The Question of Truth in Pedro da Fonseca: the Problem of the simplex apprehensio and the Foundation of Logical Identities. This article deals with the theory of truth in Pedro da Fonseca (1528-1599) as it is presented in his commentary on Aristotle’s Metaphysics (1577-1612). The first part of the paper is dedicated to Fonseca’s definition of intellective truth within the doctrinal topography of the Aristotelian tradition. The Author especially points out Fonseca’s attempt to justify the notion of a (...) “simple” truth of the “simple apprehension”, based on a specific use of Cajetan’s distinction between “signified act” and “exercised act” as well as on a (partially) nominalist account of the relationship between “simple” and “enunciative” concepts. The second part deals instead with Fonseca’s definition of transcendental truth, understood as the conformity between the intellect and the esse realis of the res, and as the conformity of the latter with exemplars in God’s mind. Here the Author also reconstructs Fonseca’s theory of divine ideas and his theory of logical identities. (shrink)

The aim of this article is to reconstruct the theory of simple apprehension held in the Kiev-Mohyla Academy in the seventeenth and eighteenth centuries. We start from Aristotle’s idea of two kinds of knowing and from the Thomist theory of the two operations of the intellect in view of the ontological distinction between essence and actuality. In dealing with the theory of the activities of the intellect in the Kiev-MohylaAcademy, we consider simple apprehension as a form of Aristotle’s immediate knowledge. (...) We conclude by introducing the notion of non-representational simple apprehension. (shrink)

This chapter focuses on the question of the specific truth granted to the human intellect’s concepts qua concepts (simplex apprehensio), as it is presented and discussed in Sebastião do Couto’s commentary on On Interpretation, included in his general commentary on Aristotle’s Dialectics (1606), the final volume of the famous and influential Cursus Conimbricensis (1592–1606). Such a topic finds it roots in a large medieval debate that runs through many authors and especially Augustine, Aquinas, Scotus, Durandus, and Ockham, reaching (...) in the Jesuit early modern context, with Pedro da Fonseca and Francisco Suárez, a complete and eclectic account that paved the way for the modern understanding of “mind.” . (shrink)

Though accepting the traditional view that truth and falsity are properties of propositions and judgments, Leibniz does not refrain from predicating truth and falsity of pre-judgmental items such as ideas, which he considers to be true iff logically consistent, and false otherwise. Elsewhere, however, Leibniz claims that ideas are true or false only insofar as they include the (true or false) affirmation that their object is possible. This paper aims to cast light on Leibniz’s doctrine of ideas as truth-bearers by (...) exploring its historical background. On the one hand, Leibniz’s pronouncements reflect his reaction to the post-Cartesian debates. On the other hand, they appear to be inspired from Aquinas’s doctrine of accidental falsity. (shrink)

it is sometimes said that one of Kant’s decisive advances over his predecessors was to have anticipated Frege’s functional theory of concepts, along with its corollary that a concept has significance only in the context of the whole proposition.1 Kant is said to break with a tradition that held that there is a self-standing species of concept-use—called apprehensio simplex, or the conceiving of an idea—in which one represents objects by having a concept before one’s mind, independently of connecting (...) it with other concepts in judgment.2 Since Kant’s use of ‘judgment’ covers what Frege calls judging as well as what he calls grasping a thought, the idea is that according to Kant the only way for a thinker to use a.. (shrink)

In the vast majority of the literature on Kant, the prevailing view is that his conception of analyticity and analytic truths suffers from obscurities and inconsistencies that render it, in the end, unintelligible. In the present paper, I try (i) to underline the meaning of these conceptions of Kant’s, (ii) to bring to the fore a crucial hidden presupposition in his account of analytic truths, and (iii) to present an interpretation that restores an intelligible account of Kantian analyticity and analytic (...) truth. Contrary to the ‘received’ view, I claim that definition is the royal way to Kant’s analyticity and analytic truth, and that the latter cannot be understood apart from a very specific kind of appeal to the intuition of the object falling under the concept being defined. I call this elusive and fragile act “simple intuition,” pointing thus to the medieval notion of apprehensio simplex (and the long history behind it). Then I try to show how this is done with reference to the most suitable species of concepts, the mathematical, and by analogy (and with expectable limitations) to the empirical ones. Of course, the present attempt to reconstruct an intelligible Kantian account of analyticity and analytic truths does not also mean that I endorse it as successful and final in the context of philosophy’s effort to clarify the possibility and kinds of a priori truths. (shrink)

In this book a noted physiologist and neuroscientist introduces the concept of simplexity, the set of solutions living organisms find that enable them to deal with information and situations, while taking into account past experiences and anticipating future ones. Such solutions are new ways of addressing problems so that actions may be taken more quickly, more elegantly, and more efficiently. In a sense, the history of living organisms may be summed up by their remarkable ability to find solutions that avoid (...) the world's complexity by imposing on it their own rules and functions. Evolution has resolved the problem of complexity not by simplifying but by finding solutions whose processes--though they can sometimes be complex--allow us to act in the midst of complexity and of uncertainty. Nature can inspire us by making us realize that simplification is never simple and requires instead that we choose, refuse, connect, and imagine, in order to act in the best possible manner. Such solutions are already being applied in design and engineering and are significant in biology, medicine, economics, and the behavioral sciences. (shrink)

We propose a reconstruction of the constellation of problems and philosophical positions on the nature and number of the primitives of logic in four authors of the nineteenth century logical scene: Peano, Padoa, Frege and Peirce. We argue that the proposed reconstruction forces us to recognize that it is in at least four different senses that a notation can be said to be simpler than another, and we trace the origins of these four senses in the writings of these authors. (...) We conclude that Frege, and even more so Peirce, developed new notations not to make drawing logical conclusions easier but in order to answer the needs of logical analysis. (shrink)

The concept of simplexity, as proposed by Alain Berthoz, is based on the assumption that solutions elaborated by living organisms to decipher and face complexity could be applicable to all complex adaptive systems. Within the pedagogical and didactic context the proposai of the French physiologist could provide a scientific research trajectory aiming at solving the tension between theory, praxis, descriptive approaches and practical needs. Thus, simplexity seems to be an operational strategy based on the identification of the principles that rule (...) and guide the didactic action through patterns of adaptation, which allow to decipher complexity in terms of data elaboration and decision making among different opportunities. (shrink)

As a student at Cambridge forty years ago I received a good training in the language and literature of classical Greece, and had the good fortune to study paleography under the late E. H. Minns. For all this I am deeply grateful. But I had no training in Byzantine Greek. It was only later, and more or less by accident, that I discovered Byzantine and Modern Greek. It is not my intention to discuss the wider aspects of this question now, (...) but to appeal, on the basis of some passages in the Oresteia, for a new approach to textual criticism, or rather for the renewal of an old approach. (shrink)

Name der Zeitschrift: Logic and Logical Philosophy Jahrgang: 22 Heft: 3 Seiten: 255-293.

Science is the basis for managing the affairs of life and human activities, and living without knowledge is a form of wandering and a kind of loss. Using scientific methods helps us understand the foundations of choice, decision-making, and adopting the right solutions when solutions abound and options are numerous. Operational research is considered the best that scientific development has provided because its methods depend on the application of scientific methods in solving complex issues and the optimal use of available (...) resources in various fields, private and governmental work in peace and war, in politics and economics, in planning and implementation, and in various aspects of life. Its basic essence is to use the data provided for the issue under study to build a mathematical model that is the optimal solution. It is the basis on which decision makers rely in managing institutions and companies, and when operations research methods meet with the neutrosophic teacher, we get ideal solutions that take into account all the circumstances and fluctuations that may occur in the work environment over time. One of the most important operations research methods is the linear programming method. Which prompted us to reformulate the linear models, the graphical method, and the simplex method, which are used to obtain the optimal solution for linear models using the concepts of neutrosophic science. In this research, and as a continuation of what we presented previously, we will reformulate the modified simplex algorithm that was presented to address the difficulty that we were facing when applying the direct simplex algorithm. It is the large number of calculations required to be performed in each step of the solution, which requires a lot of time and effort. (shrink)

Throughout the centuries, the doctrine of divine simplicity laid at the heart of Christian theology. In Thomas Aquinas’ mature thought, simplicity occupies a privileged place among other attributes of God. A simple simple being is a being that does not consist of any parts or constituents. God’s being simple means that he does not exhibit any of the seven types of composition. The arguments that serve as the justification for this thesis can be divided into four groups which I labeled: (...) the argument from the lack of potentiality, the argument from the priority of parts to the whole, the argument from the anterior maker and the argument from perfection. All of them begin with identifying God with the first cause of all things and add other premises that are specific to them. The first argument — that the first cause does not have potentiality and every composite being does have it. The second — that everything that is composite depends on it’s parts while the first cause is not dependent upon anything. The third — that every composite being needs a cause or explanation and the first cause has neither. The fourth — that the first cause is a perfectly good being and such a being cannot be composite. The analyses that were conducted show that the first two reasonings seem to be unsound. The third of the arguments provides a fine justification for the thesis in question. The fourth may serve as an additional, but weaker justification for it. (shrink)

The quantum state of a d-dimensional system can be represented by a probability distribution over the d 2 outcomes of a Symmetric Informationally Complete Positive Operator Valued Measure (SIC-POVM), and then this probability distribution can be represented by a vector of $\mathbb {R}^{d^{2}-1}$ in a (d 2−1)-dimensional simplex, we will call this set of vectors $\mathcal{Q}$ . Other way of represent a d-dimensional system is by the corresponding Bloch vector also in $\mathbb {R}^{d^{2}-1}$ , we will call this set (...) of vectors $\mathcal{B}$ . In this paper it is proved that with the adequate scaling $\mathcal{B}=\mathcal{Q}$ . Also we indicate some features of the shape of $\mathcal{Q}$. (shrink)

This paper explores Thomas Aquinas’ and Richard Swinburne’s doctrines of simplicity in the context of their philosophical theologies. Both say that God is simple. However, Swinburne takes simplicity as a property of the theistic hypothesis, while for Aquinas simplicity is a property of God himself. For Swinburne, simpler theories are ceteris paribus more likely to be true; for Aquinas, simplicity and truth are properties of God which, in a certain way, coincide – because God is metaphysically simple. Notwithstanding their different (...) approaches, some unreckoned parallels between their thoughts are brought to light. (shrink)

Herpes simplex virus (HSV)‐derived vectors are currently being developed for the introduction of foreign DNA into neurons. HSV vectors can facilitate a range of molecular studies on postmitotic neurons and may ultimately be used for somatic cell gene therapy for certain neurologic diseases. In this article, the salient features of the pathogenesis and molecular biology of HSV relevant to its use as a vector are described, along with an overview of the methods used to derive these vectors. The accomplishments (...) which have been made to date using the HSV vector system are discussed, with emphasis on the issues of this technology which remain to be addressed. HSV has the potential to be a most useful tool for neuronal cell transgenesis and it is likely that important neurobiological questions will be answered using this vector system. (shrink)

This contribution examines two related points in relation to Aquinas’s understanding of contemplation, which is a sorely neglected topic in scholarship. First, after having outlined that the final act of contemplation culminates in an intellective, simple apprehension of the truth, I will examine how this act relates to the three operations of the intellect (grasping of quiddity, judgement, and reasoning) Aquinas identifies in a number of places. Second, I argue that his view of contemplation as simple insight is significantly indebted (...) to Neoplatonic sources; therefore, we must pay attention to the way he introduces Neoplatonic elements into his Aristotelian framework. I conclude this contribution by suggesting some reasons—of a theological nature—why Aquinas would have been drawn towards a non-discursive or “intuitive” notion of contemplation. (shrink)

One of the most important theories in linear programming is the dualistic theory and its basic idea is that for every linear model has dual linear model, so that solving the original linear model gives a solution to the dual model. Therefore, when we solving the linear programming model, we actually obtain solutions for two linear models. In this research, we present a study of the models. The neutrosophic dual and the binary simplex algorithm, which works to find the (...) optimal solution for the original and dual models at the same time. The importance of this algorithm is evident in that it is relied upon in several operations research topics, such as integer programming algorithms, some nonlinear programming algorithms, and sensitivity analysis in linear programming. (shrink)

This article gives a holistic re-examination of the semantic content and syntactic structure of the concept of relative identity: it suggests and explains an expanded and enhanced dual-track characterization of relative identity. It is expanded in this sense: its due coverage is not narrowly restricted to the equal-status case of identity statements (the symmetric case for identity simplex) but also includes the category-assimilating case (the asymmetric case for identity complex), both of which are unified by the shared semantic core (...) content of relative identity. It is enhanced in this sense: it is intended to give a more refined characterization of relative identity for the sake of enhancing our understanding of the structure and content of real-life relative-identity statements in people’s basic employment of language in view of the relation between thought, language, and the world. (shrink)

Whereas geometrical oppositions (logical squares and hexagons) have been so far investigated in many fields of modal logic (both abstract and applied), the oppositional geometrical side of “deontic logic” (the logic of “obligatory”, “forbidden”, “permitted”, . . .) has rather been neglected. Besides the classical “deontic square” (the deontic counterpart of Aristotle’s “logical square”), some interesting attempts have nevertheless been made to deepen the geometrical investigation of the deontic oppositions: Kalinowski (La logique des normes, PUF, Paris, 1972) has proposed a (...) “deontic hexagon” as being the geometrical representation of standard deontic logic, whereas Joerden (jointly with Hruschka, in Archiv für Rechtsund Sozialphilosophie 73:1, 1987), McNamara (Mind 105:419, 1996) and Wessels (Die gute Samariterin. Zur Struktur der Supererogation, Walter de Gruyter, Berlin, 2002) have proposed some new “deontic polygons” for dealing with conservative extensions of standard deontic logic internalising the concept of “supererogation”. Since 2004 a new formal science of the geometrical oppositions inside logic has appeared, that is “ n -opposition theory”, or “NOT”, which relies on the notion of “logical bi-simplex of dimension m ” ( m = n − 1). This theory has received a complete mathematical foundation in 2008, and since then several extensions. In this paper, by using it, we show that in standard deontic logic there are in fact many more oppositional deontic figures than Kalinowski’s unique “hexagon of norms” (more ones, and more complex ones, geometrically speaking: “deontic squares”, “deontic hexagons”, “deontic cubes”, . . ., “deontic tetraicosahedra”, . . .): the real geometry of the oppositions between deontic modalities is composed by the aforementioned structures (squares, hexagons, cubes, . . ., tetraicosahedra and hyper-tetraicosahedra), whose complete mathematical closure happens in fact to be a “deontic 5-dimensional hyper-tetraicosahedron” (an oppositional very regular solid). (shrink)

We show that every state on an interval pseudo effect algebra E satisfying an appropriate version of the Riesz Decomposition Property (RDP for short) is an integral through a regular Borel probability measure defined on the Borel σ-algebra of a Choquet simplex K. In particular, if E satisfies the strongest type of RDP, the representing Borel probability measure can be uniquely chosen to have its support in the set of the extreme points of K.

In 1995 Slater argued both against Priest’s paraconsistent system LP (1979) and against paraconsistency in general, invoking the fundamental opposition relations ruling the classical logical square. Around 2002 Béziau constructed a double defence of paraconsistency (logical and philosophical), relying, in its philosophical part, on Sesmat’s (1951) and Blanche’s (1953) “logical hexagon”, a geometrical, conservative extension of the logical square, and proposing a new (tridimensional) “solid of opposition”, meant to shed new light on the point raised by Slater. By using n-opposition (...) theory (NOT) we analyse Beziau’s anti-Slater move and show both its right intuitions and its technical limits. Moreover, we suggest that Slater’s criticism is much akin to a well-known one by Suszko (1975) against the conceivability of many-valued logics. This last criticism has been addressed by Malinowski (1990) and Shramko and Wansing (2005), who developed a family of tenable logical counter-examples to it: trans-Suszkian systems are radically many-valued. This family of new logics has some strange logical features, essentially: each system has more than one consequence operator. We show that a new, deeper part of the aforementioned geometry of logical oppositions (NOT), the “logical poly-simplexes of dimension m”, generates new logical-geometrical structures, essentially many-valued, which could be a very natural (and intuitive) geometrical counterpart to the “strange”, new, non-Suszkian logics of Malinowski, Shramko and Wansing. By a similar move, the geometry of opposition therefore sheds light both on the foundations of paraconsistent logics and on those of many-valued logics. (shrink)

The logical hexagon (or hexagon of opposition) is a strange, yet beautiful, highly symmetrical mathematical figure, mysteriously intertwining fundamental logical and geometrical features. It was discovered more or less at the same time (i.e. around 1950), independently, by a few scholars. It is the successor of an equally strange (but mathematically less impressive) structure, the “logical square” (or “square of opposition”), of which it is a much more general and powerful “relative”. The discovery of the former did not raise interest, (...) neither among logicians, nor among philosophers of logic, whereas the latter played a very important theoretical role (both for logic and philosophy) for nearly two thousand years, before falling in disgrace in the first half of the twentieth century: it was, so to say, “sentenced to death” by the so-called analytical philosophers and logicians. Contrary to this, since 2004 a new, unexpected promising branch of mathematics (dealing with “oppositions”) has appeared, “oppositional geometry” (also called “n-opposition theory”, “NOT”), inside which the logical hexagon (as well as its predecessor, the logical square) is only one term of an infinite series of “logical bi-simplexes of dimension m”, itself just one term of the more general infinite series (of series) of the “logical poly-simplexes of dimension m”. In this paper we recall the main historical and the main theoretical elements of these neglected recent discoveries. After proposing some new results, among which the notion of “hybrid logical hexagon”, we show which strong reasons, inside oppositional geometry, make understand that the logical hexagon is in fact a very important and profound mathematical structure, destined to many future fruitful developments and probably bearer of a major epistemological paradigm change. (shrink)

In this paper, we perform theoretical analysis and experiments on the Simplex Crossover (SPX), which we have proposed. Real-coded GAs are expected to be a powerful function optimization technique for real-world applications where it is often hard to formulate the objective function. However, we believe there are two problems which will make such applications difficult; 1) performance of real-coded GAs depends on the coordinate system used to express the objective function, and 2) it costs much labor to adjust parameters (...) so that the GAs always find an optimum point efficiently. The result of our theoretical analysis and experiments shows that a performance of SPX is independent of linear coordinate transformation and that SPX always optimizes various test function efficiently when theoretical value for expansion rate, which is a parameter of SPX, is applied. We also show that BLX-α is equivalent to degenerate form of SPX. Experiments show that we have something misunderstood effect of epistasis on performance degradation of real-coded GAs. (shrink)

Herpes simplex virus type 2 is the most prevalent sexually transmitted infection in the world, despite the availability of effective anti-viral treatments. A mathematical model to explore the association between gender and HSV-2 treatment adherence is developed. Threshold parameters are determined and stabilities analyzed. Sensitivity analysis of the reproduction number and the numerical simulations suggest that treatment adherence for both females and males are equally important in keeping the reproduction as low as possible. The basic model is then extended (...) to incorporate time-dependent intervention strategies. The Pontryagin’s Maximum Principle is used to characterize the optimal level of the controls, and the resulting optimality system is solved numerically. (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)

Eco-cognitive computationalism considers computation in context, following some of the main tenets advanced by the recent cognitive science views on embodied, situated, and distributed cognition. It is in the framework of this eco-cognitive perspective that we can usefully analyze the recent attention in computer science devoted to the importance of the simplification of cognitive and motor tasks caused in organic entities by the morphological features: ignorant bodies can be domesticated to become useful “mimetic bodies”, that is able to render an (...) intertwined computation simpler, resorting to that “simplexity” of animal embodied cognition, which represents one of the main quality of organic agents. Through eco-cognitive computationalism we can clearly acknowledge that the concept of computation changes, depending on historical and contextual causes, and we can build an epistemological view that illustrates the “emergence” of new kinds of computations, such as the one regarding morphological computation. This new perspective shows how the computational domestication of ignorant entities can originate new unconventional cognitive embodiments. In the last part of the article I will introduce the concept of overcomputationalism, showing that my proposed framework helps us see the related concepts of pancognitivism, paniformationalism, and pancomputationalism in a more naturalized and prudent perspective, avoiding the excess of old-fashioned ontological or metaphysical overstatements. (shrink)

The ancient practice of metzitzah b'peh, direct oral suction, is still practiced by ultra-Orthodox Jews as part of the religious rite of male newborn circumcision. Between 2000 and 2011, 11 children have died in New York and New Jersey, following infection by herpes simplex virus, presumably from infected practitioners. The City responded by requiring signed parental consent before oral suction, with parents being warned of the dangers of the practice. This essay argues that informed consent is not an appropriate (...) response to this problem. An outright ban would a better response to a practice that is dangerous to children, but might prove unconstitutional under New York State law. (shrink)

Positive Polarity indefinites, such as some in English, are licensed in simplex negative sentences as long as they take wide scope over negation. When it surfaces under a clausemate negation, some can in principle take wide scope either by movement or by some semantic mechanism; e.g., it can take pseudoscope if it is interpreted as a choice function variable. Therefore, there is some uncertainty regarding the way in which PPI indefinites get licensed: can pseudoscope suffice? In this article we (...) show, using novel data from Hindi-Urdu and English, that pseudoscope is not sufficient, and that it is the syntactic position of PPI indefinites at LF, rather than their actual scope, which is relevant for licensing. These facts support a unified view of PPI indefinites as generalized quantifiers, and disfavor analyses where they are, or can be, interpreted as choice function variables. (shrink)

The article traces the origin of Kant's distinction between the right to a good name in the Doctrine of Right and the right to respect for human dignity in the Doctrine of Virtrue. The story begins with Pufendorf's distinction between existimatio simplex and existimatio intensiva. "Existimatio" for Pufendorf means "worth." Accordingly, existimatio simplex is plain human worth, whereas existimatio intensiva is the worth of dignitaries, meaning of persons who are ascribed special worth. For Thomasius and Barbeyrac "existimatio" becomes (...) "respect." Existimatio simplex then becomes, for example for Achenwall, simple respect, which the law requires everyone to give his fellow human beings. Existimatio intensiva becomes recognition, among other things, of another's probity. The latter existimatio intensiva is a part of ethics. Kant then looks for the existimatio simplex that can be contrasted to this existimatio intensiva. He finds it in the respect for the dignity of all of mankind.Der Beitrag sucht den Ursprung von Kants Unterscheidung zwischen dem Recht der Unbescholtenheit, das in die Rechtslehre, und dem Recht auf Achtung vor der Würde des Nebenmenschen, das in die Tugendlehre gehört. Die Geschichte beginnt mit Pufendorfs Unterscheidung von existimatio simplex und existimatio intensiva. "Existimatio" bedeutet bei Pufendorf "Würde". Existimatio simplex ist danach die schlichte Menschenwürde, existimatio intensiva die Würde von Würdenträgern , also von Personen, denen eine besondere Würde zukommt. Bei Thomasius und Barbeyrac wird "existimatio" zu "Achtung". Die existimatio simplex wird dadurch, etwa bei Achenwall, zu der schlichten Achtung, die dem Nebenmenschen entgegenzubringen das Recht fordert. Die existimatio intensiva wird zur Anerkennung unter anderem der Rechtschaffenheit eines Menschen. Die letztere existimatio intensiva gehört in die Ethik. Kant sucht die existimatio simplex zu dieser existimatio intensiva, die er in der Achtung vor der Menschenwürde des anderen findet. (shrink)

We examined how language supports the expression of temporality within sentence boundaries in English, which has a rich inventory of grammatical means to express temporality. Using a computational model that mimics how humans learn from exposure we explored what the use of different tense and aspect combinations reveals about the interaction between our experience of time and the cognitive demands that talking about time puts on the language user. Our model was trained on n-grams extracted from the BNC to select (...) the TA combination that fits the context best. It revealed the existence of two different sub-systems within the set of TA combinations, a “simplex” one that is supported lexically and is easy to learn, and a “complex” one that is supported contextually and is hard to learn. The finding that some TA combinations are essentially lexical in nature necessitates a rethink of tense and aspect as grammatical categories that form the axes of the temporal system. We argue that the system of temporal reference may be more fruitfully thought of as the result of learning a system that is steeped in experience and organised along a number of functional principles. (shrink)

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

A recent paper shows that in gene expression space the manifold spanned by normal tissues and the manifold spanned by the corresponding tumors are disjoint. The statement is based on a two-dimensional projection of gene expression data. In the present paper, we show that, for the multi-dimensional vectors defining the centers of cloud samples: 1. The closest tumor to a given normal tissue is the tumor developed in that tissue, 2. Two normal tissues define quasi-orthogonal directions, 3. A tumor may (...) have a projection onto its corresponding normal tissue, but it is quasi-orthogonal to all other normal tissues, and 4. The cancer manifold is roughly obtained by translating the normal tissue manifold along an orthogonal direction defined by a global cancer progression axis. These geometrical properties add a new characterization of normal tissues and tumors and may have biological significance. Indeed, normal tissues at the vertices of a high-dimensional simplex could indicate genotype optimization for given tissue functions, and a way of avoiding errors in embryonary development. On the other hand, the cancer progression axis could define relevant pan-cancer genes and seems to be consistent with the atavistic theory of tumors. (shrink)

The present study was conducted as part of a larger study that aimed to compare moral judgment competence and moral preferences among Pakistani students of public and private sector educational institutes and religious institutes and also to measure the pattern of development of moral judgment competence of students within these institutes. The validation study completed in two phases, during the 1st phase data were collected from the students of grade 8 to 16 from public sector schools and colleges of Rawalpindi (...) city. Very low mean c-score was observed, the test came out to be valid on preference hierarchy criterion but its validity on the cognitive-affective parallelism and Quasi- simplex structure criteria could not be established due to low c-scores of the sample. In the second phase an additional sample from one private sector and two public sector universities was collected. The analysis of the combined sample showed no significant improvement of c-scores. The test meets well the preference hierarchy criterion but on the other two criteria results remain inconclusive due to low variance in the sample. The low c-scores are explained on the basis of three assumptions; poor quality of education, dogmatic religiosity, and weak and instable political structure of Pakistani society. (shrink)

The linguistic path has been explored through several works. The present paper investigates a path underlain by the fictive motion phenomenon: The plateau goes east along the river. This itinerary, here called the ‘localization path’ discloses the FM of an item along a trajectory to highlight its immobility in space. This linguistic path is here inspected through a corpus-based analysis displaying the verbs come and go. If experiencing language is first vocal, this process also implies kinetic, non-verbal modalities. The languaging (...) experience will hence be explored through the interaction between language, space and the speaker’s body through an enactive approach. A prototypical syntactic configuration mirroring the interpretative grid of FM reality will be defined. Recurrent syntactic patterns revealing the way the speaker projects his own world through simplex models will highlight the way the complexity of visual scenari is converted into linguistic sequences. (shrink)

« On ne naît pas femme: on le devient.»: “One is not born but becomes (a) woman,” thus spake Simone de Beauvoir in Le deuxième sexe (1949), The Second Sex (1953, 2009). Which one? And how, in what language(s), would one read that line today in the age of gender variance and trans revolution? Why The Second Sex again? This article spotlights the translingual simplexity of the Beauvoirean lifeline, its conceptual genius that appears second to none, whether in French or (...) English or Korean or Chinese …. (shrink)

Eco-cognitive computationalism explores computing in context, adhering to some of the key ideas presented by modern cognitive science perspectives on embodied, situated, and distributed cognition. First of all, when physical computation is seen from the perspective of the ecology of cognition it is possible to clearly understand the role Turing assigned to the process of “education” of the machine, paralleling it to the education of human brains, in the invention of the Logical Universal Machine. It is this Turing’s emphasis on (...) education that furnishes the justification of the conceptualization of machines as “domesticated ignorant entities”, that is proposed in this article. I will show that conceptualizing machines as dynamically active in distributed physical entities of various kinds suitably transformed so that data can be encoded and decoded to obtain appropriate results sheds further light on my eco-cognitive perspective. Furthermore, it is within this intellectual framework that I will usefully analyze the recent attention in computer science devoted to the importance of the simplification of cognitive and motor tasks caused in organic entities thanks to morphological features: ignorant bodies can be computationally domesticated to make an intertwined computation simpler, relying on the “simplexity” of animal embodied cognition, which represents one of the main qualities of organic agents. Finally, eco-cognitive computationalism allows us to clearly acknowledge that the concept of computation evolves over time as a result of historical and contextual factors, and we can construct an epistemological view that depicts the “emergence” of new types of computations that exploit new substrates. This new viewpoint demonstrates how the computational domestication of ignorant entities might result in the emergence of novel unconventional cognitive embodiments. (shrink)

Polyhedral functions provide a model for an important class of problems that includes both linear programming and applications in data analysis. General methods for minimizing such functions using the polyhedral geometry explicitly are developed. Such methods approach a minimum by moving from extreme point to extreme point along descending edges and are described generically as simplicial. The best-known member of this class is the simplex method of linear programming, but simplicial methods have found important applications in discrete approximation and (...) statistics. The general approach considered in this text, first published in 2001, has permitted the development of finite algorithms for the rank regression problem. The key ideas are those of developing a general format for specifying the polyhedral function and the application of this to derive multiplier conditions to characterize optimality. Also considered is the application of the general approach to the development of active set algorithms for polyhedral function constrained problems and associated Lagrangian forms. (shrink)