An attempt is made to give a coherent account of the logical essence of the Copenhagen interpretation of quantum theory. The central point is that quantum theory is fundamentally pragmatic, but nonetheless complete. The principal difficulty in understanding quantum theory lies in the fact that its completeness is incompatible with external existence of the space—time continuum of classical physics.

Recently, Frauchiger and Renner proposed a Gedankenexperiment, which was claimed to be able to prove that quantum theory cannot consistently describe the use of itself. Here we show that the conclusions of Frauchiger and Renner actually came from their incorrect description of some quantum states. With the correct description there will be no inconsistent results, no matter which quantum interpretation theory is used. Especially, the Copenhagen interpretation can satisfy all the three assumptions,, and of Frauchiger and Renner (...) simultaneously, thus it has no problem consistently describing the use of itself. (shrink)

As the theory of the atom, quantum mechanics is perhaps the most successful theory in the history of science. It enables physicists, chemists, and technicians to calculate and predict the outcome of a vast number of experiments and to create new and advanced technology based on the insight into the behavior of atomic objects. But it is also a theory that challenges our imagination. It seems to violate some fundamental principles of classical physics, principles that eventually have become a part (...) of western common sense since the rise of the modern worldview in the Renaissance. So the aim of any metaphysical interpretation of quantum mechanics is to account for these violations. (shrink)

The Copenhagen interpretation is critically considered. A number of ambiguities, inconsistencies and confusions are discussed. It is argued that it is possible to purge the interpretation so as to obtain a consistent and reasonable way to interpret the mathematical formalism of quantum mechanics, which is in agreement with the way this theory is dealt with in experimental practice. In particular, the essential role attributed by the Copenhagen interpretation to measurement is acknowledged. For this reason it (...) is proposed to refer to it as a neo-Copenhagen interpretation. (shrink)

What is commonly known as the Copenhagen interpretation of quantum mechanics, regarded as representing a unitary Copenhagen point of view, differs significantly from Bohr's complementarity interpretation, which does not employ wave packet collapse in its account of measurement and does not accord the subjective observer any privileged role in measurement. It is argued that the Copenhagen interpretation is an invention of the mid‐1950s, for which Heisenberg is chiefly responsible, various other physicists and philosophers, including (...) Bohm, Feyerabend, Hanson, and Popper, having further promoted the invention in the service of their own philosophical agendas. (shrink)

Within the past decade there has grown an acute and highly articulate group of critics of the orthodox interpretation of quantum theory,--the so-called "Copenhagen Interpretation." The writings of people like Bopp, Janossy, and particularly Bohm and Feyerabend, must be taken very seriously indeed. The future of some important discussions in the philosophy and the logic of science rests with these individuals. But they have, in their own writings, occasionally matched the inelegancies of Bohr and Heisenberg with as (...) many inelegancies of their own. The present paper is meant to present a quintet of considerations which may possibly lead to a reassessment of the issues between Bohr, Heisenberg, and their critics, especially Bohm and Feyerabend. (shrink)

SummaryThe problem of quantum measurement is considered in the framework of a naturalized and evolutionary epistemology. Consider two simple textbook observations: a) quantum measurement is an information processing method invented for the purpose of exploring domains of the external world which are not accessible otherwise b) quantum measurement interprets signals from the external world with the help of a computing algorithm invented specifically for this purpose. Replace the words “quantum measurement” and “invented” in a) and b) by “vision” and “evolved (...) respectively”. Both sentences remain simple textbook observations; this time about vision and its biological evolution. Since both a) and b) are substantial statements whether they refer to vision or to quantum measurement the analogy between these processes suggests that quantum measurement may be viewed as a culturally evolved perceptual mode. This idea is explored further by comparing the developments of vision and of quantum measurement. The comparison reveals some interesting similarities between the two processes. One result of the comparison and of viewing quantum measurement as a perceptual mode is a realistic formulation of the Copenhagen interpretation which in turn permits a rational explanation of why, in quantum measurement, some observables exist in nature only when observed. (shrink)

The Bohr-Heisenberg scheme, which forms the basis of any current version of the standard or Copenhagen interpretation of quantum mechanics, is shown to be internally inconsistent. Although the inconsistencies demonstrated here are directly relatable to Einstein's opinion that it is unsatisfactory to interpret physical theory solely in terms of the knowledge gained from experimental outcomes, it is nevertheless shown that Einstein's view requires important modification. The implications of the Bohr-Heisenberg schem's self-inconsistency are discussed in relation to Bell's theorem (...) and Aspect's experiments. (shrink)

Popper conceived an experiment whose analysis led to a result that he deemed absurd. Popper wrote that his reasoning was based on the Copenhagen interpretation and therefore invalidated it. Many authors who have examined Popper's analysis have found in it various technical flaws which are briefly summarized here. However, the aim of the present article is not technical. My concern is to redress logical flaws in Popper's argument: the terminology he uses is ambiguous, his analysis involves counterfactual hypotheses, (...) and it violates Bohr's complementarity principle. Therefore, the absurdity of Popper's result only confirms Bohr's approach. (shrink)

Neurological Positivism’s single- and two-neuro-algorithmic referent conceptions of subjective and objective experience respectively are discussed. NP’s account of Bohr and Heisenberg’s Copenhagen interpretation of quantum reality is then described in terms of nonlinear constructions of two-neuro-algorithmic referents that are proposed also to undergird William James’s pragmatic conception of truth. In turn, qualia are depicted as nonlinear single-neuro-algorithmic referents in relation to the two-neuro-algorithmic quantum measurement procedure. Experientially, qualia are described as nonlinear "black twinkling" neuro-flux patterns which in the (...) context of overall brain organization in both phylogeny and ontogeny increase the brain’s probability of survival. It is concluded that ontological questions are really about the relationships between the two-neuro-algorithmic referent systems in the brain, and the quantum theoretical measurement procedure is the best "test" of NP’s two-neuro-algorithmic hypothesis and, as a test, greatly alters the traditional interpretation of Bell’s theorem. (shrink)

In this article, we argue that although Bohr's version of the Copenhagen interpretation is in line with several key elements of logical positivism, pragmatism is the closest approximation to a classification of the Copenhagen interpretation, whether or not pragmatists directly influenced the key figures of the interpretation. Pragmatism already encompasses important elements of operationalism and logical positivism, especially the liberalized Carnapian reading of logical positivism. We suggest that some elements of the Copenhagen interpretation, (...) which are in line with logical positivism, are also supported by pragmatism. Some of these elements are empirical realism, fallibilism, holism, and instrumentalism. However, pragmatism goes beyond logical positivism in espousing some other key elements of the Copenhagen interpretation, though imperfectly, such as the correspondence principle, complementarity, and indeterminism. (shrink)

In the quest and search for a physical theory of everything from the macroscopic large body matter to the microscopic elementary particles, with strange and weird concepts springing from quantum physics discovery, irreconcilable positions and inconvenient facts complicated physics – from Newtonian physics to quantum science, the question is- how do we close the gap? Indeed, there is a scientific and mathematical fireworks when the issue of quantum uncertainties and entanglements cannot be explained with classical physics. The Copenhagen (...) class='Hi'>interpretation is an expression of few wise men on quantum physics that was largely formulated from 1925 to 1927 namely by Niels Bohr and Werner Heisenberg. From this point on, there is a divergence of quantum science into the realms of indeterminacy, complementarity and entanglement which are principles expounded in Yijing, an ancient Chinese knowledge constructed on symbols, with a vintage of at least 3 millennia, with broken and unbroken lines to form stacked 6-line structure called the hexagram. It is premised on probability development of the hexagram in a space-time continuum. The discovery of the quantization of action meant that quantum physics could not convincingly explain the principles of classical physics. This paper will draw the great departure from classical physics into the realm of probabilistic realities. The probabilistic nature and reality interpretation had a significant influence on Bohr’s line of thought. Apparently, Bohr realized that speaking of disturbance seemed to indicate that atomic objects were classical particles with definite inherent kinematic and dynamic properties (Hanson, 1959). Disturbances, energy excitation and entanglements are processual evolutionary phases in Yijing. This paper will explore the similarities in quantum physics and the methodological ways where Yijing is pivoted to interpret observable realities involving interactions which are uncontrollable and probabilistic and forms an inseparable unity due to the entanglement, superposition Transgressing disciplinary boundaries in the discussion of Yijing, originally from the Western Zhou period (1000-750 BC), over a period of warring states and the early imperial period (500-200 BC) which was compiled, transcribed and transformed into a cosmological texts with philosophical commentaries known as the “Ten Wings” and closely associated with Confucius (551- 479 BC) with the Copenhagen Interpretation (1925-1927) by the few wise men including Niel Bohr and Werner Heisensberg would seem like a subversive undertaking. Subversive as the interpretations from Yijing is based on wisdom derived from thousands of years from ancient China to recently discovered quantum concepts. The subversive undertaking does seem to violate the sanctuaries of accepted ways in looking at Yijing principles, classical physics and quantum science because of the fortified boundaries that have been erected between Yijing and the sciences. Subversive as this paper may be, it is an attempt to re-cast an ancient framework where indeterminism, complementarity, non-linearity entanglement, superposition and probability interpretation is seen in today quantum’s realities. (shrink)

A pivotal focus of exegesis of Nāgārjuna's Mūlamadhyamakakārïkā (MMK) for the past half century has been the attempt to decipher the text's philosophy of language, and determine how this best aids us in characterizing Madhyamaka thought as a whole. In this vein, MMK 24:18 has been judged of particular weight insofar as it purportedly insists that the concepts pratītyasamutpāda (conditioned co-arising) and śūnyatā (emptiness), both indispensable to Buddhist praxis, are themselves only "nominal" or "conventional," that is, they are merely labels (...) that do not referentially signify anything that can be taken to be an ontologically ultimate reality. In various guises, as a result of this explication, Nāgārjuna's thought has been seen to embrace an overarching linguistic nominalism or conventionalism in which words, whether they are used for the purposes of theory or practice, though they serve as commonly accepted currency in the transactions of worldly business (vyavahāra), are in the end only ideas (prajñapti) or metaphysical fabrications (prapanca). This interpretation is largely due to tenaciously inaccurate translations and expositions of MMK 24:18 and their dependence on Candrakīrti's peculiar analysis of this verse in his Prasannapadā. This essay will attempt to correct both the diction of the major translations of MMK 24:18 and the fictions of nominalism and conventionalism that the consequent interpretations of this stanza have perpetuated. The argument that will be developed in the course of this essay is that Candrakīrti's reading of this verse proffers a strong form of linguistic nominalism that Nāgārjuna himself does not embrace. It will be shown, based on everything else found in the MMK, that Nāgārjuna, rather than advocating the mere nominal or conventional status of terms such as pratītyasamutpāda and sunyata, demands they be accepted as both pedagogically useful and even referentially accurate descriptions of the world as it is. (shrink)

The Copenhagen interpretation, which informs the textbook presentation of quantum mechanics, depends fundamentally on the notion of ontological wave-particle duality and a viewpoint called “complementarity.” In this paper, Bohr's own interpretation is traced in detail and is shown to be fundamentally different from and even opposed to the Copenhagen interpretation in virtually all its particulars. In particular, Bohr's interpretation avoids the ad hoc postulate of wave function ‘collapse' that is central to the Copenhagen (...) interpretation. The strengths and weakness of both interpretations are summarized. ‡I thank Edward Mackinnon, Henry Folse, and Greg Anderson for valuable comments on the penultimate draft. The final responsibility for the paper rests with the author. †To contact the author, please write to: Bhaktivedanta Institute, 2334 Stuart Street, Berkeley, CA; e-mail: [email protected]. I have been unable to achieve a sharp formulation of Bohr's principle of complementarity despite much effort I have expended on it. (Einstein 1949, 674) While imagining that I understand the position of Einstein, as regards the EPR correlations, I have very little understanding of his principal opponent, Bohr. (Bell 1987, 155) Niels Bohr brain-washed a generation of physicists into believing that the problem had been solved fifty years ago. (Gell-Mann 1979, 29) Every sentence I say must be understood not as an affirmation, but as a question. (Niels Bohr, quoted in Jammer 1966, 175) Bohr's interpretation has never been fully clarified. It needs an interpretation itself, and only that will be its defense. (Weizsäcker 1971, 25). (shrink)

According to the standard view, the so-called ‘Copenhagen interpretation’ of quantum mechanics originated in discussions between Bohr and Heisenberg in 1927, and was defended by Bohr in his classic debate with Einstein. Yet recent scholarship has shown Bohr’s views were never widely accepted, let alone properly understood, by his contemporaries, many of whom held divergent views of the ‘Copenhagen orthodoxy’. This paper examines how the ‘myth of the Copenhagen interpretation’ was constructed by situating it in (...) the context of Soviet Marxist critique of quantum mechanics in the 1950s and the response by physicists such as Heisenberg and Rosenfeld. (shrink)

The Copenhagen interpretation, which informs the textbook presentation of quantum mechanics, depends fundamentally on the notion of ontological wave-particle duality and a viewpoint called “complementarity”. In this paper, Bohr’s own interpretation is traced in detail and is shown to be fundamentally different from and even opposed to the Copenhagen interpretation in virtually all its particulars. In particular, Bohr’s interpretation avoids the ad hoc postulate of wave function ‘collapse’ that is central to the Copenhagen (...) interpretation. The strengths and weakness of both interpretations are summarized. (shrink)

In what follows, I examine three main points which may help us to understand the deep nature of Einstein's objections to quantum mechanics. After having played a fundamental pioneer role in the birth of quantum physics, Einstein was, as is well known, far less enthusiastic about its constitution as a quantum mechanics and, since 1927, he constantly argued against the pretention of its founders and proponents to have settled a definitive and complete theory. I emphasize first the importance of the (...) philosophical climate, which was dominated by the Copenhagen orthodoxy and Bohr's idea of complementarity: What Einstein was primarily reluctant to was to accept the fundamental character of quantum mechanics as such, and to modify for it the basic principles of knowledge. I thus stress the main lines of Einstein's own programme in respect to quantum physics, which is to be considered in relation to his other contemporary attempts and achievements. Finally, I show how Einstein's arguments, when dealing with his objections, have been fruitful and some of them still worthy, with regard to recent developments concerning local nonseparability as well as concerning the problems of completeness and accomplishment of quantum theory. (shrink)

A familiar interpretation of quantum mechanics (one of a number of views sometimes labeled the "Copenhagen interpretation'"), takes its empirical apparatus at face value, holding that the quantum wave function evolves by the Schrödinger equation except on certain occasions of measurement, when it collapses into a new state according to the Born rule. This interpretation is widely rejected, primarily because it faces the measurement problem: "measurement" is too imprecise for use in a fundamental physical theory. We (...) argue that this is a weak objection, as there may be many ways of making "measurement" precise. However, measurement-collapse interpretations face a more serious objection: a dilemma tied to the quantum Zeno effect. Is measurement itself an observable that can enter superpositions? If yes, then the standard measurement-collapse dynamics is ill-defined. If no, then (at least if measurement is an observable), measurements can never start or finish. The best way out is to deny that measurement is an observable, but this leads to strong and revisionary consequences. This reinforces the view that there is no nonrevisionary interpretation of quantum mechanics. (shrink)

The statistical aspects of quantum explanation are intrinsic to quantum physics; individual quantum events are created in the interactions associated with observation and are not describable by predictive theory. The superposition principle shows the essential difference between quantum and non-quantum physics, and the principle is exemplified in the classic single-photon two-slit interference experiment. Recently Mandel and Pfleegor have done an experiment somewhat similar to the optical single-photon experiment but with two independently operated lasers; interference is obtained even with beam intensity (...) so small that only one photon is in the apparatus at a time. The result can be understood in terms of the superposition of states; or, in terms of the Uncertainty Principle, which is found to forbid the determination of which of the two lasers is the source of a given photon (if conditions for interference are to obtain). The Mandel-Pfleegor experiment gives a physical argument against the continuous localization of a photon that is assumed in the hidden variable theories and therefore gives further support for the generally accepted view that an observed entity (observed state) is created in the observation event. This aspect of quantum physics implies a subjectivism on the level of individual quantum-level occurrences, since there is in quantum theory no basis for asserting the existence of the event independently of observation of it. Extension of this subjectivism to large scale, non-quantum phenomena falls within the principles of quantum theory; counter considerations that argue against such an extension are noted. (shrink)

This article proposes to interpret Nāgārjuna’s Madhyamaka philosophy as a flexible philosophical position rather than a fixed position within the metaphysical landscape. Nāgārjuna’s enigmatic mode of reasoning complicates efforts to definitively delineate his position in respect to the status of reality. Instead, it proves more worthwhile to consider his philosophical stance as dynamic, flexible, non-static, and adaptive relative to his philosophical opponents. Presenting Nāgārjuna as occupying a clearly defined metaphysical position fails to capture the full richness and complexity of the (...) Madhyamaka philosophy, and goes precisely against the Mādhyamika’s spirit and method. Nāgārjuna constantly undermines the assertions of his adversaries, expressing no fixed thesis of his own, thereby embodying the fluidity of the middle way. I contend that Nāgārjuna’s adeptness at articulating the middle way stems from his subversive-styled rhetorical strategies coupled with his application of the prasaṅga method. Furthermore, this interpretation aligns more closely with Buddhist practice in general and sheds light on the pedagogical dimensions of the Madhyamaka philosophy. (shrink)

Starting with Ratnākaraśānti’s (c. 970–1045 CE) interpretation of Nāgārjuna’s (2nd/3rd CE) _Mūlamadhyamakakārikā_ (MMK) verse 24.18 (24.18), the heart of the Middle Way doctrine, we shall revisit the different explanations of this verse transmitted in classical Chinese, Sanskrit, and classical Tibetan and highlight two hermeneutical trends under which all interpretations of 24.18 in the commentarial literature of the MMK may arguably be subsumed. On the one hand, the treble-schema school, which is best exemplified in Kumārajīva’s (鳩摩羅什, 343–413 CE) Chinese translation (...) of 24.18, the earliest textual witness to 24.18, takes 24.18 as a quotation of the Buddha’s own words, as Jízàng (吉藏, 549–623 CE) specified, from the _Fóshuō huāshǒu jīng_ (佛說華手經, T16 657, HSJ), an underappreciated tathāgatagarbhic scripture. On the other hand, the even-schema school, the most renowned advocate of which is Candrakīrti (600–650 CE), attributes emphatically 24.18 to Nāgārjuna. The exegetical ramification on the origin of 24.18 may have been the hidden drive of the doctrinal disputes and sectarian dislikes in the history of Madhyamaka, and its significance for Buddhist Studies merits and awaits further explorations. (shrink)

A review: Kristian Camilleri: Heisenberg and the interpretation of quantum mechanics: The physicist as philosopher. Cambridge University Press, Cambridge, 2009, 212 pp.

Most interpretations of Quantum Mechanics alternative to Copenhagen interpretation try to avoid the dualistic flavor of the latter. One of the basic goals of the former is to avoid the ad hoc introduction of observers and observations as an inevitable presupposition of physics. Non-Copenhagen interpretations usually trust in decoherence as a necessary mechanism to obtain a well-defined, observer-free transition from a unitary quantum description of the universe to classicality. Even though decoherence does not solve the problem of (...) the definite outcomes, it helps to explain why we do not observe superpositions and, according to Zurek’s existential interpretation, why a specific preferred basis emerges through system–environment interactions. The aim of this paper is to show why such interpretation ends up begging the question and provides little progress in understanding the quantum-to-classical transition; the ultimate reason being that preferred bases always correlate to human observation. Benefitting from the technical discussion, some remarks will be offered in the last section regarding the role of classical observations as a necessary condition to make workable the formalism of Quantum Mechanics and scientific activity itself. (shrink)

This paper proposes an interpretation of Nāgārjuna’s doctrine of the two truths that considers saṃvṛti and paramārtha-satya two visions of reality on which the Buddhas, for soteriological and pedagogical reasons, build teachings of two types: respectively in agreement with (for example, the teaching of the Four Noble Truths) or in contrast to (for example, the teaching of emptiness) the category of svabhāva. The early sections of the article show to what extent the various current interpretations of the Nāgārjunian doctrine (...) of the dve satye—despite their sometimes even macroscopic differences—have a common tendency to consider the notion of śūnyatā as a teaching not based on, but equivalent to supreme truth. This equivalence—philologically questionable—leads to interpretative paths that prove inevitably aporetic: indeed, according to whether the interpretation of śūnyatā is ‘metaphysical’ or ‘anti-metaphysical’, it gives rise to readings of Nāgārjuna’s thought incompatible, respectively, with anti-metaphysical and realistic types of verses traceable in the works of the author of the Mūla-madhyamaka-kārikā (MMK). On the contrary, by giving more emphasis to the expression samupāśritya (“based on”), which recurs in MMK.24.8, and therefore, by epistemologically separating the notion of śūnyatā from the notion of paramārtha-satya (and of some of its conceptual equivalents such as nirvāṇa, tattva and dharmatā), we may obtain an interpretation—at once realistic and anti-metaphysical—of the theory of the two truths compatible with the vast majority (or even totality) of Nāgārjuna’s verses. (shrink)

This paper proposes a critical analysis of that interpretation of the Nāgārjunian doctrine of the two truths as summarized—by both Mark Siderits and Jay L. Garfield—in the formula: “the ultimate truth is that there is no ultimate truth”. This ‘semantic reading’ of Nāgārjuna’s theory, despite its importance as a criticism of the ‘metaphysical interpretations’, would in itself be defective and improbable. Indeed, firstly, semantic interpretation presents a formal defect: it fails to clearly and explicitly express that which it (...) contains logically; the previously mentioned formula must necessarily be completed by: “the conventional truth is that nothing is conventional truth”. Secondly, after having recognized what Siderits’ and Garfield’s analyses contain implicitly, other logical and philological defects in their position emerge: the existence of the ‘conventional’ would appear—despite the efforts of semantic interpreters to demonstrate quite the contrary—definitively inconceivable without the presupposition of something ‘real’; moreover, the number of verses in Nāgārjuna that are in opposition to the semantic interpretation (even if we grant semantic interpreters that these verses do not justify a metaphysical reconstruction of Nagarjuna’s doctrine) would seem too great and significant to be ignored. (shrink)

Theological engagement with quantum physics has, to this day, been dominated by the Copenhagen interpretation. However, philosophers and physicists working in the “quantum foundations” field have largely abandoned the Copenhagen view on account of what is widely seen as its troublesome antirealism. Other metaphysical approaches have come to the fore instead, which often take a strongly realist flavor, such as de Broglie-Bohm, or Everett's “Many-Worlds” interpretation. In the spirit of recent quantum foundations work, this article introduces (...) a collection of studies aimed at taking quantum theology “beyond Copenhagen.” The present article advocates a commitment to “quantum fundamentalism,” which could resolve some of the enduring ontological problems faced by existing theological work with quantum mechanics, especially in discussions of quantum special divine action. Taking quantum fundamentalism literally would mean a departure from the Copenhagen interpretation, and the article suggests the need for a new research program to lay the groundwork in the natural theology of quantum foundations. (shrink)

Nāgārjuna, the famous founder of the Madhyamika School, proposed the positive catuṣkoṭi in his seminal work, Mūlamadhyamakakārikā: ‘All is real, or all is unreal, all is both real and unreal, all is neither unreal nor real; this is the graded teaching of the Buddha’. He also proposed the negative catuṣkoṭi: ‘“It is empty” is not to be said, nor “It is non-empty,” nor that it is both, nor that it is neither; [“empty”] is said only for the sake of instruction’ (...) and the no-thesis view: ‘No dharma whatsoever was ever taught by the Buddha to anyone’. In this essay, I adopt Gricean pragmatics to explain the positive and negative catuṣkoṭi and the no-thesis view proposed by Nāgārjuna in a way that does not violate classical logic. For Nāgārjuna, all statements are false as long as the hearer understands them within a reified conceptual scheme, according to which substance is a basic categorical concept; substances have svabhāva, and names and sentences have svabhāva. (shrink)

Kajiyama Yuich understands Nāgārjuna’s logics of catuṣkoṭi in terms of Hegelian Dialectics, while interpreting the negation formula of 4th koṭi in tetralemma as the religious truth of Madhyamika, which cannot be negated as an ultimate truth. And Richard Robinson also posits this proposition as dissolving the entire dr̥sti. Examining these approaches, this thesis argues against the dialectical interpretation of catuṣkoṭi with reference to its logical structure. For this, reference will also be made to Piṇgala and Candrakīrti’s commentary comparing them (...) to Robinson’s and Kajiyama’s. Here, focus will be put on the aspect of ‘perspectives.’ Upon further examination, it was determined that a Hegelian dialectical approach is not plausible for interpreting Nāgārjuna’s logic, which is purely negative and skeptical in its character. And through reformulating the structure of catuṣkoṭi in terms of prasaṅga, this paper compares it with a dialectical formula to more clearly evaluate the implication of negative logic for catuṣkoṭi. Thereby, it was seen that Nāgārjuna has neither equated propositions on the basis of identity, nor postulated any hierarchy through classifying the grade of these koṭis. Accordingly, on the strength of various perspectives, any proposition in the catuṣkoṭi can be understood with logical clarity, without positing any metaphysical or dialectical interpretation. Further, the possible reconstruction of Nāgārjuna’s understanding of the tetralemma supports a semantic approach to truth, while revealing the absurdity of perceiving identity or causal relations as possessing intrinsic substance. (shrink)

This paper defends a “conceptualist” interpretation of Nāgārjuna which stands in-between two other prominent accounts, the nihilist view and what I call the anti-essentialist view. The nihilist reading, recently defended by Thomas Wood, holds that for Nāgārjuna nothing exists either at the ultimate or at the conventional level. On the anti-essentialist account, supported by Jay Garfield and David Kalupahana, though Nāgārjuna rejects the ultimate existence of things as svabhāva (independent), he affirms their conventional existence as interdependent. I argue that (...) the nihilist view raises two challenges to which anti-essentialists have given no adequate response. The first alleges that the notion that all things are interdependent is incoherent. The second consists of passages from Nāgārjuna’s writings that seem to claim that whatever exists is svabhāva or depends on what is svabhāva. The conceptualist interpretation, I suggest, allows us to respond to these challenges while avoiding the implausible nihilist account. On this view, the passages in question assert a claim not about what exists but about the concept of existence, namely that it is a core part of this concept that what exists is either svabhāva or depends on what is svabhāva. Thus, contra the anti-essentialist, Nāgārjuna’s view is that there is no coherent concept of universal interdependent existence. But contra the nihilist, things can still be said to exist conventionally, since conventional discourse is precisely discourse in which subjects do not endorse the svabhāva component of the concept of existence. The upshot – again contra the anti-essentialist – is that both conventional truth and emptiness are strictly inconceivable. (shrink)

This paper presents a new Symmetrical Interpretation (SI) of relativistic quantum mechanics which postulates: quantum mechanics is a theory about complete experiments, not particles; a complete experiment is maximally described by a complex transition amplitude density; and this transition amplitude density never collapses. This SI is compared to the Copenhagen Interpretation (CI) for the analysis of Einstein’s bubble experiment. This SI makes several experimentally testable predictions that differ from the CI, solves one part of the measurement problem, (...) resolves some inconsistencies of the CI, and gives intuitive explanations of some previously mysterious quantum effects. (shrink)

Copenhagen interpretation of quantum mechanics deals with these problems is reviewed. A new interpretation of the formalism of quantum mechanics, the transactional interpretation, is presented. The basic element of this interpretation is the transaction describing a quantum event as an exchange of advanced and retarded waves, as implied by the work of Wheeler and Feynman, Dirac, and others. The transactional interpretation is explicitly nonlocal and thereby consistent with recent tests of the Bell inequality, yet (...) is relativistically invariant and fully causal. A detailed comparison of the transactional and Copenhagen interpretations is made in the context of well-known quantum-mechanical Gedankenexperimenre and "paradoxes." The transactional interpretation permits quantum-mechanical wave functions to be interpreted as real waves physically present in space rather than as "mathematical representations of knowledge" as in the Copenhagen interpretation. The transactional interpretation is shown to provide insight into the complex character of the quantum-mechanical state vector and the mechanism associated with its "collapse." It also leads in a natural way to justification of the Heisenberg uncertainty principle and the Born probability law (P = ii iij*), basic elements of the Copenhagen interpretation. (shrink)

Everettian Interpretations of Quantum Mechanics Between the 1920s and the 1950s, the mathematical results of quantum mechanics were interpreted according to what is often referred to as “the standard interpretation” or the “Copenhagen interpretation.” This interpretation is known as the “collapse interpretation" because it supposes that an observer external to a system causes the system, … Continue reading Everettian Interpretations of Quantum Mechanics →.

I describe a pedagogical scheme devised to teach efficiently to computer scientists just enough quantum mechanics to permit them to understand the theoretical developments of the last decade going under the name of ''quantum computation.'' I then note that my offbeat approach to quantum mechanics, designed to be maximally efficacious for this specific educational purpose, is nothing other than the Copenhagen interpretation.

I describe a pedagogical scheme devised to teach efficiently to computer scientists just enough quantum mechanics to permit them to understand the theoretical developments of the last decade going under the name of “quantum computation.” I then note that my offbeat approach to quantum mechanics, designed to be maximally efficacious for this specific educational purpose, is nothing other than the Copenhagen interpretation.

While the contemporary problem of the criterion raises similar epistemological issues as Agrippa’s Trilemma in ancient Pyrrhonian skepticism, the consideration of such epistemological questions has served two different purposes. On one hand, there is the purely practical purpose of Pyrrhonism, in which such questions are a means to reach suspension of judgment, and on the other hand, there is the theoretical purpose of contemporary epistemologists, in which these issues raise theoretical problems that drive the search for theoretical resolution. In classical (...) India, similar issues arise in Nāgārjuna’s Vigrahavyāvartanī, but it is not entirely clear what Nāgārjuna’s purpose is. Contrary to the theoretical interpretations of several recent scholars such as Jan Westerhoff according to which Nāgārjuna is proffering a contextualist epistemological theory, I argue that Nāgārjuna as well as the later Madhyamaka Candrakīrti, much like Pyrrhonian skeptics, employed concerns about epistemic criteria in service of purely practical purposes. There is no positive epistemological theory to be found in Nāgārjuna’s Vigrahavyāvartanī and Candrakīrti’s Prasannapadā; furthermore a putative thesis of universal emptiness is self-undermining, a conclusion which itself can be seen as part of a therapeutic program. Nonetheless, the historical persistence of these epistemological issues shows that they ought to continue to be areas of theoretical inquiry for epistemologists today. I end with reflections on the wider relevance of my conclusions, particularly with regard to demonstrating the value of philosophy. (shrink)