Raison et discours s'inscrit dans la continuite du projet initie par l'ouvrage publie un an auparavant sous le titre de Structures intellectuelles. Reflechissant sur la portee de son hexagone logique, dont il vient d'exposer la theorie, Robert Blanche pretend y trouver une preuve en faveur d'une logique developpee par reflexion sur les operations meme de la raison, qu'il oppose a une logique obtenue par analyse des resultats de ces operations dans le discours. Il s'efforce par la de justifier la legitimite (...) d'une approche reflexive ou philosophique des activites logiques de l'esprit, logique reflexive que les philosophes, abandonnant la logique aux mathematiciens comme une specialite curieuse, semblaient alors delaisser. La reflexion sur la logique operatoire ne condamne nullement a tomber dans le psychologisme: il ne s'agit aucunement ici de decrire des processus mentaux, mais bien d'expliciter et d'etudier, dans ses diverses applications, une structure objective et intemporelle. Bien plus qu'un compromis entre logique formelle et pensee modale, le projet de Robert Blanche vise une articulation efficace de la philosophie et des mathematiques. (shrink)

The square of opposition and many other geometrical logical figures have increasingly proven to be applicable to different fields of knowledge. This paper seeks to show how Blanché generalizes the classical theory of oppositions of propositions and extends it to the structure of opposition of concepts. Furthermore, it considers how Blanché restructures the Apuleian square by transforming it into a hexagon. After presenting G. Kalinowski’s formalization of Blanché’s hexagonal theory, an illustration of its applicability to mathematics, to (...) modal logic, and to the logic of norms is depicted. The paper concludes by criticizing Blanché’s claim according to which, his logical hexagon can be considered as the objective basis of the structure of the organisation of concepts, and as the formal structure of thought in general. It is maintained that within the frame of diagrammatic reasoning Blanché’s hexagon keeps its privileged place as a “nice” and useful tool, but not necessarily as a norm of thought. (shrink)

On voit quelles attitudes philosophiques l'axiomatique contrarie, quelles elle favorise. Elle répugne à un dogmatisme de la synthèse, au rêve d'un point de départ absolu qui assurerait à la déduction une sécurité définitive. C'est à la totalité de la science qu'elle étend maintenant la forme hypothético-déductive. Comme la méthode expérimentale avait discrédité l'espoir cartésien d'une physique démonstrative, aujourd'hui le logicisme, l'idée d'une science rationnelle qui ne présupposerait plus rien, se voit démenti par la régression axiomatique qui, si loin qu'elle pousse, (...) trouve devant si un " antérieur " non assimilé. Mais pas plus qu'ils ne s'imposent par une évidence intrinsèque, pas davantage les axiomes ne résultent de décrets arbitraires. ROBERT BLANCHÉ. (shrink)

The paper first introduces a cube of opposition that associates the traditional square of opposition with the dual square obtained by Piaget’s reciprocation. It is then pointed out that Blanché’s extension of the square-of-opposition structure into an conceptual hexagonal structure always relies on an abstract tripartition. Considering quadripartitions leads to organize the 16 binary connectives into a regular tetrahedron. Lastly, the cube of opposition, once interpreted in modal terms, is shown to account for a recent generalization of formal concept (...) analysis, where noticeable hexagons are also laid bare. This generalization of formal concept analysis is motivated by a parallel with bipolar possibility theory. The latter, albeit graded, is indeed based on four graded set functions that can be organized in a similar structure. (shrink)

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

. This paper aims to highlight some peculiarities of the semiotic square, whose creation is due in particular to Greimas’ works. The starting point is the semiotic notion of complex term, which I regard as one of the main differences between Greimas’ square and Blanché’s hexagon. The remarks on the complex terms make room for a historical survey in Aristotle’s texts, where one can find the philosophical roots of the idea of middle term between two contraries and its (...) relation to notions such as difference, position and motion. In the Stagirite’s non-logical works, the theory of the intermediate, or middle term, represents an important link between opposition issues and ethics: this becomes a privileged perspective from which to reconsider the semiotic use of the square, i.e., its inclusion in the semio-narrative structures articulating the sense of texts. (shrink)

The central aim of this paper is to present a Boolean algebraic approach to the classical Aristotelian Relations of Opposition, namely Contradiction and (Sub)contrariety, and to provide a 3D visualisation of those relations based on the geometrical properties of Platonic and Archimedean solids. In the first part we start from the standard Generalized Quantifier analysis of expressions for comparative quantification to build the Comparative Quantifier Algebra CQA. The underlying scalar structure allows us to define the Aristotelian relations in Boolean terms (...) and to propose a 3D visualisation by transforming a cube into an octahedron. In part two, the architecture of the CQA is shown to carry over, both to the classical quantifiers of Predicate Calculus and to the modal operators—which are given a Generalized Quantifier style re-interpretation. In this way we provide an algebraic foundation for Blanché’s Aristotelian hexagon as well as a 3D alternative to his 2D star-like visualisation. In a final part, a richer scalar structure is argued to underly the realm of Modality, thus generalizing the 3D algebra with eight (2 3 ) operators to a 4D algebra with sixteen (2 4 ) operators. The visual representation of the latter structure involves a transformation of the hypercube to a rhombic dodecahedron. The resulting 3D visualisation allows a straightforward embedding, not only of the classical Blanché star of Aristotelian relations or the paracomplete and paraconsistent stars of Béziau (Log Investig 10, 218–232, 2003) but also of three additional isomorphic Aristotelian constellations. (shrink)

Our aim is to show that translating the modal graphs of Moretti’s “n-opposition theory” (2004) into set theory by a suited device, through identifying logical modal formulas with appropriate subsets of a characteristic set, one can, in a constructive and exhaustive way, by means of a simple recurring combinatory, exhibit all so-called “logical bi-simplexes of dimension n” (or n-oppositional figures, that is the logical squares, logical hexagons, logical cubes, etc.) contained in the logic produced by (...) any given modal graph (an exhaustiveness which was not possible before). In this paper we shall handle explicitly the classical case of the so-called 3(3)-modal graph (which is, among others, the one of S5), getting to a very elegant tetraicosahedronal geometrisation of this logic. (shrink)

The main objective of this paper is devoted to two main parts. First, the paper introduces logical interpretations of classical structures of opposition that are constructed as extensions of the square of opposition. Blanché’s hexagon as well as two cubes of opposition proposed by Morreti and pairs Keynes–Johnson will be introduced. The second part of this paper is dedicated to a graded extension of the Aristotle’s square and Peterson’s square of opposition with intermediate quantifiers. These quantifiers are (...) linguistic expressions such as “most”, “many”, “a few”, and “almost all”, and they correspond to what are often called “fuzzy quantifiers” in the literature. The graded Peterson’s cube of opposition, which describes properties between two graded squares, will be discussed at the end of this paper. (shrink)

Short and accessible teachings from one of America's pioneer woman Zen teachers. Zenkei Blanche Hartman is an American Zen legend. A teacher in the lineage of Shunryu Suzuki, author of Zen Mind, Beginner's Mind, she was the first female abbot of an American Zen center. She is greatly revered, especially in the San Francisco Bay Area, where she has lived and taught for many years. This, her long-awaited first book, is a collection of short teachings taken from her talks on (...) the subject of boundlessness--the boundlessness that sees beyond our small, limited self to include all others. To live a boundless life she encourages living the vows prescribed by the Buddha and living life with the curiosity of a child. The short, stand-alone pieces can be dipped into whenever one is in need of inspiration. (shrink)

A recent French reform has revised the legal definition of the corporation. In essence, the law stipulates that the corporation must be run with due regard to the social and environmental impacts of its activity. It also introduces the notion of raison d’être and affords the possibility for any corporation to assign social or environmental purposes to itself, defined in its by-laws. This reform is similar to recent reforms in the UK and the US, but is based on an original (...) and distinctive theoretical argument. The aim of our article is to analyze the fundamental tenets of this reform and their implications for the theory of the corporation. It shows that the new law is based on a new positive definition of the enterprise as not only an economic organization or a productive entity, but more fundamentally a space for innovative collective action. We argue that this view of the enterprise challenges our conceptualization of the corporation in two important ways. First, it shows that the traditional theories overlook the activities of the enterprise and their related impacts, and that the corporation is not necessarily the appropriate legal vehicle for the innovative enterprise. Second, it suggests that the stipulation of the enterprise’s purpose or raison d’être in the corporate by-laws can provide new promising legal foundations for corporate responsibility. (shrink)

The hexagonal structure for ‘the geometry of logical opposition’, as coming from Aristoteles–Apuleius square and Sesmat–Blanché hexagon, is presented here in connection with, on the one hand, geometrical ideas on duality on triangles (construction of ‘companion’), and on the other hand, constructions of tripartitions, emphasizing that these are exactly cases of borromean objects. Then a new case of a logical interest introduced here is the double magic tripartition determining the semi-ring ${\mathcal{B}_3}$ and this is a borromean object (...) again, in the heart of the semi-ring ${{\rm Mat}_{3}(\mathbb{B}_{\rm Alg})}$ . With this example we understand better in which sense the borromean object is a deepening of the hexagon, in a logical vein. Then, and this is our main objective here, the Post-Mal’cev full iterative algebra ${\mathbb{P}_4 = \mathbb{P}(\mathbb{F}_4)}$ of functions of all arities on ${\mathbb{F}_4}$ , is proved to be a borromean object, generated by three copies of ${\mathbb{P}_2}$ in it. This fact is induced by a hexagonal structure of the field ${\mathbb{F}_4}$ . This hexagonal structure is seen as precisely a geometrical addition to standard boolean logic, exhibiting ${\mathbb{F}_4}$ as a ‘boolean manifold’. This structure allows to analyze also ${\mathbb{P}_4}$ as generated by adding to a boolean set of logical functions a very special modality, namely the Frobenius squaring map in ${\mathbb{F}_4}$ . It is related to the splitting of paradoxes, to modified logic, to specular logic. It is a setting for a theory of paradoxical sentences, seen as computations of movements on the bi-hexagonal link among the 12 classical logics on a set of 4 values. (shrink)

Based on an analysis of the category of “infinite judgments” in Kant, we will introduce the logical hexagon of predicate negation. This hexagon allows us to visualize in a single diagram the general structure of both Kant’s solution of the antinomies of pure reason and his argument in favor of Transcendental Idealism.

The name ‘Chloe’ appears four times in Horace'sOdes, once in Book 1 and three times in Book 3. Whether the ‘Chloes’ represent a woman or women from Horace's real life is probably not something we could know. Furthermore, there is no obvious reason to assume that all the ‘Chloes’ are the same person. However, there is likewise no obvious reasonnotto read the odes in which the name ‘Chloe’ appears, as some scholars have done, as referring to the same woman, fictional (...) or otherwise. This article argues both that ‘Chloe’ is a consistent character in theOdesand that the portrayal of Chloe is not only connected across odes but also sequential. Taking the poems in order, we see Chloe grow up from a girl who is inexperienced in the world of men to a mature mistress who plays the dominant role in her love affairs. (shrink)

""Published to coincide with University of Missouri-St. Louis's Golden Jubilee celebrations, this photo book by former chancellor Blanche M. Touhill invites readers to witness the inspiring story of how this school became an urban university of excellence and an important center of the community"--.

In this paper, we consider climate change as a systemic respiratory crisis, and explore how breath can function as a mode of witnessing climate catastrophe. We build on feminist environmental humanities methodologies of embodied attunement to advance a more-than-human witnessing of climate change. We suggest that a feminist “conspiratorial” witnessing of breath(lessness) can afford an embodied, situated, empathetic and systemic mode of witnessing. In this approach, the witness (e.g., “the human”) is part of what is witnessed (the climate crisis). As (...) such, breathing climate catastrophe can reveal the intimate, visceral and personal violences of global climate change, and develop empathetic approaches to climate injustice. Nevertheless, as breath’s social and multispecies differentiation reveals, no-one can witness the entirety of climate catastrophe with their own bodies. We thus advocate for collective, more-than-individual modes of knowing, such as science, art and critical analysis, to augment our own sensorial experiences of witness. (shrink)

Drawing on the theory-of-mind in B. Lonergan's Insight: A Study of Human Understanding, King forges the much-needed critical-experimental link between the reader's own written or spoken expressions and the structure of the human mind. A philosophy of education emerges that the reader-experimenter can both verify and identify with personally.

Background: Maximum safe resection of infiltrative brain tumors in eloquent area is the primary objective in surgical neuro-oncology. This goal can be achieved with direct electrical stimulation to perform a functional mapping of the brain in patients awake intraoperatively. When awake surgery is not possible, we propose a pipeline procedure that combines advanced techniques aiming at performing a dissection that respects the anatomo-functional connectivity of the peritumoral region. This procedure can benefit from intraoperative monitoring with computerized tomography scan and brain (...) shift correction. Associated with this intraoperative monitoring, the additional value of preoperative investigation combining brain mapping by navigated transcranial magnetic stimulation with various neuroimaging modalities has not yet been reported.Case Report: A 42-year-old left-handed man had increased intracranial pressure, left hand muscle deficit, and dysarthria, related to an infiltrative tumor of the right frontal lobe with large mass effect and circumscribed contrast enhancement in motor and premotor cortical areas. Spectroscopy profile and intratumoral calcifications on CT-scan suggested an WHO grade III glioma, later confirmed by histology. The aforementioned surgical procedure was considered, since standard awake surgery was not appropriate for this patient. In preoperative time, nTMS mapping of motor function was performed, combined with magnetic resonance imaging -based tractography reconstruction of 6 neural tracts and resting-state functional MRI connectivity of sensorimotor and language networks. In intraoperative time, DES mapping was performed with motor evoked response recording and tumor resection was optimized using non-rigid image transformation of the preoperative data to iCT data. Image guidance was updated with correction for brain shift and tissue deformation using biomechanical modeling taking into account brain elastic properties. This correction was done at crucial surgical steps, i.e., when tumor bulged through the craniotomy after dura mater opening and when approaching the presumed eloquent brain regions. This procedure allowed a total resection of the tumor region with contrast enhancement as well as a complete regression of IICP and dysarthria. Hand paresis remained stable with no additional deficit. Postoperative nTMS mapping confirmed the good functional outcome.Conclusion: This case report and technical note highlights the value of preoperative functional evaluation by nTMS updated intraoperatively with correction of brain deformation by iCT. This multimodal approach may become the optimized technique of reference for patients with brain tumors in eloquent areas that are unsuitable for awake brain surgery. (shrink)

Cet article entreprend d’interroger l’intérêt ambigu de Spinoza pour la théocratie hébraïque. Ambigu, car s’il en récuse la valeur de modèle et en souligne très clairement les limites, il la considère aussi, manifestement, comme une réussite politique. Nous faisons l’hypothèse que cette valorisation de la théocratie hébraïque, peu commune dans ce type de discours, s’explique en partie parce qu’elle lui sert d’exemple et de matériau pour penser un aspect central de sa théorie politique : l’attachement du citoyen à l’État. Il (...) s’agira ainsi de voir comment Spinoza fait usage d’une théocratie mosaïque jugée inadaptable au temps présent, pour dégager les fondements d’un patriotisme non théocratique, adapté aux États modernes. (shrink)

En cet article nous montrons en premier lieu que la théorie de l'hexagone logique de Blanché n'est pas, comme il le pense, le résultat d'une réflexion philosophique, mais qu'elle relève véritablement de la logique scientifique, puisqu'elle s'insère tout naturellement dans la structure d'ensemble des liaisons uninaires de la logique trivalente des propositions. Cette démonstration nous conduit, en second lieu, à renverser le jugement défavorable que E. J. Lemmon avait porté sur la toute première ébauche de cette théorie, et ainsi à (...) déVelopper la logique modale dans le sens de Blanché plutôt que dans celui de von Wright. En troisième lieu, nous complétons l'application que fait Blanché de cette théorie de l'hexagone aux liaisons binaires de la logique bivalente des propositions, en intégrant en une seule structure tétrahexaédrique l'ensemble des seize liaisons binaires, lui-même s'étant contenté d'en grouper seulement dix en une espèce d'anneau bihexagonal. (shrink)

La théorie de la quaternalité, telle que Piaget et Gottschalk l'ont appliquée aux connectifs binaires du calcul bivalent, appelle quelques précisions et compléments.Les seize connectifs ne comportent que deux quaternes complets: celui des jonctions et celui des implications. Leurs similitudes formelles ne doivent pas dissimuler une différence dans leur mode de construction. Elle apparaît sur leurs diagrammes (inspirés du “carré logique” traditionnel) par la place de la cellule initiale et par celles des signes barrés du trait vertical de la négation:En (...) effet, la dualité qui se combine avec celle de la négation contradictoire (DN, flèche diagonale) est, pour les jonctions, la dualité “morganienne” (DM, flèche verticale) et pour les implications, la dualité des réciproques (DR, flèche horizontale). Car dans les jonctions, liaisons symétriques, il n'y a point de vraies réciproques; inversement, les implications ne comportent pas (pourvu, bien sûr, qu'on ne les traduise pas en termes de jonctions) de dualité morganienne. Le quatrième terme, obtenu par la combinaison des deux relations génératrices, sera donc, pour les jonctions, une contreduale (DM× DN) et, pour les implications, une contreréciproque (DR× DN). (shrink)

Pour que ce précis soit fidèle à son titre et directement accessible à tout lecteur sans connaissances préalables, si ce n'est quelques notions élémentaires de logique classique, l'auteur a volontairement évité la présentation axiomatique et les démonstrations formelles. Il a plutôt visé à conduire progressivement l'esprit, par les voies de l'intuition, jusqu'au point où apparaissent les raisons des théories logiques contemporaines. Mais, en même temps qu'il ouvre l'accès aux développements de la logique depuis un siècle, cet ouvrage en donne une (...) large vue d'ensemble en touchant à des problèmes et à des théories que beaucoup de traités élémentaires laissent de côté. Ainsi, par son souci pédagogique de ne rien utiliser qui ne soit préalablement introduit et expliqué, en particulier en ce qui concerne les usages terminologiques ou algorithmiques, cet ouvrage, devenu un classique, constitue une remarquable introduction aux logiques modernes. (shrink)

In this short, dense essay, Jean Cavaillès evaluates philosophical efforts to determine the origin - logical or ontological - of scientific thought, arguing that, rather than seeking to found science in original intentional acts, a priori meanings, or foundational logical relations, any adequate theory must involve a history of the concept. Cavaillès insists on a historical epistemology that is conceptual rather than phenomenological, and a logic that is dialectical rather than transcendental. His famous call (cited by Foucault) to (...) abandon "a philosophy of consciousness" for "a philosophy of the concept" was crucial in displacing the focus of philosophical enquiry from aprioristic foundations toward structural historical shifts in the conceptual fabric. This new translation of Cavaillès's final work, written in 1942 during his imprisonment for Resistance activities, presents an opportunity to reencounter an original and lucid thinker. Cavaillès's subtle adjudication between positivistic claims that science has no need of philosophy, and philosophers' obstinate disregard for actual scientific events, speaks to a dilemma that remains pertinent for us today. His affirmation of the authority of scientific thinking combined with his commitment to conceptual creation yields a radical defense of the freedom of thought and the possibility of the new. (shrink)

oeuvre posthume d'un logicien humaniste, cette etude se presente avant tout comme un bilan analytique, tout en s'alimentant a l'experience personnelle de l'auteur. Robert Blanche pose d'abord un probleme de recensement et de classement. L'esthetique n'est pas plus la science exclusive du beau que la zoologie n'est la science exclusive du cheval: le sublime, le gracieux, le poetique, d'autres categories encore l'encadrent et forment systeme avec lui, s'organisant en couples antithetiques, en triades, a la limite en rosaces (classique, romantique) intercalees (...) l'une dans l'autre. Revenant sur les categories majeures, Blanche les considere ensuite une a une, chacune ayant sa problematique propre. Le beau, defini avant tout par la nettete d'une forme, maitrise (quand il s'y allie) la dimension de l'affectif et du voluptuaire. A l'inverse, le poetique n'a ni forme geometrique, ni lisibilite immediate et synoptique. Sa forme (son anti-forme) est le vague, le vaporeux. Son lieu d'election est le temps. Vient ensuite le decrescendo qui nous conduit du sublime, dont Blanche rappelle l'essence paradoxale, a la grace, categorie de l'aisance irenique, puis au joli, ou la dimension voluptuaire, le chatouillement des sens, prend toute la place, cotoyant a sa limite inferieure la sensibilite protopathique. Blanche s'interroge enfin sur le rapport entre style et categorie. Un style est un fait historique, localise et date; une categorie, au contraire, est un mode permanent d'appreciation esthetique. (shrink)