Mathematics and aesthetics are closely intertwined. Not only mathematical concepts, relationships and theorems can be aesthetically pleasing, but we also often find harmony between their results and the patterns of the world around us, and we like that. Yet, apart from rare exceptions, the beauty of mathematics, particularly in education, is mostly unrecognized: this science rarely meets the favour of students. Vedic mathematics is an approach which encapsulates the enjoyment and power of this knowledge, not only (...) in the sphere of thought process, but also in its practical utility. It highlights and develops the aesthetic dimension of learning in a very immediate sense. The aim of this article is to introduce the method – what it is and how it works – to give comparative examples of techniques and their efficacy, and to emphasize the aesthetic value it conveys. (shrink)

Mathematics has, not only a long history in India like in any other ancient civilization, but it also carries a very high value in the present-day India, basically because of its importance in engineering education. India has made some important contributions to mathematics in the last 150 years. Yet, such a description hides the fact that ‘India’ here refers to a tiny minority of Hindu dominant caste middle-class men (and a couple of women from the same socio-cultural and (...) economic background). Though precolonial India had indigenous traditions of education, the caste and gender to which one belonged determined what kind of education one could get. It is only during the colonial rule that access to education was made independent of one’s caste and it is only as late as 2009 that India made the right to education a fundamental right, making free and compulsory education available for all up to the age of fourteen. (shrink)

Several studies highlight the importance of the order of different instructional methods when designing learning environments. Correct but also erroneous worked examples are frequently used methods to foster students’ learning performance, especially in problem-solving. However, so far no study examined how the order of these example types affects learning. While the expertise reversal effect would suggest presenting correct examples first, the productive failure approach hypothesizes the reversed order to be learning-facilitating. In addition, congruency of subsequent exemplified problems was tested as (...) a moderator of the effect of order on learning. For example, with arithmetic tasks, congruent problems target exactly the same calculation while incongruent problems refer to different calculations. Following cascade theory, a model of cognitive skill acquisition, presenting correct examples first should be more effective when the subsequent exemplified problems are different. To test the hypotheses, 83 university students were assigned to one of the four conditions in a 2 × 2 between-subject design. Learners navigated through a slideshow on the topic of Vedic mathematics consisting of explicit instruction, worked examples differing in terms of the experimental condition, and transfer problems. Although no main or interaction effects were found regarding students’ learning performance, mediational analysis offered support for the expertise reversal effect, as it indicated that there is a significant indirect effect of order via mental load on learning. Presenting correct examples first and erroneous examples second resulted in a lower mental load, which in turn was associated with better learning performance. In contrast, presenting erroneous examples first and correct examples second resulted in a more accurate self-assessment of learning performance. These findings offer first insights into the question of how the presentation order of different example types impacts learning and provide practical recommendations for the design of educational media. Results are discussed in light of the ongoing debate regarding the question if less guided instructional methods should precede or succeed more guided methods. (shrink)

The Mīmā ṃ sā school of Indian philosophy elaborated complex ways of interpreting the prescriptive portions of the Vedic sacred texts. The present article is the result of the collaboration of a group of scholars of logic, computer science, European philosophy and Indian philosophy and aims at the individuation and analysis of the deontic system which is applied but never explicitly discussed in Mīmā ṃ sā texts. The article outlines the basic distinction between three sorts of principles —hermeneutic, linguistic (...) and deontic. It proposes a mathematical formalization of the deontic principles and uses it to discuss a well-known example of seemingly conflicting statements, namely the prescription to undertake the malefic Śyena sacrifice and the prohibition to perform any harm. (shrink)

Consciousness-based education and Maharishi Vedic science -- Consciousness-based education and education -- Consciousness-based education and physiology and health -- Consciousness-based education and physics -- Consciousness-based education and mathematics -- Consciousness-based education and literature -- Consciousness-based education and art -- Consciousness-based education and management -- Consciousness-based education and government -- Consciousness-based education and computer science -- Consciousness-based education and sustainability -- Consciousness-based education and world peace.

Once the Luwian hieroglyphics for God “” and Gate “” were discovered at Göbekli Tepe, this author was able to directly link the site’s carved pillars and pillar enclosures to the Abrahamic/Mosaic “Word of God”,. Archaeologists and anthropologists have long viewed the Bible as mankind’s best guide to prehistoric religion, however, archaeologist Klaus Schmidt had no reason to believe that the site he spent years excavating at Göbekli Tepe might be the legendary “Pillars of Enoch”, carved by the first Biblical (...) holy man and scribe. To make this connection, the author first had to decipher Judaism’s Razah D’Oraytah (Secret of Knowledge) from the Sefer Yetzirah (Book of Creation). The Book of Creation is the only text to explain the Secret of Knowledge, and the only text attributed to the prophet Abraham within the rabbinical community. The Zohar, Judaism’s most accessible Kabbalistic text, admits that it lacks knowledge of “deep and hidden things which issue from God’s thought and are taken up by the Voice [of God] which are not disclosed till the Word [] reveals them”. Abrahamic/Mosaic “Word of God” encrypts the mathematics of sound that emanates from God’s “Voice” in terms of ancient string theory. Just as modern string theory defines a Theory of Everything (ToE) within theoretical physics, so too does this ancient string theory define the Theory of Everything that Abraham named the “Living God”. The author’s previous paper ties Jewish sources to Göbekli Tepe, while the current paper applies this sonic “God Table” to the textual exegesis and hermeneutics structuring all religious creation allegories, including the writings of Sumer, Assyria, Babylonia, Vedic India, pre-Dynastic Egypt, Ugarit, and Israel. This paper will apply Göbekli Tepe’s structural template to archaeology’s oldest legible cuneiform tablets, including the Kesh Temple Hymn, Sumerian King List, and the Akkadian Ark Tablet. It will also be demonstrated that Göbekli Tepe holds the key to the Rig Veda, Hinduism’s oldest text, and defines the essence of Plato’s metaphysics. (shrink)

J. N. (Jitendra Nath) Mohanty (1928–2023). -/- Professor J. N. Mohanty has characterized his life and philosophy as being both “inside” and “outside” East and West, i.e., inside and outside traditions of India and those of the West, living in both India and United States: geographically, culturally, and philosophically; while also traveling the world: Melbourne to Moscow. Most of his academic time was spent teaching at the University of Oklahoma, The New School Graduate Faculty, and finally Temple University. Yet his (...) preeminent work in Husserlian phenomenology developed alongside his eminent work in Indian philosophy: describing his interests as “a fusion of disparate horizons.” -/- J. N. Mohanty was born September 26, 1928, in Cuttack (Odisha, East India). After graduating from high school, he went on to study both Indian and Western philosophy in Calcutta, earning bachelor’s and master’s degrees. There he read Whitehead and Kant’s First Critique; although he wanted to include mathematics in his curriculum, he was led instead to include Indian philosophy and Sanskrit. On the shelves of his teacher, Ras Vihar Das, he came upon a copy of the English translation (Ideas I, 1931) of Edmund Husserl’s classic Ideen I (1913), which presented Husserl’s ground-breaking conception of phenomenology. In 1952–1954 he left India for the first time, reaching Göttingen to study mathematics and philosophy, which earned him a doctorate in mathematics and “philosophy of mathematical sciences” (in his own words). In Göttingen, Mohanty found the powerful mathematical world that Husserl himself had earlier interacted with, where several Husserl students had formed the Göttingen school of phenomenology. During these years Mohanty studied primarily mathematics, alongside Kant and also Vedic Sanskrit. From his friend Günter Patzig, interpreter of Aristotle and Frege, Mohanty was drawn to Frege in relation to mathematical logic. He attended lectures of Heidegger, intrigued by his ontological thinking. Yet, despite the Husserlian legacy, Mohanty was completely self-taught in his studies of Husserl (as he has reported). With a doctorate in mathematics, and ideas from Kant and Frege in his philosophical background, Mohanty set about crafting his own conception of philosophy grounded in phenomenology, drawing on Husserl’s extensive work, critically sifting through Husserl’s texts and their emerging concepts of intentionality, meaning, subject, intersubjectivity, and world. In between he wrote his first book-length study: on phenomenological insights in Nicolai Hartmann and A. N. Whitehead (1958). -/- Over many decades Mohanty formulated and argued, in analytical detail, for a conception of phenomenology and its place in philosophy, later presented in a clear and concise book titled Transcendental Phenomenology: An Analytic Account (1989). Over these very decades the same scholar explored classical and recent Indian philosophy, thinking through kindred ideas of consciousness, self, and knowledge drawn from the Indian philosophical contexts. While writing on Nyāya theory of truth, he also pondered whether the world and finite individual are illusory or real, and whether Marx, Arendt, Gandhi (whom he heard speak in Calcutta), or Vinoba Bhave (with whom he marched across India for the land-grant movement) could best navigate post-Independent India’s social and svarāj or self-rule reforms. The two Mohantys, thinking through a vision of self and world, turned out to be “non-different” or “non-dual” as they each practiced critical phenomenology from both inside and outside the respective philosophical and cultural traditions. Numerous students, fellows, and colleagues or collaborators have benefited immensely from this infusion and unified approach to diversity in philosophical thought. In the 2000s, moving into retirement, Mohanty wrote two long books devoted to his understanding of Husserl and phenomenology and the calling of philosophy itself. This two-volume study shows Mohanty himself thinking through Husserl, critically, in The Philosophy of Edmund Husserl: A Historical Introduction (2008), and Edmund Husserl’s Freiburg Years: 1916–1938. As Mohanty worked on Husserl, he carefully indicated where he agreed and where he rejected or changed ideas, all part of his practice in phenomenology of “description and interpretation.” It was the same pattern he used in addressing the thought of Husserl vis-à-vis Kant or Frege or even Quine. -/- As Mohanty developed his understanding of phenomenology over the years, he wrote books on theory of meaning and the concept of intentionality, developing a model of ideal meaning and its foundation in intentionality, drawing on Husserl’s results. He followed these with the book Husserl and Frege (1982), linking the thought of those foundational figures for the “continental” and “analytic” traditions, respectively, in twentieth-century Western philosophy. Over his long career Mohanty addressed both traditions in his clear and accessible writing style. While developing his views on phenomenology, Mohanty regularly looked to “Husserl and his others,” evaluating views in Heidegger, Sartre, Merleau-Ponty, Ricoeur, and then Derrida and others in the wake of Husserl. With his background in Kant, Mohanty also looked toward Heidegger and Hegel in relation to Husserl’s later work in the Crisis (1935–38). Similarly, he looked to contemporary analytic philosophers, adjudicating his own, oft-wise Husserlian views in relation to Frege, Nagel, and others. Amid his active scholarly career, Mohanty co-founded the journal Husserl Studies, and was editorial advisor to Philosophy & Phenomenological Research, Philosophy East & West, Journal of Indian Philosophy, Sophia, among others. -/- Yet all this while Mohanty was also thinking and writing about Indian philosophy and its relation to phenomenology. In his own retrospective, Indian philosophy is “the permanent background” of his Husserlian thinking, while Kant is the recurrent Western background of his Husserlian phenomenology. Mohanty’s form of “transcendental phenomenology” evolved, in his own perspective, against the background of his studies of Navya-Nyāya on logic and Vedānta on consciousness, in Indian philosophy, and against the background of Kant’s First Critique on the transcendental, in Western philosophy. Accordingly, Mohanty’s study of logical form and of the intentionality of consciousness seeks a fusion of East and West in the conception of transcendental phenomenology. (Cf. Mohanty’s apt response to critics in The Empirical and the Transcendental (2000).) Even in the context of North American Husserl scholarship, Mohanty has exercised an earnest fusion of East and West. For the so-called East Coast and West Coast interpretations of Husserl’s crucial notion of noema both find a sympathetic spirit in J. N. Mohanty’s careful and nuanced interpretation of Husserlian transcendental phenomenology. With Mohanty the two faces of the noema are the logical (Fregean) and the phenomenal (Kantian), and these views of intentional structure join in consciousness—in a way resonant with Indian thought. -/- - David Woodruff Smith (UC Irvine) and Purushottama Bilimoria (SFSU, San Francisco; University of Melbourne) -/- For photo of Prof Mohanty visit APA online memorial_minutes2023 Courtesy of APA Memorial Minutes (& Proceedings) 2023 . (shrink)

Kurt Gdel was the most outstanding logician of the 20th century and a giant in the field. This book is part of a five volume set that makes available all of Gdel's writings. The first three volumes, already published, consist of the papers and essays of Gdel. The final two volumes of the set deal with Gdel's correspondence with his contemporary mathematicians, this fourth volume consists of material from correspondents from A-G.

For the purposes of this monograph, "by a degree" is meant a degree of recursive unsolvability. A degree [script bold]m is said to be minimal if 0 is the unique degree less than [script bold]m. Each of the six chapters of this self-contained monograph is devoted to the proof of an existence theorem for minimal degrees.

The nature of time is perceived by intellectuals variedly. An attempt is made in this paper to reconcile such varied views in the light of the Upanishads and related Indian spiritual and philosophical texts. The complex analysis of modern mathematics is used to represent the nature and presentation physical and psychological times so differentiated. Also the relation between time and energy is probed using uncertainty relations, forms of energy and phases of matter.

This volume presents the proceedings from the Eleventh Brazilian Logic Conference on Mathematical Logic held by the Brazilian Logic Society in Salvador, Bahia, Brazil. The conference and the volume are dedicated to the memory of professor Mario Tourasse Teixeira, an educator and researcher who contributed to the formation of several generations of Brazilian logicians. Contributions were made from leading Brazilian logicians and their Latin-American and European colleagues. All papers were selected by a careful refereeing processs and were revised and updated (...) by their authors for publication in this volume. There are three sections: Advances in Logic, Advances in Theoretical Computer Science, and Advances in Philosophical Logic. Well-known specialists present original research on several aspects of model theory, proof theory, algebraic logic, category theory, connections between logic and computer science, and topics of philosophical logic of current interest. Topics interweave proof-theoretical, semantical, foundational, and philosophical aspects with algorithmic and algebraic views, offering lively high-level research results. (shrink)

The articles by Henk Bodewitz collected in this volume, published between 1969 and 2013, deal with Vedic cosmology and ethics on basis of a systematic philological study of early Vedic texts, from the Ṛgveda to various Brāhmaṇas, Āraṇyakas and Upaniṣads.

We present a unified vision of human knowledge, the external world and ourselves in the frame of an overall unity of Everything. Two main sources of knowledge are considered to this goal: an admittedly reductionist version of Modern Science and a few key elements of Oriental Philosophy. Our view is based on an analogy between the fundamental unity of Vedic ontology and the Grand Unification scheme of Particle Physics traced along the evolution of the Universe. Our key statement is (...) that these two sources of knowledge describe the same ontological story of separation, from an original One down to the multiplicity of the phenomenological world. We further substantiate this vision by drawing an analogy between the Residue of the Vedic sacrifice and the post-Big-Bang cosmological Matter-Antimatter Asymmetry. We also discuss a Big-Bang analogy between the postulated field of Inflationary Cosmology (the Inflaton) and the Vedic dissolution-decomposition of the cosmic progenitor Prajapati – whose body, according to Brahmanas texts, provides the material substrate of which the Universe is built. (shrink)

This paper compares two ancient traditions of knowledge: The Indo-European vedic texts and the Edda poems of the Scandinavian and Germanic people. There appear to be close similarities between these two traditions in terms of four major concepts: A basic unified state lying at the foundation of the vast variety in the universe; the process of creation from within this unified field; the development of higher states of individual consciousness; and the development of higher stages in the collective consciousness (...) of society. Today this knowledge has practical implications for improving performance and quality of life, as shown by scientific research. (shrink)

Drawing on insights from Indian intellectual tradition, this book examines the conception of dharma by Jaimini in his Mīmāṃsāsūtras, assessing its contemporary relevance, particularly within ritual scholarship. Presenting a hermeneutical re-reading of the text, it investigates the theme of the relationship between subjectivity and tradition in the discussion of dharma, bringing it into conversation with contemporary discourses on ritual. The primary argument offered is that Jaimini's conception of dharma can be read as a philosophy of Vedic practice, centred on (...) the enjoinment of the subject, whose stages of transformation possess the structure of a hermeneutic tradition. Offering both substantive and methodological insights into the contentions within the contemporary study of ritual, this book will be of interest to researchers in the fields of Hindu Studies, Ritual Studies, Asian Religion and South Asian Studies. (shrink)

In This Book The Author Have Tried To Present A Historical Study Of Vedic Interpretation Confines Ourselves To The Study Of These Various Parts Of The Vedic Literature As Some Interpretation Of The Vedic Samhita. The Author Observed The Vedic Myth, Rituals And Philosophy As Interpreted By Madhvacarya The Founder Of Dvaita School Of Vedanta.

Festschrift in honor of 60th birtha anniversary of Ganesh Umakant Thite, Sanskritist; comprises contributed articles on various aspects of Vedic literature, Hinduism and Indic philosophy.

The first English collection of the work of Albert Lautman, a major figure in philosophy of mathematics and a key influence on Badiou and Deleuze.

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.

Over the past 50 years, Nelson algebras have been extensively studied by distinguished scholars as the algebraic counterpart of Nelson's constructive logic with strong negation. Despite these studies, a comprehensive survey of the topic is currently lacking, and the theory of Nelson algebras remains largely unknown to most logicians. This paper aims to fill this gap by focussing on the essential developments in the field over the past two decades. Additionally, we explore generalisations of Nelson algebras, such as N4-lattices which (...) correspond to the paraconsistent version of Nelson's logic, as well as their applications to other areas of interest to logicians, such as duality and rough set theory. A general representation theorem states that each Nelson algebra is isomorphic to a subalgebra of a rough set-based Nelson algebra induced by a quasiorder. Furthermore, a formula is a theorem of Nelson logic if and only if it is valid in every finite Nelson algebra induced by a quasiorder. (shrink)

"Vedic gods, religion, psychology, mythology, tradition, yoga.".

This article explores the way in which Madhva (1238–1317), the founder of the Dvaita Vedānta system of Hindu thought, reformulates the traditional exegetic practice of nirukta or “word derivation” to validate his pluralistic, hierarchical, and Vaiṣṇava reading of the Ṛgvedic hymns. Madhva’s Ṛgbhāṣya (RB) is conspicuous for its heavy reliance on and unique deployment of this exegetical tactic to validate several key features of his distinctive theology. These features include his belief in Viṣṇu’s unique possession of all perfect attributes (guṇaparipūrṇatva) (...) and His related conveyability by all Vedic words (sarvaśabdavācyatva). Such an understanding of Vedic language invokes the basic nirukta presupposition that words are eternally affiliated with the meanings they convey. But it is also based onMadhva’s access to a lexicon entitled Vyāsa’s Nirukti with which his critics and perhaps even his commentators seem to be unfamiliar.While the precise status of this text is the subject of ongoing debate, Madhva’s possession of special insight into the sacred canon is established in part by his unique claim to be an avatāra of the wind god Vāyu and a direct disciple of Viṣṇu Himself in the form of Vyāsa1. Thus, Madhva’s use of nirukta invokes his personal charisma to challenge not only conventional understandings of the hymns but traditional exegetic norms. Madhva’s provision of an alternative tradition of nirukta provoked sectarian debate throughout the Vijayanagara period over the extent to which one could innovate in established practices of reading the Veda. Articulating the Veda’s precise authority was a key feature of Brahmin debates during this period and reflects both the empire’s concern with promoting a shared religious ideology and the competition among rival Brahman sects for imperial patronage that this concern elicited. By looking at how two of Madhva’s most important commentators (the 14th-century Jayatīrtha and the 17th-century Rāghavendra) sought to defend his niruktis, this article will explore how notions of normative nirukta were articulated in response to Madhva’s deviations. At the same time, however, examining Madhva’s commentators’ defense of his niruktis also demonstrates the extent to which Madhva actually adhered to selected exegetic norms. This reveals that discomfort with Madhva’s particular methods for deriving words stemmed, in part, from a more general ambivalence towards this exegetical tactic whose inherent open-endedness threatened to undermine the fixity of the canon’s very substance: its language. (shrink)

First time in the history of India, in 1958, a Sankaracarya visited West. The author, His Holiness Jagadguru Sankaracarya Sri Bharati Krsna Tirtha of Puri, went to America at the invitation of the Self Realization Fellowship, Los Angeles, to spread the message of Vedanta. This book is a compilation of some of his discourses delivered there. These discourses by a saint-yogi and master of ancient Indian scriptures, also well-versed in modern sciences, give the essentials of Vedanta. They combine authenticity of (...) thought with simplicity of language. Being couched in the contemporary idiom they will be found to be particularly suited to the modern mind. Though addressed to American audiences, the discourses carry a message of eternal truth and of universal application. The steps of spiritual inquiry and the paths of God-realisation outlined in them will be of immense practical use to the readers in their quest for the Supreme. (shrink)