Una breve rassegna della vita e dell'autobiografia spirituale dell'unico mistico americano Adi Da (Franklin Jones). L'adesivo sulla copertina di alcune edizioni dice 'L'autobiografia spirituale più profonda di tutti i tempi' e questo potrebbe essere vero. Ho 70 anni e ho letto molti libri di insegnanti spirituali e sulla spiritualità, e questo è uno dei più grandi. Certamente, è by lontano il resoconto più completo e piùchiaro del processo di illuminazione che abbia mai visto. Anche se non hai alcun interesse nel (...) più affascinante di tutti i processi psicologici umani, è un documento incredibile che rivela molto sulla religione, lo yoga e la psicologia umana e sonda le profondità e i limiti delle possibilità umane. Lo descrivo in dettaglio e paragono il suo insegnamento a quello del mistico indiano contemporaneo Osho. Coloro che desiderano un quadro aggiornato completo per il comportamento umano dalla moderna vista a due systems possono consultare il mio libro 'La struttura logica dellafilosofia, psicologia, Mind e il linguaggio in Ludwig Wittgenstein e John Searle' 2nd ed (2019). Coloro che sono interessati a più dei miei scritti possono vedere 'TalkingMonkeys--Filosofia, Psicologia, Scienza, Religione e Politica su un Pianeta Condannato--Articoli e Recensioni 2006-2019 3rd ed (2019) e Suicidal Utopian Delusions in the 21st Century 4th ed (2019) . (shrink)

Yoga is a unique form of expert movement that promotes an increasingly subtle interpenetration of thought and movement. The mindful nature of its practice, even at expert levels, challenges the idea that thought and mind are inevitably disruptive to absorbed coping. Building on parallel phenomenological and ethnographic studies of skilful performance and embodied apprenticeship, we argue for the importance in yoga of mental access to embodied movement during skill execution by way of a case study of instruction and (...) practice in two related traditions, Iyengar and Anusara. Sharing a pose repertoire, they are based on distinctive philosophical systems with different teaching styles and metaphoric structures. To address relations between pedagogy and practice in embodied expertise, and to investigate the reciprocal influences of embodiment and thought, we explore in detail the linguistically mediated learning context where practitioners work with yoga teachers. Here, the mind/body problem comes to practical life. We demonstrate the effects of words on bodies, as knowledge is literally incorporated. We show why interpersonal influence on our movement capacities is sometimes needed to enhance expertise. We theorize and identify ?signature patterns of tension? among practitioners. These patterns have four sources: ghost gestures, innate differences in bodily form, functional fusing, and signature patterns of affective experience, modulation and expression. These patterns of tension produce ?silent zones?, cognitively impenetrable actions, functional fusing of a skilful, compensatory form, and signature patterns of pain and damage. We show how instruction can disrupt these silent zones, enhancing mental and physical flexibility. (shrink)

Gödel’s philosophical conceptions bear striking similarities to Cantor’s. Although there is no conclusive evidence that Gödel deliberately used or adhered to Cantor’s views, one can successfully reconstruct and see his “Cantorianism” at work in many parts of his thought. In this paper, I aim to describe the most prominent conceptual intersections between Cantor’s and Gödel’s thought, particularly on such matters as the nature and existence of mathematical entities (sets), concepts, Platonism, the Absolute Infinite, the progress and inexhaustibility of mathematics.

An interpretation of Wittgenstein’s much criticized remarks on Gödel’s First Incompleteness Theorem is provided in the light of paraconsistent arithmetic: in taking Gödel’s proof as a paradoxical derivation, Wittgenstein was drawing the consequences of his deliberate rejection of the standard distinction between theory and metatheory. The reasoning behind the proof of the truth of the Gödel sentence is then performed within the formal system itself, which turns out to be inconsistent. It is shown that the features of paraconsistent arithmetics match (...) with some intuitions underlying Wittgenstein’s philosophy of mathematics, such as its strict finitism and the insistence on the decidability of any mathematical question. (shrink)

Following Post program, we will propose a linguistic and empirical interpretation of Gödel’s incompleteness theorem and related ones on unsolvability by Church and Turing. All these theorems use the diagonal argument by Cantor in order to find limitations in finitary systems, as human language, which can make “infinite use of finite means”. The linguistic version of the incompleteness theorem says that every Turing complete language is Gödel incomplete. We conclude that the incompleteness and unsolvability theorems find limitations in our finitary (...) tool, which is our complete language. (shrink)

This article, addressed to Yoga Therapists, sorts out the historical roots of our idea of Yoga, elucidates the colonial interference and distortion of Yoga, and shows that trauma and therapy are the primary focus of Yoga. However, unlike most philosophies of therapy, Yoga's solution is primarily moral philosophical---Yoga itself being a basic ethical theory, in addition to Virtue Theory, Consequentialism and Deontology. This article goes some way to elucidating that it is quite ironic (and (...) absurd) that many feel the need to bring being “trauma-informed” into the title of Yoga education. That’s like the vacuous “chai tea” moniker (“chai” being the Hindi word for tea). Decolonizing our understanding of Yoga involves retrieving the original theory as the primary explanation of the topic, which allows us to understand how various activities, called "yoga," can be ways of practicing the moral philosophy of Yoga. The idea that "yoga" means many things and projects relies upon a contra logical methodology of interpretation which violates constraints of basic reasoning. Putting aside interpretation for explication is part of critical thinking but also our own self therapy. (Originally published in Yoga Therapy Today, a publication of the International Association of Yoga Therapists. Shared with permission.). (shrink)

Indian Philosophy is a term that refers to schools of philosophical thought that originated in the Indian subcontinent. Over the ages there has been continuity in enlarge this filed of philosophical enquiry, which as lead to a wide range of scriptures and systems of philosophy. The Yoga School, which was founded by Patanjali, was closely allied with Samkhya, and accepts its epistemology and metaphysics it was introduced by Patañjali in the 2nd century BC. The Practice of Yoga as (...) a discipline had been done since ancient times. However, since its alliance with the Samkhya, it tried to develop a specific philosophy of its own, which would be in harmony with the Samkhya Philosophy. Though the popular understanding of Yoga equates it with just the asanas, there are eight steps prescribed for its practice, which emphasize internal and external cleansing, self - discipline physical fitness, and meditation, which result in alertness and mental strength. Yoga as a term used for a system of abstract meditation or mental abstraction. Someone who practices yoga or follows the yoga philosophy with a high level of commitment is called a yogi or yogini. Virtually everyone can see physical benefits from yoga, and its practice can also give psychological benefits, such as stress reduction and a sense of well- being, and spiritual benefits, such as a feeling of connectedness with God or Spirit, or a feeling of transcendence. Mental stress is an important part of our life. It is the biggest challenge to live a life without stress and to continue with the peace of mind. In this paper it is an attempt to made the discuss yoga philosophy in present day intellectual world as well its application to maintain human well-being. (shrink)

The previous Part I of the paper discusses the option of the Gödel incompleteness statement (1931: whether “Satz VI” or “Satz X”) to be an axiom due to the pair of the axiom of induction in arithmetic and the axiom of infinity in set theory after interpreting them as logical negations to each other. The present Part II considers the previous Gödel’s paper (1930) (and more precisely, the negation of “Satz VII”, or “the completeness theorem”) as a necessary condition for (...) granting the Gödel incompleteness statement to be a theorem just as the statement itself, to be an axiom. Then, the “completeness paper” can be interpreted as relevant to Hilbert mathematics, according to which mathematics and reality as well as arithmetic and set theory are rather entangled or complementary rather than mathematics to obey reality able only to create models of the latter. According to that, both papers (1930; 1931) can be seen as advocating Russell’s logicism or the intensional propositional logic versus both extensional arithmetic and set theory. Reconstructing history of philosophy, Aristotle’s logic and doctrine can be opposed to those of Plato or the pre-Socratic schools as establishing ontology or intensionality versus extensionality. Husserl’s phenomenology can be analogically realized including and particularly as philosophy of mathematics. One can identify propositional logic and set theory by virtue of Gödel’s completeness theorem (1930: “Satz VII”) and even both and arithmetic in the sense of the “compactness theorem” (1930: “Satz X”) therefore opposing the latter to the “incompleteness paper” (1931). An approach identifying homomorphically propositional logic and set theory as the same structure of Boolean algebra, and arithmetic as the “half” of it in a rigorous construction involving information and its unit of a bit. Propositional logic and set theory are correspondingly identified as the shared zero-order logic of the class of all first-order logics and the class at issue correspondingly. Then, quantum mechanics does not need any quantum logics, but only the relation of propositional logic, set theory, arithmetic, and information: rather a change of the attitude into more mathematical, philosophical, and speculative than physical, empirical and experimental. Hilbert’s epsilon calculus can be situated in the same framework of the relation of propositional logic and the class of all mathematical theories. The horizon of Part III investigating Hilbert mathematics (i.e. according to the Pythagorean viewpoint about the world as mathematical) versus Gödel mathematics (i.e. the usual understanding of mathematics as all mathematical models of the world external to it) is outlined. (shrink)

This chapter describes Kurt Gödel's paper on the incompleteness theorems. Gödel's incompleteness results are two of the most fundamental and important contributions to logic and the foundations of mathematics. It had been assumed that first-order number theory is complete in the sense that any sentence in the language of number theory would be either provable from the axioms or refutable. Gödel's first incompleteness theorem showed that this assumption was false: it states that there are sentences of number theory that are (...) neither provable nor refutable. The first theorem is general in the sense that it applies to any axiomatic theory, which is ω-consistent, has an effective proof procedure, and is strong enough to represent basic arithmetic. Their importance lies in their generality: although proved specifically for extensions of system, the method Gödel used is applicable in a wide variety of circumstances. Gödel's results had a profound influence on the further development of the foundations of mathematics. It pointed the way to a reconceptualization of the view of axiomatic foundations. (shrink)

Although Kurt Gödel does not figure prominently in the history of computabilty theory, he exerted a significant influence on some of the founders of the field, both through his published work and through personal interaction. In particular, Gödel’s 1931 paper on incompleteness and the methods developed therein were important for the early development of recursive function theory and the lambda calculus at the hands of Church, Kleene, and Rosser. Church and his students studied Gödel 1931, and Gödel taught a seminar (...) at Princeton in 1934. Seen in the historical context, Gödel was an important catalyst for the emergence of computability theory in the mid 1930s. (shrink)

The relationship between the physical body and the conscious human mind has been a deeply problematic topic for centuries. Physicalism is the 'orthodox' metaphysical stance in contemporary Western thought, according to which reality is exclusively physical/material in nature. However, in the West, theoretical dissatisfaction with this type of approach has historically lead to Cartesian-style dualism, wherein mind and body are thought to belong to distinct metaphysical realms. In the current discussion I compare and contrast this standard Western approach with an (...) alternative form of dualism developed in the Sāṃkhya-Yoga philosophical tradition, where matter and pure consciousness are held to belong to distinct and independent realms, but where the mind is placed on the material side of the ontological divide. I argue that this model possesses a number of theoretical advantages over Cartesian-style dualism, and constitutes a compelling theoretical framework for re-conceptualizing the mind-body problem. (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)

Gödel's ontological argument is related to Gödel's view that causality is the fundamental concept in philosophy. This explicit philosophical intention is developed in the form of an onto-theological Gödelian system based on justification logic. An essentially richer language, so extended, offers the possibility to express new philosophical content. In particular, theorems on the existence of a universal cause on a causal "slingshot" are formulated.

The paper shows that it is possible to obtain a "slingshot" result in Gödel's theory of positiveness in the presence of the theorem of the necessary existence of God. In the context of the reconstruction of Gödel's original "slingshot" argument on the suppositions of non-Fregean logic, this is a natural result. The "slingshot" result occurs in sufficiently strong non-Fregean theories accepting the necessary existence of some entities. However, this feature of a Gödelian theory may be considered not as a trivialisation, (...) but as an intended consequence of Gödel's ontotheological views. (shrink)

Comparative philosophy has been subjected to much criticism in the latter half of the last century, though some of these criticisms were appropriate and justified. However, in our present cultural milieu, where traditions and culture transcend their geographical boundaries, seeping through the global network of views and ideas, it seems to be a legitimate enterprise to understand one’s own traditions and culture through the critical lens of the ‘other culture’. It is such cross-cultural understanding that paved the way towards legitimizing (...) “human rights” as a universal discourse. So also, the discourse on “environmental ethics” has gained acceptance in a similar manner across cultures and traditions. The paper attempts at an understanding of “Indian Philosophy” as a theoretical practice by exemplifying the notion of “sādhanā” in the Yoga system of Indian Philosophy through a reading of the notion of ‘phenomenological reduction’ as espoused in the transcendental phenomenology of Husserl. Thus, we reject the claim that philosophy as a pure rational activity was unique to the West as proclaimed in some Eurocentric readings. It is pertinent to recall here that the Sāṅkhya philosophy, which the Yoga system accepts as an allied school of thought was atheistic in its origin and attempted to explain the universe in terms of an evolutionary theory—the “prakṛti pariṇāma vāda”. (shrink)

'Godel's Way'에서 세 명의 저명한 과학자들은 부정성, 불완전성, 임의성, 계산성 및 파라불일치와 같은 문제에 대해 논의합니다. 나는 완전히 다른 해결책을 가지고 두 가지 기본 문제가 있다는 비트 겐슈타인의 관점에서 이러한 문제에 접근. 과학적 또는 경험적 문제가 있다, 관찰 하 고 철학적 문제 언어를 어떻게 이해할 수 있는 (수학 및 논리에 특정 질문을 포함) 에 대 한 조사 해야 하는 세계에 대 한 사실,우리가 실제로 특정 컨텍스트에서 단어를 사용 하는 방법을 보고 하 여 결정 될 필요가. 우리가 어떤 언어 게임을 (...) 하고 있는지 명확히 알 면, 이 주제는 다른 언어와 마찬가지로 평범한 과학적이고 수학적 질문으로 보입니다. 비트겐슈타인의 통찰력은 거의 동등하지 않았고 결코 능가하지 않았으며, 그가 블루와 브라운 북을 지시했을 때 80 년 전과 마찬가지로 오늘날과 관련이 있습니다. 완성된 책이 아닌 일련의 노트가 실패했음에도 불구하고, 이것은 반세기 이상 물리학, 수학, 철학의 출혈 가장자리에서 일해온 이 세 명의 유명한 학자들의 작품의 독특한 원천입니다. 다 코스타와 도리아는 울퍼트에 의해 인용된다 (그들은 보편적 인 계산에 쓴 이후 울퍼트와 야노프스키의 '이성의 외부 한계'에 대한 내 리뷰에, 대한 내 리뷰) 그리고 그의 많은 업적 중, 다 코스타는 파라 불일치의 선구자입니다. 현대 의 두 systems보기에서인간의 행동에 대한 포괄적 인 최신 프레임 워크를 원하는 사람들은 내 책을 참조 할 수 있습니다'철학의 논리적 구조, 심리학, 민d와 루드비히 비트겐슈타인과 존 Searle의언어' 2nd ed (2019). 내 글의 더 많은 관심있는 사람들은 '이야기 원숭이를 볼 수 있습니다-철학, 심리학, 과학, 종교와 운명 행성에 정치 - 기사 및 리뷰 2006-2019 3 rd 에드 (2019) 및 21st 세기 4번째 에드 (2019) 및 기타에서 자살 유토피아 망상. (shrink)

Letter to the Editors in response to Alasdair Richmond's 'Time Travelers'.

The chapter focuses on the yogic and other ascetic practices of the sadhus of the Ramananda Sampraday, the largest renunciant order in the world.

Self-knowledge, at first glance, seems to be naturally and easily accessible to each of us. We commonly believe that we need much less effort to understand ourselves than to understand the world. The authoress of the paper uncovers the fallacy of this popular view referring to the fundamental conceptions and philosophical ideas of the classical Yoga. She tries to demystify our deceptive self-understanding explaining the definitions of ignorance (avidya), I-am-ness (asmita), desire (raga), aversion (dvesha) and fear of death (abhinivesha) (...) given by the author of the oldest Yoga treatise. Besides, the paper discusses briefly how we can make use of our limited, incorrect self-knowledge as far as we are aware that it needs to be transcended. In the final part of the paper, the issue of self-discipline consisting basically in cultivation of detachment and the practice of meditation is addressed. (shrink)

As a senior physicist colleague and our friend, Robert N. Boyd, wrote in a journal (JCFA, Vol. 1,. 2, 2022), Our universe is but one page in a large book [4]. For example, things and Beings can travel between Universes, intentionally or unintentionally. In this short remark, we revisit and offer short remark to Neil’s ideas and trying to connect them with geometrization of musical chords as presented by D. Tymoczko and others, then to Escher staircase and then to Jacob’s (...) ladder which seems to point to possibility to interpret Jacob’s vision as described in the ancient book of Genesis as inter dimensional or heavenly staircase, e.g. an inter dimensional bridge between heaven and earth (see also classic book: Hofstadter, Godel, Escher, Bach). Jacob’s vision of angels going down to earth from that staircase has been depicted for instance in William Blake art etc. In our communication with others via physics literature and discussions etc, we came to several conclusions as follows: Firstly, possibility of quantum wormhole effect to mirror particle universe, which sometimes it is termed non-orientable wormhole. While such mirror particles effect have been more than 50 years predicted with the so-called parity violation (cf. Lee & Yang, 1950s), and that is called symmetry breaking. Secondly, a series of extended experiments on laser irradiated cold water may suggest possible transition from a phase of water to be at least partially fourth phase of water, which may be composed of crystalline water (see e.g. Gerald Pollack, and also Harold Aspden on liquid crystalline). If we can imagine laser cooling effect can be done in protracted time, then we can achieve a physical representation of Aspden’s liquid crystalline. Therefore, in subsequent article (Part II) we outlined simple model of such an effect of tunneling via quantum liquid crystalline Universe, which may likely be modeled with iced-water. It is interesting to remark here that certain experiments by Stockholm University scientists have shown that X-ray triggered water can exhibit properties just like liquid crystal (cf. PRL, 2020). That is why we consider it possible that there can be quantum phase transition where liquid water (comprised of iced cubes and water) can exhibit effects such as tunneling in quantum liquid crystalline Universe. Last but not least, we admit that what we outlined here is just an initial phase; and if you wish, perhaps we can call such experiments as “wormhole-at-lab” experiments (abbreviated: WHALE). (shrink)

The present article was partly inspired by G. Pollack’s book, and also Dadoloff, Saxena & Jensen (2010). As a senior physicist colleague and our friend, Robert N. Boyd, wrote in a journal (JCFA, Vol. 1, No. 2, 2022), for example, things and Beings can travel between Universes, intentionally or unintentionally [4]. In this short remark, we revisit and offer short remark to Neil Boyd’s ideas and trying to connect them with geometry of musical chords as presented by D. Tymoczko and (...) others, then to Escherian staircase and then to Jacob’s ladder which seems to pointto possibility to interpret Jacob’s vision as described in the ancient book of Genesis as interdimensional staircase, e.g. an interdimensional bridge between heaven and earth (cf. classic book: Hofstadter, Godel, Escher, Bach). Jacob’s vision of angels going down to earth from that staircase has been depicted for instance in William Blake art etc. In our communication with others via physics literature and discussions etc, we came to several conclusions as follows: Firstly, possibility of wormhole effect to mirror particle universe, which sometimes it is termed non-orientable wormhole. While such mirror particles effect have been more than 50 years predicted with the so-called parity violation (cf. Lee & Yang, 1950s), and that is called symmetry breaking. Secondly, a series of extended experiments on laser irradiated cold water may suggest possible transition from a phase of water to be at least partially fourth phase of water, which may be composed of crystalline water (see e.g. Gerald Pollack, and also Harold Aspden on liquid crystalline). If we can imagine laser cooling effect can be done in protracted time, then we can achieve a physical representation of Aspden‘s liquid crystalline. Therefore, in this article we outline a series of simple experiments of laser irradiated iced-water along with beryl and selenite crystals in order to see possibility of such a quantum tunneling via quantum liquid crystalline Universe hypothesis, which may likely be modeled with iced-water. It is interesting to remark here that certain experiments by Stockholm University scientists have shown that X-ray triggered water can exhibit properties just like liquid crystal (cf. PRL, 2020). That is why we consider it possible that there can be quantum phase transition where liquid water (comprised of iced cubes and water) can exhibit effects such as tunneling in quantum liquid crystalline Universe. Last but not least, we admit that what we outlined here is just aninitial phase; and if you wish, perhaps we can call such experiments as “wormhole-at-lab” experiments (abbreviated: WHALE). (shrink)

The present first part about the eventual completeness of mathematics (called “Hilbert mathematics”) is concentrated on the Gödel incompleteness (1931) statement: if it is an axiom rather than a theorem inferable from the axioms of (Peano) arithmetic, (ZFC) set theory, and propositional logic, this would pioneer the pathway to Hilbert mathematics. One of the main arguments that it is an axiom consists in the direct contradiction of the axiom of induction in arithmetic and the axiom of infinity in set theory. (...) Thus, the pair of arithmetic and set are to be similar to Euclidean and non-Euclidean geometries distinguishably only by the Fifth postulate now, i.e. after replacing it and its negation correspondingly by the axiom of finiteness (induction) versus that of finiteness being idempotent negations to each other. Indeed, the axiom of choice, as far as it is equivalent to the well-ordering “theorem”, transforms any set in a well-ordering either necessarily finite according to the axiom of induction or also optionally infinite according to the axiom of infinity. So, the Gödel incompleteness statement relies on the logical contradiction of the axiom of induction and the axiom of infinity in the final analysis. Nonetheless, both can be considered as two idempotent versions of the same axiom (analogically to the Fifth postulate) and then unified after logicism and its inherent intensionality since the opposition of finiteness and infinity can be only extensional (i.e., relevant to the elements of any set rather than to the set by itself or its characteristic property being a proposition). So, the pathway for interpreting the Gödel incompleteness statement as an axiom and the originating from that assumption for “Hilbert mathematics” accepting its negation is pioneered. A much wider context relevant to realizing the Gödel incompleteness statement as a metamathematical axiom is consistently built step by step. The horizon of Hilbert mathematics is the proper subject in the third part of the paper, and a reinterpretation of Gödel’s papers (1930; 1931) as an apology of logicism as the only consistent foundations of mathematics is the topic of the next second part. (shrink)

Monográfico: Yoga: Historia, Filosofía y Prácticas. Aposta. Revista de Ciencias Sociales, 94 (2022) .

Materialist and fundamentalist reductive ideologies obscure our capacity to directly experience the numinous. Thus, importantly, given the weight of the observable and measurable in orthodox science, and oftentimes a dismissal of both the soul and the subjective, a viable means of reconciling science and religious experience has continued to elude us. As a counter-measure to this obscuration, Jungian-oriented depth psychology has developed as an empirical science of the unconscious, researching both subject and object and offering theories and practices that foster (...) the psychospiritual development of the personality. Despite cultural and epochal differences, comparable evidence to Jung's process of psychospiritual development can be found in the Eastern liberatory tradition of Patañjali's Classical Yoga. However, given the elevated presence of neuroscience, no psychology, and especially no psychology that supports the soul, seems likely to survive much longer without finding an alliance with the objective measures of brain science. When considering the radically empirical measures of Jung and Patañjali, affective neuroscience may offer us a contemporary and objective means of languaging the bridge between the transcendent and immanent and fostering a contemporary science of the sacred. (shrink)

Entailment in propositional Gödel logics can be defined in a natural way. While all infinite sets of truth values yield the same sets of tautologies, the entailment relations differ. It is shown that there is a rich structure of infinite-valued Gödel logics, only one of which is compact. It is also shown that the compact infinite-valued Gödel logic is the only one which interpolates, and the only one with an r.e. entailment relation.

In his "Ontological proof", Kurt Gödel introduces the notion of a second-order value property, the positive property P. The second axiom of the proof states that for any property φ: If φ is positive, its negation is not positive, and vice versa. I put forward that this concept of positiveness leads into a paradox when we apply it to the following self-reflexive sentences: (A) The truth value of A is not positive; (B) The truth value of B is positive. Given (...) axiom 2, sentences A and B paradoxically cannot be both true or both false, and it is also impossible that one of the sentences is true whereas the other is false. (shrink)

Since the millennium, first person accounts of experience have been accepted as philosophically valid, potentially useful sources of information about the nature of mind and self. Several Vedic sciences rely on such first person accounts to discuss experience and consciousness. This paper shows that their insights define the information structure of experience in agreement with a scientific theory of mind fulfilling all presently known philosophical and scientific conditions. Experience has two separate components, its information content, and a separate ‘witness aspect’, (...) which can reflect on all forms of experience, and with training be strengthened until its power of reflection identifies it as the innermost aspect of ‘self’. The Vedic sciences, Sankhya, Yoga and Vedanta develop these themes. Sankhya identifies the different aspects of experience, outer and inner; Yoga practices lead the mind to inner states without information content (samadhi) in which the experience of the witness (sakshi) is strengthened and deepened. Vedanta states the nature of the ‘self’ is to know itself directly without intermediary. All this requires the witness to have a singular loop structure. The information structure of experience therefore has two aspects, information content plus a singular loop endowing it with a subjective sense of ‘Self’. (shrink)

We can simply define Gödel 1931 Incompleteness away by redefining the meaning of the standard definition of Incompleteness: A theory T is incomplete if and only if there is some sentence φ such that (T ⊬ φ) and (T ⊬ ¬φ). This definition construes the existence of self-contradictory expressions in a formal system as proof that this formal system is incomplete because self-contradictory expressions are neither provable nor disprovable in this formal system. Since self-contradictory expressions are neither provable nor disprovable (...) only because they are self-contradictory we could define them as unsound instead of defining the formal system as incomplete. (shrink)

INTRODUCTION Yoga is very ancient, certainly much older than the archaeological record, which is the only reliable one we have at present. ...

In the Appendix I of his "Remarks on the Foundations of Mathematics", Wittgenstein elaborates a different interpretation of Gödel’s First Incompleteness Theorem, which we have come to refer to as "Gödel’s Theorem" or "Incompleteness Theorem". This nomenclature arises from the recognition that the so-called "Second Incompleteness Theorem" is essentially a corollary of the primary theorem. Wittgenstein aims to reassess Gödel’s conclusion that there exist true formulas not demonstrable within formal systems capable of representing a sufficient amount of arithmetic theory. Gödel’s (...) initial reaction, as well as other commentators, was that Wittgenstein had not understood the proof. Nevertheless, recent commentators view worthy commentaries in wittgensteinian writings: some commentators, such as Juliet Floyd and Hilary Putnam, distinguish between mathematical proof and philosophical prose that surrounds the theorem, making it possible to understand Wittgenstein’s remarks. Ultimately, Wittgenstein’s observations serve as a lens through which Gödel’s theorem can be reconsidered within the realm of non-classical logics, such as paraconsistent logic. (shrink)

The determinism-free will debate is perhaps as old as philosophy itself and has been engaged in from a great variety of points of view including those of scientific, theological, and logical character. This chapter focuses on two arguments from logic. First, there is an argument in support of determinism that dates back to Aristotle, if not farther. It rests on acceptance of the Law of Excluded Middle, according to which every proposition is either true or false, no matter whether the (...) proposition is about the past, present or future. In particular, the argument goes, whatever one does or does not do in the future is determined in the present by the truth or falsity of the corresponding proposition. The second argument coming from logic is much more modern and appeals to Gödel's incompleteness theorems to make the case against determinism and in favour of free will, insofar as that applies to the mathematical potentialities of human beings. The claim more precisely is that as a consequence of the incompleteness theorems, those potentialities cannot be exactly circumscribed by the output of any computing machine even allowing unlimited time and space for its work. The chapter concludes with some new considerations that may be in favour of a partial mechanist account of the mathematical mind. (shrink)

This is what Daniel Simpson has to say of it: An entertaining polemic that takes heartfelt swipes at Western scholars, accusing them of misreading Tantra. "Hinduism is Tantric in essence," the essay says, without proving that Tantra predates other influences, or that "Yoga in its various forms, arises out of Tantra". The latter seems at odds with the earliest descriptions of austerities, or the ascetic objective of bodily transcendence (which Tantric teachings later modified, as evinced by hatha yoga (...) texts). Meanwhile, Patanjali is said to be Tantric because he describes a silent mind - despite not mentioning kundalini (as the author implies). And quoting Abhinavagupta does not mean that Vedanta is based on his framework. Yoga and experiential insight might be inseparable, but a history of ideas can still be written, however tangential it might seem to the practices it alludes to. If "that which is comprehensible is reductionist and is an exercise in structural scrutiny which is disastrous to Indology," then why compose an essay reducing Hinduism to Tantra, while dismissing all else as misguided archiving? Regardless, I enjoyed its invective. (shrink)

[Theism and Theology in Classical Yoga] .

O objetivo deste artigo é analisar o conceito de yoga da Bhagavad-gītā. Cinco concepções de yoga encontradas no texto são descritas: yoga enquanto disciplina ou prática, yoga enquanto disciplina qualificada, yoga enquanto estado mental de equanimidade e renúncia, yoga enquanto estado de união e yoga enquanto poder místico. As relações existentes entre essas concepções são explicitadas e o que podemos chamar de a estrutura do yoga na Bhagavad-gītā é pormenorizada.

The paper continues the consideration of Hilbert mathematics to mathematics itself as an additional “dimension” allowing for the most difficult and fundamental problems to be attacked in a new general and universal way shareable between all of them. That dimension consists in the parameter of the “distance between finiteness and infinity”, particularly able to interpret standard mathematics as a particular case, the basis of which are arithmetic, set theory and propositional logic: that is as a special “flat” case of Hilbert (...) mathematics. The following four essential problems are considered for the idea to be elucidated: Fermat’s last theorem proved by Andrew Wiles; Poincaré’s conjecture proved by Grigori Perelman and the only resolved from the seven Millennium problems offered by the Clay Mathematics Institute (CMI); the four-color theorem proved “machine-likely” by enumerating all cases and the crucial software assistance; the Yang-Mills existence and mass gap problem also suggested by CMI and yet unresolved. They are intentionally chosen to belong to quite different mathematical areas (number theory, topology, mathematical physics) just to demonstrate the power of the approach able to unite and even unify them from the viewpoint of Hilbert mathematics. Also, specific ideas relevant to each of them are considered. Fermat’s last theorem is shown as a Gödel insoluble statement by means of Yablo’s paradox. Thus, Wiles’s proof as a corollary from the modularity theorem and thus needing both arithmetic and set theory involves necessarily an inverse Grothendieck universe. On the contrary, its proof in “Fermat arithmetic” introduced by “epoché to infinity” (following the pattern of Husserl’s original “epoché to reality”) can be suggested by Hilbert arithmetic relevant to Hilbert mathematics, the mediation of which can be removed in the final analysis as a “Wittgenstein ladder”. Poincaré’s conjecture can be reinterpreted physically by Minkowski space and thus reduced to the “nonstandard homeomorphism” of a bit of information mathematically. Perelman’s proof can be accordingly reinterpreted. However, it is valid in Gödel (or Gödelian) mathematics, but not in Hilbert mathematics in general, where the question of whether it holds remains open. The four-color theorem can be also deduced from the nonstandard homeomorphism at issue, but the available proof by enumerating a finite set of all possible cases is more general and relevant to Hilbert mathematics as well, therefore being an indirect argument in favor of the validity of Poincaré’s conjecture in Hilbert mathematics. The Yang-Mills existence and mass gap problem furthermore suggests the most general viewpoint to the relation of Hilbert and Gödel mathematics justifying the qubit Hilbert space as the dual counterpart of Hilbert arithmetic in a narrow sense, in turn being inferable from Hilbert arithmetic in a wide sense. The conjecture that many if not almost all great problems in contemporary mathematics rely on (or at least relate to) the Gödel incompleteness is suggested. It implies that Hilbert mathematics is the natural medium for their discussion or eventual solutions. (shrink)

John P. Burgess kritisiert Kurt Gödels Begriff der mathematischen oder rationalen Anschauung und erläutert, warum heuristische Intuition dasselbe leistet wie rationale Anschauung, aber ganz ohne ontologisch überflüssige Vorannahmen auskommt. Laut Burgess müsste Gödel einen Unterschied zwischen rationaler Anschauung und so etwas wie mathematischer Ahnung, aufzeigen können, die auf unbewusster Induktion oder Analogie beruht und eine heuristische Funktion bei der Rechtfertigung mathematischer Aussagen einnimmt. Nur, wozu benötigen wir eine solche Annahme? Reicht es nicht, wenn die mathematische Intuition als Heuristik funktioniert? Für (...) Gödel sind Mengen Extensionen von Begriffen und er beharrt beispielsweise auf dem ontologischen Objektstatus von Mengen, weil Denken für ihn einen Input benötigt, den es selbst nicht zu liefern im Stande ist. Im Falle der mathematischen Anschauung darf dieser Input allerdings nicht subjektiv kontingent sein, wenn es sich um objektiv gültige Theorien handeln soll. (Zudem vertritt Gödel eine Korrespondenztheorie der Wahrheit.) Der Begriff der heuristischen Intuition, den Burgess expliziert, stammt hingegen nicht zuletzt aus der kognitiven Psychologie, der bei der Verarbeitung impliziter, also unbewusster Informationen ansetzt und so das menschliche Vermögen erklärt, Entscheidungen und Urteile zu fällen, ohne sich der Urteilsgrundlagen bewusst zu sein. Über den ontologischen oder erkenntnistheoretischen Status dieser Urteilsgrundlagen sagen diese Theorien nichts aus. Sie könnten auch subjektiv kontingent zustande gekommen sein. Ihr normativer Anspruch ergibt sich lediglich aus „dem Funktionieren“, nicht daraus, dass es sich um Gesetze des Wahrseins handelt. (shrink)

Mathematical instrumentalism construes some parts of mathematics, typically the abstract ones, as an instrument for establishing statements in other parts of mathematics, typically the elementary ones. Gödel’s second incompleteness theorem seems to show that one cannot prove the consistency of all of mathematics from within elementary mathematics. It is therefore generally thought to defeat instrumentalisms that insist on a proof of the consistency of abstract mathematics from within the elementary portion. This article argues that though some versions of mathematical instrumentalism (...) are defeated by Gödel’s theorem, not all are. By considering inductive reasons in mathematics, we show that some mathematical instrumentalisms survive the theorem. (shrink)

This paper is a critical examination of Stephen Neale's *The Philosophical Significance of Godel's slingshot*. I am sceptical of the philosophical significance of Godel’s Slingshot (and of Slingshot arguments in general). In particular, I do not believe that Godel’s Slingshot has any interesting and important philosophical consequences for theories of facts or for referential treatments of definite descriptions. More generally, I do not believe that any Slingshot arguments have interesting and important philosophical consequences for theories of facts (...) or for referential treatments of definite descriptions. Friends of facts and referential treatments of definite descriptions can, and should, proceed with the construction of their theories, blithely ignoring the many Slingshots which now litter the landscape. (Of course, there may be other considerations which should give such theorists pause -- but those are other considerations.). (shrink)

Although written in Japanese, this article handles historical and technical survey of Gödel's incompleteness theorem thoroughly.

This book sheds new light on the fascinating - at times dark and at times hopeful - reception of classical Yoga philosophies in Germany during the nineteenth century. Written for non-specialists, Indian Philosophy and Yoga in Germany will be of interest to students and scholars working on 19th-century philosophy, Indian philosophy, comparative philosophy, Hindu studies, intellectual history, and religious history.

Valmiki , The Sage of 5th century B.C wrote The Ramayana not to narrate the story of Rama in an absorbing style. Though the epic poem presents Rama’s Journey of life in enchanting poetry , the story and the enchanting poetry are sugar coating or honey to the organic medicine called Kundalini Yoga. Maharshi Valmiki wrote the Ramayana to spread / propagate Kundalini Yoga among the masses. Thus the soul of The Ramayana is Kundalini Yoga / Sri (...) Vidya. Valmiki embedded Kundalini Yoga in the Chapter titled “ Sundara Kanda” . Hanuman and Ravana are Kundalini Yogis of Samaya and Kaula Paths. And in Sundara Kanda , he inserted “ Trijata Swapna “ , dream sequence of a demon and in it embedded the Gayathri Mantra. The concepts of Vishnu and Avatar (reincarnation) were nonexistent during the Ramayana Period. Seshendra Sharma , Scholar - Poet in his Magnum Opus of Research “ Shodasi : Secrets of The Ramayana “ reveals these secrets lying hidden for thousands of years . (shrink)

Since the onset of logical positivism, the general wisdom of the philosophy of science has it that the kantian philosophy of (space and) time has been superseded by the theory of relativity, in the same sense in which the latter has replaced Newton’s theory of absolute space and time. On the wake of Cassirer and Gödel, in this paper I raise doubts on this commonplace by suggesting some conditions that are necessary to defend the ideality of time in the sense (...) of Kant. In the last part of the paper I bring to bear some contemporary physical theories on such conditions. (shrink)

This essay deals with Gödel's Theorems in relationship to Philosophy of Science; firstly, in outlining Ludwig Wittgenstein's position on the limits of philosophical truth that we can derive from Gödel (and how this in turn impacts modern-philosophical conceptions of science), and secondly, the deeper uncertainty about consciousness that Gödel's theorems point to, most notably elucidated by Sir Roger Penrose.

After introductory reminder of and comments on Gödel’s ontological proof, we discuss the collapse of modalities, which is provable in Gödel’s ontological system GO. We argue that Gödel’s texts confirm modal collapse as intended consequence of his ontological system. Further, we aim to show that modal collapse properly fits into Gödel’s philosophical views, especially into his ontology of separation and union of force and fact, as well as into his cosmological theory of the nonobjectivity of the lapse of time. As (...) a result, modal collapse should not be conceived in Gödel so much as a deficit, but rather as a kind of the rise of modalities to the “perfect” being. We further show that, in accordance with Gödel’s ontology, the concepts of modality and time should be derived in terms of the “fundamental philosophical concept” of cause. To give an example of how a formalization of such causative Gödelian ontology and ontological proof might look, we propose the transformation of GO into a kind of causally re-interpreted justification logic. (shrink)

It is shown that Gqp↑, the quantified propositional Gödel logic based on the truth-value set V↑ = {1 - 1/n : n≥1}∪{1}, is decidable. This result is obtained by reduction to Büchi's theory S1S. An alternative proof based on elimination of quantifiers is also given, which yields both an axiomatization and a characterization of Gqp↑ as the intersection of all finite-valued quantified propositional Gödel logics.

“Slingshot Arguments” are a family of arguments underlying the Fregean view that if sentences have reference at all, their references are their truth-values. Usually seen as a kind of collapsing argument, the slingshot consists in proving that, once you suppose that there are some items that are references of sentences (as facts or situations, for example), these items collapse into just two items: The True and The False. This dissertation treats of the slingshot dubbed “Gödel’s slingshot”. Gödel argued that there (...) is a deep connection between these arguments and definite descriptions. More precisely, according to Gödel, if one adopts Russell’s interpretation of definite descriptions (which clashes with Frege’s view that definite descriptions are singular terms), it is possible to evade the slingshot. We challenge Gödel’s view in two manners, first by presenting a slingshot even with a Russellian interpretation of definite descriptions and second by presenting a slingshot even when we change from singular terms to plural terms in the light of new developments of the so-called Plural Logic. The text is divided in three chapters, in the first, we present the discussion between Russell and Frege regarding definite descriptions, in the second, we present Gödel’s position and reconstructions of Gödel’s argument and in the third we prove our slingshot argument for Plural Logic. In light of these results we conclude that we can maintain the validity of slingshot arguments even within a Russellian interpretation of definite descriptions or in the context of Plural Logic. (shrink)

Modern science, based on the laws of physics, claims validity for all events in space and time. However, it also reveals its own limitations, such as the indeterminacy of quantum physics, the limits of decidability, and, presumably, limits of decodability of the mind-brain relationship. At the philosophical level, these intrinsic limitations allow for different interpretations of the relation between human cognition and the natural order. In particular, modern science may be logically consistent with religious as well as agnostic views of (...) humans and the universe. These points are exemplified through the transcript of a discussion between Kurt Gödel and Rudolf Carnap that took place in 1940. Gödel, discoverer of mathematical undecidability, took a proreligious view; Carnap, one of the founders of analytical philosophy, an antireligious view. By the time of the discussion, Carnap had liberalized his ideas on theoretical concepts of science: he believed that observational terms do not suffice for an exhaustive definition of theoretical concepts. Then, responded Gödel, one should formulate a theory or metatheory that is consistent with scientific rationality, yet also encompasses theology. Carnap considered such theories unproductive. The controversy remained unresolved, but its emphasis shifted from rationality to wisdom, not only in the Gödel-Carnap discussion but also in our time. -/- . (shrink)

In 1956, a few writings of Wittgenstein that he didn't publish in his lifetime were revealed to the public. These writings were gathered in the book Remarks on the Foundations of Mathematics (1956). There, we can see that Wittgenstein had some discontentment with the way philosophers, logicians, and mathematicians were thinking about paradoxes, and he even registered a few polemic reasons to not accept Gödel’s incompleteness theorems.

Those incompleteness theorems mean the relation of (Peano) arithmetic and (ZFC) set theory, or philosophically, the relation of arithmetical finiteness and actual infinity. The same is managed in the framework of set theory by the axiom of choice (respectively, by the equivalent well-ordering "theorem'). One may discuss that incompleteness form the viewpoint of set theory by the axiom of choice rather than the usual viewpoint meant in the proof of theorems. The logical corollaries from that "nonstandard" viewpoint the relation of (...) set theory and arithmetic are demonstrated. (shrink)

A cognitive science perspective of yoga system of thought will be developed in conjugation with the Samkhya Darsana. This development will be further advanced using Advaita Vedanta and will be translated into modern scientific terms to arrive at an idea about cognition process. The stalling of the cognitive process and stilling the mind will be critically discussed in the light of this perspective. This critical analysis and translation into cognitive science and modern scientific terms will be presented together with (...) its implications and applications to the disciplines of mind-machine modeling, natural language comprehension branch of artificial intelligence and physiological psychology. (shrink)