We present the logic K/2 which is a logic with classical implication and only the left part of classical negation.We show that it is possible to define a classical negation into K/2 and that the classical proposition logic K can be translated into this apparently weaker logic.We use concepts from model-theory in order to characterized rigorously this translation and to understand this paradox. Finally we point out that K/2 appears, following Haack's distinction, both as a deviation and an extension of (...) K. (shrink)

This paper introduces the special issue on Formal Approaches to the Ontological Argument of the Journal of Applied Logics (College Publications). The issue contains the following articles: Formal Approaches to the Ontological Argument, by Ricardo Sousa Silvestre and Jean-Yves Béziau; A Brief Critical Introduction to the Ontological Argument and its Formalization: Anselm, Gaunilo, Descartes, Leibniz and Kant, by Ricardo Sousa Silvestre; A Mechanically Assisted Examination of Begging the Question in Anselm’s Ontological Argument, by John Rushby; A Tractarian Resolution to the (...) Ontological Argument, by Erik Thomsen; On Kant’s Hidden Ambivalence Toward Existential Generalization in his Critique of the Ontological Argument, by Giovanni Mion; The Totality of Predicates and the Possibility of the Most Real Being, by Srećko Kovač; An Even More Leibnizian Version of Gödel’s Ontological Argument, by Kordula Świętorzecka and Marcin Łyczak; A Case Study On Computational Hermeneutics: E. J. Lowe’s Modal Ontological Argument, by David Fuenmayor. (shrink)

This is a volume containing papers honoring Patrick Suppes (1922-2014). All contributors have worked directly with Suppes or/and with his ideas. The book also contains one of the last papers by Suppes (co-authored by two of his collaborators). -/- The work of Suppes touches many different areas, ranging from meteorology to physics, through logic, mathematics, psychology, neuroscience, education, painting, but he was first of all and above all a philosopher, always questioning, but not in vain. There are not many philosophers (...) who can be proud of having written influential math textbooks, contributed decisively to the philosophical foundations of science, helped to develop research in real labs, promoted new forms o education (computer-assisted learning and the EGPY – Education Program for Gifted Youth). -/- Since the range of interest of Suppes was very broad, so is the variety of topics dealt with in this volume. The work of a researcher is certainly not limited to his own writings, but also has to be appreciated through the work of the people he has been working with and influenced. From this point of view the work of Suppes is very impressive, and the present book contributes to show that. -/- This is a follow up of a special issue of the journal Synthese, New Directions in the Foundations of Science, edited by Béziau and Krause, after a meeting they organized with Suppes in Florianópolis (Brazil) in 2002 for his 80th birthday. -/- Jean-Yves Béziau worked with Suppes at Stanford University for two years (2000 and 2001) and has been continuously working in the Suppes tradition of logic, methodology and philosophy of science, which emphasizes structures and models. -/- Décio Krause has used Suppes’ approach to the axiomatization of scientific theories in many fields. With J.C.M. Magalhães, he presented a ``Suppes predicate” for genetics and natural selection and with S. French he developed a Suppes predicate for quantum field theories via Fock spaces. (shrink)

We discuss aspects of the logic of negation bearing on an issue raised by Jean-Yves Béziau, recalled in §1. Contrary- and subcontrary-forming operators are introduced in §2, which examines some of their logical behaviour, leading on naturally to a consideration in §3 of dual intuitionistic negation (as well as implication), and some further operators related to intuitionistic negation. In §4, a historical explanation is suggested as to why some of these negation-related connectives have attracted more attention than others. The remaining (...) sections (§§5, 6) briefly address a question about a certain notion of global contrariety and the provision of Kripke semantics for the various operators in play in our discussion. (shrink)

This is a collection of new investigations and discoveries on the theory of opposition (square, hexagon, octagon, polyhedra of opposition) by the best specialists from all over the world. The papers range from historical considerations to new mathematical developments of the theory of opposition including applications to theology, theory of argumentation and metalogic.

Using methods of abstract logic and the theory of valuation, we prove that there is no paraconsistent negation obeying the law of double negation and such that $\neg(a\wedge\neg a)$ is a theorem which can be algebraized by a technique similar to the Tarski-Lindenbaum technique.

Information can be public among a group. Whether or not information is public matters, for example, for accounts of interdependent rational choice, of communication, and of joint intention. A standard analysis of public information identifies it with (some variant of) common belief. The latter notion is stipulatively defined as an infinite conjunction: for p to be commonly believed is for it to believed by all members of a group, for all members to believe that all members believe it, and so (...) forth. This analysis is often presupposed without much argument in philosophy. Theoretical entrenchment or intuitions about cases might give some traction on the question, but give little insight about why the identification holds, if it does. The strategy of this paper is to characterize a practical-normative role for information being public, and show that the only things that play that role are (variants of) common belief as stipulatively characterized. In more detail: a functional role for “taking a proposition for granted” in non-isolated decision making is characterized. I then present some minimal conditions under which such an attitude is correctly held. The key assumption links this attitude to beliefs about what is public. From minimal a priori principles, we can argue that a proposition being public among a group entails common commitment to believe among that group. Later sections explore partial converses to this result, the factivity of publicity and publicity from the perspective of outsiders to the group, and objections to the aprioricity of the result deriving from a posteriori existential presuppositions. (shrink)

Ned Block argues that the higher-order (HO) approach to explaining consciousness is ‘defunct’ because a prominent objection (the ‘misrepresentation objection’) exposes the view as ‘incoherent’. What’s more, a response to this objection that I’ve offered elsewhere (Weisberg 2010) fails because it ‘amounts to abusing the notion of what-it’s-like-ness’ (xxx).1 In this response, I wish to plead guilty as charged. Indeed, I will continue herein to abuse Block’s notion of what-it’s-like-ness. After doing so, I will argue that the HO approach accounts (...) for the sense of what-it’s-like-ness that matters in a theory of consciousness. I will also argue that the only incoherence present in the HO theory is that generated by embracing Block’s controversial notion of what-it’s-like-ness, something no theorist of any stripe ought to do. Block is famous for (among other things) having introduced the notion of ‘phenomenal consciousness’ into contemporary philosophy of mind (Block 1995). This term is widely employed in the philosophical literature and it even appears in the empirical literature. But wide-speared usage has brought about divergent interpretations of the term. We can distinguish a ‘moderate’ and a ‘zealous’ reading of ‘phenomenal consciousness’. On the moderate reading, ‘phenomenal consciousness’ just means ‘experience’. Many people have embraced this sense of the term and use it to roughly pick out conscious experience involving sensory quality (states like conscious visual experiences or conscious pains, for example).2 On the zealous reading, however, phenomenal consciousness is held to be ‘distinct from any cognitive, intentional, or functional property’ (Block 1995: 234). That is, any explanation of phenomenal consciousness in exclusively cognitive, intentional, or functional terms will fail to capture, without remainder, what is really distinctive about phenomenal consciousness. Block, of course, is fully clear about embracing the zealous reading; indeed, his initial introduction of the notion is in those terms. The same ambiguity occurs with the much-used (and abused) idea of ‘what-it’s-like-ness’.. (shrink)

This special issue of Logica Universalis (Springer) deals with the relations between logic and religion, broadly conceived. It contains the following articles: Logic and Religion, by Jean-Yves Beziau and Ricardo Silvestre; Thinking Negation in Early Hinduism and Classical Indian Philosophy, by Purushottama Bilimoria; Karma Theory, Determinism, Fatalism and Freedom of Will, by Ricardo Sousa Silvestre; From Logic in Islam to Islamic Logic, by Musa Akrami; Leibniz’s Ontological Proof of the Existence of God and the Problem of Impossible Objects, by (...) Wolfgang Lenzen; A Logical Analysis of the Anselm’s Unum Argumentum (from Proslogion), by Jean-Pierre Desclés; Monotonic and Non-monotonic Embeddings of Anselm’s Proof, by Jacob Archambault; Computer-Assisted Analysis of the Anderson–Hájek Ontological Controversy, by C. Benzmüller, L. Weber and B. Woltzenlogel Paleo. (shrink)

A proof is presented showing that there is no paraconsistent logics with a standard implication which have a three-valued characteristic matrix, and in which the replacement principle holds.

Telling a patient that the outcome of his illness is not good, or even hopeless, requires sensitivity and the ability to communicate with him in the setting of a hospital which is an unnatural environment divorced from family and friends. It is a task which must be taught and learned by doctors and nurses.

The hexagon of opposition is an improvement of the square of opposition due to Robert Blanché. After a short presentation of the square and its various interpretations, we discuss two important problems related with the square: the problem of the I-corner and the problem of the O-corner. The meaning of the notion described by the I-corner does not correspond to the name used for it. In the case of the O-corner, the problem is not a wrong-name problem but a no-name (...) problem and it is not clear what is the intuitive notion corresponding to it. We explain then that the triangle of contrariety proposed by different people such as Vasiliev and Jespersen solves these problems, but that we don’t need to reject the square. It can be reconstructed from this triangle of contrariety, by considering a dual triangle of subcontrariety. This is the main idea of Blanché’s hexagon. We then give different examples of hexagons to show how this framework can be useful to conceptual analysis in many different fields such as economy, music, semiotics, identity theory, philosophy, metalogic and the metatheory of the hexagon itself. We finish by discussing the abstract structure of the hexagon and by showing how we can swing from sense to non-sense thinking with the hexagon. (shrink)

The existential analysis -- The death of dasein -- The timeliness of dasein -- The derivation of time -- The time of being.

The achievements of the textile industry in Roman Britain are often underestimated as a result of the meagreness of our available evidence. The Edict on maximum prices issued by Diocletian in A.D. 301 shows that British capes commanded high prices on the markets of the Empire, and that in the late third century A.D. British rugs were the best in the world. In view of the competition from the traditional centres of rug manufacture in the East, this is an astonishing (...) achievement. (shrink)

The received translation and interpretation of many of the technical terms current in the textile industry of the Roman Empire are inaccurate, because lexicographers have either fought shy of being precise, or have thought that they recognized in the ancient world technical processes which originated at a much later date. The evidence is often equivocal or insufficient, but may still yield details that have been overlooked. The textile expression scutulatus, to take an example, deserves more attention than Blümner has devoted (...) to it. When it refers to the appearance of a garment, Lewis and Short, s.v. scutulatus, translate ‘diamond or lozenge-shaped, checkered’. It seems worth while to attempt a more precise translation, and, if possible, to estimate the significance in context of the goods so designated. (shrink)

Living out of silence, out of a fully functioning, lovingly attentive mind, and not just out of thought, out of a partially functioning mind, is requisite for depth or profundity in living or relating. A fully attentive, truly silent or meditative mind sees that there is real dualism of time and the timeless and that time and the timeless each has its own unique value. The timeless, or real silence, that which alone can make for depth in one's living and (...) relating, can be there only when, in one's awareness, time and all that is related to time, have come to an end. An examination of a wide variety of statements made by writers, both past and present, shows that these understandings are seldom there in contemporary writings, just as they were not there in writings that have come down to us from the past. 'Living beyond the One and the Many' invites readers to consider the possibility that what is presented in it can bring deep meaning to one's way of living in the world"--Publisher's description, back cover. (shrink)

If the world itself is metaphysically indeterminate in a specified respect, what follows? In this paper, we develop a theory of metaphysical indeterminacy answering this question.

This paper introduces the special issue on Logic and Religion of the journal Logica Universalis (Springer). The issue contains the following articles: Logic and Religion, by Jean-Yves Beziau and Ricardo Silvestre; Thinking Negation in Early Hinduism and Classical Indian Philosophy, by Purushottama Bilimoria; Karma Theory, Determinism, Fatalism and Freedom of Will, by Ricardo Sousa Silvestre; From Logic in Islam to Islamic Logic, by Musa Akrami; Leibniz’s Ontological Proof of the Existence of God and the Problem of Impossible Objects, by (...) Wolfgang Lenzen; A Logical Analysis of the Anselm’s Unum Argumentum (from Proslogion), by Jean-Pierre Desclés; Monotonic and Non-monotonic Embeddings of Anselm’s Proof, by Jacob Archambault; Computer-Assisted Analysis of the Anderson–Hájek Ontological Controversy, by C. Benzmüller, L. Weber and B. Woltzenlogel Paleo. (shrink)

Jean-Yves Béziau Abstract In this paper I relate the story about the new rising of the square of opposition: how I got in touch with it and started to develop new ideas and to organize world congresses on the topic with subsequent publications.

Jeffrey Collins’ new book aims to presents Locke’s views on religious toleration in the light of Thomas Hobbes’ political philosophy. At first blush, Hobbes seems an unusual choice as a point of co...

The theory of the square of opposition has been studied for over 2,000 years and has seen a resurgence in new theories and research since the second half of the twentieth century. This volume collects papers presented at the Sixth World Congress on the Square of Opposition, held in Crete in 2018, developing an interdisciplinary exploration of the theory. Chapter authors explore subjects such as Aristotle’s ontological square, logical oppositions in Avicenna’s hypothetical logic, and the power of the square of (...) opposition to solve theological problems regarding predestination and theodicy. Other topics covered include: Hegel’s opposition to diagrams De Morgan’s unpublished octagon of opposition turnstile figures of opposition institutional model-theoretic treatment of oppositions Lacan’s four formulas of sexuation the theory of oppositional poly-simplexes The Exoteric Square of Opposition will appeal to pure logicians, historians of logic, semioticians, philosophers, theologians, mathematicians, and psychoanalysts. (shrink)

We present a paraconsistent logic, called Z, based on an intuitive possible worlds semantics, in which the replacement theorem holds. We show how to axiomatize this logic and prove the completeness theorem.

We are pleased to present this special issue of the journal History and Philosophy of Logic dedicated to the square of opposition.The square of opposition is a diagram and a theory of opposition re...

After recalling the distinction between logic as reasoning and logic as theory of reasoning, we first examine the question of relativity of logic arguing that the theory of reasoning as any other science is relative. In a second part we discuss the emergence of universal logic as a general theory of logical systems, making comparison with universal algebra and the project of mathesis universalis. In a third part we critically present three lines of research connected to universal logic: logical pluralism, (...) non-classical logics and cognitive science. (shrink)

We present the logic K/2 which is a logic with classical implication and only the left part of classical negation.We show that it is possible to define a classical negation into K/2 and that the classical proposition logic K can be translated into this apparently weaker logic.We use concepts from model-theory in order to characterized rigorously this translation and to understand this paradox. Finally we point out that K/2 appears, following Haack's distinction, both as a deviation and an extension of (...) K. (shrink)

According to Boole it is possible to deduce the principle of contradiction from what he calls the fundamental law of thought and expresses as \. We examine in which framework this makes sense and up to which point it depends on notation. This leads us to make various comments on the history and philosophy of modern logic.

Contradiction is often confused with contrariety. We propose to disentangle contrariety from contradiction using the hexagon of opposition, providing a clear and distinct characterization of three notions: contrariety, contradiction, incompatibility. At the same time, this hexagonal structure describes and explains the relations between them.

I discuss the origin and development of logic prizes around the world. In a first section I describe how I started this project by creating the Newton da Costa Logic Prize in Brazil in 2014. In a second section I explain how this idea was extended into the world through the manifesto A Logic Prize in Every Country! and how was organized the Logic Prizes Contest at the 6th UNILOG in Vichy in June 2018 with the participation of 9 logic (...) prizes winners from 9 countries. In a third section I discuss how this project will develop in the future with the creation of more logic prizes, an Encyclopædia of Logic, the book series Logic PhDs, as well as the creation of a World Logic Day, January 14, day of birth of Alfred Tarski and of death of Kurt Gödel. (shrink)