what represents). Graham Hough writes, for example: "In discussing whatever it is we mean by style we assume mat the primary choice, the choice of subject-matter in the large sense, has already been made.... We can talk about the secondary choice, the stylistic one, in various ways.... But whatever point of view we adopt, it will be the verbal ordonnance that we discuss, not the oudines of die mym, the facts of the case, the ideological or biographical substructure."2 Yet, as I have more than suggested, any what has (or can have) a corresponding how. Besides, both 59 60Philosophy and Literature in formal criticism and informal exchanges, we frequently seem to refer to the how of a signified. When we say, for instance, that a given short story is Kafkaesque, we do not, I think, have its verbal style in mind; and when we claim that a novelistic episode or character comes right out of Alice in Wonderland, we are not talking about linguistic matters. Of course, the fact mat we seem to refer to the how of signifieds (or that we do refer to the how of signifiers) does not necessarily mean mat mere are such things (or that we can describe them). But I suspect that there are (and that we can). I would like to discuss in what follows some of the ways in which we might be able to talk of the style of represented "worlds" more or less meaningfully and systematically and some of the problems attending such talk. For the sake of convenience and because of personal affinities, I will restrict myself to verbal narratives. I will not make a distinction between literary and non-literary ones, since such a distinction is formally and even pragmatically quite problematic. IfI concentrate on fictional narratives, it is, again, because of personal affinities and not because I mink that, when it comes to style, (ontological or other) differences between fiction and nonfiction make very much of a difference. As I will argue, style is in the eye ofthe beholder and, from that point of view, whether or not something is compossible with one's knowledge of the "real world" does not necessarily make it function as fictional or nonfictional; indeed, I am constandy surprised by the real world and I could easily recount... (shrink)

Many different modes of definition have been proposed over time, but none of them allows for circular definitions, since, according to the prevalent view, the term defined would then be lacking a precise signification. I argue that although circular definitions may at times fail uniquely to pick out a concept or an object, sense still can be made of them by using a rule of revision in the style adopted by Anil Gupta and Nuel Belnap in the theory (...) of truth. (shrink)

We introduce a Gentzen-style sequent calculus axiomatization for Basic Predicate Calculus. Our new axiomatization is an improvement of the previous axiomatizations, in the sense that it has the subformula property. In this system the cut rule is eliminated.

RULE or restricted utilitarianism is frequently propounded and just as frequently criticized in the literature. Its various refinements initially involve conceptual adjustments such as clarifying the logical relations between some stateable rule of utility and other moral rules or the specification of a criterion for ranking rules in case of conflict and so forth. It soon becomes clear, comparatively speaking, that a cluster of problems involving justice, personal rights and the denotation of ‘intrinsic good’ cannot be resolved without (...) extending rule utilitarianism as a theory of right conduct and justification; thus the origin of the appellation ‘extended’ rule utilitarianism. In this paper I shall: render an interpreted model of rule utilitarianism that possesses all the logical features of alternative interpretations. Describe a style of argument for extending rule utilitarianism to incorporate a rule of distribution. Such an extension preserves the consistency of rule utilitarianism. Describe a second style of argument for extending rule utilitarianism to incorporate a rule of distribution. Such an extension does not preserve the consistency of rule utilitarianism. (shrink)

In this article, I argue that we need to reconsider some of the stylistic principles that govern writing in analytic philosophy. I suggest that the rules are much more difficult to justify than might be thought at first sight; and may possibly be gendered, given what we know about the reading preferences and writing styles of men and women.

The original text, written in the language and style of 1909, is almost completely unreadable in 2011. I have taken the liberty of editing it and paraphrasing it for the sake of readability; I have made every effort to preserve the author’s original meaning. Section headings and tables have been added by Prof. Steinhart. Note that Figure 1 is by Adams.

This paper argues that Lemmon-style proof systems (those that consist of only introduction and elimination inference rules) have several pedagogical benefits over Copi-style systems (those that make use of inference rules and equivalence rules). It is argued that Lemmon-style systems are easier to learn as they do not require memorizing as many rules, they do not require learning the subtle distinction between a rule of inference and a rule of replacement, and deriving material conditionals is (...) more straightforward. Finally, it is argued that the need for learning provisional assumptions in Lemmon-style rules is not a significant enough reason for choosing the Copi-style system. (shrink)

I consider various principles which might explain our intuitive obligation to rescue people from imminent death at great cost, even when the same resources could produce more benefit elsewhere. Our obligation to rescue is commonly explained in terms of the identifiability of the rescuee, but I reject this account. Instead, I offer two considerations which may come into play. Firstly, I explain the seeming importance of identifiability in terms of an intuitive obligation to prioritise life-extending interventions for people who face (...) a high risk of an early death, and I explain this in turn with a fair innings-style principle which prioritises life-extending interventions for people expected to die young. However, this account is incomplete. It does not explain why we would devote the same resources to rescuing miners stuck down a mine even if they are elderly. We are averse to letting people die suddenly, or separated from friends and family. And so, secondly, I give a new account that explains this in terms of narrative considerations. We value life stories that follow certain patterns, classic patterns which are reflected in many popular myths and stories. We are particularly averse to depriving people of the opportunity to follow some such pattern as they approach death. This means allowing them to sort out their affairs, say goodbyes to family and friends, review their life, or come to terms with death itself. Such activities carry a lot of meaning as ways of closing our life story in the right way. So, for someone who has not been given much notice of their death, an extra month is worth much more than for other patients. Finally, I review the UK National Health Service's end of life premium, which gives priority to patients with short life expectancy. I suggest it falls short in terms of such considerations. For example, the NHS defines its timings in terms of how long the patient can expect to live as at the time of the treatment decision, whereas the timings should be specified in terms of time from diagnosis. (shrink)

The calculus DNL results from the non-associative Lambek calculus NL by splitting the product functor into the right (⊲) and left (⊳) product interacting respectively with the right (/) and left () residuation. Unlike NL, sequent antecedents in the Gentzen-style axiomatics of DNL are not phrase structures (i.e., bracketed strings) but functor-argument structures. DNL − is a weaker variant of DNL restricted to fa-structures of order ≤ 1. When axiomatized by means of introduction/elimination rules for / and , it (...) shows a perfect analogy to NL which DNL lacks. (shrink)

The semantical structures called T x W frames were introduced in (Thomason, 1984) for the Ockhamist temporal-modal language, $[Unrepresented Character]_{o}$ , which consists of the usual propositional language augmented with the Priorean operators P and F and with a possibility operator ◇. However, these structures are also suitable for interpreting an extended language, $[Unrepresented Character]_{so}$ , containing a further possibility operator $\lozenge^{s}$ which expresses synchronism among possibly incompatible histories and which can thus be thought of as a cross-history 'simultaneity' operator. (...) In the present paper we provide an infinite set of axioms in $[Unrepresented Character]_{so}$ , which is shown to be strongly complete for T x W-validity. Von Kutschera (1997) contains a finite axiomatization of T x W-validity which however makes use of the Gabbay Irreflexivity Rule (Gabbay, 1981). In order to avoid using this rule, the proof presented here develops a new technique to deal with reflexive maximal consistent sets in Henkin-style constructions. (shrink)

James Robert Brown’s Who Rules in Science? is an engaging, candid discussion of various postmodern and sociological challenges that have recently been launched at the orthodoxy of science. Interspersed throughout the book are various, largely introductory discussions of issues pertaining to the history of philosophy of science, issues such as realism, unification, instrumentalism, novel predictions, objectivity, and so forth. At the end of the book Brown takes up topics relevant to the politics of science. Altogether it is a pleasant book (...) to read, written with the same warm flair that is characteristic of Brown’s accessible lecturing style. (shrink)

The paper deals with the problem of axiomatizing a system T1 of discrete tense logic, where one thinks of time as the set Z of all the integers together with the operations +1 ("immediate successor") and-1 ("immediate predecessor"). T1 is like the Segerberg-Sundholm system WI in working with so-called infinitary inference ruldes; on the other hand, it differs from W I with respect to (i) proof-theoretical setting, (ii) presence of past tense operators and a "now" operator, and, most importantly, with (...) respect to (iii) the presence in T1 of so-called systematic frame constants, which are meant to hold at exactly one point in a temporal structure and to enable us to express the irreflexivity of such structures. Those frame constants will be seen to play a paramount role in our axiomatization of T1. (shrink)

This study investigates the relationship among ethical philosophy, thinking style, and managerial ethical decision-making. Based on the premise that business ethics is a function of culture and time, we attempt to explore two important questions as to whether the national differences in managerial ethical philosophies remain over time and whether the relationship between thinking style and ethical decision-making is consistent across different national contexts. We conducted a survey on Korean managers’ ethical decision-making and thinking style and made (...) a cross-cultural, cross-temporal comparison with the results presented by previous studies that surveyed Korean and US managers with the same questionnaire at different points in time. Our analysis revealed that Korean managers have become more reliant on rule utilitarianism for ethical decision-making over the last two decades, which is dominantly used by US managers, corroborating our convergence hypothesis built on social contracts theory. However, as opposed to previous research, we found that managers with a balanced linear and nonlinear thinking style do not necessarily make more ethical decisions compared to those with a predominantly linear or nonlinear thinking style. This study contributes to international business ethics literature by presenting a theoretical framework that may explain the convergence of ethical philosophies employed by managers in different national contexts over time, and that the relationship between thinking style and managerial ethical decision-making may not be universal, but contingent on contextual factors. (shrink)

This paper contains a formal treatment of the system of quantified epistemic logic sketched in Appendix II of Carlson (1983). Section 1 defines the syntax and recapitulates the model set rules and principles of the Appendix system. Section 2 defines a possible worlds semantics for this system, and shows that the Appendix system is complete with respect to this semantics. Section 3 extends the system by an explicit truth operatorT it is true that and considers quantification over nonexistent individuals. Section (...) 4 formalizes the idea of variable identity criteria typical of Hintikkian epistemic logic. (shrink)

This paper argues that Lemmon-style proof systems (those that consist of only introduction and elimination inference rules) have several pedagogical benefits over Copi-style systems (those that make use of inference rules and equivalence rules). It is argued that Lemmon-style systems are easier to learn as they do not require memorizing as many rules, they do not require learning the subtle distinction between a rule of inference and a rule of replacement, and deriving material conditionals is (...) more straightforward. Finally, it is argued that the need for learning provisional assumptions in Lemmon-style rules is not a significant enough reason for choosing the Copi-style system. (shrink)

Assorted fruit from forty years' writing, these essays by David Braybrooke discuss (in Part One of the book) a variety of concrete, practical topics that ethical concerns bring into politics: people's interests; their needs as well as their preferences; their work and their commitment to work; their participation in politics and in other group activities. Essays follow on the justice with which theme matters are arranged for and on the common good in which they are consolidated. Justice here inspires a (...) 'departures' approach, which moves from agreement on departures from commutative justice to agreement on measures of distributive justice needed to forestall such departures. Another essay (first published here) radically undermines the odd but entrenched belief that utilitarianism classically licenced, even prescribed, systematically sacrificing the happiness of some people to give others greater pleasure. Part II and Part III of the book concentrate upon the subject of settled social rules, which are devices for securing the objectives treated in Part I. Part II shows that rules are ubiquitous in ethics, since there are no virtues without rules, just as there are no (justified) rules; without virtues. Part Two also shows that rules are as ubiquitous in social phenomena as the causal regularities sought by one school of social science. Part III captures the dialectic of history at least in part by a logical analysis of changes in rules following the onset of quandaries. It then considers how political choices can be both prudent, by keeping within duly considered incremental limits, and yet imaginative enough to escape the recent embarrassments generated by social choice theory. Characteristically versatile in topic and style, Braybrooke offers original light on all theme subjects. One reader has commented, ' His] prose is elegant and always a pleasure to read. Some of the pieces are nothing short of brilliant.' Which did the reader have in mind? Readers may differ (they already have) on just which pieces they would rank highest. (shrink)

We give a Hilbert style axiomatization for the set of formulas in the temporal language with Until and Since which are valid over the real number flow of time. The axiomatization, which is orthodox in the sense of only having the usual temporal rules of inference, is complete with respect to single formulas.

The Babylonian Talmud, compiled from the 2nd to 7th centuries C.E., is the primary source for all subsequent Jewish laws. It is not written in apodeictic style, but rather as a discursive record of (real or imagined) legal (and other) arguments crossing a wide range of technical topics. Thus, it is not a simple matter to infer general methodological principles underlying the Talmudic approach to legal reasoning. Nevertheless, in this article, we propose a general principle that we believe helps (...) to explain the variety of methods used by the Rabbis of the Talmud for resolving uncertainty in matters of Jewish Law (henceforth: Halakhah). Such uncertainty might arise either if the facts of a case are clear but the relevant law is debatable or if the facts themselves are unclear. (shrink)

American-plan semantics with 4 values 1, 0, { {1, 0}} {{}}, interpretable as True, False, Both and Neither, are furnished for a range of logics, including relevant affixing systems. The evaluation rules for extensional connectives take a classical form: in particular, those for negation assume the form 1 (A, a) iff 0 (A, a) and 0 (A, a) iff 1 (A, a), so eliminating the star function *, on which much criticism of relevant logic semantics has focussed. The cost of (...) these classical features is a further relation (or operation), required in evaluating falsity assignments of implication formulae.Two styles of 4 valued relational semantics are developed; firstly a semantics using notions of double truth and double validity for basic relevant systemB and some extensions of it; and secondly, since the first semantics makes heavy weather of validating negation principles such as Contraposition, a reduced semantics using more complex implicational rules for relevant systemC and various of its extensions. To deal satisfactorily with elite systemsR,E andT, however, further complication is inevitable; and a relation of mateship (suggested by the Australian plan) is introduced to permit cross-over from 1 to 0 values and vice versa. (shrink)

In the collection under review, Boghossian assembles 14 of his papers from the last 20 years. 1 They are presented in four groups. The first three groups are focused on, respectively, the nature of mental content, the links of content with self-knowledge and the links of content with a priori knowledge. The two papers of the last group, written with David Velleman, deal with colour and colour concepts. Each group of papers is followed by a bibliography, where responses and possible (...) further reading are listed. Since Boghossian has been a notable contributor on all the topics mentioned, at the very least this collection provides a useful entry point to worthwhile literature on good problems. But one can say much more. Boghossian writes with acuity and ingenuity and his style is clear and direct. He is prepared to challenge and rethink venerable doctrines and is also prepared to revise his own views when good arguments are brought against them. He shows admirable persistence, in returning to topics from different angles, bringing out more implications of the positions explored and the complexity of the issues. He does not at any point gloss over difficulties or pretends to more completeness or decisiveness than the material warrants. So we have here much rigorous and judicious discussion of a thought-provoking kind.The fourth group of papers, on colour, is not closely linked in theme to the rest of the collection. And although the issues merit further consideration we will not pursue them here. Let me just note that in these papers Boghossian and Velleman lay out two of the more attractive realist accounts of colour, dispositional and physicalist, and argue that no current version of such theories is acceptable.In the sections which follow, I shall first consider briefly the papers on content and …. (shrink)