A possible world semantics for standard modal languages is presented, where the valuation functions are allowed to be partial, the truth--functional connectives are interpreted according to weak Kleene matrices, and the necessity operator is given a "weak" interpretation. Completeness and incompleteness results for some (axiomatic) systems are then established. Extensions of these modal logics in which figure "statability" operators are also examined.

At the end of the 19th century in the fundamentals of mathematics appeared a crisis. It was caused by the paradoxes found in Cantor’s set theory. One of the ideas a resolving the crisis was intuitionism – one of the constructivist trends in the philosophy of mathematics. Its creator was Brouwer, the main representative was Heyting. In this paper described will be attempt to construct a suitable logic for philosophical intuitionism theses. In second paragraph Heyting system will be present – (...) its axioms and matrices truth-. Later Gödel theorem about the inadequacy of finite dimensional matrices for this system will be explained. At the end this paper an infinite sequence of matrices adequate for Heyting axioms proposed by Jaśkowski will be described. (shrink)

A possible world semantics for standard modal languages is presented, where the valuation functions are allowed to be partial, the truth–functional connectives are interpreted according to weak Kleene matrices, and the necessity operator is given a “weak” interpretation. Completeness and incompleteness results for some (axiomatic) systems are then established. Extensions of these modal logics in which figure “statability” operators are also examined.

RÉSUMÉ Cette étude met en perspective le précédent constitué par les travaux précoces du jeune Nietzsche où ce dernier fait valoir la force structurante de la métaphore comme matrice des facultés cognitives. Nous offrons d’abord une brève esquisse des postulats et des acquis des grammaires cognitives associées aux travaux d’Eleanor Rosch, ensuite de George Lakoff et Mark Johnson, ainsi qu’à la notion d’inscription corporelle de l’esprit développée par Francesco Varela. Cet exercice sert de propédeutique à une série de lectures tangentes (...) mobilisant divers angles d’approche appelés à faciliter noter évaluation des contributions de Nietzsche au domaine de la cognition. Les travaux examinés nous situent dans la période contemporaine de la publication de son premier grand ouvrage, La naissance de la tragédie : les notes pour le cours intitulé Présentation de la rhétorique ancienne, prononcé au semestre d’hiver 1872-1873 à l’Université de Bâle, ensuite ses Theoretische Studien, datant de l’été 1873, avec un renvoi aux développements plus tardifs dans le Gai Savoir. La thèse de Nietzsche peut être résumée comme suit : tous les éléments de l’appareil catégorial et du régime conceptuel à l’aide desquels nous appréhendons la réalité, a fortiori la notion de vérité qui en est le garant, sont le « précipité » ou le résidu d’un faisceau de métaphores qui constituent la force structurante des facultés cognitives. Si chez Kant nous n’avons accès qu’aux phénomènes et non au noumène, chez Nietzsche nous n’avons affaire qu’à des perspectives ou des points de vues alors que la réalité nous est monnayée sous forme de vérités qui sont des fictions ou des métaphores usées. Il ressort de cet examen que le tropisme endogène de la langue constitue une force majeure dans l’implémentation d’une conceptualité qui a la vertu d’oblitérer sa préhistoire et de se ménager un statut qui est incessamment implosé par le reflux de l’imagination créatrice nourrie par la force métaphorique qui répond à une impulsion foncière que Nietzsche associe à une « force artiste » qui tend à démultiplier les perspectives dont la généalogie se conjugue à l’exponentiel. ABSTRACT This paper highlights the precedent, managed by the precocious insights of the young Nietzsche who advocated the structuring force of the metaphor as the matrix of cognitive powers. We first provide a short sketch of the postulates and gains of cognitive grammars. We examine the guidelines of the works on cognitive research led by great Eleanor Rosch, George Lakoff and Mark Johnson, as well as the concept of embodied mind developed by Francesco Varela. This summary survey is a crash introduction to a series of angular readings from a large array of perspectives on Nietzsche's early contributions to the field of cognition. The works prospected are contemporary of the publication of Nietzsche first great work, "The Birth of the Tragedy", including his notes for the lecture course on rhetoric taught at the University of Basel during the winter semester, in 1872-73, then his "Theoretische Studien", written during summer 1873, with a consideration of later developments in his "Gay Science". The overall thesis advocated by Nietzsche in these works could be summarized as follows: all the elements of the categorical apparatus and the conceptual framework by which we assess reality, a fortiori the notion of truth which vouches for it, are the "precipitate" or the residue of a cluster of metaphors which constitute the structuring force of cognitive powers. The instinct of conservation and a subtle form of dissimulation lead to the elision of the tropic dynamics of language to the benefit of a literalism bound to a structuring amnesia. If for Kant we get access only to phenomena and not to noumenon, for Nietzsche we always deal with perspectives or points of view, whilst reality is traded to us by mean of truths which are mere fictions or worn out metaphors. So we come to acknowledge that the endogenous tropism displayed by language uses constitutes a major force in the implementation of conceptuality, that last one being eager to absorb its own prehistory into oblivion and to endow itself a status which is in close to timelessly imploded by the ebb of creative imagination fuelled by sheer metaphoric force, a spontaneous impulsion that Nietzsche ties to an "artistic force" which tends to multiply the perspectives whose genealogy is driven by an exponential factor. (shrink)

We explore the technical details and historical evolution of Charles Peirce's articulation of a truth table in 1893, against the background of his investigation into the truth-functional analysis of propositions involving implication. In 1997, John Shosky discovered, on the verso of a page of the typed transcript of Bertrand Russell's 1912 lecture on ?The Philosophy of Logical Atomism? truth table matrices. The matrix for negation is Russell's, alongside of which is the matrix for material implication in (...) the hand of Ludwig Wittgenstein. It is shown that an unpublished manuscript identified as composed by Peirce in 1893 includes a truth table matrix that is equivalent to the matrix for material implication discovered by John Shosky. An unpublished manuscript by Peirce identified as having been composed in 1883?1884 in connection with the composition of Peirce's ?On the Algebra of Logic: A Contribution to the Philosophy of Notation? that appeared in the American Journal of Mathematics in 1885 includes an example of an indirect truth table for the conditional. (shrink)

Theories where truth is a naive concept fall under the following dilemma: either the theory is subject to Curry’s Paradox, which engenders triviality, or the theory is not trivial but the resulting conditional is too weak. In this paper we explore a number of theories which arguably do not fall under this dilemma. In these theories the conditional is characterized in terms of non-deterministic matrices. These non-deterministic theories are similar to infinitely-valued Łukasiewicz logic in that they are consistent (...) and their conditionals are quite strong. The difference is the following: while Łukasiewicz logic is \-inconsistent, the non-deterministic theories might turn out to be \-consistent. (shrink)

Involutive Stone algebras were introduced by R. Cignoli and M. Sagastume in connection to the theory of $n$-valued Łukasiewicz–Moisil algebras. In this work we focus on the logic that preserves degrees of truth associated to S-algebras named Six. This follows a very general pattern that can be considered for any class of truth structure endowed with an ordering relation, and which intends to exploit many-valuedness focusing on the notion of inference that results from preserving lower bounds of (...) class='Hi'>truth values, and hence not only preserving the value $1$. Among other things, we prove that Six is a many-valued logic that can be determined by a finite number of matrices. Besides, we show that Six is a paraconsistent logic. Moreover, we prove that it is a genuine Logic of Formal Inconsistency with a consistency operator that can be defined in terms of the original set of connectives. Finally, we study the proof theory of Six providing a Gentzen calculus for it, which is sound and complete with respect to the logic. (shrink)

Łukasiewicz 3-valued logic Ł3 is often understood as the set of all valid formulas according to Łukasiewicz 3-valued matrices MŁ3. Following Wojcicki, in addition, we shall consider two alternative interpretations of Ł3: ‘truth-preserving’ Ł3a and ‘well-determined’ Ł3b defined by two different consequence relations on the 3-valued matrices MŁ3. The aim of this article is to provide a Routley–Meyer ternary semantics for each one of these three versions of Łukasiewicz 3-valued logic: Ł3, Ł3a and Ł3b.

The aim of this article is to explore the class of intermediate logics between the truth-preserving Lukasiewicz logic L and its degree-preserving companion L<⁠. From a syntactical point of view, we introduce some families of inference rules (that generalize the explosion rule) that are admissible in L< and derivable in L and we characterize the corresponding intermediate logics. From a semantical point of view, we first consider the family of logics characterized by matrices defined by lattice filters in (...) ⁠[0,1], but we show there are intermediate logics falling outside this family. Finally, we study the case of finite-valued Lukasiewicz logics where we axiomatize a large family of intermediate logics defined by families of matrices (A,F) such that A is a finite MV-algebra and F is a lattice filter. (shrink)

This chapter contains sections titled: Abstract Introduction Paradigms, Disciplinary Matrices, and Epistemological Relativism Incommensurability The Transcendence of Truth World ‐ Change, Idealism, and Ontological Relativism Relativism in the Sociology of Science and the History of Science References.

Despite being fairly powerful, finite non-deterministic matrices are unable to characterize some logics of formal inconsistency, such as those found between mbCcl and Cila. In order to overcome this limitation, we propose here restricted non-deterministic matrices (in short, RNmatrices), which are non-deterministic algebras together with a subset of the set of valuations. This allows us to characterize not only mbCcl and Cila (which is equivalent, up to language, to da Costa's logic C_1) but the whole hierarchy of da (...) Costa's calculi C_n. This produces a novel decision procedure for these logics. Moreover, we show that the RNmatrix semantics proposed here induces naturally a labelled tableau system for each C_n, which constitutes another decision procedure for these logics. This new semantics allows us to conceive da Costa's hierarchy of C-systems as a family of (non deterministically) (n+2)-valued logics, where n is the number of "inconsistently true" truth-values and 2 is the number of "classical" or "consistent" truth-values, for every C_n. (shrink)

Trying to overcome Dugundji’s result on uncharacterisability of modal logics by finite logical matrices, Kearns and Ivlev proposed, independently, a characterisation of some modal systems by means of four-valued multivalued truth-functions , as an alternative to Kripke semantics. This constitutes an antecedent of the non-deterministic matrices introduced by Avron and Lev . In this paper we propose a reconstruction of Kearns’s and Ivlev’s results in a uniform way, obtaining an extension to another modal systems. The first part (...) of the paper is devoted to four-valued Nmatrices, including Kearns’s and Ivlev’s. Besides proving with full details Kearns’s results for T, S4 and S5, we also obtain a characterisation of the system B by four-valued Nmatrices with level valuations. Concerning Ivlev’s results, two new modal systems are introduced and char.. (shrink)

In this paper, we define the family FiCn:={FiCn}n∈ω of logics by means of semantics of bivaluations. This family is a variant of the family of paraconsistent bivaluated Ciun-logics, defined and studied by J. Ciuciura. We will show that every logic in FiCn can be alternatively defined by means of finite matrices. This result arises from the characterisation of the truth-values of the involved matrices (relative to each FiCn-logic) as being specific finite sequences of elements of the set (...) 2 := {0,1}. Moreover, we will show in this paper that such characterisation is related to the well-known standard Fibonacci Sequence, which is presented here by means of its binary expansion. (shrink)

Trivalence is quite natural for deontic action logic, where actions are treated as good, neutral or bad.We present the ideas of trivalent deontic logic after J. Kalinowski and its realisation in a 3-valued logic of M. Fisher and two systems designed by the authors of the paper: a 4-valued logic inspired by N. Belnap’s logic of truth and information and a 3-valued logic based on nondeterministic matrices. Moreover, we combine Kalinowski’s idea of trivalence with deontic action logic based (...) on boolean algebra. (shrink)

We consider an example of four valued semantics partially inspired by quantum computations and negation-like operations occurred therein. In particular we consider a representation of so called square root of negation within this four valued semantics as an operation which acts like a cycling negation. We define two variants of logical matrices performing different orders over the set of truth values. Purely formal logical result of our study consists in axiomatizing the logics of defined matrices as the (...) systems of binary consequence relation and proving correctness and completeness theorems for these deductive systems. (shrink)

It is well known that every propositional logic which satisfies certain very natural conditions can be characterized semantically using a multi-valued matrix ([Los and Suszko, 1958; W´ ojcicki, 1988; Urquhart, 2001]). However, there are many important decidable logics whose characteristic matrices necessarily consist of an infinite number of truth values. In such a case it might be quite difficult to find any of these matrices, or to use one when it is found. Even in case a logic (...) does have a finite characteristic matrix it might be difficult to discover this fact, or to find such a matrix. The deep reason for these difficulties is that in an ordinary multi-valued semantics the rules and axioms of a system should be considered as a whole, and there is no method for separately determining the semantic effects of each rule alone. (shrink)

According to Suszko's Thesis,any multi-valued semantics for a logical system can be replaced by an equivalent bivalent one. Moreover: bivalent semantics for families of logics can frequently be developed in a modular way. On the other hand bivalent semantics usually lacks the crucial property of analycity, a property which is guaranteed for the semantics of multi-valued matrices. We show that one can get both modularity and analycity by using the semantic framework of multi-valued non-deterministic matrices. We further show (...) that for using this framework in a constructive way it is best to view "truth-values" as information carriers, or "information-values". (shrink)

This chapter contains sections titled: Abstract Introduction The Tacit ‐ Agreement Approach to Morality as Social Construction Speaker Relativism What it Might Mean for Morality to be Constructed as Part of Human Culture Explaining Moral Commonalities and Differences Across Cultures Relativism and the Meaning of Moral Terms Explaining Intra ‐ Group Disagreement Why Fundamental Intragroup Disagreement Might Be Inevitable References.

Nilpotent Minimum logic (NML) is a substructural algebraizable logic that is a distinguished member of the family of systems of Mathematical Fuzzy logic, and at the same time it is the axiomatic extension with the prelinearity axiom of Nelson and Markov’s Constructive logic with strong negation. In this paper our main aim is to characterize and axiomatize paraconsistent variants of NML and its extensions defined by (sets of) logical matrices over linearly ordered NM-algebra with lattice filters as designated values, (...) with special emphasis on those that only exclude the falsum truth-value, called non-falsity preserving logics. We also consider turning these non-falsity preserving logics into Logics of Formal Inconsistency by expanding them with a consistency operator, and we axiomatize them as well. Finally, we provide a full description of the logics defined by finite products of matrices over finite NM-chains. (shrink)

The formation of the education professional has been a top subject of studies during the history of education in Brazil and must be a human formation directly related to his or her emancipation as a social, individual person. This is his or her truth citizenship and sine qua non to the formation of a new man for the construction of a human culture. In this sense, the concept of man is the fundamental axis of formation of the education professional. (...) Theoretical matrices that have given rise to individualism and its powerful concepts are analyzed, as well as the new dominant ideas that, in an explicit or implicit way, construct in our society by different forms of social consciousness. There is a firm conviction that the understanding of man as alive, active, and conscious in material existence, according to concrete life, looks as the formation of consensus, organic emancipating scientific fundamental of radial change in social relations on a global society and with the possibility of human culture. (shrink)

In this pioneering work, the author develops a fundamental formulation of logic in terms of theory of matrices and vector spaces. The discovery of matrix logic represents a landmark in the further formalization of logic. For the first time the power of direct mathematical computation is applied to the whole set of logic operations, allowing the derivation of both the classical and modal logics from the same formal base. The new formalism allows the author to enlarge the alphabet of (...) the truth-values with negative logic antivalues and to link matrix logic descriptions with the Dirac formulation of quantum theory - a result having fundamental implications and repercussions for science as a whole. As a unified language which permits a logical examination of the underlying phenomena of quantum field theory and vice versa, matrix logic opens new avenues for the study of fundamental interactions and gives rise to a revolutionary conclusion that physics as such can be viewed and studied as a logic in the fundamental sense. Finally, modelling itself on exact sciences, matrix logic does not refute the classical logic but instead incorporates it as a special deterministic limit. The book requires multidisciplinary knowledge and will be of interest to physicists, mathematicians, computer scientists and engineers. (shrink)

In this work, we investigate the representation of counterfactual conditionals using the vector logic, a matrix-vector formalism for logical functions and truth values. Inside this formalism, the counterfactuals can be transformed in complex matrices preprocessing an implication matrix with one of the square roots of NOT, a complex matrix. This mathematical approach puts in evidence the virtual character of the counterfactuals. This happens because this representation produces a valuation of a counterfactual that is the superposition of the two (...) opposite truth values weighted, respectively, by two complex conjugated coefficients. This result shows that this procedure gives an uncertain evaluation projected on the complex domain. After this basic representation, the judgement of the plausibility of a given counterfactual allows us to shift the decision towards an acceptance or a refusal. This shift is the result of applying for a second time one of the two square roots of NOT. (shrink)

The first part of the papaer contains desiderata for a realistic epistemic system as opposed to idealistic ones. One of the main characteristics of idealistic epistemic systems is their deductive infallibility or deductive omniscience. The system presented avoids deductive infallibility though having a strong concept of knowledge. The second part contains the theorems of the system. The system is detailed in so far as it distinguishes between two concepts of belief and one of assumption and interrelates them to the concept (...) of knowledge. Though all concepts satisfy certain consistency criteria the strongest ones hold for the concept of knowledge; whereas a belief in or a assumption (assertion) of a proposition which has inconsistent consequences (not known or believed or assumed by the believer or assumer) does not entail the commitment of believing in (or assuming of) an explicit contradiction. Moreover the system contains a lot of distinctions and details concerning propositions with a second person involved like "a knows that b knows whether p is the case" etc. The third part of the paper contains the semantics of the system which consists of many-valued truth-tables. Since the matrices are finite the system is consistent and decidable. (shrink)

The work's central thesis is that meaningful discourse would be impossible unless the discoursers had distributive access to realities structured independently of language, such an access in fact as can service a metaphysically significant correspondence theory of truth. The thesis is deployed against the view, advanced by Hilary Putnam and by Richard Rorty, that we cannot exit the circle of words so as to secure any version of external realism. ;To establish the thesis, an intentionalist hermeneutics is developed: Due (...) to the plasticity of lexical meanings, the meaning of a text cannot be compositionally derived from linguistic conventions alone; the author's intentions, constituted in part by the extra-linguistic narrative matrices framing his life, must be consulted. The finding that a text's ontological commitments are determined by authorial intentions blocks Putnam's attempt to derive the ontological indeterminacy of human discourse from the Lowenheim-Skolem theorem. And his charge that this appeal to intentions is circular is faulted for its reliance on an inadequate, psycholinguistic model of intentions. ;It is then argued that meaningful discourse must be anchored, through narratively coherent transactions conducted without words, to realities structured beyond words: Our pre-linguistic ancestors could never have developed a meaningful description scheme unless its terms elicited among its original users sub-linguistic reality-negotiating strategies appropriate to encountered realities, strategies like those displayed by alexic brutes. The internal realist's claim that our grasp of reality is everywhere structured by language is consequently afforded a corrective supplement: That our grasp of language is everywhere structured by a sub-linguistic grasp of reality. The strategies our pre-linguistic ancestors used to locate and manage encountered realities indispensably underlie our present use of language and provide us with an extra-linguistic access to those realities, an access that is sufficient, it is argued, to support a substantive correspondence theory of truth: An assertion corresponds to reality as long as the reality-negotiating strategies it conjugates can be successfully implemented. And this truth-conferring conception of correspondence, constituted by an appropriateness to reality, can arguably sustain a robust version of realism. (shrink)

Is there any link between the doctrine of logical fatalism and prime numbers? What do logic and prime numbers have in common? The book adopts truth-functional approach to examine functional properties of finite-valued Łukasiewicz logics Łn+1. Prime numbers are defined in algebraic-logical terms and represented as rooted trees. The author designs an algorithm which for every prime number n constructs a rooted tree where nodes are natural numbers and n is a root. Finite-valued logics Kn+1 are specified that they (...) have tautologies if and only if n is a prime number. It is discovered that Kn+1 have the same functional properties as Łn+1 whenever n is a prime number. Thus, Kn+1 are 'logics' of prime numbers. Amazingly, combination of logics of prime numbers led to uncovering a law of generation of classes of prime numbers. Along with characterization of prime numbers author also gives characterization, in terms of Łukasiewicz logical matrices, of powers of primes, odd numbers, and even numbers. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Womb as Synecdoche: Introduction to Irigaray’s Deconstruction of Plato’s CaveKristi L. Krumnow (bio)“Le prisonnier n’était déjà plus dans une matrice mais dans une caverne, tentative de figuration, de métaphorisation, de la cavité utérine.”(347)1Entering the used bookstore in a university city not too far from Paris, I was anxious to find a copy of a certain Luce Irigaray book. When asked, the bookstore owner politely mocked me about wanting one (...) of her books. What could I possibly want that for? After all, the study of Irigaray was very popular in the 1970s and 1980s, but today, “C’est bien passé, Madame,” he enlightened me. While the bookshop owner was correct in assessing a time frame of the academic popularity of Irigaray’s work, I would argue that the work she did at the onset of 1970s feminism is no more passé than the philosophers she deconstructed. For this reason, I read Irigaray’s work alongside the work of founder-philosopher-father Plato, in order to highlight the timeless relevance of a supposed irrelevant work as “passé” as Luce Irigaray’s Spéculum de l’autre femme. In this analysis, I argue that the negligence of her reading of Plato’s cave and subsequent amnesia of it clearly substantiate her steadfast claim that masculine universality eradicates the feminine and does so quite ironically and even jarringly, as shown by the critical dismissal of Plato’s cave in Spéculum.2Irigaray’s work does indeed come out of a French national context highly invested in the studies of antiquity and, by the postwar ’60s and ’70s, in the questioning of social, cultural, and political institutions (Egéa-Kuehne 200; Leonard, “Irigaray’s Cave” 159–64; Leonard, “Classics” 143; Leonard,Athens 1–14), but this historical fact does not marginalize her work nor subject it to a mere temporal estrangement of feminism, as the male bookstore owner had insinuated. It certainly is a point of fact that Irigaray questioned the father of Western philosophical truth. In fact, reconsidering Plato was tempting to someone, like Luce Irigaray, invested in cultural and academic revolutions, someone who questioned and doubted, like other cultural revolutionaries3 of the late 1960s and early ’70s. The bookstore owner seemed to be saying that the tide has returned to normal, that is, the “normal” that signifies complacency, the “normal” that no longer questions the supposed truth-bearers. He seemed to be pontificating, “it is no longer status quo not to be status quo,” or more precisely, “The revolution is over. Now, go home, girls.” [End Page 69]Spéculum de l’autre femme, the WholeLuce Irigaray’s work Spéculum de l’autre femme [Speculum of the Other Woman]4 is anything but status quo. In an idiosyncratic prose indicative of her deconstructive project, Irigaray daringly reads untouched historical and philosophical works, ones that for millennia have remained a critical and foundational part of Western discourse. Her methodology is complex and knotty because the rhetoric used twists and winds through its own words, sentences, scenes, and discourse, thereby intentionally effecting an implosion within language.5 While on the one hand she innocently participates in an evaluation of Platonism that Derrida made fashionable a few years prior with “deconstruction” of “La Pharmacie de Platon” (Leonard, Athens 190), what she unveils by rereading Plato’s work à la Derrida is the proliferation and predominance of certain philosophical images and ideas. She names this proliferation “patriarchy,” referencing the “phallus” as the symbol of patriarchy and its dominant masculine discourse, thereby calling every thing masculine-related “phallologic,” all of which are neologisms borrowed and employed from either Derrida or her teacher Lacan. Inevitably, she centers her whole argument on certain Western texts as the cause and consequent advancement of the masculine. Spéculum appears daunting in its 462-page French original,6 although no less truncated, albeit ordered, footnoted, and proportionally spaced, in the English translation (Gill 9). In order to facilitate comprehension of a charged and impressive topic, Irigaray relies on images to elucidate her reading by employing ambitious albeit ancient Greek philosophical metaphors of light, sun, and vision. As she does... (shrink)

The present study is an interrogation of theories of culture and nation in the context of spectacular sports. It proposes a view of nationalism as discourses that articulate and produce nations through narrative acts. A wide array of concepts and tools are drawn from the work of Pierre Bourdieu and contrasted with methods and notions from discursive and semiotic analysis to interrogate a national-sports nexus in which sports are vehicles to embody nations, their matrices of thought and perception, and (...) their dominant order of masculinity and heteronormativity in the national subject, so that this order appears natural and commonsensical. Particular attention is given to the case of South Africa’s participation in the 1998 World Cup, and the way the epic genre was employed to frame the event and produce a particular kind of national body. -/- Spectacular sports events provide nations with opportunities to disseminate narratives that regulate desire and conjure a particular kind of national fantasy – what Bourdieu referred to as illusio – in subjects. This work makes a distinction between an epic body of nationalism, a body enmeshed in "the natural and authentic," and an excessive body. However, mediations of sports are never merely reflections of social events but themselves participate in producing these events as meaningful and anchor them as national. Furthermore, an actively interpreting subject is required for the production of meaning, and in this regard the thesis offers a critique of Bourdieu’s limited view on what it entails for a recipient of nationalist discourse to be active. The questions addressed by this study is twofold: how and what kind of national order of the body and desire is manufactured through spectacular sports events, and how are mediations of such events made meaningful in subjects? -/- The open-ended character of signification means that beneath the level of nationalist anchorage of spectacular sports events other articulations are possible. Drawing on Bourdieu’s view of sports as forms of silent dressage, the thesis suggests that there is a potential excess of meaning that enables such events to become potential sites of subjective truth: as viewers realise the fantasmatic character of such mediations they may come to question the notion that spectacular sports are something more than just a game. (shrink)

Les dérives politiques, au XIXe siècle, du thème du Royaume de Dieu et des attentes messianiques, et les désillusions qui en résultent aujourd’hui, invitent à mieux souligner le caractère théologal de l'espérance chrétienne en lien avec la foi au Dieu créateur.Confesser la création, en effet, désacralise la nature et donc aussi l'histoire et renvoie ainsi la fin ultime au-delà des aspirations aux satisfactions d’ordre mondain. La logique de l'incarnation également, tout en inscrivant notre action dans le monde, projette notre vérité (...) au-delà de lui, en Dieu seul. La fin ultime est pascale : en lien avec l'humain et le monde, mais en rupture avec l'histoire et la nature, et non en prolongement ni en comblement de l’une ni de l'autre. La matrice apocalyptique disjoint le Règne de Dieu de l’ordre de ce monde. L'ultime habite et transforme le présent, mais il n’est pas le terme du déroulement du temps.Le chrétien est institué témoin du Règne de Dieu sur ce monde, « théâtre de sa gloire » : c'est pourquoi son espérance est hétérogène à ce monde. En tant que vertu théologale, elle n'oublie pas de faire mémoire du passé pour se disposer à recevoir le futur, mais elle ne fait pas du futur qui vient de Dieu l'accomplissement d'un sens de l'histoire, pas plus que l’éternité ne se situe sur la ligne du temps. The political deviations in the 19th century of the theme of the Kingdom of God and of Messianic expectations, and the disillusions that are the result today, invite us to underline better the theological character of Christian hope connected with faith in a creator God.To avow the creation, indeed, desacralizes nature and, therefore, also history, thereby sending the ultimate end beyond aspirations to satisfactions of a worldly kind. The logic of the Incarnation, while writing our action in the world, also projects our truth beyond it, in God alone. The ultimate end is paschal : in connection with the human and the world, but in rupture with history and nature, and not in prolonging nor in filling up of the one nor of the other. The apocalyptic matrix disconnects the Kingdom of God from the nature of this world. The ultimate inhabits and transforms the present, but it is not the end of the passing of time.The Christian is made witness to the Kingdom of God in this world, « theatre of his glory » : that is why his hope is heterogeneous to this world. As a theological virtue it does not fail to remember the past in order to dispose itself to receive the future. But hope does not make of the future that comes from God the accomplishment of a sense of history, no more than eternity is situated on the time-line. (shrink)

“What characterizes the act of justice is not resort to a court and to judges; it is not the intervention of magistrates. What characterizes the juridical act, the process or the procedure in the broad sense, is the regulated development of a dispute. And the intervention of judges, their opinion or decision, is only ever an episode in this development. What defines the juridical order is the way in which one confronts one another, the way in which one struggles. The (...) rule and the struggle, the rule in the struggle, this is the juridical.” - Michel Foucault Penal Theories and Institutions is the title Michel Foucault gave to the lectures he delivered at the Collège de France from November 1971 to March 1972. In these lectures Michel Foucault presents for the first time his approach to the question of power that will be the focus of his research up to the writing of Discipline and Punish and beyond. His analysis starts with a detailed account of Richelieu’s repression of the Nu-pieds revolt and then goes on to show how the apparatus of power developed by the monarchy on this occasion breaks with the system of juridical and judicial institutions of the Middle Ages and opens out onto a “judicial State apparatus”, a “repressive system”, whose function is focused on the confinement of those who challenge its order. Michel Foucault systemizes the approach of a history of truth on the basis of the study of “juridico-political matrices” that he had begun in the previous year’s lectures and which is at the heart of the notion of “knowledge-power”. In these lectures Foucault develops his theory of justice and penal law. The appearance of this volume marks the end of the publication of the series Foucault’s courses at the Collège de France. (shrink)

“What characterizes the act of justice is not resort to a court and to judges; it is not the intervention of magistrates (even if they had to be simple mediators or arbitrators). What characterizes the juridical act, the process or the procedure in the broad sense, is the regulated development of a dispute. And the intervention of judges, their opinion or decision, is only ever an episode in this development. What defines the juridical order is the way in which one (...) confronts one another, the way in which one struggles. The rule and the struggle, the rule in the struggle, this is the juridical.” - Michel Foucault Penal Theories and Institutions is the title Michel Foucault gave to the lectures he delivered at the Collège de France from November 1971 to March 1972. In these lectures Michel Foucault presents for the first time his approach to the question of power that will be the focus of his research up to the writing of Discipline and Punish (1975) and beyond. His analysis starts with a detailed account of Richelieu’s repression of the Nu-pieds revolt (1639-1640) and then goes on to show how the apparatus of power developed by the monarchy on this occasion breaks with the system of juridical and judicial institutions of the Middle Ages and opens out onto a “judicial State apparatus”, a “repressive system”, whose function is focused on the confinement of those who challenge its order. Michel Foucault systemizes the approach of a history of truth on the basis of the study of “juridico-political matrices” that he had begun in the previous year’s lectures (Lectures on the Will to Know) and which is at the heart of the notion of “knowledge-power”. In these lectures Foucault develops his theory of justice and penal law. The appearance of this volume marks the end of the publication of the series Foucault’s courses at the Collège de France (the first volume of which was published in 1997). (shrink)

L’analyse du pouvoir que propose Merleau-Ponty dans sa confrontation avec le Marxisme et le bolchévisme tente de penser ce paradoxe : le phénomène du pouvoir contient deux sous-phénomènes: premièrement, le pouvoir d’une entité politique (Prince, Etat, Parti etc.) est reconnu s’il est perçu comme donné (moment de reconnaissance) ; deuxièmement, le pouvoir de cette entité dépend de ladite reconnaissance (moment d’institution). Le premier moment constate le donné alors que l’autre le conteste. L’article se propose de comprendre, premièrement, dans quelle mesure (...) le pouvoir doit être compris comme l’union de la reconnaissance et de l’institution, et deuxièmement, dans quelle mesure cette unité doit être comprise comme une matrice productrice d’histoire. La première question sera résolue par appel à la notion de foi perceptive, qui est la version ontologique d’une telle unité ; et la seconde par appel à la notion politique de représentation héritée de Machiavel et développée dans les analyses critiques du thème de la représentation du prolétariat par le Parti. Le résultat est une reconfiguration des relations entre discours de vérité (dans ce cas, l’ontologie) et action politique ; une reconfiguration de la notion de pouvoir, et une hypothèse pour rendre compte de l’unité des travaux « théoriques » et « politiques » de Merleau-Ponty.The analysis of power that Merleau-Ponty proposes in his confrontation with Marxism and Bolshevism tries to think through the following paradox. The phenomenon of power is composed of two sub-phenomena. Firstly, the power of a political entity (Prince, State, Party, etc.) is recognized if it is perceived as given (moment of recognition). Secondly, the power of that entity depends on the said recognition (moment of institution). The first moment notices the given, while the other contests it. This article aims to elucidate, firstly, to what extent power must be understood as the union of recognition and institution, and secondly, to what extent that unity must be understood as a matrix productive of history. The first question will be resolved by appealing to the notion of the perceptual faith, which is the ontological version of such a unity; and the second, by appealing to the political notion of representation inherited from Machiavelli and developed in the critical analyses of the theme of the representation of the proletariat by the Party. The result is a reconfiguration of the relations between discourses of truth (in this case, ontology) and political action. It is a reconfiguration of the notion of power and a hypothesis that wants to account for the unity of Merleau-Ponty’s “theoretical” and “political” efforts.L’analisi del potere che Merleau-Ponty propone attraverso il confronto tra marxismo e bolscevismo tenta di pensare questo paradosso: il fenomeno del potere contiene due sotto-fenomeni: in primo luogo, il potere di un’entità politica (il Principe, lo Stato, il Partito, ecc.) è riconosciuto se è percepito come dato (momento di riconoscimento); in secondo luogo, il potere di questa entità dipende dal suddetto riconoscimento (momento di istituzione). Il primo momento constata ciò che è dato, mentre l’altro lo contesta. L’articolo si propone di comprendere, in primis, in quale misura il potere deve essere inteso come unione del riconoscimento e dell’istituzione, e in seconda battuta, in quale misura quest’unità deve essere compresa come una matrice produttrice di storia. La prima questione sarà risolta tramite il riferimento alla nozione politica di rappresentazione ereditata da Machiavelli e sviluppata nelle analisi critiche del tema della rappresentazione del proletariato attraverso il Partito. Il risultato è una riconfigurazione delle relazioni tra discorso di verità (in questo caso, l’ontologia) e azione politica; una riconfigurazione della nozione di potere, e un’ipotesi che renda conto dell’unità dei lavori “teorici” e “politici” di Merleau-Ponty. (shrink)

Contents INTRODUCTION: PHENOMENOLOGICAL APPROACHES TO THE POLITICAL IN PATOČKA AND MERLEAU-PONTY 11 1. Memory and community 11 2. Patočka 18 3. Merleau-Ponty, Husserl and institution 22 4. The political context 28 5. Status of the current research 32 6. Overview of the chapters 34 CHAPTER 1: THE PHENOMENOLOGICAL EPOCHĒ AND THE POLITICAL 39 1. Introduction 39 2. Criticism of Husserl’s notion of the lifeworld 46 3. The a priori of the World 49 4. The subject and the epochē 56 5. (...) Epochē to polis 61 6. Two ways into the epochē: myth and “le bouc émissaire” 76 7. A “public/private” distinction in the performing of the epochē 84 CHAPTER 2: THE BODY AT THE FRONT: CORPOREITY AND COMMUNITY IN JAN PATOČKA’S HERETICAL ESSAYS IN THE PHILOSOPHY OF HISTORY. 89 1. Introduction 89 2. The front 94 3. The double determination of life: Patočka and Foucault on “war” 98 4. Rooting 126 5. The body at the front 135 CHAPTER 3: LOOKING-IN ON EUROPE 145 1. Introduction 145 2. Post-Europe 147 3. Globalization as shaking 157 4. The idea of culture 162 5. Looking-in on Europe 164 6. The borders of Europe: towards a post-European democracy 175 a. Polemos and boundary 175 b. The skin and the soul 178 c. Europe and the boundary 190 CHAPTER 4: HUSSERL ON STIFTUNG AND STYLE 201 1. Introduction 201 2. Husserl’s concepts of retention institution and the possibility of an “institutional unconscious” 202 a. Retention 202 b. Husserl’s notion of institution in §50 of the Cartesian Meditations 210 c. Difficulties 220 d. Retention as unconscious 221 3. Husserl´s concept of style in Ideas II 236 a. Introduction 236 b. Institution and style 237 c. Style 243 d. Style and intersubjectivity 248 e. Style and politics in Merleau-Ponty 254 4. §15 of the Crisis of the European Sciences and Transcendental Phenomenology: “Reflection on the method of our historical manner of investigation” 259 a. Stiftung as the task of history 259 b. Endstiftung 269 c. Endstiftung and Style 272 5. Community and surrounding world in section three of Ideas II 274 6. “The Origin of Geometry” 291 CHAPTER 5: STIFTUNG AND STYLE IN MERLEAU-PONTY 303 1. Introduction 303 2. Institution and Style 304 a. event/advent 304 b. The opening of a field 308 c. The relation to the past, or subterranean communication across time: Urstiftung—Nachstiftung—Endstiftung 310 d. Style 312 e. Latency 314 3. Three painters: Matisse, Cézanne, and Vermeer 319 a. Matisse 319 b. Cézanne 325 c. Vermeer 337 4. The historical field 344 a. The field of praxis 344 b. Symbolic matrices 355 c. Matrix institutions 361 CHAPTER 6: THE NOBLE MEMORY: SURVIVAL, DEMOCRACY AND RESISTANCE 371 1. Introduction 371 a. “Resistance” and “survival” 371 b. The plaque 372 c. “Inertia” and “movement” 378 d. Difficulties 383 e. Vulnerability 385 2. Institution and parliamentary democracy 391 a. Merleau-Ponty’s support for parliamentary democracy 391 b. An institution of institutions 396 c. “Regime” and “corps de l’État” 400 d. Survival 406 e. Institution and reparation 421 f. Institution and revolution 423 g. Democracy, epochē, and virtù 424 h. Concrete political action 429 3. Resistance 430 a. The “mythical” past and the “verbal-Wesen of society” 432 b. The generality of freedom and the unconscious 441 c. Endstiftung, Telos and Truth 442 CONCLUSIONS 451 BIBLIOGRAPHY 471. (shrink)

The aim of this article is to discuss pure variable inclusion logics, that is, logical systems where valid entailments require that the propositional variables occurring in the conclusion are included among those appearing in the premises, or vice versa. We study the subsystems of Classical Logic satisfying these requirements and assess the extent to which it is possible to characterise them by means of a single logical matrix. In addition, we semantically describe both of these companions to Classical Logic in (...) terms of appropriate matrix bundles and as semilattice-based logics, showing that the notion of consequence in these logics can be interpreted in terms of truth (or non-falsity) and meaningfulness (or meaninglessness) preservation. Finally, we use Płonka sums of matrices to investigate the pure variable inclusion companions of an arbitrary finitary logic. -/- . (shrink)

According to Frege's principle the denotation of a sentence coincides with its truth-value. The principle is investigated within the context of abstract algebraic logic, and it is shown that taken together with the deduction theorem it characterizes intuitionistic logic in a certain strong sense.A 2nd-order matrix is an algebra together with an algebraic closed set system on its universe. A deductive system is a second-order matrix over the formula algebra of some fixed but arbitrary language. A second-order matrix A (...) is Fregean if, for any subset X of A, the set of all pairs a,b such that X{a} and X{b} have the same closure is a congruence relation on A. Hence a deductive system is Fregean if interderivability is compositional. The logics intermediate between the classical and intuitionistic propositional calculi are the paradigms for Fregean logics. Normal modal logics are non-Fregean while quasi-normal modal logics are generally Fregean.The main results of the paper: Fregean deductive systems that either have the deduction theorem, or are protoalgebraic and have conjunction, are completely characterized. They are essentially the intermediate logics, possibly with additional connectives. All the full matrix models of a protoalgebraic Fregean deductive system are Fregean, and, conversely, the deductive system determined by any class of Fregean second-order matrices is Fregean. The latter result is used to construct an example of a protoalgebraic Fregean deductive system that is not strongly algebraizable. (shrink)

The aim of this paper is to combine several Ivlev-like modal systems characterized by 4-valued non-deterministic matrices (Nmatrices) with $$\mathcal {IDM}4$$, a 4-valued expansion of Belnap–Dunn’s logic $$FDE$$ with an implication introduced by Pynko in 1999. In order to do this, we introduce a new methodology for combining logics which are characterized by means of swap structures, based on what we call superposition of snapshots. In particular, the combination of $$\mathcal {IDM}4$$ with $$Tm$$, the 4-valued Ivlev’s version of KT, (...) will be analyzed with more details. From the semantical perspective, the idea is to combine the 4-valued swap structures (Nmatrices) for $$Tm$$ (and several of its extensions) with the 4-valued twist structure (logical matrix) for $$\mathcal {IDM}4$$. This superposition produces a universe of 6 snapshots, with 3 of them being designated. The multioperators over the new universe are defined by combining the specifications of the given swap and twist structures. This gives rise to 6 different paradefinite Ivlev-like modal logics, each one of them characterized by a 6-valued Nmatrix, and conservatively extending the original modal logic and $$\mathcal {IDM}4$$. This important feature allows to consider the proposed construction as a genuine technique for combining logics. In addition, it is possible to define in the combined logics a classicality operator in the sense of logics of evidence and truth (LETs). A sound and complete Hilbert-style axiomatization is also presented for the 6 combined systems, as well as a Prolog program which implements the swap structures semantics for the 6 systems, producing a decision procedure for satisfiability, refutability and validity of formulas in these logics. (shrink)

How can the reference of theoretical terms be stable over changes of theory? I defend an approach to this that does not depend on substantive metasemantic theories of reference. It relies on the idea that in contexts of use, terms may play a role in a theory that in turn points to a further (possibly unknown) theory. Empirical claims are claims about the nature of the further theories, and the falsification of these further theories is understood not as showing that (...) a term in the original theory fails to refer, but rather that a scientific hypothesis encapsulated by the further theory is mistaken. Introduction 1.1 Two theories involving ‘cat’ 1.2 Some objections 1.3 Doing it with matrices 1.4 The theory so far Approximate truth 2.1 Modes of reference 2.2 Papineau's solution Meaning, analyticity and verbal dispositions 3.1 Theory 1 and the folk theory 3.2 Is the armchair too comfortable? 3.3 What role for the armchair? 3.4 How can we be mistaken about our dispositions? 3.5 The theory of reference and the theory of meaning. (shrink)

The first part of the papaer contains desiderata for a realistic epistemic system as opposed to idealistic ones. One of the main characteristics of idealistic epistemic systems is their deductive infallibility or deductive omniscience. The system presented avoids deductive infallibility though having a strong concept of knowledge. The second part contains the theorems of the system. The system is detailed in so far as it distinguishes between two concepts of belief and one of assumption and interrelates them to the concept (...) of knowledge. Though all concepts satisfy certain consistency criteria the strongest ones hold for the concept of knowledge; whereas a belief in or a assumption (assertion) of a proposition which has inconsistent consequences (not known or believed or assumed by the believer or assumer) does not entail the commitment of believing in (or assuming of) an explicit contradiction. Moreover the system contains a lot of distinctions and details concerning propositions with a second person involved like "a knows that b knows whether p is the case" etc. The third part of the paper contains the semantics of the system which consists of many-valued truth-tables. Since the matrices are finite the system is consistent and decidable. (shrink)

We consider a 2-valued non-deterministic connective \({\wedge \!\!\!\!\!\vee }\) defined by the table resulting from the entry-wise union of the tables of conjunction and disjunction. Being half conjunction and half disjunction we named it _platypus_. The value of \({\wedge \!\!\!\!\!\vee }\) is not completely determined by the input, contrasting with usual notion of Boolean connective. We call non-deterministic Boolean connective any connective based on multi-functions over the Boolean set. In this way, non-determinism allows for an extended notion of truth-functional (...) connective. Unexpectedly, this very simple connective and the logic it defines, illustrate various key advantages in working with generalized notions of semantics (by incorporating non-determinism), calculi (by allowing multiple-conclusion rules) and even of logic (moving from Tarskian to Scottian consequence relations). We show that the associated logic cannot be characterized by any finite set of finite matrices, whereas with non-determinism two values suffice. Furthermore, this logic is not finitely axiomatizable using single-conclusion rules, however we provide a very simple analytic multiple-conclusion axiomatization using only two rules. Finally, deciding the associated multiple-conclusion logic is \(\mathbf {coNP}\) -complete, but deciding its single-conclusion fragment is in \({\mathbf {P}}\). (shrink)

. The paper presents a method for transforming a given sound and complete n-sequent proof system into an equivalent sound and complete system of ordinary sequents. The method is applicable to a large, central class of (generalized) finite-valued logics with the language satisfying a certain minimal expressiveness condition. The expressiveness condition decrees that the truth-value of any formula φ must be identifiable by determining whether certain formulas uniformly constructed from φ have designated values or not. The transformation preserves the (...) general structure of proofs in the original calculus in a way ensuring preservation of the weak cut elimination theorem under the transformation. The described transformation metod is illustrated on several concrete examples of many-valued logics, including a new application to information sources logics. (shrink)

Henry M. Sheffer: a bibliography (p. xv-xvi)--Structure: A formulation of the logic of sense and denotation, by A. Church. Notes on the logic of intension, by C.I. Lewis. The logic of terms, by J.W. Miller. Two-valued truth tables for modal functions, by H.S. Leonard. N-valued Boolean algebra, by P. Henle. Triangular matrices determined by two sequences, by L.L. Silverman. The ordered pair in number theory, by W.V. Quine.

Łukasiewicz three-valued logic Ł3 is often understood as the set of all 3-valued valid formulas according to Łukasiewicz’s 3-valued matrices. Following Wojcicki, in addition, we shall consider two alternative interpretations of Ł3: “well-determined” Ł3a and “truth-preserving” Ł3b defined by two different consequence relations on the 3-valued matrices. The aim of this paper is to provide (by using Dunn semantics) dual equivalent two-valued under-determined and over-determined interpretations for Ł3, Ł3a and Ł3b. The logic Ł3 is axiomatized as an (...) extension of Routley and Meyer’s basic positive logic following Brady’s strategy for axiomatizing many-valued logics by employing two-valued under-determined or over-determined interpretations. Finally, it is proved that “well determined” Łukasiewicz logics are paraconsistent. (shrink)

Łukasiewicz three-valued logic Ł3 is often understood as the set of all 3-valued valid formulas according to Łukasiewicz’s 3-valued matrices. Following Wojcicki, in addition, we shall consider two alternative interpretations of Ł3: “well-determined” Ł3a and “truth-preserving” Ł3b defined by two different consequence relations on the 3-valued matrices. The aim of this paper is to provide dual equivalent two-valued under-determined and over-determined interpretations for Ł3, Ł3a and Ł3b. The logic Ł3 is axiomatized as an extension of Routley and (...) Meyer’s basic positive logic following Brady’s strategy for axiomatizing many-valued logics by employing two-valued under-determined or over-determined interpretations. Finally, it is proved that “well determined” Łukasiewicz logics are paraconsistent. (shrink)

It is proposed in this paper to develop a method by which the most general problem of the algebra of propositions is solved. This problem is to construct all propositions whose truth is independent of the form of the variables. As might be expected this method will enable us to determine without the use of matrices the consistency and independence of propositions, except in the case of those fundamental properties, which taken together define consistency itself. In the discussion (...) which follows no limitations are placed on the meaning of the terms and the word proposition is used simply in the sense of a variable. If we were to say, for example, that our variables must be restricted to zero or one values, we would be introducing a limitation which would reduce the generality of our science. A logic may be false in the sense that its postulates lead to contradictory theorems, or it may be false in the sense that it lacks generality, and the situation is not saved by calling it a two-valued, or a three-valued logic, or a logic of “propositions,” or by designating it by some other euphuism. (shrink)

I examine the theory of consequentia of the medieval logician, John Buridan. Buridan advocates a strict commitment to what we now call proposition-tokens as the bearers of truth-value. The analysis of Buridan's theory shows that, within a token-based semantics, amendments to the usual notions of inference and consequence are made necessary, since pragmatic elements disrupt the semantic behaviour of propositions. In my reconstruction of Buridan's theory, I use some of the apparatus of modern two-dimensional semantics, such as two-dimensional (...) class='Hi'>matrices and the distinction between the context of formation and the context of evaluation of utterances. (shrink)

This paper explores a notion of “the strong version” of a sentential logic S, initially defined in terms of the notion of a Leibniz filter, and shown to coincide with the logic determined by the matrices of S whose filter is the least S-filter in the algebra of the matrix. The paper makes a general study of this notion, which appears to unify under an abstract framework the relationships between many pairs of logics in the literature. The paradigmatic examples (...) are the local and the global consequences associated with a normal modal logic, and the logics preserving degrees of truth and preserving truth associated with certain substructural and many-valued logics. For protoalgebraic logics the results in the paper coincide with those obtained by two of the authors in 2001, so the main novelty of the approach is its suitability for all kinds of logics. The paper also studies three kinds of definability of the Leibniz filters, and their consequences for the determination of the strong version. In a second part of the paper several case studies are developed, comprising positive modal logic, Dunn–Belnap’s four-valued logic, the large family of substructural logics, and some relevance logics. (shrink)

As the title indicates, this most recent of Hartshorne's works blends doctrinal exposition with analyses of methodological issues. Each of the sixteen chapters can be read as an independent essay, although the entire work is intended as "an essay in systematic metaphysics." The paradox is resolved once we realize that Hartshorne does not separate substantive discussion and the examination of methodological principles--the text exemplifies the principles latent in "creative synthesis" as he understands it. Each chapter takes shape out of a (...) position-matrix in terms of which a number of possible positions on problems of relations, modality, and temporality are exhibited and finally sifted in order to determine the most viable for future philosophic inquiry. Portions of six of the chapters had previously been published, one as early as 1958; the remaining ten appear for the first time in this volume. Although much of the doctrinal content will be familiar to those who have read Hartshorne's earlier works, the clarity and coherence of these essays make it an especially valuable work for students of metaphysics, whether they accept the neoclassical position or not. In the first chapter, "A Philosophy of Shared Creative Experience," Hartshorne presents his case for the inclusive priority of "becoming" over "being"; in the next three chapters, he turns to a more detailed analysis of technical problems in metaphysics--the specification of the domain of metaphysical inquiry, the viability of the notion of inclusive contrast as the heart of "relativity", and the ultimate coincidence of modal and temporal categories as the summit of the analyses of "abstractions". Each of these chapters is an excellent example of Hartshorne's working through "position-matrices"; but for those who are unfamiliar with Hartshorne's work, or for those who desire a less 'naïve' approach to metaphysical inquiry it might be advisable to turn to Chapters V and VI immediately after Chapter I. In these two essays, Hartshorne presents a general exposition of the structure of his system, exposing and defending the conception of relativity which lies at the heart of his system: the triadicity [[sic]] of creative synthesis must be construed relatively, the contrast of relative and absolute being included within the relative member of the contrast. In the succeeding chapters, the difficulties which such a conception must face are explored in detail. Among the difficulties which Hartshorne focuses upon are the possibility of "non-restrictive or necessary existential truths", the psychological reeducation which a conception of the priority of events necessitates, the explanatory power of directed or asymmetrical relations as opposed to non-directed, symmetrical ones, and the critique of the notion of ens realissimum and its substitution by the universal forms of dependence and independence. It is interesting that at various places in this work Hartshorne indicates that the importance of the problem of the relations among contemporaries must be relegated to secondary status in the philosophy of shared creative experience. It becomes increasingly evident that were the author to stress its importance, he should have to turn to a conception of eternal objects functioning relationally or affirm interaction between God and any other individual in strictly simultaneous states. Either move would necessitate a major shift in his methodological principles and substantive doctrines. That he has struggled with the problem of the relations among contemporaries for so long shows his willingness to confront the possibility of such a shift. This is one of the major criteria for evaluating metaphysicians, as Hartshorne notes; in the light of this criterion, Hartshorne's newest work will be judged a significant contribution to metaphysical inquiry.--R. L. C. (shrink)

Logics of significance have been proposed in an attempt to overcome the shortcomings of classical logic as a model of reasoning in the presence of nonsignificant (e.g., meaningless, ill-formed, unverifiable) sentences. Many-valued logicians have addressed this problem by introducing logics with infectious truth values. Cases in point are the weak Kleene logics B3 (paracomplete weak Kleene logic) and PWK (paraconsistent weak Kleene logic). Over time, it has become clear that the valid entailments of these significance logics obey variable inclusion (...) patterns that link them to other, usually better known, logics—such patterns, however, allow for disturbing exceptions. Logics of pure (left or right) variable inclusion have been introduced with an eye to removing these exceptions. In this paper, we consider the pure left variable inclusion companion of classical logic and give a complete description of its subclassical extensions. We also provide relative axiomatizations and characteristic (sets of) matrices for each one of these extensions, as well as syntactic descriptions (in terms of variable inclusion criteria) for the valid entailments of some of them, and determine in each case the algebra reducts of the Suszko-reduced matrix models. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Haiti Can't BreatheNéhémy Pierre-Dahomey (bio)Translated by David F. BellI'm not particularly familiar with recent politics in Haiti. Nor, as it were, with the contemporary history of the country. In some sense, the difference between recent politics and contemporary history is rather delicate. History would be the most profound social, political, and economic points of contention behind the daily lives of a population under siege. Not simply those talked about (...) while people travel in public transportation (Haitians talk a lot while in public transportation), but also the interpretive matrices mobilized to speak about these problems. As for current events, they are the province of newspaper headlines, those front pages and editorial pages most often read and shared, the public opinion machine.Of course, a few snippets of news come to me: the rise of kidnapping, political instability, the opposition declaring that the presidential mandate has ended, a government sponsored referendum to change the constitution, upcoming elections. As I write this piece (summer 2021), armed banditry is rife in many working-class neighborhoods. There are victims by the dozens nearly every day.As I was asking myself how best to express the bicentennial dyspnea of the Haitian people, I learned about the assassination of the president of the Republic in his private residence.Haiti could not breathe. Now it is suffocating.I recently published a novel entitled Combats (March 2021) in which the characters live in a nineteenth-century rural setting. They experience the full force of the first consequences provoked by the infamous independence debt, well understood by Haitians and analyzed by international specialists such as David Graeber and Thomas Piketty.After its independence in 1804, Haiti was not accepted into the concert of nations. The country, founded by hordes of previously enslaved Blacks and by freed Mulattos, was a bad example, a model not to be emulated so geographically near a slave society, the United States, and the Antilles belonging to France. No economic power, that is, no white country defining itself as such, recognized the independence of the new Black, abolitionist, and egalitarian population. The isolation of Haiti thus began at the very moment of its foundation. [End Page 165]In a vain attempt to escape the embargo and to construct a collective destiny at the international level, Haiti accepted a colossal debt imposed on it by France. Charles X, king of France and Navarre, forced Jean-Pierre Boyer, supreme leader of the Haitian nation, to assume the responsibility for a ransom of 120 million francs. The economist Thomas Piketty calculates that this was equivalent to 28 billion euros in today's currency. David Graeber, in his Debt: The First 500 Years, considers it to be the most egregious debt in history. In truth, for Haitians, this strange transaction consisted in buying lands they had already conquered in their independence struggle, having taken them from the previous colonial settlers representing the French state.Since the previously emancipated ancestors were considered the colonial settlers' property, Haitians, under threat from the French army, assumed the weight of this debt, which really consisted in purchasing—from their previous torturers—their very persons and those of their grandparents. In other words, after the war of independence, begun by Black Maroons as soon as they arrived on the island of Haiti, pursued by Toussaint Louverture against slavery, brought successfully to a conclusion by Jean Jacques Dessalines through victorious military battles (November 1803 at Vertières, for example), after this long road toward emancipation, France, supported by all the foreign powers of the period, extracted from Haiti recognition of the debt in 1826, that is, during the first half of the nineteenth century, at the very moment when the independent countries of the world were beginning to undergo a massive industrialization.Haiti clearly missed out on this entrance into the industrial age of the steam engine. It remained an "essentially agricultural" country because every year it had to pay debt service—including interest—every year until the second half of the 20th century!Like many others I saw the images of the white man, Derek Chauvin, resting his knee on George Floyd's neck for eight... (shrink)

Three competing ‘methods’ have been endorsed for inferring phylogenetic hypotheses: parsimony, likelihood, and Bayesianism. The latter two have been claimed superior because they take into account rates of sequence substitution. Can rates of substitution be justified on its own accord in inferences of explanatory hypotheses? Answering this question requires addressing four issues: (1) the aim of scientific inquiry, (2) the nature of why-questions, (3) explanatory hypotheses as answers to why-questions, and (4) acknowledging that neither parsimony, likelihood, nor Bayesianism are inferential (...) actions leading to explanatory hypotheses. The aim of scientific inquiry is to acquire causal understanding of effects. Observation statements of organismal characters lead to implicit or explicit why-questions. Those questions, conveyed in data matrices, assume the truth of observation statements, which is contrary to subsequently invoking substitution rates within inferences to phylogenetic hypotheses. Inferences of explanatory hypotheses are abductive in form, such that some version of an evolutionary theory(ies) is/are included or implied. If rates of sequence evolution are to be considered, it must be done prior to, rather than within abduction, which requires renaming those putatively-shared nucleotides subject to substitution rates. There are, however, no epistemic grounds for renaming characters to accommodate rates, calling into question the legitimacy of causally accounting for sequence data. (shrink)