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)

Philologus, founded in 1846, is one of the oldest and most respected periodicals in the field of Classics. It publishes articles on Greek and Latin literature, historiography, philosophy, history of religion, linguistics, reception, and the history of scholarship. The journal aims to contribute to our understanding of Greco-Roman culture and its lasting influence on European civilization. The journal Philologus, conceived as a forum for discussion among different methodological approaches to the study of ancient texts and their reception, publishes original scholarly (...) contributions with a strong international focus. Publications languages are: German, English, Italian, French. As of 2014 the publication of supplementary volumes will be resumed. The series Philologus. Supplemente / Philologus. Supplementary Volumes will publish monographs and edited volumes pertaining to all aspects of the study of ancient literature and its reception, with a special focus on topics concerning literary theory, philosophy and the history of scholarship from an interdisciplinary perspective. (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)

This article considers the issue of changes in the understanding of symbols as an integral part of spiritual life in Neoplatonic philosophy. It seems that ancient Neoplatonic philosophers were the first who clearly realized the importance of symbols to spiritual life. However, it happened due to the influence of the mystical Chaldean and Egyptian thought transferred to philosophical investigation by the Chaldean oracles and Corpus hermeticum. The late Neoplatonic thought of Iamblichus and Eastern Neoplatonic schools used symbols and rituals as (...) integral parts of philosophical investigation, understood as having a mystical goal. Especially mathematical symbols played a significant role, because they were used in the most advanced theurgical rituals. This analysis of the pagan Neoplatonic philosophy permits us to show properly the thought of Pseudo- Dionysius the Areopagite, who creatively transformed the teaching of his pagan predecessors, by incorporating ancient Neoplatonic tradition into Christian theology. Pseudo-Dionysius excludes liturgical symbols from the order of the cosmos and transfers them to the plane of Salvation grounded in Biblical Revelation. Only true symbols are used in the liturgy of the Church, and thus mathematical symbols are no longer needed in the ascent of the soul to unity with God. The third part analyzes the meaning of symbolism in the thought of Nicolas of Cusa. Thanks to the rediscovery of ancient pagan Neoplatonism and Pythagorean thought, Cusanus also brings new life to the mystical meaning of mathematics. Mathematical symbols once again become an im- portant part of the mystical ascent of the soul, but this time without their ritual context. (shrink)

This paper, looking over the life and the texts of the greek philosophers and analyzing the Pythagorean harmony, the two stories of Thales, the outstanding personality of Xenophanes, the humorous sense of Democritus and the Socratic irony, shows that philosophy in the beginning was understood not like an abstract reflection, but like a joyful search of the excellence in the human life.

This is a comprehensive, authoritative and innovative account of Pythagoras and Pythagoreanism, one of the most enigmatic and influential philosophies in the West. In twenty-one chapters covering a timespan from the sixth century BC to the seventeenth century AD, leading scholars construct a number of different images of Pythagoras and his community, assessing current scholarship and offering new answers to central problems. Chapters are devoted to the early Pythagoreans, and the full breadth of Pythagorean thought is explored including politics, (...) religion, music theory, science, mathematics and magic. Separate chapters consider Pythagoreanism in Plato, Aristotle, the Peripatetics and the later Academic tradition, while others describe Pythagoreanism in the historical tradition, in Rome and in the pseudo-Pythagorean writings. The three great lives of Pythagoras by Diogenes Laertius, Porphyry and Iamblichus are also discussed in detail, as is the significance of Pythagoras for the Middle Ages and Renaissance. (shrink)

This volume presents the first Italian translation with commentary of the Doric Pseudo-Pythagorean texts, which are ascribed to Archytas and Brontinus and deal with metaphysical, logical, and epistemological questions. These texts probably date from the 1st century BCE and are the product of a re-emerging dogmatic interpretation of Plato's dialogues.

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 _Aristotle’s Empiricism_, Jean De Groot argues that an important part of Aristotle’s natural philosophy has remained largely unexplored and shows that much of Aristotle’s analysis of natural movement is influenced by the logic and concepts of mathematical mechanics that emerged from late Pythagorean thought. De Groot draws upon the pseudo-Aristotelian_ Physical Problems_ XVI to reconstruct the context of mechanics in Aristotle’s time and to trace the development of kinematic thinking from Archytas to the Aristotelian _Mechanics_. She shows (...) the influence of kinematic thinking on Aristotle’s concept of power or potentiality, which she sees as having a physicalistic meaning originating in the problem of movement. De Groot identifies the source of early mechanical knowledge in kinesthetic awareness of mechanical advantage, showing the relation of Aristotle’s empiricism to more ancient experience. The book sheds light on the classical Greek understanding of imitation and device, as it questions both the claim that Aristotle’s natural philosophy codifies opinions held by convention and the view that the cogency of his scientific ideas depends on metaphysics. (shrink)

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)

En 1965, H. Thesleff offrait le premier recueil des textes pseudopythagoriciens parvenus (The Pythagorean texts of the Hellenistic period, Abo Akademi, Abo). Certains d’entre eux ont depuis fait l’objet d’études spécifiques : le traité Sur la nature du monde et de l’âme du Pseudo-Timée de Locres par M. Baltes (Leiden, 1972), le traité Sur les catégories du Pseudo-Archytas par T. A. Szlezák (Berlin / New York, 1972) et les traités éthiques attribués à Archytas, Métopos, Théagès et Euriphamos (...) p... (shrink)

Ancient Greek music was purely or predominantly melodic; and in such music subtleties of intonation count for much. If our sources of information about the intervals used in Greek music are not always easy to interpret, they are at any rate fairly voluminous. On the one hand we have Aristoxenus, by whom musical intervals were regarded spatially and combined and subdivided by the processes of addition and subtraction; for him the octave consisted of six tones, and the tone was exactly (...) divisible into fractions such as the half and quarter, so that the fourth was equal to two tones and a half, the fifth to three tones and a half, and so on. On the other hand we have preserved for us in Ptolemy's Harmonics the computations of a number of mathematicians, who realized correctly that intervals could only be expressed as ratios , that the octave was less than the sum of six whole tones and that this tone could not be divided into equal parts. These authorities are Archytas, the Pythagorean of the early fourth century, Eratosthenes , Didymus and Ptolemy himself . To these we must add the scale of Plato's Timaeus and, closely related to it, the computations of the pseudo-Philolaus and of Boethius himself . Aristoxenus is less easy to understand than the mathematicians because of the unscientific nature of his postulates. His importance, however, is very great, not only from his comparatively early date but because he claims to champion the direct musical consciousness against the scientific approach of some of his predecessors and contemporaries. (shrink)

Pythagoreans dominated the political scene in southern Italy for nearly a century in the late 6th to 5th century BC. What was the secret of their political success and can their political, social and economic policies be assessed in the customary terms with which historians try to analyse ancient societies? I argue that they cannot, and that the Pythagorean approach to politics was sui generis, and successful because it was based on ideas, not force or popular demagogy.

We develop and test a model of pseudo-transformational leadership. Pseudo-transformational leadership is manifested by a particular combination of transformational leadership behaviors, and is differentiated from both transformational leadership and laissez-faire -leadership. Survey data from senior managers show differential outcomes of transformational, pseudo-transformational, and laissez-faire leadership. Possible extensions of the theoretical model and directions for future research are offered.

In Pythagorean Women, classical scholar Sarah B. Pomeroy discusses the groundbreaking principles that Pythagoras established for family life in Archaic Greece, such as constituting a single standard of sexual conduct for women and men. Among the Pythagoreans, women played an important role and participated actively in the philosophical life. While Pythagoras encouraged women to be submissive to men, his reasoning was based on the desire to preserve harmony in the home. -/- Pythagorean Women provides English translations of all (...) the earliest extant examples of literary Greek prose by Neopythagorean women, shedding light on their attitudes about marriage, the home, music, and the cosmos. Pomeroy sets the Pythagorean and Neopythagorean women vividly in their historical, ecological, and intellectual contexts, illustrated with original photographs of sites and artifacts known to these women. (shrink)

The Pythagorean women are a group of female philosophers who were followers of Pythagoras and are credited with authoring a series of letters and treatises. In both stages of the history of Pythagoreanism – namely, the fifth-century Pythagorean societies and the Hellenistic Pythagorean writings – the Pythagorean woman is viewed as an intellectual, a thinker, a teacher, and a philosopher. The purpose of this Element is to answer the question: what kind of philosopher is the (...) class='Hi'>Pythagorean woman? The traditional picture of the Pythagorean female sage is that of an expert of the household. The author argues that the available evidence is more complex and conveys the idea of the Pythagorean woman as both an expert on the female sphere and a well-rounded thinker philosophising about the principles of the cosmos, human society, the immortality of the soul, numbers, and harmonics. (shrink)

: Some of the great physicists' belief in the existence of a connection between the aesthetical features of a theory (such as beauty and simplicity) and its truth is still one of the most intriguing issues in the aesthetics of science. In this paper I explore the philosophical credibility of a version of this thesis, focusing on the connection between the mathematical beauty and simplicity of a theory and its truth. I discuss a heuristic interpretation of this thesis, attempting to (...) clarify where the appeal of this Pythagorean view comes from and what are the arguments favoring its acceptance or rejection. Along the way, I sketch the historical context in which this heuristic interpretation gained credibility (the quantum crisis in physics in the 1920s), as well as the more general implications of this thesis for physicists' metaphysical outlook. (shrink)

In both ancient tradition and modern research Pythagoreanism has been understood as a religious sect or as a philosophical and scientific community. Numerous attempts have been made to reconcile these pictures as well as to analyze them separately. The most recent scholarship compartmentalizes different facets of Pythagorean knowledge, but this offers no context for exploring their origins, development, and interdependence. This collection aims to reverse this trend, addressing connections between the different fields of Pythagorean knowledge, such as eschatology, (...) metempsychosis, metaphysics, epistemology, arithmology and numerology, music, dietetics and medicine as well as politics. In particular, the contributions discuss how the Pythagorean way of life related to more doctrinal aspects of knowledge, such as Pythagorean religion and science. The volume explores the effects of this interdependence between different kinds of knowledge both within the Pythagorean corpus and in its later reception. Chapters cover historical periods from the Archaic Period (6th century BC) to Neoplatonism, Early Christianity, the European and Arabic Middle Ages, and the Renaissance through to the Early Modern Period (17th century AD). (shrink)

Reconstruction of the versions of Aristoxenos and Dikaiarchos.--The sources of Dikaiarchos and Aristoxenos and the reliability of their accounts. --Reconstruction of Timaios' version and the reliability of his accounts.--The chronological questions and the numismatic evidence.--The character of the "Pythagorean rule" in southern Italy.--Appendix.

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)

According to some cosmologists, the big bang cosmogony and even the (now largely defunct) steady-state theory pose a scientifically insoluble problem of matter-energy creation. But I argue that the genuine problem of the origin of matter-energy or of the universe has been fallaciously transmuted into the pseudo-problem of creation by an external cause. A fortiori, it emerges that the initial "true" and "false" vacuum states of quantum cosmology do not vindicate biblical divine creation ex nihilo at all.

In ancient tradition, Pythagoras emerges as a wise teacher, an outstanding mathematician, an influential politician, and as a religious and ethical reformer. This volume offers a comprehensive study of Pythagoras, Pythagoreanism, and the early Pythagoreans through an analysis of the many representations of the individual and his followers.

Pythagorean Women Philosophers argues for a rewriting of Greek philosophical history so as to include female intellectuals. Dutsch presents testimonies regarding the role of women in the Pythagorean school as demonstrating their active contribution to the philosophical tradition.

The problem of the relationship between mathematics and objective reality, which arose in early antiquity, is still a subject of heated discussion. The discussions are mainly about the question that probably was posed most clearly by Immanuel Kant in his Critique of Pure Reason: "How do subjective conditions of thought have objective validity, that is, how do they become conditions of the possibility of all knowledge of objects?" Is it because they are themselves elements of objective reality, or because they (...) are contained in thought a priori, before and independently of experience, or, finally, because they are subjective images of corresponding facets and aspects of objective reality? (shrink)

The obstacle to more objective knowledge of early Pythagoreanism is the ideological conflict over the proper mission of historiography. Not only the confusing evidence, but also the different investigative procedures and theories of history employed, make solving the Pythagorean problem difficult. I analyze the historiographic methodologies of some modern historians of Pythagoreanism in respect to the kinds of historical explanation they provide. Immediately ideological controversy arises between idealist and materialist historians. ;My critical evaluation proceeds from two theses. The content (...) of ideas reflects their social referents. Consequently, one must identify the class interests of early Pythagoreans. Writing history is a contemporary undertaking by which historians reflect their own social interests. Therefore, historiographic methodology continually must be objectified to overcome the subjectivism of historical relativism. ;I review the reconstructions of six historians. John Burnet, an empiricist, held that the Greeks entirely broke from their religious past to develop philosophy. F. M. Cornford, a Durkheimian, used anthropology to reveal philosophy's totemic content. J. E. Raven is a philologist; he maintaned that ancient philosophy was the Eleatic-Pythagorean debate. W. K. C. Guthrie, an eclectic, held that science served Pythagorean religious interests. These idealist historians attributed the Greek achievement to absolutized temperaments or racial factors; the development of ideas is not mediated by practical necessity. George Thomson and Alban Winspear are historical materialists. They explained ancient philosophy by showing the class interests of philosophers in a mercantile economy based on slave labor. ;After introducing the Pythagorean problem, I present, by chapter, first an exposition of each historian's account of the causes of Greek philosophy and then his exposition of early Pythagoreanism. My analyses follow each section. In the first part of the final chapter I discuss each historian in the context of the ideological controversy. In the second part I present a general outline of procedure for scientific historiography. (shrink)

This study attempts to answer the question of the origins of the non-biblical features of the Essenes' way of life. It is clear that their project was founded in biblical and Jewish realities. Where did those elements come from that appear not to have been derived from these sources? That they have their origins in Greek, and specifically Pythagorean, customs is an idea that recurs regularly in the history of scholarship and has had some notable supporters in the 19th (...) and first half of the 20th centuries, including E Zeller, E Schuer, I Levy, F C Cumont and M J Lagrange. Recent scholars seem more reluctant to accept such views. The inquiry will take the reader through the available sources, then a series of comparative studies with possible parallels in Greece and elsewhere, to see whether and in what terms the question of Pythagorean influences on Essenism can be answered. (shrink)

Pseudo-Concrete Ideals of a Good Life What has happened in the late and concluding stages of postmodern culture is that concrete ideas of a good life have been reduced to pseudo-concrete ideals. With the aid of simulacra, the experience of everyday life is turning into a show, into narcissistic emptiness and single bodily pleasures.

At Metaphysics A 5 986a22-b2, Aristotle refers to a Pythagorean table, with two columns of paired opposites. I argue that 1) although Burkert and Zhmud have argued otherwise, there is sufficient textual evidence to indicate that the table, or one much like it, is indeed of Pythagorean origin; 2) research in structural anthropology indicates that the tables are a formalization of arrays of “symbolic classification” which express a pre-scientific world view with social and ethical implications, according to which (...) the presence of a principle on one column of the table will carry with it another principle within the same column; 3) a close analysis of Aristotle's arguments shows that he thought that the table expresses real causal relationships; and 4) Aristotle faults the table of opposites with positing its principles as having universal application and with not distinguishing between those principles that are causally prior and those that are posterior. Aristotle's account of scientific explanation and his own explanations that he developed in accordance with this account are in part the result of his critical encounter with this prescientific Pythagorean table. (shrink)

This anthology, the largest collection of Pythagorean writings ever to appear in English, contains the four ancient biographies of Pythagoras and over 25 Pythagorean and Neopythagorean writings from the Classical and Hellenistic periods. The material of this book is indispensable for anyone who wishes to understand the real spiritual roots of Western civilization.

Pseudo‐mechanistic explanations in psychology and cognitive neuroscienceThis paper focuses on the level of systems/cognitive neuroscience. It argues that the great majority of explanations in psychology and cognitive neuroscience is “pseudo‐mechanistic.” On the basis of various case studies, Hommel argues that cognitive neuroscience should move beyond what he calls an “Aristotelian phase” to become a mature “Galilean” science seeking to discover actual mechanisms of cognitive phenomena.

This paper explores the influence of the fifth-century Christian Neoplatonist Pseudo-Dionysius the Areopagite (Denys) on the twentieth-century philosopher of science Paul Feyerabend. I argue that the later Feyerabend took from Denys a metaphysical claim—the ‘doctrine of ineffability’—intended to support epistemic pluralism. The paper has five parts. Part one introduces Denys and Feyerabend’s common epistemological concern to deny the possibility of human knowledge of ultimate reality. Part two examines Denys’ arguments for the ‘ineffability’ of God as presented in On the (...) Divine Names . Part three then explores how Feyerabend imported Denys’ account of divine ineffability into his own metaphysics to provide a novel argument for epistemic pluralism. Part four explains the significance of an appreciation of Dionyius’ influence for our understanding of Feyerabend. I conclude that Denys was a significant and neglected influence upon the later Feyerabend. (shrink)

This commentary provides valuable insight into the basic tenets of an unknown sect from the formative years of Hellenistic Pythagoreanism, a movement which had a major impact on the morality and philosophy of the Greco-Roman world.

This paper argues that Hindi incorporation is, in fact, pseudoincorporation, involving noun phrases rather than nouns. Furthermore, it shows that there is no requirement that the incorporated nominal form a morphological or even a syntactic unit with the verb. Such loosely aligned nominals can nevertheless be identified as incorporation on the basis of semantic intuitions having to do with number interpretation, anaphora, and certain properties typically associated with lexical processes. Contrary to standard assumptions, it is argued that the targets of (...) pseduo-incorporation are specified for number. Singular incorporated nominals in Hindi are shown to be semantically singular, with number neutrality arising as a consequence of interaction with aspectual specification. Taking aspectual information into account is also shown to have interesting implications for current approaches to the semantics of incorporation, one in which the incorporated nominal introduces a discourse referent, and one in which it functions as a predicate modifier. A closer look at the effect of aspect on anaphora, for example, does not unequivocally support the predicate modification view of pseudoincorporation. The paper also explores the cross-linguistic applicability of the claims made on the basis of Hindi. Most notably, a distinction between Hungarian verbs with respect to incorporation of bare singulars provides striking confirmation of the claims that number morphology is semantically visible in pseudo-incorporation. It also discusses the restrictions on the productivity of pseudo-incorporation in light of the findings for Hindi and Hungarian. (shrink)

In coal mining industry, the running state of mine ventilators plays an extremely significant role for the safe and reliable operation of various industrial productions. To guarantee the better reliability, safety, and economy of mine ventilators, in view of early detection and effective fault diagnosis of mechanical faults which could prevent unscheduled downtime and minimize maintenance fees, it is imperative to construct some viable mathematical models for mine ventilator fault diagnosis. In this article, we plan to establish a data-based mine (...) ventilator fault diagnosis method to handle situations where engineers are absent or they are incapable of coming to a conclusion from multisource data. In the process of building the mine ventilator fault diagnosis model, considering that probabilistic rough sets could reduce the errors triggered by incompleteness, inconsistency, and inaccuracy without needing any additional assumptions and Pythagorean fuzzy multigranulation rough sets over the two universes’ model could effectively handle data representation, fusion, and analysis issues, we generalize the existing PF MGRSs over the two universes’ model to the PRS setting, as well as to further establish a novel model named Pythagorean fuzzy multigranulation probabilistic rough sets over two universes. In the granular computing paradigm, three types of PF MG-PRSs over two universes based on the risk attitude of engineers are proposed at first. Afterwards, several basic propositions of the newly proposed model are explored. Moreover, a PF multigranulation probabilistic model for mine ventilator fault diagnosis based on PF MG-PRSs over two universes is investigated. At last, a real-world case study of dealing with a mine ventilator fault diagnosis problem is given to illustrate the practicality of the presented model, and a validity test, a sensitivity analysis, and a comparison analysis are further explored to demonstrate the effectiveness of the presented model. (shrink)

Allusions to a cosmogony contained in a Vedic hymn present striking analogies to a cosmogony attributed to the Pythagoreans by Aristotle, Simplicius and Stobaeus. The aim of the paper is to evaluate the extent to which they are similar and to which their differences respond to different cultural premises.