This paper discusses continuity between ancient Pythagoreanism and the pseudo-Pythagorean writings, which began to appear after the end of the Pythagorean school ca. 350 BC. Relying on a combination of temporal, formal and substantial criteria, I divide Pseudopythagorica into three categories: 1) early Hellenistic writings ascribed to Pythagoras and his family members; 2) philosophical treatises written mostly, yet not exclusively, in pseudo-Doric from the turn of the first century BC under the names of real or fictional (...) Pythagoreans; 3) writings attributed to Pythagoras and his relatives that continued to appear in the late Hellenistic and Imperial periods. I will argue that all three categories of pseudepigrapha contain astonishingly little that is authentically Pythagorean. (shrink)

The polis, as a gathering of various citizens, may be threatened by discord and finally may collapse because of the stasis, the internal conflict between different groups of people with diverging interests. This scheme is tackled by Plato in Gorgias, and more thoroughly in the Republic. Both dialogues were a source of inspiration for the pseudo-Pythagorean writings which flourished between the second half of the 4th century B.C. and the Hellenistic period. Among them, the treaties attributed to Kleinias, (...) Metopus, Theages, Lysis and Hippodamus frequently use the concept of stasis and pleonexia to describe how a city may be governed and what kind of danger may appear if the citizens’ behavior is not controlled. In general, these treaties adapt the vision of Plato concerning conflict to some Pythagorean images and teachings. By mingling both influences, they blur the frontier between Platonism and Pythagoreanism and create a genre of intertwined literature which may be qualified as bricolage, according to Lévi-Strauss’s concept. These philosophical texts use a range of material mostly traced back to the Hellenistic period, but also some fragments related to the conception of conflicts and violence in early Pythagoreanism. (shrink)

The paper offers a running commentary on ps-Archytas’ On Intellect and Sense Perception (composed ca. 80 BCE), with the aim to provide a clear description of Hellenistic/post-Hellenistic Pythagorean epistemology. Through an analysis of the process of knowledge and of the faculties that this involves, ps-Archytas presents an original epistemological theory which, although grounded in Aristotelian and Platonic theories, results in a peculiar Pythagorean criteriology that accounts for the acquisition and production of knowledge, as well as for the specific (...) competences of each cognitive faculty. (shrink)

In his Exhortation to Philosophy (Protrepticus), the Neoplatonic philosopher Iamblichus famously preserves material culled from lost works of ancient philosophy, including dialogues of Aristotle. He also preserves a work entitled On Wisdom and ascribed to the Pythagorean philosopher Archytas of Tarentum, who was a friend and challenger of Plato. The text On Wisdom is a later Hellenistic production, probably written in the 1st century BCE, but it presents an important piece in the puzzle of reconstructing Pythagoreanism for the Hellenistic (...) and Post-Hellenistic periods. On Wisdom provides ps-Archytas' views on the nature, pursuit, and purposes of philosophy, as well as the division of the parts of knowledge. This article presents the first complete modern translation into English and analysis of this work, whilst also explaining the precise ways in which its first critic, Iamblichus, appropriates its content to Neoplatonic theories. (shrink)

In this paper, I challenge a familiar argument -- a composite of arguments in the literature -- for the view that “Why be moral?” is a pseudo-question. I do so by refuting a component of that argument, a component that is not only crucial to the argument but important in its own right. That component concerns the status of moral reasons in replies to “Why be moral?”; consequently, this paper concerns reasons and rationality no less than it concerns (...) morality. The work I devote to those topics shows not only that the argument I address is unsound, but that the conclusion of that argument is false. “Why be moral?” is no pseudo-question. (shrink)

Here we propose a discussion about the "mandorla" or "vesica piscis". It is a type of 2-dimensional lens, that is, a geometric shape formed by the intersection of two circles with the same radius, intersecting in such a way that the centre of each circle lies on the perimeter of the other. The aim of the discussion is that of understanding when such a geometric shape became a symbol and when this symbol received a specific name. We will find that (...) the name "mandorla" was used long before the term "vesica piscis", which is the Latin translation of the German "fischblosen" used by Albrecht Dürer in his book on geometry. Therefore, the name invented by Dürer was not used by the painter for a sacred form. However, after the middle of the nineteenth century the term "vesica piscis" exploded in literature. Its use was criticized and, at the same time, it was stressed that the proper term for the symbol is "mandorla". Nonetheless, the "vesica piscis" continues to be largely used in the sacred geometry, which ascribes symbolic and sacred meanings to certain geometric shapes and proportions. In the proposed discussion, we will also show that, recently, the 2-dimensional lenticular symbol has been related to the Pythagorean philosophy. It is told that the followers of this philosophy had the habit of using an apple for symbolic communications. Sliced across, the core of the apple is displaying a pentagram, but sliced lengthwise it forms two intersecting circles, that is a "mandorla". Then, the investigation about terms and related uses of this specific geometric shape is the core of the matter of our discussion or, let us tell, the "core of the apple", in a Pythagorean-like approach to find how a German "fischblosen" evolved into a sacred symbol, thanks to a translation into Latin. (shrink)

Archytas of Tarentum, a contemporary and associate of Plato, was a famous Pythagorean, mathematician, and statesman of Tarentum. Although his works are lost and most of the fragments attributed to him were composed in later eras, they nevertheless contain valuable information about his thought. In particular, the fragments of On Law and Justice are likely based on a work by the early Peripatetic biographer Aristoxenus of Tarentum. The fragments touch on key themes of early Greek ethics, including: written and (...) unwritten laws; freedom and self-sufficiency; moderation of the emotions and cultivation of virtues; equality and the competence of the majority to participate in government; criticism of “rule by an individual”; a theory of the ideal “mixed constitution”; distributive and corrective justice and punishment, and of the rule of law. The fragments also contain one of the only positive accounts of democracy in ancient Greek philosophy. (shrink)

In the literature, new types of neutrosophic sets have been introduced in the meantime by the growing neutrosophic community. We present a few: Pythagorean Neutrosophic Set, Fermatean Neutrosophic Set, Generalized Fermatean Neutrosophic Set, n-power Neutrosophic Set, Cubic Spherical Neutrosophic Set, Spherical Neutrosophic Set, n-HyperSpherical Neutrosophic Set, Refined n-HyperSpherical Neutrosophic Set.

The paper discusses Hilbert mathematics, a kind of Pythagorean mathematics, to which the physical world is a particular case. The parameter of the “distance between finiteness and infinity” is crucial. Any nonzero finite value of it features the particular case in the frameworks of Hilbert mathematics where the physical world appears “ex nihilo” by virtue of an only mathematical necessity or quantum information conservation physically. One does not need the mythical Big Bang which serves to concentrate all the violations (...) of energy conservation in a “safe”, maximally remote point in the alleged “beginning of the universe”. On the contrary, an omnipresent and omnitemporal medium obeying quantum information conservation rather than energy conservation permanently generates action and thus the physical world. The utilization of that creation “ex nihilo” is accessible to humankind, at least theoretically, as long as one observes the physical laws, which admit it in their new and wider generalization. One can oppose Hilbert mathematics to Gödel mathematics, which can be identified as all the standard mathematics until now featureable by the Gödel dichotomy of arithmetic to set theory: and then, “dialectic”, “intuitionistic”, and “Gödelian” mathematics within the former, according to a negative, positive, or zero value of the distance between finiteness and infinity. A mapping of Hilbert mathematics into pseudo-Riemannian space corresponds, therefore allowing for gravitation to be interpreted purely mathematically and ontologically in a Pythagorean sense. Information and quantum information can be involved in the foundations of mathematics and linked to the axiom of choice or alternatively, to the field of all rational numbers, from which the pair of both dual and anti-isometric Peano arithmetics featuring Hilbert arithmetic are immediately inferable. Noether’s theorems (1918) imply quantum information conservation as the maximally possible generalization of the pair of the conservation of a physical quantity and the corresponding Lie group of its conjugate. Hilbert mathematics can be interpreted from their viewpoint also after an algebraic generalization of them. Following the ideas of Noether’s theorem (1918), locality and nonlocality can be realized both physically and mathematically. The “light phase of the universe” can be linked to the gap of mathematics and physics in the Cartesian organization of cognition in Modernity and then opposed to its “dark phase”, in which physics and mathematics are merged. All physical quantities can be deduced from only mathematical premises by the mediation of the most fundamental physical constants such as the speed of light in a vacuum, the Planck and gravitational constants once they have been interpreted by the relation of locality and nonlocality. (shrink)

This paper critically examines the use of the name 'Pseudo-Archytas' to refer to two aspects of the reception of Archytas of Tarentum in antiquity: the 'author-inflection' and the 'authority-inflection'. In order to make progress on our understanding of authority and authorship within the Pythagorean tradition, it attempts to reconstruct Porphyry's views on the importance of Archytas as guarantor of Pythagorean authenticity in the former's lost work On the History of the Philosophers by considering a fragment preserved in (...) Arabic by Ibn Abī Uṣaybi‘a. The article finally argues that a range of problems attend our use of the term 'pseudo-Archytas', which is not fit for purpose when considering the evidence regarding authorship and authority in the Pythagorean tradition. It recommends a more critical approach to the notion of authenticity within the Pythagorean tradition and suggests a new term, 'Archytism', as a more useful point of reference. (shrink)

Recent research on algebraic models of _quasi-Nelson logic_ has brought new attention to a number of classes of algebras which result from enriching (subreducts of) Heyting algebras with a special modal operator, known in the literature as a _nucleus_. Among these various algebraic structures, for which we employ the umbrella term _intuitionistic modal algebras_, some have been studied since at least the 1970s, usually within the framework of topology and sheaf theory. Others may seem more exotic, for their primitive (...) operations arise from algebraic terms of the intuitionistic modal language which have not been previously considered. We shall for instance investigate the variety of _weak implicative semilattices_, whose members are (non-necessarily distributive) meet semilattices endowed with a nucleus and an implication operation which is not a relative pseudo-complement but satisfies the postulates of Celani and Jansana’s strict implication. For each of these new classes of algebras we establish a representation and a topological duality which generalize the known ones for Heyting algebras enriched with a nucleus. (shrink)

The primary quantum mechanical equation of motion entails that measurements typically do not have determinate outcomes, but result in superpositions of all possible outcomes. Dynamical collapse theories (e.g. GRW) supplement this equation with a stochastic Gaussian collapse function, intended to collapse the superposition of outcomes into one outcome. But the Gaussian collapses are imperfect in a way that leaves the superpositions intact. This is the tails problem. There are several ways of making this problem more precise. But many authors dismiss (...) the problem without considering the more severe formulations. Here I distinguish four distinct tails problems. The first (bare tails problem) and second (structured tails problem) exist in the literature. I argue that while the first is a pseudo-problem, the second has not been adequately addressed. The third (multiverse tails problem) reformulates the second to account for recently discovered dynamical consequences of collapse. Finally the fourth (tails problem dilemma) shows that solving the third by replacing the Gaussian with a non-Gaussian collapse function introduces new conflict with relativity theory. (shrink)

In the context of feminist and postmodern thought, traditional conceptions of masculinity and what it means to be a “Real Man” have been critiqued. In Genevieve Lloyd's The Man of Reason, this critique takes the form of exposing the effect that the distinctive masculinity of the “man of reason” has had on the history of philosophy. One major feature of the masculine-feminine dichotomy will emerge as a key notion for understanding the rest of the paper: the dichotomy of reason-feeling, a (...) parallel and a foundational aspect to the dichotomy of masculinity and femininity. In exploring the history of symbolic conceptions of masculinity in ancient Greece, the Renaissance, and the present, one finds that the oppression of women is integrally linked to the traditional tie between masculinity and reason. There have been many efforts in recent feminist philosophy to rewrite or redefine “Woman” in such a way as to alleviate the oppression of women. I argue that the effectiveness of rewriting Woman for this purpose is problematic, primarily because any rewriting of this type must occur in the current historical context of hierarchical dualisms, like Man-Woman, masculine-feminine, male-female. These binary oppositions arguably find their roots in Pythagorean philosophy and can be traced through the Renaissance to our current historical context. It is these dualisms that have traditionally valued the masculine side of the Man-Woman dichotomy more than the feminine. Further, it will be argued that the hierarchical dualism of Man and Woman is so pervasive that if we rewrite or redefine the inferior, deprivileged side of that dualism, we cannot correct its devalued status. Instead, we redefine that which is undervalued but retain its devalued status. This particular aspect of attempts to critique hierarchical dualisms like reason and feeling has been reflected in the writings of many feminists, male and female. This paper will show that in cases where women attempt to redefine the dichotomy by revaluing the traditionally feminine (like feelings and emotions) over the traditionally masculine (like reason) their work is often mistakenly criticized for being purely political; conversely, when men attempt to redefine the same dichotomy in an attempt to allow men to “get back in touch with their feelings,” to be nurturers, their work is described in terms of providing a better epistemology. The current literature on masculinity explores alternatives to rewriting or redefining Woman that try to avoid the problem of status remaining with redefinition. This alternative is rewriting or redefining Man. Through redefining Man, one may be able to reconceptualize the privileged side of the hierarchical dualism in such a way that it is no longer privileged. Deprivileging, as well as redefining Man, is argued by theorists of masculinity to be possible because while the devalued status of the inferior side of a hierarchical dualism tends to keep the same status when redefined, it may be possible to redefine the privileged side of the dualism in such a way that it loses its privileged status. Unfortunately, many of these attempts to rewrite or redefine masculinity have detrimental faults of their own. Finally, this paper will discuss more promising possibilities for new definitions of Man, as well as a vision for better interaction between the work of women and men in general. (shrink)

Medieval and early modern Jewish philosophers developed their thinking in conversation with various bodies of literature. The influence of ancient Greek – primarily Aristotle (and pseudo-Aristotle) – and Arabic sources was fundamental for the very constitution of medieval Jewish philosophical discourse. Toward the late Middle Ages Jewish philosophers also established a critical dialogue with Christian scholastics. Next to these philosophical corpora, Jewish philosophers drew significantly upon Rabbinic sources (Talmud and the numerous Midrashim) and the Hebrew Bible. In order (...) to clarify the unique as well as shared elements in the thought of medieval Jewish philosophers, we will begin this chapter with a brief study of some early Rabbinic sources on the purpose of the world, i.e., why it came to be and why it is sustained in existence. In the second part of this chapter, we will study Maimonides’ critique of the veracity and usefulness of the belief in (anthropocentric) teleology, and the critical reception of his views by later philosophers. The third part will address discussions of divine teleology in Kabbalistic literature. Our exposition will concentrate mostly on a specific early-eighteenth-century text that is one of the most lucid and rigorous presentations of Lurianic Kabbalah. The fourth and final section will elucidate Spinoza’s critique of teleology, its precise target and scope, and its debt to earlier sources discussed in this chapter. (shrink)

Recent feminist and postmodern thought has critiqued traditional conceptions of masculinity, describing the effect that the distinctive masculinity of the "man of reason" has had on the history of philosophy, on consciousness, and on the academy. A common characteristic of the recent literature on masculinity is that it reflects the historical and cultural context in which it is written -- a context of binary, hierarchical dualisms which involve certain symbolic associations. These dualisms, such as Man-Woman, masculine-feminine, and reason-emotion, arguably (...) find their roots in Pythagorean philosophy and can be traced through the Renaissance to our current historical context. One example is our conception of reason: the association of maleness with a clear, determinate mode of thought, i.e. reason, was incorporated into the form-matter distinction that was central to Greek thought. This paper will show that in cases where women attempt to redefine the dichotomy by revaluing the traditionally feminine (like feelings and emotions) over the traditionally masculine (like reason) their work is often mistakenly criticized for being purely political; conversely, when men attempt to redefine the same dichotomy in an attempt to allow men to "get back in touch with their feelings," to be nurturers, their work is described in terms of providing a better epistemology. The current literature on masculinity explores alternatives to rewriting or redefining Woman that try to avoid the problem of status remaining with redefinition. This alternative is rewriting or redefining Man. Through redefining Man, one may be able to reconceptualize the privileged side of the hierarchical dualism in such a way that it is no longer privileged. Deprivileging, as well as redefining Man, is argued by theorists of masculinity to be possible because while the devalued status of the inferior side of a hierarchical dualism tends to keep the same status when redefined, it may be possible to redefine the privileged side of the dualism in such a way that it loses its privileged status. Unfortunately, many of these attempts to rewrite or redefine masculinity have detrimental faults of their own. Finally, this paper will discuss more promising possibilities for new definitions of Man, as well as a vision for better interaction between the work of women and men in general. (shrink)

Popper's account of refutation is the linchpin of his famous view that the method of science is the method of conjecture and refutation. This thesis critically examines his account of refutation, and in particular the practice he deprecates as avoiding a refutation. I try to explain how he comes to hold the views that he does about these matters; how he seeks to make them plausible; how he has influenced others to accept his mistakes, and how some of the ideas (...) or responses to Popper of such people are thus similarly mistaken. I draw some distinctions necessary to the provision of an adequate account of the so-called practice of avoiding a refutation, and try to rid the debate about this practice of at least one red herring. I analyse one case of 'avoiding' a refutation in detail to show how the rationality of scientific practice eludes both Popper and many of his commentators. Popper's skepticism about contingent knowledge prevents him from providing an acceptable account of contingent refutation, and so his method is really the method of conjecture and conjecture. He cannot do without the concepts of knowledge and refutation, however, if his account of science is to be plausible or persuasive, and so he equivocates between, amongst other things, refutation as disproof and refutation as the weaker notion of discorroboration. I criticise David Stove's account of this matter, in particular to show how he misses this point. An additional advantage Popper would secure from this equivocation is that if refutations were mere discorroborations they would be easier to achieve, and hence more common in science, than is the case. On Popper's weak notion of refutation, it would be possible to refute true theories since corroboration does not entail truth. There are two other related doctrines Popper holds about refutation which, if accepted, make some refutations seem easier to obtain than is the case. I call these doctrines 'Strong Popperian Falsificationism' (SPF) and 'Weak Popperian Falsificationism' (WPF). SPF is the false doctrine that if a prediction from some theory is refuted then that theory is refuted. Popper does not always endorse SPF. In particular, when confronted with a counterexample to it, he retreats to WPF, which is the false doctrine that if a prediction from some theory is refuted then that theory is prima facie refuted. WPF , or even SPF, can seem plausible if one has in mind predictions derived from theories in strong or conclusive tests of those theories, which I suggest Popper characteristically does. v Popper is disposed to describe any such case of predictive failure which does not lead to the refutation of the theory concerned as one in which that refutation has been avoided. To reinforce his portrayal of the refutation, or the attempted refutation, of major scientific theories as the rational core of scientific practice, Popper treats the so-called practice of avoiding a refutation as untypical of science, and much so-called avoidance he dismisses as unscientific or pseudo-scientific. I argue that his notion of avoiding a refutation is incoherent. Popper is further driven to believe that such avoidance is possible, however, because he conflates sentences with propositions and propositions with propositional beliefs. Also, he wishes to avoid being saddled with the relativisim that is a consequence of his weak account of refutation as discorroboration. Popper believes that ad hoc hypotheses are the most important of the unscientific means of avoiding a refutation. I argue that his account of such hypotheses is also incoherent, and that several hypotheses thought to be ad hoc in his sense are not. Such hypotheses appear to be so largely because of Popper's use of rhetoric and partly because these hypotheses are unacceptable for other reasons. I conclude that to know that a hypothesis is ad hoc in Popper's sense does not illuminate scientific practice. Popper has also attempted to explicate ad hocness in terms of some undesirable, or allegedly undesirable, properties of hypotheses or the explanations they would provide. The first such property is circularity, which is undesirable; the second such property is reduction in empirical content, which is not. In the former case I argue that non-circularity is clearly preferable to non-ad hocness as a criterion for a satisfactory explanation or explanans, as the case may be, and in the latter case that Popper is barking up the wrong tree. Some cases of so-called avoidance are obviously not unscientific. The discovery of Neptune from a prediction based on the reasonable belief that there were residual perturbations in the motion of Uranus is an important case in point, and one that is much discussed in the literature. The manifest failure of astronomers to account for Uranus's motion did not lead to the refutation of Newton's law of gravitiation, yet significant scientific progress obviously did result. Retreating to WPF, Popper claims that Newton's law was prima facie refuted. In general, astronomers have never shared this view, and they are correct in not doing so. I argue that the law of gravitation would have been prima facie refuted only if there had been good reason at the time to believe as false what is true, namely, that an unknown trans-Uranian planet was the cause of those Uranian residuals. Knowledge of the trans-Uranian region was then so slight that it was merely a convenient assumption, one which there was little reason to believe was false, that the known influences on Uranus's motion were the only such influences. I conclude that in believing vi or supposing that it was this assumption that was false, rather than the law of gravitation, Leverrier and Adams, the co-predictors of Neptune, were acting rationally and intelligently. Popper's commentators offer a variety of accounts of the alleged practice of avoiding a refutation, and of this case in particular. I analyse a sample of their accounts to show how common is the acceptance of some of Popper's basic mistakes, even amongst those who claim to reject his falsificationism, and to display the effects on their accounts of this acceptance of his mistakes. Many commentators recognize that anomalies are typically dealt with by changes in the boundary conditions or in other of the auxiliary propositions employed. Where many still go wrong, however, is in retaining the presupposition of WPF which encouraged Popper to hold the contradictory view about anomalies in the first place. Thus Imre Lakatos and others, for example, have developed a 'siege mentality' about major scientific theories; they see them as under continual threat of refutation from anomalies, and so come to believe that dogmatism is essential in science if such theories are to survive as they do. I examine various such doomed attempts to reconcile Popper with the history of science. It is a common failure in this literature to conflate or to fail to see the need to distinguish a belief from a supposition, and an epistemic reason from a pragmatic reason. I argue that only if one does draw these distinctions can one give an adequate account of how anomalies are rationally dealt with in science. The other important strand in Popper's thinking about 'avoidance' of refutation which has seriously misled some of his commentators is his unfounded belief in the dangers of ad hoc hypotheses. I examine the accounts that a sample of such commentators provide of the trans-Uranian planet hypotheses of Leverrier and Adams. These commentators imply or assert what Popper only hints at, namely, that there is something fishy about this hypothesis. I provide a further defence of the rationality of entertaining this hypothesis at the time. I conclude with a few remarks about Popper's dilemma in respect of scientific practice and his long standing emphasis on refutations. (shrink)

The Pythagorean tradition dominates the understanding of beauty up until the end of the 18th Century. According to this tradition, the experience of beauty is stimulated by certain relations perceived to be between an object/construct's elements. As such, the object of the experience of beauty is indeterminate: it has neither a determinate perceptual analogue (one cannot simply identify beauty as you can a straight line or a particular shape) nor a determinate concept (there are no necessary and sufficient conditions (...) for beauty at the semantic level). By the 13th Century in the West, the pleasure experienced in beauty is characterized as disinterested. Yet, on the basis that all cultural manifestations of the pythagorean theory of beauty recognize that judgments of beauty are genuine judgments, we would want to say that judgments of beauty are lawful. In addition, from ancient times, up until after Kant, philosophers of beauty within this tradition recognize two kinds of beauty: a universal, unchanging beauty coexisting with a relative, dynamic beauty. These two kinds of beauty and the tensions discussed above, are reconciled and dissolved respectively, according to the metaphysical/religious commitments of the particular author. As yet, however, these features of beauty have not been reconciled within a physicalist worldview. This is what I set out to do. (shrink)

Time as the key to a theory of everything became recently a renewed topic in scientific literature. Social constructivism applied to physics abandons the inevitable essentials of nature. It adopts uncertainty in the scope of the existential activity of scientific research. We have enlightened the deep role of social constructivism of the predetermined Newtonian time and space notions in natural sciences. Despite its incompatibility with determinism governing the Newtonian mechanics, randomness and entropy are inevitable when negative localized energy is (...) transformed into spatially dissipative heat. In sharp contrast to the Newtonian notion, social constructivism makes room for the temporal twin of cyclic conservation and pseudo-linearly structural evolution both reconciling mechanical order and thermodynamic chaos in Leibnizian space-time. In the broad scope of natural sciences this triad nature of time produces a multiple reality and gives appropriate answers on virtual physical paradoxes. (shrink)

The commentary is a detailed analysis of one of the shortest writings (25 verses) and, according to an already classic definition, "The Most Neglected Book in the New Testament” (cf. D. J. Rowston). Thus, it covers an existing gap in the specialized theological literature and is among the newer concerns of biblical scholars, attentive to the enhancement of the corpus of the Catholic Epistles. The interest in such an inspired text lies primarily in the approximately ten new topics it (...) uniquely addresses in the New Testament literature, and also in the issues it exposes, regarding those who have always disturbed the peace of Christian communities: agitators, impostor pseudo-prophets, schismatic heretics, ultimately sectarians. The volume is divided into three essential parts, as announced in the subtitle of the writing: an Isagogical part that reaches the main points related to the authorship, the authority, the structure and the dating of the writing, a more consistent part materialized in a very elaborate Commentary of the text itself. said (verse by verse, we could even say word for word), preceded each time by an adequate Translation of the basic Greek text (also highlighted at the beginning of each section, in bilingual columns) and also a final part which highlights the main Theological Themes of the Letter (Triadology, Eschatology, Angelology, Soteriology, etc.). Through the methods of analysis used, the commentary is a very useful tool for biblical scholars and historians, an informed guide for priests and believers interested in reading and the history of the Holy Scriptures of the New Testament, the reflection on these texts, and their profound theological meaning. (shrink)

There are two aspects to Wittgenstein’s method of deconstructing pseudo-philosophical problems that need to be distinguished: (1) describing actual linguistic practice, and (2) constructing hypothetical ‘language-games’. Both methods were, for Wittgenstein, indispensable means of clarifying the ‘grammar’ of expressions of our language -- i.e., the appropriate contexts for using those expressions – and thereby dissolving pseudo-philosophical problems. Though (2) is often conflated with (1), it is important to recognize that it differs from it in important respects. (1) can (...) be seen as functioning as a direct method of ‘proof’ (i.e., attempt to convince the reader of some thesis), and (2) as an indirect method of ‘proof’ -- proof by reductio ad absurdum. This essay will be devoted to clarifying (2) by forging an analogy with surrealism in art. (shrink)

This essay is part of larger project in which I attempt to show that Western formal logic, from its inception in Aristotle onward, has both been partially constituted by, and partially constitutive of, what has become known as racism. More specifically, (a) racist/quasi-racist/proto-racist political forces were part of the impetus for logic’s attempt to classify the world into mutually exclusive, hierarchically-valued categories in the first place; and (b) these classifications, in turn, have been deployed throughout history to justify and empower (...) racism/quasi-racism/proto-racism. In other words, (a) an important part of the chaos and messiness that so troubles logic has been the natural bio-cultural diversity of human beings as described by concepts such as race and ethnicity; and (b) once these concepts were historically in place, taken for granted, buttressed with pseudo-science, and had their origins forgotten, they became tools for the oppression of diverse human groups. The central thesis of this essay is that close readings of a variety of Leibniz’s writings (including several essays and one letter) will reveal a pattern of mutual dependency and creation in regard to logic and racism in Leibniz. My conclusion will be that there is a meaningful connection between logic and racism (or at least between logic and politics in general) in Leibniz such that one should be skeptical of his logic’s claim to offer transparent and neutral descriptions of the world as well as imperatives for action. Put differently, I want to ask the following specific question: how do Leibniz’s own racially-informed political goals, along with the emergence of race-centric European colonialism, both invest and disguise themselves within Leibniz’s mathematizing of logic? (shrink)

This paper generalizes rationalizability of a choice function by a single acyclic binary relation to rationalizability by a set of such relations. Rather than selecting those options in a menu that are maximal with respect to a single binary relation, a weakly pseudo-rationalizable choice function selects those options that are maximal with respect to at least one binary relation in a given set. I characterize the class of weakly pseudo-rationalizable choice functions in terms of simple functional properties. This (...) result also generalizes Aizerman and Malishevski's characterization of pseudo-rationalizable choice functions, that is, choice functions rationalizable by a set of total orders. (shrink)

We present a game mechanic called pseudo-visibility for games inhabited by non-player characters (NPCs) driven by reinforcement learning (RL). NPCs are incentivized to pretend they cannot see pseudo-visible players: the training environment simulates an NPC to determine how the NPC would act if the pseudo-visible player were invisible, and penalizes the NPC for acting differently. NPCs are thereby trained to selectively ignore pseudo-visible players, except when they judge that the reaction penalty is an acceptable tradeoff (e.g., (...) a guard might accept the penalty in order to protect a treasure because losing the treasure would hurt even more). We describe an RL agent transformation which allows RL agents that would not otherwise do so to perform some limited self-reflection to learn the training environments in question. (shrink)

Is all explanations causal explanation? Puzzles about barometer readings "explain" storms and shadow lengths "explaining" flagpole heights make it attractive to think so. Wesley Salmon (1984) has endorsed this causal thesis. One way to test this thesis is to assess the explanatory import of pseudo-processes. I do so by discussing the concept of heritability, which measures a pseudo-process, and one role it played in the theory of natural selection: explaining response to selection. This will show, not just that (...) heritability has heuristic or predictive utility, but that it can be explanatory. Possible responses to this case are also discussed. (shrink)

The Quine/Putnam indispensability argument is regarded by many as the chief argument for the existence of platonic objects. We argue that this argument cannot establish what its proponents intend. The form of our argument is simple. Suppose indispensability to science is the only good reason for believing in the existence of platonic objects. Either the dispensability of mathematical objects to science can be demonstrated and, hence, there is no good reason for believing in the existence of platonic objects, or their (...) dispensability cannot be demonstrated and, hence, there is no good reason for believing in the existence of mathematical objects which are genuinely platonic. Therefore, indispensability, whether true or false, does not support platonism. (shrink)

Eugene Afonasin highlights the wealth of information on Pythagoras and his tradition preserved in Clement of Alexandria’s Stromateis and presents them against the background of Later Platonic philosophy. He  rst outlines what Clement knew about the Pythagoreans, and then what he made of the Pythagorean ideal and how he reinterpreted it for his own purposes. Clement clearly occupies an intermediate position between the Neopythagorean biographical tradition, rmly based on Nicomachus, and that more or less vague and difuse literary (...) situation which preceded the later developments, and in this respect is a very good source, worth studying for its own sake and as supplementary material which can help to understand the great Pythagorean synthesis attempted by Iamblichus. Developing their variants of the “exhortation to philosophy” (protreptikoi logoi), these men were much concerned with the educational value of the Pythagorean way of life rather than biographical circumstances, designed to place the ancient sage in the proper cultural context. (shrink)

In the twenty-fourth aporia of Theophrastus' Metaphysics, there appears an important, if ‘bafflingly elliptical’, ascription to Plato and the ‘Pythagoreans’ of a theory of reduction to the first principles via ‘imitation’. Very little attention has been paid to the idea of Platonic and ‘Pythagorean’ reduction through the operation of ‘imitation’ as presented by Theophrastus in his Metaphysics. This article interrogates the concepts of ‘reduction’ and ‘imitation’ as described in the extant fragments of Theophrastus’ writings – with special attention to (...) his Metaphysics – in an attempt to make sense of how, precisely, Theophrastus characterizes the metaphysical systems of Plato and the ‘Pythagoreans’. A fuller examination of Aporia 24 produces important new understandings of the nature of the Early Academy in the mid fourth century B.C.E. Specifically, by ascribing the concept of reduction via ‘imitation’ to Plato and the ‘Pythagoreans’, Theophrastus is actually describing theories about the structure of the universe held by an important Platonist competitor and the contemporary head of the Academy in Athens, Xenocrates of Chalcedon (396/5–314/13 B.C.E.), who (a) took it upon himself to establish a Platonic doctrine that could be associated with his master’s writings and (b) coordinated that doctrine with the philosophical precepts of the Pythagoreans. As a consequence, we are prompted to question Aristotle’s famous ascription of a theory of ‘imitation’ to the metaphysics of the genuine contemporary or recently deceased Pythagoreans (such as Philolaus of Croton or Archytas of Tarentum) and consider how Xenocrates’ writings on Plato and the ‘Pythagoreans’ might be informing both Theophrastus’ and Aristotle’s descriptions of the Platonic and Pythagorean philosophical system(s). (shrink)

This paper traces how the dualism of body and soul, cosmic and human, is bridged in philosophical and religious traditions through appeal to the notion of ‘breath’ (πνεῦμα). It pursues this project by way of a genealogy of pneumatic cosmology and anthropology, covering a wide range of sources, including the Pythagoreans of the fifth century BCE (in particular, Philolaus of Croton); the Stoics of the third and second centuries BCE (especially Posidonius); the Jews writing in Hellenistic Alexandria in the first (...) century BCE (Philo); and the Christians of the first century CE (the gospel writers and Paul). Starting from the early Pythagoreans, ‘breath’ and ‘breathing’ function to draw analogies between cosmogony and anthropogony – a notion ultimately rejected by Plato in the Timaeus and Aristotle in his cosmological works, but taken up by the Posidonius (perhaps following the early Stoa) and expanded into a rich and challenging corporeal metaphysics. Similarly, the Post-Hellenistic philosopher and biblical exegete Philo of Alexandria, who was deeply influenced by both Platonist and Stoic physics, approaches the cosmogony and anthropogony described in Genesis (1:1–3 and 1:7) through Platonist-Stoic philosophy, in his attempt to provide a philosophically rigorous explanation for why Moses employed certain terms or phrases when writing his book of creation. Finally, the chapter sees a determined shift in the direction of rejecting pneumatic cosmology for a revised pneumatic anthropogony in the writings of the New Testament: by appeal to the ‘Holy Spirit’ or ‘Holy Breath’ (πνεῦμα ἅγιον), early Christians effectively adapted the Stoic metaphysics of ‘breath’, with its notions of divine intelligence and bonding, to the prophetic and ecclesiastical project of building a Christian community conceived of as the ‘body of Christ’. Hence, the spiritual cosmogony of the Pythagoreans, Stoics, and Philo is effectively subordinated to the spiritual anthropogony that facilitates the construction of the Christian kosmopolis, only fully realised in the form of New Jerusalem, the ‘bride’ which, in tandem with the Holy Spirit, calls to the anointed. At the end of the Christian worldview, the kosmos of Greek philosophy is supplanted by the pneumatic kosmopolis. (shrink)

In this paper, we introduce the concepts of Pythagorean fuzzy valued neutrosophic set (PFVNS) and Pythagorean fuzzy valued neutrosophic (PFVNV) constructed by considering Pythagorean fuzzy values (PFVs) instead of numbers for the degrees of the truth, the indeterminacy and the falsity, which is a new extension of intuitionistic fuzzy valued neutrosophic set (IFVNS). By means of PFVNSs, the degrees of the truth, the indeterminacy and the falsity can be given in Pythagorean fuzzy environment and more sensitive (...) evaluations are made by a decision maker in decision making problems compared to IFVNSs. In other words, such sets enable a decision maker to evaluate the degrees of the truth, the indeterminacy and the falsity as PFVs to model the uncertainty in the evaluations. (shrink)

The ability to communicate in a specific language like Chinese typically indicates that the speaker understands the language. A counterexample to this belief is John Searle’s Chinese room experiment. It has been shown in this experiment that in certain circumstances we can communicate with a Chinese speaker without intuitively acknowledging that the Chinese language is understood in the conversation. In the present paper, we aim to present another counterexample showing that, in certain circumstances, we can communicate using a specific language (...) by converting its words to those of our natural language, and understand what is expressed using the language without understanding it. Using a specific conversion process introduced in the present paper, symbols and even sounds of a language like the Chinese language lose their original function and act as a tool to express one’s natural language. To better understand this, imagine the English language has another writing or phonological system in addition to its current writing system. (shrink)

The paper considers a generalization of Peano arithmetic, Hilbert arithmetic as the basis of the world in a Pythagorean manner. Hilbert arithmetic unifies the foundations of mathematics (Peano arithmetic and set theory), foundations of physics (quantum mechanics and information), and philosophical transcendentalism (Husserl’s phenomenology) into a formal theory and mathematical structure literally following Husserl’s tracе of “philosophy as a rigorous science”. In the pathway to that objective, Hilbert arithmetic identifies by itself information related to finite sets and series and (...) quantum information referring to infinite one as both appearing in three “hypostases”: correspondingly, mathematical, physical and ontological, each of which is able to generate a relevant science and area of cognition. Scientific transcendentalism is a falsifiable counterpart of philosophical transcendentalism. The underlying concept of the totality can be interpreted accordingly also mathematically, as consistent completeness, and physically, as the universe defined not empirically or experimentally, but as that ultimate wholeness containing its externality into itself. (shrink)

This study aimed to determine the levels of pre-service teachers' nature of science (NOS) knowledge, assess their pseudo-scientific beliefs, and examine the relationship between aspects of their NOS knowledge and these beliefs. It also aimed to determine whether NOS knowledge and pseudo-scientific beliefs depended on the discipline and gender. A survey method was conducted in this study. Data were collected from 215 pre-service teachers who are being educated in different fields in a state university. Two different five-point Likert (...) scales were applied. Scale 1, which hasthree factors, measured pseudo-scientific beliefs, while Scale 2, which has seven factors, measured NOS knowledge. As a result, preservice teachers' NOS knowledge was found to be inadequate and their pseudoscientific beliefs were excessive. All factors of Scale 1 were positively correlated with each other, and they were correlated with some components of NOS knowledge. Significant differences were found between disciplines in the analysis of the factors of Scale 2; however, no significant differences were found between genders. (shrink)

In his recent "Thomas vs. Thomas: A New Approach to Nagel's Bat Argument", Yujin Nagasawa interprets Thomas Nagel as making a certain argument against physicalism and objects that this argument transgresses a principle, laid down by Thomas Aquinas, according to which inability to perform a pseudo-task does not count against an omnipotence claim. Taking Nagasawa's interpretation of Nagel for granted, I distinguish different kinds of omnipotence claims and different kinds of pseudo-tasks, and on that basis show that Nagasawa's (...) criticism of Nagel is unsuccessful. I also show how his reflections do nonetheless point to a limitation of the approach he means to criticize. (shrink)

The well-known connection between the extant fragments of Philolaus and Plato’s Philebus is examined in its methodological aspect. By drawing on more texts, it is shown that Plato was aware of an explanatory scheme that can be attributed to Pythagoreanism. His attempt to modify it is also outlined, which sets the historical-philosophical perspective.

India dropped its target of 500 GW of renewable energy capacity fossil fuel sources by 2030. Its responsibilities the United Nations Framework Convention Climate Change [UNFCCC],and reducing radiations by one billion tonnes by the end of the decade at the COP26 conference, held in Glasgow in November 2022. Researchers are continually searching for inexhaustible and reasonable energy sources. Solar energy is one of the greenest sources of energy and is also one of the cleanest. The most important factor in using (...) solar energy is the location of the solar power plant. The main objective of this study is to find the best location for a new solar power plant in a specific region called Bundelkhand region of Uttar Pradesh in India. Here we offer an extension of ELECTRE III method as two-phase Pythagorean neutrosophic elimination and choice translating reality PN-ELECTRE-III) method to adapt with fuzzy, ambiguous, unsure, and indeterminate criteria. The Pythagorean neutrosophic numbers [PNNs] used by the group decision support system of PN-ELECTRE III to measure performance of the alternatives. The options are entirely outclassed in the subsequent stage in view of the past stage's evaluations of them. By defining PNN we describe the technique of indifference threshold functions, preference treshold and veto threshold functions, which provide a more stable basis to drop outranking relations. By calculating the concordance credibility, discordance credibility and net credibility degrees of each alternative, the ranking module of the PN-ELECTRE III approach is made simpler. In order to confirm the applicability of the strategy suggested in this paper, the location selection problem for solar plants is finaly solved. (shrink)

Alors que le débat sur le caractère scientifique ou pseudo-scientifique de l’agriculture biodynamique occupe régulièrement le débat public, l’histoire et la philosophie des sciences ne semblent que très peu s’être emparées de ce sujet. La thèse défendue ici est double : tout d’abord, si l’agriculture biodynamique rencontre un relatif succès aujourd’hui, cela tient sans doute au fait que son théoricien, R. Steiner, a été un des premiers à critiquer le paradigme qui domine l’agronomie, ou en tout cas l’agriculture, depuis (...) plus d’un siècle. Cette critique semble d’ailleurs se maintenir dans ses motifs tout au long du XXe siècle, jusqu’à une certaine critique contemporaine de l’agro-industrie et de ses conséquences désastreuses sur l’environnement. Or, et c’est la seconde thèse défendue ici, cette critique semble méconnaître voire occulter la réalité des débats internes qui ont traversé l’agronomie au cours du XXe siècle et qui continuent de l’agiter aujourd’hui : l’agronomie système a ainsi par exemple intégré dans ses objets des éléments de l’agriculture biodynamique. Selon nous, le problème principal est que l’agronomie est souvent abordée selon une approche externaliste, qui doit impérativement être complétée par une approche internaliste afin tout d’abord de distinguer ce qui relève de la science et ce qui relève du mysticisme, et ensuite de saisir toute la richesse historique et épistémologique de l’agronomie. (shrink)

The paper provides to give a minimal contribution about a typical argumentation scheme which called "ad hominem". Especially, this mode of conduct a dialogue and arguing towards an opponent has been revisited by not long past approaches on Argumentation Theory with the aim to re-legitimate it in logical context and re-consider its consequences in terms of validity, consistence and alethic thinking. Ad hominem argument is part of rational discussion and informs audience about the coherence between speaker and his favored thesis.

I provide a characterization of weakly pseudo-rationalizable choice functions---that is, choice functions rationalizable by a set of acyclic relations---in terms of hyper-relations satisfying certain properties. For those hyper-relations Nehring calls extended preference relations, the central characterizing condition is weaker than (hyper-relation) transitivity but stronger than (hyper-relation) acyclicity. Furthermore, the relevant type of hyper-relation can be represented as the intersection of a certain class of its extensions. These results generalize known, analogous results for path independent choice functions.

Mathematics appears to play an explanatory role in science. This, in turn, is thought to pave a way toward mathematical Platonism. A central challenge for mathematical Platonists, however, is to provide an account of how mathematical explanations work. I propose a property-based account: physical systems possess mathematical properties, which either guarantee the presence of other mathematical properties and, by extension, the physical states that possess them; or rule out other mathematical properties, and their associated physical states. I explain why Platonists (...) should accept that physical systems have mathematical properties, and why a property based account is better than existing accounts of mathematical explanation. I close by considering whether nominalists can accept the view I propose here. I argue that they cannot. (shrink)

The Doppelgänger or Double presents literature as the “double” of philosophy. There are historical reasons for this. The genesis of the Doppelgänger is literature’s response to the philosophical focus on subjectivity. The Doppelgänger was coined by the German author Jean Paul in 1796 as a critique of Idealism’s assertion of subjective autonomy, individuality and human agency. This critique prefigures post-War extrapolations of the subject as decentred. From this perspective, the Doppelgänger has a “family resemblance” to current conceptualizations of (...) subjectivity. It becomes the emblematic subject of modernity. This is the first significant study on the Doppelgänger’s influence on philosophical thought. The Doppelgänger emerges as a hidden and unexplored element both in conceptions of subjectivity and in philosophy’s relation to literature. Vardoulakis demonstrates this by employing the Doppelgänger to read literature philosophically and to read philosophy as literature. The Doppelgänger then appears instrumental in the self-conception of both literature and philosophy. (shrink)

ABSTRACT In order to explore what it means to pursue philosophical investigations for theological reasons, this paper argues that Ludwig Wittgenstein continues and corrects Pseudo-Denys’ project in The Divine Names. I first argue that The Divine Names should be interpreted as attempting to render human thought transparent to the divine by relativizing our concepts. The success of this project is compromised because the concept of ‘unity’ is not relativized. I then develop the claim that Wittgenstein does relativize unity in (...) a similar way and for similar religious reasons to Pseudo-Denys. As such, he can be read as continuing and correcting the Pseudo-Dionysian project. I conclude by reflecting on several of this argument’s implications for the relationship between philosophy and Christian systematic theology. (shrink)

This contribution aims to explore the historical predecessors of the Five Percenter model of self-realization, as popularized by Hip Hop artists such as Supreme Team, Rakim Allah, Brand Nubian, Wu-Tang Clan, or Sunz of Man. As compared to frequent considerations of the phenomenon as a creative mythological background for a socio-political struggle, Five Percenter teachings shall be discussed as contemporary interpretations of historical models of self-realization in various philosophical, religious, and esoteric systems. By putting the coded system of the tenfold (...) Supreme Mathematics as one of its core teachings in context with the Pythagorean Tetractys, an arrangement of ten points in four lines, the commonalities between the sequence and concepts attributed to the respective numbers will be demonstrated. (shrink)

Argues that John of Salisbury's Institutio Traiani is a pseudo-classical forgery. 34: "In my opinion this framework within which John presents his opinions is a pseudo-classical invention of his own, and an invention which in its combination of clerical and classical features is characteristic of the author.".

There is a long tradition in philosophy and literary theory defending the view that engagement with literature promotes readers’ empathy. Until the last century, few of the empirical claims adduced in that tradition were investigated experimentally. Recent work in psychology and neuropsychology has now shed new light on the interplay of empathy and literature. This article surveys the experimental findings, addressing three central questions: What is it to read empathically? Does reading make us more empathic? What characteristics of (...) literature, if any, affect readers’ empathy? While experimental studies have delivered no conclusive answers to these questions, it has exposed their psychological complexity and constructed a more nuanced picture of the diverse ways in which literature interacts with our empathic capacities. (shrink)

The main objective of this paper is to present a reinterpretation of Karl Popper’'s position on the methodological and sociopolitical views of Karl Marx. In spite of the weaknesses of the Popper’'s critique of the achievements of Marx, special attention will be focused on the explanation of contradictions within the epistemological position of the former. This will be of great importance in the context of the analysis of Marx’s historicism, and will also help undermine the coherence view of the founder (...) of falsi
cationism. Additionally, this newly developed perspective will serve as a starting point for evaluation of Marx’s intellectual output, as well as conceptions that refer to him. (shrink)

Many great authors claim that reading literature can expand your phenomenal imagination and allow you to imagine experiences you have never had. How is this possible? Your phenomenal imagination is constrained by your phenomenal concepts, which are in turn constrained by the phenomenology of your own actual past experiences. Literature could expand your phenomenal imagination, then, by giving you new phenomenal concepts. This paper explains how this can happen. Literature can direct your attention to previously unnoticed phenomenal (...) properties of your own past experiences, as brought to mind by involuntary memory. This process gives you the opportunity to notice those phenomenal properties for the first time, and so also to form phenomenal concepts of those properties. Forming a new phenomenal concept strictly expands the range of your phenomenal imagination. It gives you the capacity to imagine more than you could have before, including certain specific kinds of experience that you yourself have never enjoyed firsthand. Literature’s capacity to expand your phenomenal imagination in this way is central to its social, moral, and epistemic value. (shrink)

Neutrosophic set is a new mathematical tool for handling problems involving imprecise, indetermi nacy and inconsistent data. Pseudo-BCI algebra is a kind of non-classical logic algebra in close connection with various non-commutative fuzzy logics. Recently, we applied neutrosophic set theory to pseudo-BCI al gebras. In this paper, we study neutrosophic filters in pseudo-BCI algebras. The concepts of neutrosophic regular filter, neutrosophic closed filter and fuzzy regular filter in pseudo-BCI algebras are introduced, and some basic properties are (...) discussed. Moreover, the relationships among neutrosophic regular filter, fuzzy filters and anti-grouped neutrosophic filters are prese nted, and the results are proved: a neutrosophic filter (fuzzy filter) is a neutrosophic regular filter (fuzzy regular filter), if and only if it is both a neutrosophic closed filter (fuzzy closed filter) and an anti-grouped neutrosophic filter (fuzzy anti-grouped filter). (shrink)