Contemporary research offers a more compelling account on the complex emotion of envy than the traditional view of envy as simply something bad. This essay explains how Logic-Based Therapy can use this account to coach individuals struggling with negative species of envy. Given that jealousy and envy are often equated, the essay differentiates the two; explains the conditions that make the four species of envy possible; identifies cardinal fallacies associated with negative species of envy; proposes counteractive virtues, (...) and describes ways to help people struggling with negative species of envy acquire these virtues. (shrink)

In my presentation I argue for the utility of a philosophical counseling method, called logic-based therapy (LBT), in the treatment of addicted populations. In the context of addiction treatment LBT could be also classified as a philosophical psychotherapy. Philosophical psychotherapy can be understood as an umbrella term for interventions designed to treat mental health disorders, with theoretical foundations that are philosophical. Philosophical psychotherapy would be distinct from philosophical counseling, as the latter does not directly treat mental health (...) disorders. I suggest that LBT has utility beyond philosophical counseling and is a viable intervention in the treatment of certain mental health disorders, like substance use disorders. I provide a brief overview of LBT and then discuss a LBT case study with a client suffering diagnosed with a substance use disorder. In the case study the client was advised to apply the moral philosophy of Friedrich Nietzsche as an uplifting philosophical framework to counteract his unproductive worldview and fallacious thinking. Considering that there is an ostensibly low efficacy rate for the treatment of addiction, articulating the value of philosophical psychotherapies in the context of addiction treatment can assist in the development of novel philosophically-based addiction treatment and recovery-oriented programs––thus expanding the treatment and recovery options available for those seeking recovery from addiction. (shrink)

The phenomenon of self-love elicits conflicting reactions. Some believe it is the key to happiness, while others are skeptical. This essay defines self-love as wholehearted concern for one's well-being, argues that it does not imply selfishness, arrogance, or vanity, discusses reasons to value self-love, and describes ways Logic-Based Therapy can be used to help people love themselves.

In article I explore how Logic-based Therapy (LBT) can inform a philosophically oriented recovery pathway for individuals in addiction recovery. Considering that there is an ostensibly low efficacy rate for the treatment of addiction, there is significant value in highlighting the utility of LBT for the development of novel philosophically based addiction treatment and recovery-oriented programs, which would expand the treatment and recovery options. I propose that LBT may be a suitable intervention when challenging the unrealistic (...) conclusions derived from illogical premises in practical reasoning that contribute to addiction, because it can contest irrational beliefs in a way that could mitigate the fragmentation anxiety that often arises when individuals relinquish maladaptive self-object organizations. (shrink)

In this essay I argue that a comprehensive understanding of addiction and its treatment should include an existential perspective. I provide a brief overview of an existential perspective of addiction and recovery, which will contextualize the remainder of the essay. I then present a case study of how the six-step philosophical practice method of Logic-Based Therapy can assist with issues that often arise in addiction treatment framed through an existential perspective.

In this essay I explore the notion of philosophy as a way of life as a recovery pathway for individuals in addiction recovery. My hypothesis is that philosophy as a way of life can be a compelling, and legitimate recovery pathway for individuals in addiction recovery, as one of many recovery pathways. I will focus on logic-based therapy applied in the context of addiction recovery. The aim of presenting a case study is to show how a client (...) receiving LBT is provided with techniques and a worldview that can contribute to a philosophically oriented recovery program. In the case study the client was advised to apply the moral philosophy of Friedrich Nietzsche as an uplifting philosophical framework to counteract his unproductive worldview and fallacious thinking. Considering that there is an ostensibly low efficacy rate for the treatment of addiction, articulating the value of philosophy as a way of life as a recovery pathway provides a conceptual and methodological framework for the development of novel philosophically-based addiction treatment and recovery-oriented programs—thus expanding the treatment and recovery options available for those seeking recovery from addiction. (shrink)

Logic-Based Therapy is a proposed modality of philosophical counseling developed by philosopher Elliot D. Cohen beginning in the mid-1980s. This Socratic dialogue illustrates the techniques used by Philosophical Counselors in helping their clients work through life problems. Philosophical Counseling is based on Stoic Philosophy and practitioners assist clients to identify faulty reasoning that leads to poor behavioral choices or unwanted emotions. Dialogues such as this can serve as teaching resources for students working towards certification in Practical (...) Philosophy or Philosophical Counseling. (shrink)

Introduction to logic-based therapy. This Socratic dialogue illustrates the techniques used by Philosophical Counselors in helping their clients work through life problems. Philosophical Counseling is based on Stoic Philosophy and practitioners assist clients to identify faulty reasoning that leads to poor behavioral choices or unwanted emotions. Dialogues such as this can serve as teaching resources for students working towards certification in Practical Philosophy or Philosophical Counseling.

The paper presents a method for interpreting religious texts for use in psychotherapy. In particular, the paper takes the example of the pivotal character Arjuna in Bhagavad-Gita as having low frustration tolerance and uses the collective philosophy of the Bhagavad-Gita and Bhagavata-Purana through six steps of Logic-Based Therapy to overcome it. Although the paper uses Hindu religious texts, the treatment of these texts will speak to anyone interested in the possibility of integrating religious texts into psychotherapy.

Central to philosophical practice is the application of philosophers' work by philosophical practitioners to inspire, educate, and guide their clients. For example, in Logic-Based Therapy (LBT) philosophical practitioners help their clients to find an uplifting philosophy that promotes guiding virtues that counteract unrealistic and often self-defeating conclusions derived from irrational premises. I will present the argument that Simone de Beauvoir’s existentialist ethics can be applied as an uplifting philosophy as per LBT methodology, and therefore has utility for (...) philosophical practice. Additionally, I will propose that Beauvoir’s existentialist ethics, as an uplifting philosophy, may act as an antidote for ideological obsession and ideology addiction. I will also suggest that LBT may be a suitable intervention when challenging the unrealistic conclusions derived from illogical premises in practical reasoning that contribute to ideological obsession, because it can contest irrational beliefs in a way that could mitigate the fragmentation anxiety that often arise when individuals relinquish maladaptive self-object organizations. (shrink)

This article explores the potential utility of the theory of Holism as developed by South African philosopher, British Commonwealth statesman and military leader, Jan Smuts, for philosophical counselling or practice. Central to the philosophical counseling process is philosophical counsellors or practitioners applying the work of philosophers to inspire, educate and guide their counselees in dealing with life problems. For example, Logic-Based Therapy, a method of philosophical counselling developed by Elliot Cohen, provides a rational framework for confronting problems (...) of living, where the counselor helps the counselee find an uplifting philosophy that promotes a guiding virtue that acts as an antidote to unrealistic and often self-defeating conclusions derived from irrational premises. We present the argument that Holism is one such uplifting philosophy which can be of utility to philosophical counselors or practitioners to help their counselees with confronting problems of living. Furthermore, we argue that Smuts’ articulation of freedom can act as a guiding virtue within this uplifting philosophy of Holism in accordance with the methodology of LBT. Smuts’ contribution to philosophy and psychology is arguably inadequately credited, and for this reason, and to the best of our knowledge, Smuts’ theory of Holism has yet to be discussed in the context of philosophical counseling or practice. Given these omissions, we begin this article with a discussion of his influence on 20th Century Anglo-American psychology. We then provide a brief historical context, and an introduction to the central argument of Smuts’ Holism, as well as a brief overview of the origins of Smut’s Holism and an introduction to his book Holism and Evolution. In the remainder of the article, we discuss several foundational concepts that underlie Smuts’ theory of Holism, as articulated and developed in his book Holism and Evolution, to substantiate our arguments. We conclude by highlighting the limitations of our article, limitations to Smuts’ model, and the challenges inherent in the use of a now largely antiquated theory, even by Smuts’ own admission nineteen years after its publication, for the purposes of contextualizing and substantiating the arguments and recommendations presented herein. (shrink)

This article explores the utility of Nietzsche’s ethical thought for philosophical counselling. Central to the philosophical counseling process is philosophical counsellors applying the work of philosophers to inspire, educate, and guide their counselees in dealing with life problems. For example, Logic-Based Therapy (LBT), a method of philosophical counselling developed by Elliot Cohen, provides a rational framework for confronting problems of living, where the counselor helps the counselee find an uplifting philosophy that promotes a guiding virtue that acts (...) as an antidote to unrealistic and often self-defeating conclusions derived from irrational premises. I present the argument that Nietzsche’s moral philosophy, and more specifically his analysis of suffering, is one such uplifting philosophy which can be of utility to philosophical counselors to help their counselees with confronting problems of living. According to Bernard Reginster, suffering forms the bedrock of Nietzsche's life-affirming concept of the will to power. Nietzsche’s notion of the will to power radically alters our conception and significance of suffering – and that the will to power is best understood as man’s desire for the activity of overcoming resistance. Nietzsche's analysis implies that the fundamental human impulse is not to avoid suffering, but instead to will nothing less than suffering itself. To find meaning in suffering is tantamount to affirming life itself. (shrink)

Central to the philosophical practice is the application of philosophers' work by philosophical practitioners to inspire, educate, and guide their clients. For example, in Logic-Based Therapy (LBT), a philosophical practice methodology developed by Elliot Cohen, philosophical practitioners help their clients to find an uplifting philosophy that promotes a guiding virtue that acts as an antidote to unrealistic and often self-defeating conclusions derived from irrational premises. In this essay, I will explore the existential ethics of Simone de Beauvoir, (...) a French existentialist philosopher, and writer. I present the argument that Beauvoir’s existential ethics, more specifically her articulation of ambiguity, can act as an uplifting philosophy, as per LBT methodology, which could be of value to philosophical practitioners to inspire, educate and guide their counselees for confronting problems of living. I will present my discussion of Beauvoir’s existential ethics in the context of ideological obsession and ideology addiction, which is often supported by the reasoning that underlies the cardinal fallacy of existential perfectionism. I will argue that Beauvoir’s existential ethics could serve as a prophylactic for ideological obsession and ideology addiction. I will also suggest that LBT may be particularly suited when addressing the self-defeating, unrealistic conclusions derived from irrational premises in practical reasoning that may fuel ideological obsession because it could provide a methodology to address irrational beliefs in a way that could mitigate the fragmentation anxiety that may arise when relinquishing maladaptive self-object organizations. (shrink)

This paper argues for global sharing of COVID‐19 treatments during the COVID‐19 pandemic and beyond based on principles of global solidarity. It starts by distinguishing two types of COVID‐19 treatments and models sharing strategies for each in small‐group scenarios, contrasting groups that are solidaristic with those composed of self‐interest maximizers to show the appeal of solidaristic reasoning. It then extends the analysis, arguing that a similar logic should apply within and between nations. To further elaborate global solidarity, the (...) paper distinguishes morally voluntary, sliding‐scale, and mandatory versions. It argues for an all‐hands‐on‐deck approach and gives examples to illustrate. The paper concludes that during the COVID‐19 crisis, global solidarity is a core value, and global sharing of COVID‐19 treatments should be considered a duty of justice, not of charity. (shrink)

In this essay I address the notions of motivation and self-deception by exploring the value of philosophy in the context of addiction treatment. More specifically, in this essay I explore the notion of philosophy as a way of life as a recovery pathway for individuals in addiction recovery. My hypothesis is that philosophy as a way of life can be a compelling, and legitimate recovery pathway for individuals in addiction recovery, as one of many recovery pathways. I will focus on (...) logic-based therapy (LBT) applied in the context of addiction recovery. The aim of presenting a case study is to show how a client receiving LBT is provided with techniques and a worldview that can contribute to a philosophically oriented recovery program. In the case study the client was advised to apply the moral philosophy of Friedrich Nietzsche as an uplifting philosophical framework to counteract his unproductive worldview and fallacious thinking. Considering that there is an ostensibly low efficacy rate for the treatment of addiction, articulating the value of philosophy as a way of life as a recovery pathway provides a conceptual and methodological framework for the development of novel philosophically-based addiction treatment and recovery-oriented programs–thus expanding the treatment and recovery options available for those seeking recovery from addiction. (shrink)

Deontic logic is devoted to the study of logical properties of normative predicates such as permission, obligation and prohibition. Since it is usual to apply these predicates to actions, many deontic logicians have proposed formalisms where actions and action combinators are present. Some standard action combinators are action conjunction, choice between actions and not doing a given action. These combinators resemble boolean operators, and therefore the theory of boolean algebra offers a well-known athematical framework to study the properties of (...) the classic deontic operators when applied to actions. In his seminal work, Segerberg uses constructions coming from boolean algebras to formalize the usual deontic notions. Segerberg’s work provided the initial step to understand logical properties of deontic operators when they are applied to actions. In the last years, other authors have proposed related logics. In this chapter we introduce Segerberg’s work, study related formalisms and investigate further challenges in this area. (shrink)

A wide family of many-valued logics—for instance, those based on the weak Kleene algebra—includes a non-classical truth-value that is ‘contaminating’ in the sense that whenever the value is assigned to a formula φ⁠, any complex formula in which φ appears is assigned that value as well. In such systems, the contaminating value enjoys a wide range of interpretations, suggesting scenarios in which more than one of these interpretations are called for. This calls for an evaluation of systems with multiple (...) contaminating values. In this paper, we consider the countably infinite family of multiple-conclusion consequence relations in which classical logic is enriched with one or more contaminating values whose behavior is determined by a linear ordering between them. We consider some motivations and applications for such systems and provide general characterizations for all consequence relations in this family. Finally, we provide sequent calculi for a pair of four-valued logics including two linearly ordered contaminating values before defining two-sided sequent calculi corresponding to each of the infinite family of many-valued logics studied in this paper. (shrink)

The rapid increase of the old age people imposes the reconsideration of the rehabilitation techniques and procedures and/or the development of the existing ones, at least from two points of view: the limitation use of the pharmaceutical drugs because of their secondary effects in the debilitated organisms and their avoidance; the high risk of the induced anxiety states, depression or other symptoms as a consequence of the main disease, i.e. the neuro-degenerative or mobility dysfunctions, limiting again the use of such (...) excessive drug medication. Moreover, Alzheimer’s or Parknson’s diseases are otherwise incurable, so the application of rehabilitating procedures like music-based therapy becomes preferential. The advances both in the identification of the specific auditory musical-sensitive circuits and of the non- musical neuro-connections but activated indirectly by music, otherwise inaccessible by other techniques, and in the understanding of consciousness, which can be described by seven cognitive centers, allows to improve and develop the music based therapy. A multitask procedure based on the activation of these cognition centers is presented, allowing to increase the personal psychical engagement of the patient in the recommended music based therapeutic program, addressed both to the rehabilitation of the main degenerative disease and to the secondary induced dysfunctions. This procedure combines the evidence based medicine assisted by laboratory expertise for the determination of a correct diagnostic, and narrative based medicine allowing to quantify the personal engaging qualities of the patient with respect to the proposed music based program, reducing in this way the gap between these two basic procedures and bringing in a first plane the patient care, not only the disease, with beneficial consequence for the therapy efficiency and for the patient-medical care relations. (shrink)

In this work we present NERVOUS, an intelligent recommender system exploiting a probabilistic extension of a Description Logic of typicality to dynamically generate novel contents in AllMusic, a comprehensive and in-depth resource about music, providing data about albums, bands, musicians and songs. The tool can be used for both the generation of novel music genres and styles, described by a set of typical properties characterizing them, and the reclassification of the available songs within such new genres.

Mathematics textbooks teach logical reasoning by example, a practice started by Euclid; while logic textbooks treat logic as a subject in its own right without practical application to mathematics. Stuck in the middle are students seeking mathematical proficiency and educators seeking to provide it. To assist them, the article explains in practical detail how to teach logic-based skills such as: making mathematical reasoning fully explicit; moving from step to step in a mathematical proof in logically correct (...) ways; and checking to make sure inferences are logically correct. The methodology can easily be extended beyond the four examples analyzed. (shrink)

The evidence based medicine movement has championed the need for objective and transparent methods of clinical guideline development. The Grades of Recommendation, Assessment, Development, and Evaluation (GRADE) framework was developed for that purpose. Central to this framework is criteria for assessing the quality of evidence from clinical studies and the impact that body of evidence should have on our confidence in the clinical effectiveness of a therapy under examination. Grades of Recommendation, Assessment, Development, and Evaluation has been adopted (...) by a number of professional medical societies and organizations as a means for orienting the development of clinical guidelines. As a result, the method of GRADE has implications on how health care is delivered and patient outcomes. In this paper, we reveal several issues with the underlying logic of GRADE that warrant further discussion. First, the definitions of the “grades of evidence” provided by GRADE, while explicit, are functionally vague. Second, the “criteria for assigning grade of evidence” is seemingly arbitrary and arguably logically incoherent. Finally, the GRADE method is unclear on how to integrate evidence grades with other important factors, such as patient preferences, and trade‐offs between costs, benefits, and harms when proposing a clinical practice recommendation. Much of the GRADE method requires judgement on the part of the user, making it unclear as to how the framework reduces bias in recommendations or makes them more transparent—both goals of the programme. It is our view that the issues presented in this paper undermine GRADE's justificatory scheme, thereby limiting the usefulness of GRADE as a tool for developing clinical recommendations. (shrink)

Formalisms based on one or other flavor of Description Logic (DL) are sometimes put forward as helping to ensure that terminologies and controlled vocabularies comply with sound ontological principles. The objective of this paper is to study the degree to which one DL-based biomedical terminology (SNOMED CT) does indeed comply with such principles. We defined seven ontological principles (for example: each class must have at least one parent, each class must differ from its parent) and examined the (...) properties of SNOMED CT classes with respect to these principles. Our major results are: 31% of these classes have a single child; 27% have multiple parents; 51% do not exhibit any differentiae between the description of the parent and that of the child. The applications of this study to quality assurance for ontologies are discussed and suggestions are made for dealing with the phenomenon of multiple inheritance. The advantages and limitations of our approach are also discussed. (shrink)

Logical pluralism is the view that there is more than one correct logic. A key objection to logical pluralism is that it collapses into monism. The core of the Collapse Objection is that only the pluralist’s strongest logic does any genuine normative work; since a logic must do genuine normative work, this means that the pluralist is really a monist, who is committed to her strongest logic being the one true logic. This paper considers a (...) neglected question in the collapse debate: what is it for a logic to do genuine normative work? As well as having wider upshot for the connection between logic and normativity, grappling with this question provides a new response to the Collapse Objection on behalf of the pluralist. I suggest that we should allow logics to generate pro tanto reasons in a way that bears not just on combinations of attitudes but on how an agent’s attitudes are based on one another. This motivates adopting normative principles that allow the pluralist’s weaker logics to earn their normative keep. Rather than being ad hoc, these principles capture a sense in which good reasoning goes beyond the consistency of an agent’s attitudes. Good reasoning is also concerned with how an agent’s attitudes are based on one another. (shrink)

Temporal epistemic logics are known, from results of Halpern and Vardi, to have a wide range of complexities of the satisfiability problem: from PSPACE, through non-elementary, to highly undecidable. These complexities depend on the choice of some key parameters specifying, inter alia, possible interactions between time and knowledge, such as synchrony and agents' abilities for learning and recall. In this work we develop practically implementable tableau-based decision procedures for deciding satisfiability in single-agent synchronous temporal-epistemic logics with interactions between time (...) and knowledge. We discuss some complications that occur, even in the single-agent case, when interactions between time and knowledge are assumed and show how the method of incremental tableaux can be adapted to work in EXPSPACE, respectively 2EXPTIME, for these logics, thereby also matching the upper bounds obtained for them by Halpern and Vardi. (shrink)

In proof-theoretic semantics, meaning is based on inference. It may be seen as the mathematical expression of the inferentialist interpretation of logic. Much recent work has focused on base-extension semantics, in which the validity of formulas is given by an inductive definition generated by provability in a ‘base’ of atomic rules. Base-extension semantics for classical and intuitionistic propositional logic have been explored by several authors. In this paper, we develop base-extension semantics for the classical propositional modal systems (...) K, KT , K4, and S4, with □ as the primary modal operator. We establish appropriate soundness and completeness theorems and establish the duality between □ and a natural presentation of ♢. We also show that our semantics is in its current form not complete with respect to euclidean modal logics. Our formulation makes essential use of relational structures on bases. (shrink)

Philosophers of logic are particularly interested in understanding the aims, epistemology, and methodology of logic. This raises the question of how the philosophy of logic should go about these enquires. According to the practice-based approach, the most reliable method we have to investigate the methodology and epistemology of a research field is by considering in detail the activities of its practitioners. This holds just as true for logic as it does for the recognised empirical and (...) abstract sciences. If we wish to systematically understand the aims and epistemology of logic, we are best placed achieving this by looking at what logicians do, rather than reflecting upon the nature of logic itself. In this entry, we outline the motivations for a practice-based approach towards the philosophy of logic and highlight its advantages over more “top-down” approaches, which attempt to infer conclusions about the nature of logic and its methodology on the basis of traditional assumptions about knowledge, metaphysics, or logic itself. We end by addressing several prominent concerns raised against the practice-based approach. (shrink)

In the 89th letter to Lucilius Seneca divides philosophy into three parts, namely ethics, physics, and logic. As philosophy in general he also divides its ethical parts into three parts: the first one has to do with value judgments, the second with impulses, and the third with actions. But instead of characterizing each of these parts and giving an overview of their contents he rather describes an ideal action: first, one makes a correct value judgment, then, one initiates a (...) regulated and ordered impulse, and finally, one brings this impulse into harmony with one’s external action by paying attention to the circumstances under which one intends to act. If each of these action moments has the mentioned character, one is consistent with oneself—an important step towards reaching full self-consistency, i.e., virtue. If those moments do not have the mentioned character, as for example in a passion, one cannot be consistent with oneself. As a result, one diverges from the goal of full self-consistency and thus from virtue. The thesis of my book takes up the parallel Seneca is drawing between ethics and its parts on the one hand and an action and its moments on the other hand. I argue that his ethics is based on an action theory that has as its main moments a judgment, an impulse and an external action. Within this theoretical framework, Seneca gives an answer to the question of what one should do in order to reach full self-consistency, i.e., virtue, which for a Stoic like him is a necessary and sufficient condition for happiness. My book, correspondingly, has two major parts: first, I am working out Seneca’s action theory and its philosophical origins, then, I am concerned with his ethics. In the first main chapter, I further argue that his action theory stems for the most part from the early Stoics, but that unlike them he has a concept of will. This concept, as I want to show in the second part, plays an important role in his ethics, too. (shrink)

Currently available systems of action deontic logic are not designed to model procedures to assess the conduct of an agent which take into account the intentions of the agent and the circumstances in which she is acting. Yet, procedures of this kind are essential to determine what counts as culpable not doing. In light of this, we design an action logic, AL, in which it is possible to distinguish actions that are objectively possible for an agent, viz. there (...) are no objective impediments for the agent to do them, and actions that, besides being objectively possible, are compatible with the setting or intentions of the agent. (shrink)

The classical theory of computation does not represent an adequate model of reality for simulation in the social sciences. The aim of this paper is to construct a methodological perspective that is able to conciliate the formal and empirical logic of program verification in computer science, with the interpretative and multiparadigmatic logic of the social sciences. We attempt to evaluate whether social simulation implies an additional perspective about the way one can understand the concepts of program and computation. (...) We demonstrate that the logic of social simulation implies at least two distinct types of program verifications that reflect an epistemological distinction in the kind of knowledge one can have about programs. Computer programs seem to possess a causal capability (Fetzer, 1999) and an intentional capability that scientific theories seem not to possess. This distinction is associated with two types of program verification, which we call empirical and intentional verification. We demonstrate, by this means, that computational phenomena are also intentional phenomena, and that such is particularly manifest in agent-based social simulation. Ascertaining the credibility of results in social simulation requires a focus on the identification of a new category of knowledge we can have about computer programs. This knowledge should be considered an outcome of an experimental exercise, albeit not empirical, acquired within a context of limited consensus. The perspective of intentional computation seems to be the only one possible to reflect the multiparadigmatic character of social science in terms of agent-based computational social science. We contribute, additionally, to the clarification of several questions that are found in the methodological perspectives of the discipline, such as the computational nature, the logic of program scalability, and the multiparadigmatic character of agent-based simulation in the social sciences. (shrink)

Simple partial logic (=SPL) is, broadly speaking, an extensional logic which allows for the truth-value gap. First I give a system of propositional SPL by partializing classical logic, as well as extending it with several non-classical truth-functional operators. Second I show a way based on SPL to construct a system of tensed ontology, by representing tensed statements as two kinds of necessary statements in a linear model that consists of the present and future worlds. Finally I (...) compare that way with other two ways based on Łukasiewicz’s three-valued logic and branching temporal logic. (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)

We develop a conceptually clear, intuitive, and feasible decision procedure for testing satisfiability in the full multi\-agent epistemic logic \CMAELCD\ with operators for common and distributed knowledge for all coalitions of agents mentioned in the language. To that end, we introduce Hintikka structures for \CMAELCD\ and prove that satisfiability in such structures is equivalent to satisfiability in standard models. Using that result, we design an incremental tableau-building procedure that eventually constructs a satisfying Hintikka structure for every satisfiable input set (...) of formulae of \CMAELCD\ and closes for every unsatisfiable input set of formulae. (shrink)

Infectious logics are systems that have a truth-value that is assigned to a compound formula whenever it is assigned to one of its components. This paper studies four-valued infectious logics as the basis of transparent theories of truth. This take is motivated as a way to treat different pathological sentences differently, namely, by allowing some of them to be truth-value gluts and some others to be truth-value gaps and as a way to treat the semantic pathology suffered by at least (...) some of these sentences as infectious. This leads us to consider four distinct four-valued logics: one where truth-value gaps are infectious, but gluts are not; one where truth-value gluts are infectious, but gaps are not; and two logics where both gluts and gaps are infectious, in some sense. Additionally, we focus on the proof theory of these systems, by offering a discussion of two related topics. On the one hand, we prove some limitations regarding the possibility of providing standard Gentzen sequent calculi for these systems, by dualizing and extending some recent results for infectious logics. On the other hand, we provide sound and complete four-sided sequent calculi, arguing that the most important technical and philosophical features taken into account to usually prefer standard calculi are, indeed, enjoyed by the four-sided systems. (shrink)

The new logic of partitions is dual to the usual Boolean logic of subsets (usually presented only in the special case of the logic of propositions) in the sense that partitions and subsets are category-theoretic duals. The new information measure of logical entropy is the normalized quantitative version of partitions. The new approach to interpreting quantum mechanics (QM) is showing that the mathematics (not the physics) of QM is the linearized Hilbert space version of the mathematics of (...) partitions. Or, putting it the other way around, the math of partitions is a skeletal version of the math of QM. The key concepts throughout this progression from logic, to logical information, to quantum theory are distinctions versus indistinctions, definiteness versus indefiniteness, or distinguishability versus indistinguishability. The distinctions of a partition are the ordered pairs of elements from the underlying set that are in different blocks of the partition and logical entropy is defined (initially) as the normalized number of distinctions. The cognate notions of definiteness and distinguishability run throughout the math of QM, e.g., in the key non-classical notion of superposition (= ontic indefiniteness) and in the Feynman rules for adding amplitudes (indistinguishable alternatives) versus adding probabilities (distinguishable alternatives). (shrink)

Main results are: (i) number e^{e} is transcendental; (ii) the both numbers e+π and e-π are irrational.

An introductory text describing the author’s approach to epistemology in terms of self-referential argumentation and self-validating proofs. The text emphasizes a skill-based, rather than content-based, approach to the study of epistemology. The book is a simply stated, basic text whose purpose is to introduce students to the technical approach to epistemology developed by the author in other publications. ●●●●● -/- 2022 UPDATE: The approach of this book has been updated and developed further in the author’s 2021 book _Critique (...) of Impure Reason: Horizons of Possibility and Meaning_. The book is available both in a printed edition (under ISBN 978-0-578-88646-6 from Barnes & Noble, Amazon, and other booksellers) and an Open Access eBook edition (available through Philpapers under the book’s title and other philosophy online archives). (shrink)

The incompleteness of set theory ZF C leads one to look for natural nonconservative extensions of ZF C in which one can prove statements independent of ZF C which appear to be “true”. One approach has been to add large cardinal axioms.Or, one can investigate second-order expansions like Kelley-Morse class theory, KM or Tarski-Grothendieck set theory T G or It is a nonconservative extension of ZF C and is obtained from other axiomatic set theories by the inclusion of Tarski’s axiom (...) which implies the existence of inaccessible cardinals. See also related set theory with a filter quantifier ZF (aa). In this paper we look at a set theory NC# ∞# , based on bivalent gyper infinitary logic with restricted Modus Ponens Rule In this paper we deal with set theory NC# ∞# based on bivalent gyper infinitary logic with Restricted Modus Ponens Rule. Nonconservative extensions of the canonical internal set theories IST and HST are proposed. (shrink)

In To be is to be the object of a possible act of choice the authors defended Boolos’ thesis that plural quantification is part of logic. To this purpose, plural quantification was explained in terms of plural reference, and a semantics of plural acts of choice, performed by an ideal team of agents, was introduced. In this paper, following that approach, we develop a theory of concepts that—in a sense to be explained—can be labeled as a theory of logical (...) concepts. Within this theory, we propose a new logicist approach to natural numbers. Then, we compare our logicism with Frege’s traditional logicism. (shrink)

An AC servomotor which is mostly a two-phase induction motor with two stator field coils placed 90 electrical degrees apart used for controlling position, speed and acceleration in manufacturing industries. In this paper, a two-phase induction motor has been designed with a fuzzy logic and observer based controllers to improve the performance of the system. Comparison of the AC servomotor with the proposed controllers for tracking a step and a square desired position signal input has been done using (...) Matlab/Simulink toolbox and a promising result obtained. (shrink)

Epistemic logics based on the possible worlds semantics suffer from the problem of logical omniscience, whereby agents are described as knowing all logical consequences of what they know, including all tautologies. This problem is doubly challenging: on the one hand, agents should be treated as logically non-omniscient, and on the other hand, as moderately logically competent. Many responses to logical omniscience fail to meet this double challenge because the concepts of knowledge and reasoning are not properly separated. In this (...) paper, I present a dynamic logic of knowledge that models an agent’s epistemic state as it evolves over the course of reasoning. I show that the logic does not sacrifice logical competence on the altar of logical non- omniscience. (shrink)

In this article Russell’s paradox and Cantor’s paradox resolved successfully using intuitionistic logic with restricted modus ponens rule.

Sports physicians are continuously confronted with new biotechnological innovations. This applies not only to doping in sports, but to all kinds of so-called enhancement methods. One fundamental problem regarding the sports physician's self-image consists in a blurred distinction between therapeutic treatment and non-therapeutic performance enhancement. After a brief inventory of the sports physician's work environment I reject as insufficient the attempts to resolve the conflict of the sports physician by making it a classificatory problem. Followed by a critical assessment of (...) some ideas from the US President's Council on Bioethics, the formulation of ethical codes and attempts regarding a moral topography, it is argued that the sports physician's conflict cannot be resolved by the distinction between therapy and enhancement. Instead, we also have to consider the possibility that the therapy-based paradigm of medicine cannot do justice to the challenges of the continuously increasing technical manipulability of the human body and even our cognitive functions as well. At the same time we should not adhere to transhumanist ideas, because non-therapeutic interventions require clear criteria. Based on assistive technologies an alternative framework can be sketched that allows for the integration of therapeutic and non-therapeutic purposes. After a thorough definition of standards and criteria, the role of the sports physician might be defined as that of an assistant for enhancement. Yet the process of defining such an alternative framework is a societal and political task that cannot be accomplished by the sports physicians themselves. Until these questions are answered sports physicians continue to find themselves in a structural dilemma that they partially can come to terms with through personal integrity. (shrink)

In this book set theory INC# based on intuitionistic logic with restricted modus ponens rule is proposed. It proved that intuitionistic logic with restricted modus ponens rule can to safe Cantor naive set theory from a triviality.

In this opinion piece we propose the investigation of psychedelic-assisted psychotherapy for the treatment of body dysmorphic disorder (BDD). BDD is a psychiatric disorder characterised by appearance-based preoccupations and accompanying compulsions. While safe and effective treatments for BDD exist, non-response and relapse rates remain high. Therefore, there is a need to investigate promising new treatment options for this highly debilitating condition. Preliminary evidence suggests safety, feasibility, and potential efficacy of psychedelic treatments in disorders that share similar psychopathological mechanisms with (...) BDD. Drawing on this evidence, as well as on relevant qualitative reports and theoretical proposals, we argue that it would be worthwhile to conduct a phase 2a study aimed at assessing the safety and feasibility of psychedelic-assisted psychotherapy in BDD. We also offer some suggestions for how future research ought to proceed. (shrink)

Desire is an important philosophical topic that deeply impacts everyday life. Philosophical practice is an emerging trend that uses philosophical theories and methods as a guide to living a eu‐ daimonic life. In this paper, we define desire philosophically and compare different theories of desire in specific Eastern and Western traditions. Based on the Lacanian conceptual–terminological triad of “Need‐Demand‐Desire”, the research of desire is further divided into three dimensions, namely, the subject of desire, the object of desire, and the (...) desire itself. The concept of desire is then an‐ alyzed from this triad and these three dimensions through different philosophical theories. This paper selects Buddhism as the representative of Eastern tradition, and Stoicism as the representative of the West, paying special attention to Stoicism’s “spiritual exercises” following Pierre Hadot. By exploring and comparing the Buddhist paths to liberation from suffering (i.e., the Four Noble Truths and the Noble Eightfold Path) and the two theoretical pillars in Stoicism (i.e., the notions of “living according to nature” and “the dichotomy of control”), practical guidance is then provided for un‐ derstanding and regulating desire in times of crisis. This understanding and regulation of desire constitutes a philosophical therapy for today’s troubles, particularly those caused by excessive or irrational desires. (shrink)

When one thinks—knows, believes, imagines—that something is the case, one’s thought has a topic: it is about something, towards which one’s mind is directed. What is the logic of thought, so understood? This book begins to explore the idea that, to answer the question, we should take topics seriously. It proposes a hyperintensional account of the propositional contents of thought, arguing that these are individuated not only by the set of possible worlds at which they are true, but also (...) by their topic: what they are about. The book then builds epistemic, doxastic, probabilistic, and conditional logics based on this view. It applies them to issues ranging from dogmatism, scepticism, and epistemic fallibilism, to imagination and suppositional reasoning, belief revision, framing effects, and the acceptability of indicative conditionals. (shrink)

Abstract This article proposes and outlines an integrally informed 12 Step-based therapy that is adapted for treating addicted populations. Integrated Recovery Therapy (IRT) as a therapeutic orientation is an Integral Methodological Pluralism to therapy for treating addiction. Its two main features are paradigmatic and meta-paradigmatic. The paradigmatic aspect refers to the recognition, compilation and implementation of various methodologies in a comprehensive and inclusive manner. The meta-paradigmatic aspect refers to IRT’s capacity to weave together, relate and integrate (...) the various paradigmatic practices. IRT is a meta-therapy derived from the Integrated Recovery Model, which is a comprehensive, balanced, multi-phased and multi-disciplinary clinical model designed for in-patient addiction treatment. As with the Integrated Recovery Model, IRT’s philosophy is derived from an integration of the 12-step abstinence-based philosophy, mindfulness, positive psychology, and Integral theory. It is suggested here that the application of IRT as a meta-therapy provides a truly comprehensive and integrated therapeutic orientation for therapists who treat addicted populations. -/- Keywords: Integrated Recovery Therapy, Integrated Recovery model; 12 Steps; mindfulness; Integral theory; positive psycholog. (shrink)

Based on Kolchinsky and Wolpert’s work on the semantics of autonomous agents, I propose an application of Mathematical Logic and Probability to model cognitive processes. In this work, I will follow Bateson’s insights on the hierarchy of learning in complex organisms and formalize his idea of applying Russell’s Type Theory. Following Weaver’s three levels for the communication problem, I link the Kolchinsky–Wolpert model to Bateson’s insights, and I reach a semantic and conceptual hierarchy in living systems as an (...) explicative model of some adaptive constraints. Due to the generality of Kolchinsky and Wolpert’s hypotheses, I highlight some fundamental gaps between the results in current Artificial Intelligence and the semantic structures in human beings. In light of the consequences of my model, I conclude the paper by proposing a general definition of knowledge in probabilistic terms, overturning de Finetti’s Subjectivist Definition of Probability. (shrink)

The Bounds of Logic presents a new philosophical theory of the scope and nature of logic based on critical analysis of the principles underlying modern Tarskian logic and inspired by mathematical and linguistic development. Extracting central philosophical ideas from Tarski’s early work in semantics, Sher questions whether these are fully realized by the standard first-order system. The answer lays the foundation for a new, broader conception of logic. By generally characterizing logical terms, Sher establishes a (...) fundamental result in semantics. Her development of the notion of logicality for quantifiers and her work on branching are of great importance for linguistics. Sher outlines the boundaries of the new logic and points out some of the philosophical ramifications of the new view of logic for such issues as the logicist thesis, ontological commitment, the role of mathematics in logic, and the metaphysical underpinning of logic. She proposes a constructive definition of logical terms, reexamines and extends the notion of branching quantification, and discusses various linguistic issues and applications. (shrink)