Logic arguably plays a role in the normativity of reasoning. In particular, there are plausible norms of belief/disbelief whose antecedents are constituted by claims about what follows from what. But is logic also relevant to the normativity of agnostic attitudes? The question here is whether logical entailment also puts constraints on what kinds of things one can suspend judgment about. In this paper I address that question and I give a positive answer to it. In particular, I advance two logical (...) norms of agnosticism, where the first one allows us to assess situations in which the subject is agnostic about the conclusion of a valid argument and the second one allows us to assess situations in which the subject is agnostic about one of the premises of a valid argument. (shrink)

A logic is called 'paraconsistent' if it rejects the rule called 'ex contradictione quodlibet', according to which any conclusion follows from inconsistent premises. While logicians have proposed many technically developed paraconsistent logical systems and contemporary philosophers like Graham Priest have advanced the view that some contradictions can be true, and advocated a paraconsistent logic to deal with them, until recent times these systems have been little understood by philosophers. This book presents a comprehensive overview on paraconsistent logical systems to change (...) this situation. The book includes almost every major author currently working in the field. The papers are on the cutting edge of the literature some of which discuss current debates and others present important new ideas. The editors have avoided papers about technical details of paraconsistent logic, but instead concentrated upon works that discuss more 'big picture' ideas. Different treatments of paradoxes takes centre stage in many of the papers, but also there are several papers on how to interpret paraconistent logic and some on how it can be applied to philosophy of mathematics, the philosophy of language, and metaphysics. (shrink)

Philosophy of biology is often said to have emerged in the last third of the twentieth century. Prior to this time, it has been alleged that the only authors who engaged philosophically with the life sciences were either logical empiricists who sought to impose the explanatory ideals of the physical sciences onto biology, or vitalists who invoked mystical agencies in an attempt to ward off the threat of physicochemical reduction. These schools paid little attention to actual biological science, and as (...) a result philosophy of biology languished in a state of futility for much of the twentieth century. The situation, we are told, only began to change in the late 1960s and early 1970s, when a new generation of researchers began to focus on problems internal to biology, leading to the consolidation of the discipline. In this paper we challenge this widely accepted narrative of the history of philosophy of biology. We do so by arguing that the most important tradition within early twentieth-century philosophy of biology was neither logical empiricism nor vitalism, but the organicist movement that flourished between the First and Second World Wars. We show that the organicist corpus is thematically and methodologically continuous with the contemporary literature in order to discredit the view that early work in the philosophy of biology was unproductive, and we emphasize the desirability of integrating the historical and contemporary conversations into a single, unified discourse. (shrink)

Philosophers such as Nietzsche, Heidegger, Derrida, Deleuze and Gendlin pronounce that difference must be understood as ontologically prior to identity. They teach that identity is a surface effect of difference, that to understand the basis of logico-mathematical idealities we must uncover their genesis in the fecundity of differentiation. In this paper, I contrast Heidegger’s analyses of the present to hand logico-mathematical object, which he discuses over the course of his career in terms of the ‘as’ structure, temporalization and enframing , (...) with the approaches of Gendlin and Deleuze, supplementing this discussion with Husserl’s investigations of mathematical idealities. Deleuze and Gendlin distinguish between the representational power a logical pattern has in itself, apart from its virtual generative source, to exactly repeat itself, and the way this self-same pattern is generated and changed by the larger situational texture within which it is embedded. In so doing, they misconstrue the empty, meaningless temporalization of logical calculation as the explicitly preserving carrying-through of already instituted implicit sense. For Heidegger, by contrast, logical inference is less a supplement to or development of implicit experience than a narrowing of its scope , a deficient mode of handiness. Experiencing something as present to hand extension modifies the relevant usefulness of ‘as’ structured comportment by stripping away what is meaningful in our relation with beings, and in the process stripping away its intelligibility. Thus, contrary to the assertions of Deleuze and Gendlin, extensive repetition does not carry through intelligible, relevant meaning, it dissolves understanding into the nihilism of empty calculation. (shrink)

This paper analyses a hitherto unknown technique of using logic diagrams to create argument maps in eristic dialectics. The method was invented in the 1810s and -20s by Arthur Schopenhauer, who is considered the originator of modern eristic. This technique of Schopenhauer could be interesting for several branches of research in the field of argumentation: Firstly, for the field of argument mapping, since here a hitherto unknown diagrammatic technique is shown in order to visualise possible situations of arguments in a (...) dialogical controversy. Secondly, the art of controversy or eristic, since the diagrams do not analyse the truth of judgements and the validity of inferences, but the persuasiveness of arguments in a dialogue. (shrink)

The logicality of language is the hypothesis that the language system has access to a ‘natural’ logic that can identify and filter out as unacceptable expressions that have trivial meanings—that is, that are true/false in all possible worlds or situations in which they are defined. This hypothesis helps explain otherwise puzzling patterns concerning the distribution of various functional terms and phrases. Despite its promise, logicality vastly over-generates unacceptability assignments. Most solutions to this problem rest on specific stipulations about the properties (...) of logical form—roughly, the level of linguistic representation which feeds into the interpretation procedures—and have substantial implications for traditional philosophical disputes about the nature of language. Specifically, contextualism and semantic minimalism, construed as competing hypotheses about the nature and degree of context-sensitivity at the level of logical form, suggest different approaches to the over-generation problem. In this paper, I explore the implications of pairing logicality with various forms of contextualism and semantic minimalism. I argue that to adequately solve the over-generation problem, logicality should be implemented in a constrained contextualist framework. (shrink)

This paper examines the role of ?situations? in John Dewey's philosophy of logic. To do this properly it is necessary to contrast Dewey's conception of experience and mentality with views characteristic of modern epistemology. The primary difference is that, rather than treat experience as peripheral and or external to mental functions (reason, etc.), we should treat experience as a field in and as a part of which thinking takes place. Experience in this broad sense subsumes theory and fact, hypothesis and (...) evidence, reason and observation, thought and perception. Logic in this view is a formal study of the generic features of all possible kinds of experience in this broad (thick, deep, wide, multifaceted) sense. The goal of this paper is to explain what Dewey thinks a situation is in the context of this view of experience, and to argue for the fundamental importance of that idea for logic and philosophy in general. (shrink)

Modal logic is one of philosophy’s many children. As a mature adult it has moved out of the parental home and is nowadays straying far from its parent. But the ties are still there: philosophy is important to modal logic, modal logic is important for philosophy. Or, at least, this is a thesis we try to defend in this chapter. Limitations of space have ruled out any attempt at writing a survey of all the work going on in our field—a (...) book would be needed for that. Instead, we have tried to select material that is of interest in its own right or exemplifies noteworthy features in interesting ways. Here are some themes that have guided us throughout the writing: • The back-and-forth between philosophy and modal logic. There has been a good deal of give-and-take in the past. Carnap tried to use his modal logic to throw light on old philosophical questions, thereby inspiring others to continue his work and still others to criticise it. He certainly provoked Quine, who in his turn provided—and continues to provide—a healthy challenge to modal logicians. And Kripke’s and David Lewis’s philosophies are connected, in interesting ways, with their modal logic. Analytic philosophy would have been a lot different without modal logic! • The interpretation problem. The problem of providing a certain modal logic with an intuitive interpretation should not be conflated with the problem of providing a formal system with a model-theoretic semantics. An intuitively appealing model-theoretic semantics may be an important step towards solving the interpretation problem, but only a step. One may compare this situation with that in probability theory, where definitions of concepts like ‘outcome space’ and ‘random variable’ are orthogonal to questions about “interpretations” of the concept of probability. • The value of formalisation. Modal logic sets standards of precision, which are a challenge to—and sometimes a model for—philosophy. Classical philosophical questions can be sharpened and seen from a new perspective when formulated in a framework of modal logic. On the other hand, representing old questions in a formal garb has its dangers, such as simplification and distortion. • Why modal logic rather than classical (first or higher order) logic? The idioms of modal logic—today there are many!—seem better to correspond to human ways of thinking than ordinary extensional logic. (Cf. Chomsky’s conjecture that the NP + VP pattern is wired into the human brain.) In his An Essay in Modal Logic (1951) von Wright distinguished between four kinds of modalities: alethic (modes of truth: necessity, possibility and impossibility), epistemic (modes of being known: known to be true, known to be false, undecided), deontic (modes of obligation: obligatory, permitted, forbidden) and existential (modes of existence: universality, existence, emptiness). The existential modalities are not usually counted as modalities, but the other three categories are exemplified in three sections into which this chapter is divided. Section 1 is devoted to alethic modal logic and reviews some main themes at the heart of philosophical modal logic. Sections 2 and 3 deal with topics in epistemic logic and deontic logic, respectively, and are meant to illustrate two different uses that modal logic or indeed any logic can have: it may be applied to already existing (non-logical) theory, or it can be used to develop new theory. (shrink)

I use modal logic and transfinite set-theory to define metaphysical foundations for a general theory of computation. A possible universe is a certain kind of situation; a situation is a set of facts. An algorithm is a certain kind of inductively defined property. A machine is a series of situations that instantiates an algorithm in a certain way. There are finite as well as transfinite algorithms and machines of any degree of complexity (e.g., Turing and super-Turing machines and more). There (...) are physically and metaphysically possible machines. There is an iterative hierarchy of logically possible machines in the iterative hierarchy of sets. Some algorithms are such that machines that instantiate them are minds. So there is an iterative hierarchy of finitely and transfinitely complex minds. (shrink)

Today, there are many natural sciences, one of which is physics, but there is no science in the sense of a Theory of Nature. In our everyday life, the opinion is rightly held that there is only one nature, but whether this opinion stands up to reflection is questionable. When we apply the speculation that Aristotle developed in Metaphysics Λ to his Physics, we will see, that Aristotle has developed a Theory of Nature that consists in posing the question of (...) the being of the natural being (Frage nach dem Sein des Naturseienden). The standardinterpretation wants us to believe that Aristotle founded a substance metaphysics with a corresponding theology, and that he practised natural science. But, our hermeneutical situation could lead us to an "Aristotle today" and free us from old beliefs so that we, like Thomas Aquinas and others, could learn from a contemporary Aristotle as an immediate interlocutor. One of the learning points, for example, would be that questions are more crucial than new assertions, even if they are sophisticated, and that unassertive thinking (unbehauptendes Denken) in a topical attitude can lead us to insight into the multiplicity of worlds. This insight would have immediate consequences for our behaviour towards our co-inhabitants of our planet and towards our environment. (shrink)

Those who conceive logic as a science have generally favoured one of two alternative conceptions as to what the subject-matter of this science ought to be. On the one hand is the nowadays somewhat old-fashioned-seeming view of logic as the science of judgment, or of thinking or reasoning activities in general. On the other hand is the view of logic as a science of ideal meanings, 'thoughts', or 'propositions in themselves'. There is, however, a third alternative conception, which enjoyed only (...) a brief flowering in the years leading up to the first World War, but whose lingering presence can be detected in the background of more recent ontologising trends in logic, as for example in the 'situation semantics' of Barwise and Perry. This third conception sees logic as a science of special objects called 'Sachverhalte' or 'states of affairs'. A view of this sort is present in simplified form in the works of Meinong, but it received its definitive formulation in the writings of Adolf Reinach, a student of Husserl who is otherwise noteworthy for having anticipated, in a monograph of 1913, large chunks of what later became known as the theory of speech acts.(1). (shrink)

In researching presuppositions dealing with logic and dynamic of belief we distinguish two related parts. The first part refers to presuppositions and logic, which is not necessarily involved with intentional operators. We are primarily concerned with classical, free and presuppositonal logic. Here, we practice a well known Strawson’s approach to the problem of presupposition in relation to classical logic. Further on in this work, free logic is used, especially Van Fraassen’s research of the role of presupposition in supervaluations logical systems. (...) At the end of the first part, presuppositional logic, advocated by S.K. Thomason, is taken into consideration. The second part refers to the presuppositions in relation to the logic of the dynamics of belief. Here the logic of belief change is taken into consideration and other epistemic notions with immanent mechanism for the presentation of the dynamics. Three representative and dominant approaches are evaluated. First, we deal with new, less classical, situation semantics. Besides Strawson’s theory, the second theory is the theory of the belief change, developed by Alchourron, Gärdenfors, and Makinson (AGM theory). At the end, the oldest, universal, and dominant approach is used, recognized as Hintikka’s approach to the analysis of epistemic notions. (shrink)

This paper has two aims. First, it sets out an interpretation of the relevant logic E of relevant entailment based on the theory of situated inference. Second, it uses this interpretation, together with Anderson and Belnap’s natural deduc- tion system for E, to generalise E to a range of other systems of strict relevant implication. Routley–Meyer ternary relation semantics for these systems are produced and completeness theorems are proven. -/- .

2nd edition. Many-valued logics are those logics that have more than the two classical truth values, to wit, true and false; in fact, they can have from three to infinitely many truth values. This property, together with truth-functionality, provides a powerful formalism to reason in settings where classical logic—as well as other non-classical logics—is of no avail. Indeed, originally motivated by philosophical concerns, these logics soon proved relevant for a plethora of applications ranging from switching theory to cognitive modeling, and (...) they are today in more demand than ever, due to the realization that inconsistency and vagueness in knowledge bases and information processes are not only inevitable and acceptable, but also perhaps welcome. The main modern applications of (any) logic are to be found in the digital computer, and we thus require the practical knowledge how to computerize—which also means automate—decisions (i.e. reasoning) in many-valued logics. This, in turn, necessitates a mathematical foundation for these logics. This book provides both these mathematical foundation and practical knowledge in a rigorous, yet accessible, text, while at the same time situating these logics in the context of the satisfiability problem (SAT) and automated deduction. The main text is complemented with a large selection of exercises, a plus for the reader wishing to not only learn about, but also do something with, many-valued logics. (shrink)

We reconsider the pragmatic interpretation of intuitionistic logic [21] regarded as a logic of assertions and their justi cations and its relations with classical logic. We recall an extension of this approach to a logic dealing with assertions and obligations, related by a notion of causal implication [14, 45]. We focus on the extension to co-intuitionistic logic, seen as a logic of hypotheses [8, 9, 13] and on polarized bi-intuitionistic logic as a logic of assertions and conjectures: looking at the (...) S4 modal translation, we give a de nition of a system AHL of bi-intuitionistic logic that correctly represents the duality between intuitionistic and co-intuitionistic logic, correcting a mistake in previous work [7, 10]. A computational interpretation of cointuitionism as a distributed calculus of coroutines is then used to give an operational interpretation of subtraction.Work on linear co-intuitionism is then recalled, a linear calculus of co-intuitionistic coroutines is de ned and a probabilistic interpretation of linear co-intuitionism is given as in [9]. Also we remark that by extending the language of intuitionistic logic we can express the notion of expectation, an assertion that in all situations the truth of p is possible and that in a logic of expectations the law of double negation holds. Similarly, extending co-intuitionistic logic, we can express the notion of conjecture that p, de ned as a hypothesis that in some situation the truth of p is epistemically necessary. (shrink)

In this work we propose an encoding of Reiter’s Situation Calculus solution to the frame problem into the framework of a simple multimodal logic of actions. In particular we present the modal counterpart of the regression technique. This gives us a theorem proving method for a relevant fragment of our modal logic.

In this paper I try to clarify and systematize some contributions with regard to (a) the main aspects of crisis situations that impose the management of emotions, (b) the correlation of certain social emotions with the factors that trigger them and their related tendencies to act, (c) the essential elements of emotional experience, (d) the differentiation of appropriate emotional reactions to a crisis situation from the inappropriate ones; (e) the in-stances in which emotions can be managed, and (f) the balance (...) between rationality and affectivity in the organization’s response to the risks or crises which it faces. By means of logical correlations I arrived at the following conclusions. Regardless of the social sphere in which the crisis makes itself felt, regardless of its type, phase or damage control strategies, the rational control of emotions contributes significantly to overcoming the crisis situation. Beyond the specificities, crises involve digressions form the norms of rightful conduct, breaches of the social norms that support institutions (as spontaneous order structures) and maladaptive reactions to reality. They can be corrected through a good management of emotions, with the caveat that we are not dealing with a problem of knowledge, but rather with one of will and character. All people can identify the adaptive emotional responses to a crisis situation, but only a few prefer them and train assiduously to use them. (shrink)

Analogy-making is finding analogies between different situations. In this paper, we provide a new model of computational analogy-making which uses Situation Theory as its formal background. Situation Theory is a semantic and logical theory which provides a naturalistic way to represent relations in situations. The system described in this paper is aimed at solving analogy problems made by basic geometric figures in a chessboard-like environment.

The aim of this paper is to introduce a system of dynamic deontic logic in which the main problems related to the de finition of deontic concepts, especially those emerging from a standard analysis of permission in terms of possibility of doing an action without incurring in a violation of the law, are solved. The basic idea is to introduce two crucial distinctions allowing us to differentiate (i) what is ideal with respect to a given code, which fixes the types (...) of action that are abstractly prescribed, and what is ideal with respect to the specific situation in which the agent acts, and (ii) the transitions associated with actions and the results of actions, which can obtain even without the action being performed. (shrink)

According to Jago (2014a), logical omniscience is really part of a deeper paradox. Jago develops an epistemic logic with principles of indeterminate closure to solve this paradox, but his official semantics is difficult to navigate, it is motivated in part by substantive metaphysics, and the logic is not axiomatized. In this paper, I simplify this epistemic logic by adapting the hyperintensional semantic framework of Sedlár (2021). My first goal is metaphysical neutrality. The solution to the epistemic paradox should not require (...) appeal to a metaphysics of truth-makers, situations, or impossible worlds, by contrast with Jago’s official semantics. My second goal is to elaborate on the proof theory. I show how to axiomatize a family of logics with principles of indeterminate epistemic closure. (shrink)

The investigation into logical form and structure of natural sciences and mathematics covers a significant part of contemporary philosophy. In contrast to this, the metatheory of normative theories is a slowly developing research area in spite of its great predecessors, such as Aristotle, who discovered the sui generis character of practical logic, or Hume, who posed the “is-ought” problem. The intrinsic reason for this situation lies in the complex nature of practical logic. The metatheory of normative educational philosophy and theory (...) inherits all the difficulties inherent in the general metatheory but has also significantly contributed to its advancement. In particular, the discussion on its mixed normative-descriptive character and complex composition has remained an important part of research in educational philosophy and theory. The two points seem to be indisputable. First, the content of educational philosophy and theory is a complex one, connecting different disciplines. Second, these disciplines are integrated within the logical form of practical inference or means-end reasoning. On the other hand, the character of consequence relation in this field, although generally recognized as specific, represents an unresolved prob- lem, a solution of which requires a sophisticated logical theory and promises to influence the self- understanding of educational philosophy and theory. (shrink)

In this paper, I attempt to clarify the heart of Dewey’s philosophy: his method (denotative method (DM) / pattern of inquiry (PI)). Despite the traditional understanding of Dewey as anti-foundationalist, I want to show that Dewey did have metaphysical foundations for his method: the principle of continuity or theory of emergentism. I also argue that Dewey’s metaphysical position is better named as ‘cultural emergentism’, rather than his own term ‘cultural naturalism’. What Dewey called ‘common sense’ in his Logic, Husserl termed (...) as the ‘life-world’ in his Crisis. I compare two perspectives of dealing with the phenomenon and conclude that for Dewey, the difference between natural sciences and the common sense inquiry is that of subject-matter but not of method. Thus, the goal is to find the unified method to be applied in both domains. Whereas Husserl was more pessimistic: for him, the difference was not only in subject-matter, but in the very methods. Following that discussion, I also attempt to reformulate the hard problem of consciousness in Deweyan terms. In the end, I compare Dewey’s DM / PI with Popper’s understandings of scientific method and conclude that there is no significant difference between the two and that Dewey’s method could also be looked at as hypothetic-deductive method, with the only difference in emphases. (shrink)

"A Little More Logical" is the perfect guide for anyone looking to improve their critical thinking and logical reasoning skills. With chapters on everything from logic basics to fallacies of weak induction to moral reasoning, this book covers all the essential concepts you need to become a more logical thinker. You'll learn about influential figures in the field of logic, such as Rudolph Carnap, Betrrand Russell, and Ada Lovelace, and how to apply your newfound knowledge to real-world situations. Whether you're (...) looking to engage in debates with others, make better decisions in your personal and professional life, or simply want to improve your overall critical thinking skills, "A Little More Logical" has you covered. So why wait? Start learning and become a little more logical today! -/- "A Little More Logical" differs from typical logical textbooks in a number of ways. One key difference is its emphasis on engaging and relatable examples and case studies. Rather than simply presenting dry definitions and concepts, the book uses fables, stories, and real-world situations to illustrate key ideas and make them more relatable for readers. -/- Another unique aspect of "A Little More Logical" is its inclusion of "Minds that Mattered" sections, which highlight the contributions and insights of influential figures in the field of logic and critical thinking. These sections provide readers with a deeper understanding of the history and development of logical principles and offer valuable context for the concepts being discussed. -/- Additionally, "A Little More Logical" covers a wide range of topics beyond the basics of logic and argument evaluation. Chapters on moral reasoning, probability and inductive logic, scientific reasoning, conspiracy theories, statistical reasoning, and the history of formal logic offer a more comprehensive and well-rounded understanding of logic and critical thinking. -/- Overall, "A Little More Logical" stands out as a dynamic and engaging resource for anyone looking to improve their logical reasoning abilities. Its relatable examples, historical context, and broad coverage make it a valuable resource for anyone interested in mastering the principles of logic. -/- This is a free, Creative-Commons-licensed book. (shrink)

The thesis that the two-valued system of classical logic is insufficient to explanation the various intermediate situations in the entity, has led to the development of many-valued and fuzzy logic systems. These systems suggest that this limitation is incorrect. They oppose the law of excluded middle (tertium non datur) which is one of the basic principles of classical logic, and even principle of non-contradiction and argue that is not an obstacle for things both to exist and to not exist at (...) the same time. However, contrary to these claims, there is no inadequacy in the two-valued system of classical logic in explanation the intermediate situations in existence. The law of exclusion and the intermediate situations in the external world are separate things. The law of excluded middle has been inevitably accepted by other logic systems which are considered to reject this principle. The many-valued and the fuzzy logic systems do not transcend the classical logic. Misconceptions from incomplete information and incomplete research are effective in these criticisms. In addition, it is also effective to move the discussion about the intellectual conception (tasawwur) into the field of judgmental assent (tasdiq) and confusion of the mawhum (imaginable) with the ma‘kûl (intellegible). (shrink)

Gila Sher approaches knowledge from the perspective of the basic human epistemic situation—the situation of limited yet resourceful beings, living in a complex world and aspiring to know it in its full complexity. What principles should guide them? Two fundamental principles of knowledge are epistemic friction and freedom. Knowledge must be substantially constrained by the world (friction), but without active participation of the knower in accessing the world (freedom) theoretical knowledge is impossible. This requires a grounding of all knowledge, empirical (...) and abstract, in both mind and world, but the fall of traditional foundationalism has led many to doubt the viability of this ‘classical’ project. Sher challenges this skepticism, charting a new foundational methodology, foundational holism, that differs from others in being holistic, world-oriented, and universal (i.e., applicable to all fields of knowledge). Using this methodology, Epistemic Friction develops an integrated theory of knowledge, truth, and logic. This includes (i) a dynamic model of knowledge, incorporating some of Quine’s revolutionary ideas while rejecting his narrow empiricism, (ii) a substantivist, non-traditional correspondence theory of truth, and (iii) an outline of a joint grounding of logic in mind and world. The model of knowledge subjects all disciplines to demanding norms of both veridicality and conceptualization. The correspondence theory is robust and universal yet not simplistic or naive, admitting diverse forms of correspondence. Logic’s grounding in the world brings it in line with other disciplines while preserving, and explaining, its strong formality, necessity, generality, and normativity. (shrink)

Hilbert’s choice operators τ and ε, when added to intuitionistic logic, strengthen it. In the presence of certain extensionality axioms they produce classical logic, while in the presence of weaker decidability conditions for terms they produce various superintuitionistic intermediate logics. In this thesis, I argue that there are important philosophical lessons to be learned from these results. To make the case, I begin with a historical discussion situating the development of Hilbert’s operators in relation to his evolving program in the (...) foundations of mathematics and in relation to philosophical motivations leading to the development of intuitionistic logic. This sets the stage for a brief description of the relevant part of Dummett’s program to recast debates in metaphysics, and in particular disputes about realism and anti-realism, as closely intertwined with issues in philosophical logic, with the acceptance of classical logic for a domain reflecting a commitment to realism for that domain. Then I review extant results about what is provable and what is not when one adds epsilon to intuitionistic logic, largely due to Bell and DeVidi, and I give several new proofs of intermediate logics from intuitionistic logic+ε without identity. With all this in hand, I turn to a discussion of the philosophical significance of choice operators. Among the conclusions I defend are that these results provide a finer-grained basis for Dummett’s contention that commitment to classically valid but intuitionistically invalid principles reflect metaphysical commitments by showing those principles to be derivable from certain existence assumptions; that Dummett’s framework is improved by these results as they show that questions of realism and anti-realism are not an “all or nothing” matter, but that there are plausibly metaphysical stances between the poles of anti-realism and realism, because different sorts of ontological assumptions yield intermediate rather than classical logic; and that these intermediate positions between classical and intuitionistic logic link up in interesting ways with our intuitions about issues of objectivity and reality, and do so usefully by linking to questions around intriguing everyday concepts such as “is smart,” which I suggest involve a number of distinct dimensions which might themselves be objective, but because of their multivalent structure are themselves intermediate between being objective and not. Finally, I discuss the implications of these results for ongoing debates about the status of arbitrary and ideal objects in the foundations of logic, showing among other things that much of the discussion is flawed because it does not recognize the degree to which the claims being made depend on the presumption that one is working with a very strong logic. (shrink)

The goal of the present paper is to construct a formal explication of the pluralistic ignorance explanation of the bystander effect. The social dynamics leading to inaction is presented, decomposed, and modeled using dynamic epistemic logic augmented with ‘transition rules’ able to characterize agent behavior. Three agent types are defined: First Responders who intervene given belief of accident; City Dwellers, capturing ‘apathetic urban residents’ and Hesitators, who observe others when in doubt, basing subsequent decision on social proof. It is shown (...) how groups of the latter may end in a state of pluralistic ignorance leading to inaction. Sequential models for each agent type are specified, and their results compared to empirical studies. It is concluded that only the Hesitator model produces reasonable results. (shrink)

I construct a quantum-logical model of the type of situation that seems to be at the root of the problem of interpreting the projection postulate (Luders' rule) as a criterion of minimal disturbance. It is shown that the most natural way of characterizing minimal disturbance leads to contradictory conclusions concerning the final state.

In the paper we provide an overview of issues related to the models used in the research on the logic of norms and actions. We present two models of the variability of the world: temporal (acyclic) and atemporal (cyclic). In the first one the past is always clearly defined, and the future is potentially “branched”. The second type of model allows for a return to the situation that took place. Next we describe different approaches towards agency modeling. We present the (...) most important paradigms, including the logic of actions, where actions are interpreted as transitions between the situations and STIT logic, which states only the responsibility of the agent for particular states of affairs. We discuss questions of determinism and indeterminism of actions, identification of basic actions and operations and the issue of identity. The final part of the paper is devoted to deontic categories. In particular, the applicability of the concepts of strong and weak permission and prohibition in different situational contexts, and their relationship to the two concepts of obligation: abstract and derived. (shrink)

This article provides the foundation for a new predictive theory of animal learning that is based upon a simple logical model. The knowledge of experimental subjects at a given time is described using logical equations. These logical equations are then used to predict a subject’s response when presented with a known or a previously unknown situation. This new theory suc- cessfully anticipates phenomena that existing theories predict, as well as phenomena that they cannot. It provides a theoretical account for phenomena (...) that are beyond the domain of existing models, such as extinction and the detection of novelty, from which “external inhibition” can be explained. Examples of the methods applied to make predictions are given using previously published results. The present theory proposes a new way to envision the minimal functions of the nervous system, and provides possible new insights into the way that brains ultimately create and use knowledge about the world. (shrink)

Edward Nieznański developed two logical systems to deal with the problem of evil and to refute religious determinism. However, when formalized in first-order modal logic, two axioms of each system contradict one another, revealing that there is an underlying minimal set of axioms enough to settle the questions. In this article, we develop this minimal system, called N3, which is based on Nieznański’s contribution. The purpose of N3 is to solve the logical problem of evil through the defeat of a (...) version of religious determinism. On the one hand, these questions are also addressed by Nieznański’s systems, but, on the other hand, they are obtained in N3 with fewer assumptions. Our approach can be considered a case of logic of religion, that is, of logic applied to religious discourse, as proposed by Józef Maria Bocheński; in this particular case, it is a discourse in theodicy, which is situated in the context of the philosophy of religion. (shrink)

In the paper we present a formal system motivated by a specific methodology of creating norms. According to the methodology, a norm-giver before establishing a set of norms should create a picture of the agent by creating his repertoire of actions. Then, knowing what the agent can do in particular situations, the norm-giver regulates these actions by assigning deontic qualifications to each of them. The set of norms created for each situation should respect (1) generally valid deontic principles being the (...) theses of our logic and (2) facts from the ontology of action whose relevance for the systems of norms we postulate. (shrink)

The aim of this paper is to emphasize the fact that for all finitely-many-valued logics there is a completely systematic relation between sequent calculi and tableau systems. More importantly, we show that for both of these systems there are al- ways two dual proof sytems (not just only two ways to interpret the calculi). This phenomenon may easily escape one’s attention since in the classical (two-valued) case the two systems coincide. (In two-valued logic the assignment of a truth value and (...) the exclusion of the opposite truth value describe the same situation.). (shrink)

Developing a suggestion of Wittgenstein, I provide an account of truth tables as formulas of a formal language. I define the syntax and semantics of TPL (the language of Tabular Propositional Logic), and develop its proof theory. Single formulas of TPL, and finite groups of formulas with the same top row and TF matrix (depiction of possible valuations), are able to serve as their own proofs with respect to metalogical properties of interest. The situation is different, however, for groups of (...) formulas whose top rows differ. For them I provide (i) a tree-style system of ‘row tree proofs’, which is shown to be sound and complete, and (ii) an alternative, re-writing strategy. (shrink)

Abstract. Traditional epistemology of knowledge and belief can be succinctly characterized as JTB-epistemology, i.e., it is characterized by the thesis that knowledge is justified true belief. Since Gettier’s trail-blazing paper of 1963 this account has become under heavy attack. The aim of is paper is to study the Gettier problem and related issues in the framework of topological epistemic logic. It is shown that in the framework of topological epistemic logic Gettier situations necessarily occur for most topological models of knowledge (...) and belief. On the other hand, there exists a special class of topological models (based on so called nodec spaces) for which traditional JTB-epistemology is valid. Further, it is shown that for each topological model of Stalnaker’s combined logic KB of knowledge and belief a canonical JTB-model (its JTB-doppelganger) can be constructed that shares many structural properties with the original model but is free of Gettier situations. The topological model and its JTB-doppelganger both share the same justified belief operator and have very similar knowledge operators. Seen from a somewhat different perspective, the JTB-account of epistemology amounts to a simplification of a more general epistemological account of knowledge and belief that assumes that these two concepts may differ in some cases. The JTB-account of knowledge and belief assumes that the epistemic agent’s cognitive powers are rather large. Thereby in the JTB-epistemology Gettier cases do not occur. Eventually, it is shown that for all topological models of Stalnaker’s KB-logic Gettier situations are topologically characterized as nowhere dense situations. This entails that Gettier situations are epistemologically invisible in the sense that they can neither be known nor believed with justification with respect to the knowledge operator and the belief operator of the models involved. (shrink)

This paper attempts to demonstrate that the logical problematic of signification, has a very dangerous socio-political effect due to the ontological implication that is connected to the signification of terms in logic. It expounds the notion of signification in Formal Logic as exposed by William of Ockham. It thus, employs this notion of signification of terms, to discuss the term “Fulani”, to show the danger potent in distorting the signification of the term “Fulani” as in every conventional and connotative terms. (...) This work claims that as a result of the connection between logic and ontology, conceptualization and perception, names and reality, the distortion of terms, which are the building blocks of propositions in logic could lead to a dangerous cognition and perception of ontological realities. To this end, it posits a critique on the dangerous change in the signification of the term “Fulani”, in the conceptualization and perception of present day Nigeria people, of West Africa. A dangerous change, as this paper claims, if not speedily reconstructed and re-conceptualized, could lead to a disastrous situation in the socio-political reality of the Nigerian State. (shrink)

Traditional epistemology of knowledge and belief can be succinctly characterized as JTB-epistemology, i.e., it is characterized by the thesis that knowledge is justified true belief. Since Gettier’s trail-blazing paper of 1963 this account has become under heavy attack. The aim of is paper is to study the Gettier problem and related issues in the framework of topological epistemic logic. It is shown that in the framework of topological epistemic logic Gettier situations necessarily occur for most topological models of knowledge and (...) belief. On the other hand, there exists a special class of topological models (based on so called nodec spaces) for which traditional JTB-epistemology is valid. Further, it is shown that for each topological model of Stalnaker’s combined logic KB of knowledge and belief a canonical JTB-model (its JTB-doppelganger) can be constructed that shares many structural properties with the original model but is free of Gettier situations. The topological model and its JTB-doppelganger both share the same justified belief operator and have very similar knowledge operators. Seen from a somewhat different perspective, the JTB-account of epistemology amounts to a simplification of a more general epistemological account of knowledge and belief that assumes that these two concepts may differ in some cases. The JTB-account of knowledge and belief assumes that the epistemic agent’s cognitive powers are rather large. Thereby in the JTB-epistemology Gettier cases do not occur. Eventually, it is shown that for all topological models of Stalnaker’s KB- logic Gettier situations are topologically characterized as nowhere dense situations. This entails that Gettier situations are epistemologically invisible in the sense that they can neither be known nor believed with justification with respect to the knowledge operator and the belief operator of the models involved. Keywords. Stalnaker’s logic KB of knowledge and belief; Topological epistemology; Epistemic Invisibility; Doxastic invisibility; Gettier cases; . (shrink)

The previous Part I of the paper discusses the option of the Gödel incompleteness statement (1931: whether “Satz VI” or “Satz X”) to be an axiom due to the pair of the axiom of induction in arithmetic and the axiom of infinity in set theory after interpreting them as logical negations to each other. The present Part II considers the previous Gödel’s paper (1930) (and more precisely, the negation of “Satz VII”, or “the completeness theorem”) as a necessary condition for (...) granting the Gödel incompleteness statement to be a theorem just as the statement itself, to be an axiom. Then, the “completeness paper” can be interpreted as relevant to Hilbert mathematics, according to which mathematics and reality as well as arithmetic and set theory are rather entangled or complementary rather than mathematics to obey reality able only to create models of the latter. According to that, both papers (1930; 1931) can be seen as advocating Russell’s logicism or the intensional propositional logic versus both extensional arithmetic and set theory. Reconstructing history of philosophy, Aristotle’s logic and doctrine can be opposed to those of Plato or the pre-Socratic schools as establishing ontology or intensionality versus extensionality. Husserl’s phenomenology can be analogically realized including and particularly as philosophy of mathematics. One can identify propositional logic and set theory by virtue of Gödel’s completeness theorem (1930: “Satz VII”) and even both and arithmetic in the sense of the “compactness theorem” (1930: “Satz X”) therefore opposing the latter to the “incompleteness paper” (1931). An approach identifying homomorphically propositional logic and set theory as the same structure of Boolean algebra, and arithmetic as the “half” of it in a rigorous construction involving information and its unit of a bit. Propositional logic and set theory are correspondingly identified as the shared zero-order logic of the class of all first-order logics and the class at issue correspondingly. Then, quantum mechanics does not need any quantum logics, but only the relation of propositional logic, set theory, arithmetic, and information: rather a change of the attitude into more mathematical, philosophical, and speculative than physical, empirical and experimental. Hilbert’s epsilon calculus can be situated in the same framework of the relation of propositional logic and the class of all mathematical theories. The horizon of Part III investigating Hilbert mathematics (i.e. according to the Pythagorean viewpoint about the world as mathematical) versus Gödel mathematics (i.e. the usual understanding of mathematics as all mathematical models of the world external to it) is outlined. (shrink)

In appearance, Husserl’s writings seem not to have had any influence on linguistic research, nor does what the German philosopher wrote about language seem to be worth a place in the history of linguistics. The purpose of the paper is exactly to contrast this view, by reassessing both the position and the role of Husserl’s early masterpiece — the Logical Investigations — within the history of linguistics. To this end, I will focus mainly on the third (On the theory of (...) wholes and parts) and fourth (The distinction between independent and non-independent meanings) Investigations, paying special attention to Husserl’s mereology and to the idea of a general pure grammar. The paper tries to situate the third and fourth Logical Investigation within the general context of late nineteenth-century and early twentieth-century linguistics and furthermore attempts to show the historical and theoretical importance of the Logical Investigations for the birth and the development of one of the most important linguistic “schools” of the twentieth century, namely structural linguistics. (shrink)

There is widespread agreement that while on a Dummettian theory of meaning the justified logic is intuitionist, as its constants are governed by harmonious rules of inference, the situation is reversed on Huw Price's bilateralist account, where meanings are specified in terms of primitive speech acts assertion and denial. In bilateral logics, the rules for classical negation are in harmony. However, as it is possible to construct an intuitionist bilateral logic with harmonious rules, there is no formal argument against intuitionism (...) from the bilateralist perspective. Price gives an informal argument for classical negation based on a pragmatic notion of belief, characterised in terms of the differences they make to speakers' actions. The main part of this paper puts Price's argument under close scrutiny by regimenting it and isolating principles Price is committed to. It is shown that Price should draw a distinction between A or ¬A making a difference. According to Price, if A makes a difference to us, we treat it as decidable. This material allows the intuitionist to block Price's argument. Abandoning classical logic also brings advantages, as within intuitionist logic there is a precise meaning to what it might mean to treat A as decidable: it is to assume A ∨ ¬A. (shrink)

In recent years, the human ability to reasoning about mental states of others in order to explain and predict their behavior has come to be a highly active area of research. Researchers from a wide range of fields { from biology and psychology through linguistics to game theory and logic{ contribute new ideas and results. This interdisciplinary workshop, collocated with the Thirteenth International Conference on Theoretical Aspects of Rationality and Knowledge (TARK XIII), aims to shed light on models of social (...) reasoning that take into account realistic resource bounds. People reason about other people's mental states in order to understand and predict the others' behavior. This capability to reason about others' knowledge, beliefs and intentions is often referred to as theory of mind. Idealized rational agents are capable of recursion in their social reasoning, and can reason about phenomena like common knowledge. Such idealized social reasoning has been modeled by modal logics such as epistemic logic and BDI (belief, desire, intention) logics and by epistemic game theory. However, in real-world situations, many people seem to lose track of such recursive social reasoning after only a few levels. The workshop provides a forum for researchers that attempt to analyze, understand and model how resource-bounded agents reason about other minds. (shrink)

This paper considers non-standard analysis and a recently introduced computational methodology based on the notion of ①. The latter approach was developed with the intention to allow one to work with infinities and infinitesimals numerically in a unique computational framework and in all the situations requiring these notions. Non-standard analysis is a classical purely symbolic technique that works with ultrafilters, external and internal sets, standard and non-standard numbers, etc. In its turn, the ①-based methodology does not use any of these (...) notions and proposes a more physical treatment of mathematical objects separating the objects from tools used to study them. It both offers a possibility to create new numerical methods using infinities and infinitesimals in floating-point computations and allows one to study certain mathematical objects dealing with infinity more accurately than it is done traditionally. In these notes, we explain that even though both methodologies deal with infinities and infinitesimals, they are independent and represent two different philosophies of Mathematics that are not in a conflict. It is proved that texts :539–555, 2017; Gutman and Kutateladze in Sib Math J 49:835–841, 2008; Kutateladze in J Appl Ind Math 5:73–75, 2011) asserting that the ①-based methodology is a part of non-standard analysis unfortunately contain several logical fallacies. Their attempt to show that the ①-based methodology can be formalized within non-standard analysis is similar to trying to show that constructivism can be reduced to the traditional Mathematics. (shrink)

In the paper, certain rational postulates for protocols describing real communicating are introduced.These rational postulates, on the one hand, allow assigning a certain typology of real systems of interactions, which is consistent with the reality of epistemic argumentation in systems of communicating, and on the other one – defining rules of using argumentation in real situations. Moreover, the presented postulates for protocols characterize information networks and administering knowledge in real interactivity systems. Due to the epistemic character of the considerations, the (...) problem undertaken in the paper concerns working out fundamental assumptions that refer to building of epistemic logics. They allow establishing the correctness of the discourse defined by rational postulates of protocols of real communication. In the context of the presented problem there are the following two research questions distinguished: 1) How do we determine the rule of building of real dynamic epistemic logics? and 2) How should we define semantics for these logics? Within the framework of considerations relating to the research questions asked, certain epistemic operators, relativized to types of communicating, are introduced. Basic logical relations between using these operators are established for these operators. The relations are presented by a diagram called the square of epis temic operators. On the basis of these logical relations some axioms for real dynamic epistemic logics are presented. The semantics of real dynamic epistem ic logics is extended by the methods of lower and upper approximation of formula evaluating. This allows defining ‘approximation Kripke models’. The results of conceptualization of knowledge on real premises of epistemic argum entation presented in this paper can be applied to rhetoric in real systems of interaction. (shrink)

In this article, I argue that G. A. Cohen’s defense of the feminist slogan, “The personal is political”, his argument against Rawls’s restriction of principles of justice to the basic structure of society, depends for its intelligibility on the ability to distinguish—with reasonable but perhaps not perfect precision—between those situations in which what Nancy Rosenblum has called “the logic of congruence” is validly invoked and those in which it is not. More importantly, I suggest that the philosophical shape of Cohen’s (...) critique makes it difficult for him to supply the required criterion, and that the methodological “intuitionism” he claims to be committed to is at odds with his larger argument against Rawls concerning the subject of justice. (shrink)

This book presents a (new) attempt to apply the notion of an underlying logic to Aristotle’s Organon and certain passages of the Metaphysics. The author situates his approach as part of a ‘deductio...

The present essay is a critical study of Barwise and Perry’s book, emphasizing the logical and model-theoretical aspects of their work. I begin by presenting the authors’ criticism of the classical view of logic and semantics within the tradition of Frege, Russell and Tarski. In this connection, I discuss the so-called Frege argument (“the slingshot”). I try to show that the argument appears inconclusive, not only from a situation-theoretic perspective, but also from such alternative perspectives as orthodox Fregean semantics or (...) Russellian semantics. I then discuss the ontology of situation semantics and the way it is modeled within set theory. In particular, I compare the notion of an abstract situation with that of a possible world. The last two sections concern the model-theoretic aspects of the authors’ theory. In Section 7, I discuss how the “partial” perspective of situation semantics differs from that of classical model theory. Finally, in Section 8, different model-theoretic accounts of attitude reports within situation semantics are discussed, in particular the “relations to situations”-approach presented by the authors in Chapter 9 of S & A. The usual problems of “logical omniscience” that appear in standard Hintikka-style epistemic logic are avoided in situation semantics. I argue, however, that situation semantics is faced with analogous counter-intuitive results, unless the expressive power of the language under study is suitably restricted. (shrink)

Peirce wrote that Hume’s argument against miracles (which is generally liked by twentieth century philosophers for its antireligious conclusion) "completely misunderstood the true nature of" ’abduction’. This paper argues that if Hume’s argumentative strategy were seriously used in all situations (not just those in which we seek to "banish superstition"), it would deliver a choking epistemological conservatism. It suggests that some morals for contemporary naturalistic philosophy may be drawn from Peirce’s argument against Hume.

Human actions and decisions are most of the times not only grounded on emotional reactions, they are irrationally debasing. While such emotions and heuristics were perhaps suitable for dealing with life in the Stone Age, they are woefully inadequate in the Silicon Age. The substitution of traditional news agencies and communication platforms in Nigeria with social media networks has not only increased human capacities, it has aided the common good and further eased communication and increased the human knowledge base. For (...) instance, the Silicon Valley in the state of California in the United State of America has proved the extent to which human ingenuity can be exerted in beneficial ways. Here in, the top of the multibillion-dollar communication companies like Apple, eBay, Cisco, Lockheed, Hewlett Packard (HP), Google, Netflix, Facebook, Oracle, Tesla, etc. whose yearly budgets far exceed the entire yearly budget of Nigeria, has proved that, ICT remains the building blocks of contemporary communities. The state of California for instance prides herself as the 6th largest economy of the world after France and Brazil. This romantic picture of ICT is but only one chapter of the ICT divide. In today’s world, the scale and speed of the highly partisan news and falsehoods that circulate in the human environment is deafening. In politics and governance for instance, the populist have exploited the ICT effectively and without restraints, to access power and authority. Today, we are in the era of post-truth, an era in which objective facts are less influential in shaping public opinion than appeals to emotion and personal belief. An era that harbours corruption of intellectual integrity and damage to the whole fabric of democracy. The battle to protect information integrity and expose fake news becomes sine qua non. We shall in this paper explore the dark side of the age of information, a side that has been exploited by the media mavens, political hacks, and ideological propagandists who promote lies, illusion, confusion, and other forms of demented or manipulated imagination. In doing this, we shall proceed as follows: i. Historicize the concept of ‘fake news’ here referred to as post-truth. ii. Interrogate the concept of ‘information’ and its goal in human affairs iii. Evaluate the nexus between ‘truth’ values in ‘information’, ‘Misinformation’ and ‘dis-information’ iv. Situate the role of Philosophy in the era of post-truth. (shrink)