This pioneering book presents a reconstitution of Charles Sanders Peirce philosophical system as a coherent architecture of concepts that form a unified theory of reality. Historically, the majority of Peircean scholars adopted a thematic approach to study isolated topics such as semiotics and pragmatism without taking into account the author’s broader philosophical framework, which led to a poor and fragmented understanding of Peirce’s work. In this volume, professor Ivo Assad Ibri, past president of The Charles Sanders Peirce Society and a (...) leading figure in the Brazilian community of Peircean scholars, adopts a systemic approach to Peirce’s thought and presents Peirce’s scientific metaphysics as a deep ontological architecture based on a semiotic logic and on pragmatism as criteria of meaning. Originally published in Portuguese, this book became a classic among Brazilian Peircean scholars by presenting a conceptual matrix capable of providing a clear reference system to ground the thematic studies into the broader Peircean system. Now translated to English, this reviewed, amplified and updated edition aims to make this contributions available to the international community of Peircean scholars and to serve as a tool to understand Peirce’s work in a more systemic way by integrating concepts such as experience, phenomenon, existence and reality, as well as theories such as Chance, Continuity, Objective Idealism, Cosmology and Pragmatism, in a coherent system that reveals Peirce’s complex metaphysical architecture. "As the philosophical reputation of Charles S. Peirce continues to rise to first-tier prominence in the history of American philosophy, Ivo Ibri’s Kósmos Noetós assumes a unique status in both a pioneering and a magisterial work of transcontinental Peirce scholarship. This original work of this internationally renowned scholar and editor, and Professor of Philosophy at the Pontifical Catholic University of San Paulo, penetrates to the heart of Peirce’s architectonic system of phenomenological, metaphysical, and semiotic categories which heuristically characterize our world as “a universe perfused with signs.” Ibri’s own synergistic commentary on the radiating registers of Peirce’s cosmogonically and pragmatistically conceived “one intelligible theory of the universe” also instructively contributes to the illumination of significant nodes of interface with a range of relevant theoretical trends in the contemporary academy; as well, it places Peirce in the company of such thinkers as Plato, Aristotle, Plotinus, Kant, and Schelling who preceded Peirce in providing a legacy of first-tier reasoning on our intelligibly developing world. Kosmos Noetos impresses as Ibri’s pure, lucid, passionately thought-loving, philosophical articulation of his own and as the indispensable prolegomena to all future Peirce studies." David Dilworth, State University of New York at Stone Brook – USA "Ivo Ibri has offered us in this exquisite work a framing of the inner logic of Charles S. Peirce's core metaphysical vision and its existential implications. It is a deep and nuanced exploration of the internal dynamics of Peirce’s central metaphysical categories, developed through rigorous and detailed attention to the evolution of Peirce’s thought on the ‘vitally important topics’ of the appearing, the reality, and the intelligibility of the world. The two-leveled format of the book, an intricate weaving of Peirce’s texts and discursive elaboration and linkage by Ibri, gives it a distinctive feel and is the bedrock of its value. The book is a remarkable combination of presentation and analysis. It is informed by Ibri’s deep philosophical culture and is a gentle and convincing argument for the centrality of metaphysics in understanding Peirce’s thought. It offers in a new way indispensable suggestions for our own attempts to think about our places in an evolving universe with the aid of Peirce and offers threads of thought to be followed up by others." Robert E. Innis, University of Massachusetts Lowell – USA. (shrink)

In Transparent Intensional Logic we can recognize two distinct notions of computation that loosely correspond to term rewriting and term interpretation as known from lambda calculus. Our goal will be to further explore these two notions and examine some of their properties.

The main objective of this paper is to sketch unifying conceptual and formal framework for inference that is able to explain various proof techniques without implicitly changing the underlying notion of inference rules. We base this framework upon the so-called two-dimensional, i.e., deduction to deduction, account of inference introduced by Tichý in his seminal work The Foundation’s of Frege’s Logic (1988). Consequently, it will be argued that sequent calculus provides suitable basis for such general concept of inference and therefore should (...) not be seen just as technical tool, but philosophically well-founded system that can rival natural deduction in terms of its “naturalness”. (shrink)

In this paper we examine two approaches to the formal treatment of the notion of problem in the paradigm of algorithmic semantics. Namely, we will explore an approach based on Martin-Löf’s Constructive Type Theory, which can be seen as a direct continuation of Kolmogorov’s original calculus of problems, and an approach utilizing Tichý’s Transparent Intensional Logic, which can be viewed as a non-constructive attempt of interpreting Kolmogorov’s logic of problems. In the last section we propose Kolmogorov and CTT-inspired modifications to (...) TIL-based approach. The focus will be on non-empirical problems only. (shrink)

Let Uq be the quantum group associated to sl2 with char≠2 and qk not a root of unity. The article is devoted to the model-theoretic study of the quantum plane kq[x,y], considered as an -structure, where is the language of representations of Uq. It is proved that the lattice of definable k-subspaces of kq[x,y] is complemented. This is deduced from the same result for the Uq-module M, which is defined to be the direct sum of all finite dimensional representations of (...) Uq. It follows that the ring of definable scalars for the quantum plane is a von Neumann regular epimorphic ring extension of the quantum group Uq. (shrink)

Is there a poetic ground in Peirce's philosophy? While this question may sound interesting, it is somehow odd, as Peirce is well–known as a logician, and it is also known by scholars that he was not an expert in poetry, literature, art, or even theories concerning art in general. This paper hypothesizes that there is a starting point in his philosophy that is poetical in its nature. Moreover, Peirce's system is obviously logical in its form, but also keeps the spirit (...) of the original silent feeling of poetry that seems to have fascinated him. Also, I claim there is a Schellingian heritage in Peirce's philosophy that is partially responsible for that poetic starting point. This idea also has, as a support, the supposition that a realistic view of the world provides a hypothesis of symmetry between the human and natural worlds, which provides the basic form for his ontological theories and for the theoretical harmony among Peirce's doctrines. This quality of Peirce's philosophy is a kind of a Greek beauty that is only evident for those who can view his thought not in fragments but as a complex system that has the potency of not only answering classical philosophical questions, but also of giving rise to a new philosophy which needs to be further developed. (shrink)

In this paper, we will be interested in the notion of a computable proposition. It allows for feasible computational semantics of empirical sentences, despite the fact that it is in general impossible to get to the truth value of a sentence through a series of effective computational steps. Specifically, we will investigate two approaches to the notion of a computable proposition based on constructive type theory and transparent intensional logic. As we will see, the key difference between them is their (...) accounts of denotations of empirical sentences. (shrink)

Proofs from assumptions are amongst the most fundamental reasoning techniques. Yet the precise nature of assumptions is still an open topic. One of the most prominent conceptions is the placeholder view of assumptions generally associated with natural deduction for intuitionistic propositional logic. It views assumptions essentially as holes in proofs, either to be filled with closed proofs of the corresponding propositions via substitution or withdrawn as a side effect of some rule, thus in effect making them an auxiliary notion subservient (...) to proper propositions. The Curry–Howard correspondence is typically viewed as a formal counterpart of this conception. I will argue against this position and show that even though the Curry–Howard correspondence typically accommodates the placeholder view of assumptions, it is rather a matter of choice, not a necessity, and that another more assumption-friendly view can be adopted. (shrink)

In this paper, we consider the ex falso quodlibet rule (EFQ) as a derived rule and propose a new justification for it based on a rule we call the collapse rule. The collapse rule is a mix between EFQ and disjunctive syllogism (DS). Informally, it says that a choice between a proposition A and ⊥, which is understood as nullary disjunction, is no choice at all and it defaults to A. Thus, we can regard it as capturing the idea of (...) an implosion principle in contrast to EFQ’s explosion principle. Furthermore, we show that the collapse rule can also be used to justify DS and that all these three rules have the same deductive strength: they are all interderivable. Thus, the discussions about the justification of EFQ or DS be reduced to a discussion about the justification of the collapse rule. (shrink)

Jeder weiss, dass er sterben muss. Er weiss nur nicht wann. Wüsste er es, er könnte den Tod nicht mehr aus seinem Leben verdrängen. Dieses Buch geht von einer utopischen Situation aus: Durch eine gentechnische Analyse wird bei jedem Menschen gleich nach seiner Geburt festgestellt, wann sein "Endtag", also sein Todestag, sein wird. Frühere Todesfälle gibt es nur bei Unfall oder Mord, spätere nie. Das Wissen um den Endtag verändert das Leben jedes Einzelnen, die Familien, die Gesellschaft, Ausbildung, Beziehungen und (...) Lebensplanung, Laufbahnen im Beruf, das Rentensystem u.v.m. Was für die einen ein "Horrorszenario" sein kann, entpuppt sich für die anderen als ein Segen: Alle können ihren Lebensabend planen und zur rechten Zeit bewusst Abschied nehmen. Und an diesem Punkt wird das Szenario von Ivo W. Greiter zum Plädoyer: Versucht euch täglich bewusst zu sein und zu akzeptieren, dass Ihr nicht ewig leben werdet. Rechnet mit dem Tod, redet über das Sterben, räumt eure Sachen auf. Und: Der Tod kann seinen Schrecken verlieren, wenn er am Leben teilhaben darf. "Und immer wieder stellte ich mir die Frage: Wenn ich weiss, was ich ändern würde, wenn ich in vier Monaten sterben würde, warum ändere ich es dann nicht gleich?" DR. GREITER, geb. 1940, ist Rechtsanwalt in Innsbruck; er ist vielfach in Berufsverbänden und ehrenamtlich engagiert, so als österreichischer Vorsitzender der internationalen Juristenorganisation World Jurist Association, Washington, als Vizepräsident des Österreichischen Juristentages und des österreichischen Anwaltsvereins u. a.; von 1983 bis 1989 war Dr. Greiter Mitglied des Gemeinderates von Innsbruck und von 1993 bis 2010 französischer Honorarkonsul in Innsbruck. Er befasst sich unter anderem mit Rechtsfragen für Menschen über 66; zahlreiche sonstige fachbezogene Veröffentlichungen. (shrink)

Following the theory of Boolean algebras with modal operators , in this paper we investigate Boolean algebras with sufficiency operators and mixed operators . We present results concerning representability, generation by finite members, first order axiomatisability, possession of a discriminator term etc. We generalise the classes BAO, SUA, and MIA to classes of algebras with the families of relative operators. We present examples of the discussed classes of algebras that arise in connection with reasoning with incomplete information.

In a recent paper, we have shown that the class of Boolean contact algebras (BCAs) has the hereditary property, the joint embedding property and the amalgamation property. By Fraïssé’s theorem, this shows that there is a unique countable homogeneous BCA. This paper investigates this algebra and the relation algebra generated by its contact relation. We first show that the algebra can be partitioned into four sets {0}, {1}, K, and L, which are the only orbits of the group of base (...) automorphisms of the algebra, and then show that the contact relation algebra of this algebra is finite, which is the first non-trivial extensional BCA we know which has this property. (shrink)

The designation of Diego Maradona’s ‘handball’ goal, that it was an intervention by God himself, brings the phenomena of sport and religion into an interrelationship. The basic thesis of this paper is that, despite many of their phenomenal similarities, explicit religion is not, and cannot be, substantially related to sport, as the two manifest themselves in different ways of being. This thesis is supported by arguments from three philosophical areas: 1. The ontological dimension of the manifestation of the sacred in (...) the profane through the process of hierophany in sport does not refer to a specific deity or God, and is therefore not a presentation but an indirect representation of the sacred; 2. The epistemological perspective of the intentional relation of consciousness to religious ritual justifies the necessity of situating them in an overall horizon of references and meanings to the horizon of the lifeworld; 3. The existential and experiential aspects of transformative sport experiences transform the horizon of meanings of empirical reality, but lack the sacramental perspective. Implicit religion as a possibility of transition on a continuum of complementary existential states is a suitable explicative framework for analyzing the phenomenal similarities and essential differences of religion and sport. (shrink)

Contact relations have been studied in the context of qualitative geometry and physics since the early 1920s, and have recently received attention in qualitative spatial reasoning. In this paper, we present a sound and complete proof system in the style of Rasiowa and Sikorski (1963) for relation algebras generated by a contact relation.

Before examining de Moivre's contributions to the science of mathematics, this article reviews the source materials, consisting of the printed works and the correspondence of de Moivre, and constructs his biography from them. The analytical part examines de Moivre's contributions and achievements in the study of equations, series, and the calculus of probability. De Moivre contributed to the continuing development from Viète to Abel and Galois of the theory of solving equations by means of constructing particular equations, the roots of (...) which can be written in the form $$\sqrt[n]{{a + \sqrt b }} + \sqrt[n]{{a - \sqrt b }}$$. He also discovered the reciprocal equations. In the course of this work de Moivre discovered an expression equivalent to (cos α+i sin α) n =cos n α+i sin n α and, following Cotes, he succeeded in expressing the nth roots of unity in trigonometric form. In the theory of series, de Moivre developed a polynomial theorem encom-passing Newton's binomial theorem and, in particular, a theorem of recurrent series useful in the calculus of probability. The demands of the calculus of probability led de Moivre to an approximation for the binomial coefficients $$\left( {_m^n } \right)$$ for large values of n. The interaction between de Moivre and James Stirling, particularly in regard to the asymptotic series for log (n!), is treated at length. This work supplied the foundation for de Moivre's limit theorem for the binomial distribution. The calculus of probability, which occupied him from 1708 onward, became in time ever more the center of de Moivre's inquiries. Proceeding from contemporary collections of gambling exercises, de Moivre, by introducing an explicit measure of probability for the so-called Laplace experiments, found the beginnings of a theory of probability. De Moivre expanded the classic application of probability calculus to games of chance by addressing himself to the problem of annuities and by adopting Halley's work with its conception of “Probability of life”. De Moivre was the first to publish a mathematically formulated law for the decrements of life derived from mortality tables. (shrink)

Natural law as a discipline was definitively institutionalized at universities in the Habsburg monarchy during the reforms of Maria Theresia after 1752. The guiding principles of these reforms were set in the instruction for the chair of natural law in Vienna which was given to Carl Anton Martini. It was Catholic in conception, but it ordered the professor to draw on Grotius. Our article reconstructs the elementary structure of Martini’s theory of natural law with a focus on his conception of (...) state. The article proves that Martini did not adopt Wolff’s conception of deducing duties and obligations from the highest principle for that would conflict with the Catholic emphasis on freedom of will. Instead of that, Martini derived duties and rights from the three God-given ends. Martini perceived the state as based on social contract, after the model of Christian Wolff. However, it seems that Martini rejected the two-contract model and acknowledged only the contract of submission as binding. Martini sought to hold the middle ground between Machiavellians arguing that the subjects lose all rights after the social contract, and radical ‘monarchomachs’ who believe that the ‘populus’ retains the supreme power. Martini argues that the ruler is limited by natural laws; the subjects retain rights to life and to property, but they are denied any right to resistance. Since Martini derived the monarch’s powers from the unlimited duty to guarantee security, he admitted even encroachments on religious freedom. He admitted coercion in matters that would threaten salus civitatis, but respected the inner libertas conscientiae. He also acknowledged a peculiar division of powers differentiating between a legislative, an inspectorial and an executive power. Even though the aim of this division was not a system of checks and balances, a precise description of the scope of the executive power helped to delimit a sphere of individual freedom. (shrink)

We introduce and study a class ofbetweenness algebras—Boolean algebras with binary operators, closely related to ternary frames with a betweenness relation. From various axioms for betweenness, we chose those that are most common, which makes our work applicable to a wide range of betweenness structures studied in the literature. On the algebraic side, we work with two operators ofpossibilityand ofsufficiency.

This essay focuses on the concept of consciousness in C. S. Peirce’s work, revealing how its ways of being are associated with the three Peircean phenomenological categories. In this article, I intend to reflect on the heuristic power of the mind, namely, its ability to bring about new ideas, which, within Peirce’s logic of inquiry, is called by the well-known term of abduction. The abductive logical step promotes a synthesis of signs that constitutes a logical structure capable of proposing a (...) new mediation or representation of a new phenomenon. I make use of a metaphorical passage from Peirce not only to give the title to this essay, but also to highlight the importance of the first category as a sort of synechistic envelopment of an unprecedented logical structure of signs that composes a new synthesis. Two continua intertwine themselves, namely, those of the first and third categories, to account for what appears as a fact of the world in the theater of secondness. The essay also seeks to bring to light the core realism of Peirce’s philosophy, the genetic aspect of this bottomless lake, through its cosmology, where the generalization of forms and the acquisition of habits of reality are the proper ground of his Objective Idealism. One of the heuristic aspect of the lake metaphor is a sort of invitation to extend the concept of synthesis from the realm of logical structures to that one of arts, which in this essay will remain as a suggestion for a further reflection. (shrink)

We approach the topic of solution equivalence of propositional problems from the perspective of non-constructive procedural theory of problems based on Transparent Intensional Logic (TIL). The answer we put forward is that two solutions are equivalent if and only if they have equivalent solution concepts. Solution concepts can be understood as a generalization of the notion of proof objects from the Curry-Howard isomorphism.

In die Geschichte sind Franz Josef Graf von Thun (1734-1801) und seine Frau Wilhelmine (1744-1800) als Gonner des Geniemusikers Wolfgang Amadeus Mozart eingegangen. Der "sonderbare Cavalier", wie er von Mozart genannt wurde, war seinen Zeitgenossen eher als Geisterbeschworer und Magnetiseur, denn als Musikliebhaber und Schriftsteller bekannt. Erst 2009 tauchte im Familienarchiv Thun-Hohenstein das Manuskript der umfangreichen esoterischen Enzyklopadie auf, in der Graf von Thun seine Ansichten uber den Menschen, uber das Weltall und uber die Franzosische Revolution darlegt. Ivo Cerman stellt (...) hier die Philosophie des Grafen vor dem Hintergrund des Illuminismus des 18. Jahrhunderts vor und ediert die wichtigsten Artikel seiner esoterischen Enzyklopadie. Auf der Grundlage dieser gerade entdeckten wichtigen Quelle kann die Frage nach dem Verhaltnis zwischen Aufklarung und Illuminismus neu beantwortet werden. (shrink)

We investigate complex algebras of the form arising from a frame where, and exhibit their abstract algebraic and logical counterparts.

The Kosovo conflict -- The Israeli-Palestinian conflict -- The conflict in the Democratic Republic of Congo.

ABSTRACT Two objects o1, o2 of an information system are said to be complementary with respect to attribute a if α(o1) = -α(o2), where α(o) is the set of values of attribute a assigned to o. They are said to be complementary with respect to a set of attributes A if they are complementary with respect to each attribute α ε A. A multi-modal logical language for reasoning about complementarity relations is presented, with modalities [A] and ?A? parameterised by subsets (...) of a given set ATTR of attributes. Two complete deduction system for the language are presented: a Rasiowa-Sikorski style system using signed formulae, and an equivalent sequent calculus system in Gentzen style complete for theories. (shrink)

Based on Alasdair Urquhart’s representation of not necessarily distributive bounded lattices we exhibit several discrete dualities in the spirit of the “duality via truth” concept by Orłowska and Rewitzky. We also exhibit a discrete duality for Urquhart’s relevant algebras and their frames.