The scientific paradigm which I rely upon in the framework of this article is quantum mechanics, whose “cognitive revolution” consisted of replacing the classical principle of separability with the principle of nonseparability or global intercorrelation. According to this intercorrelation, highlighted at the subatomic level, the part cannot be separated from the whole, because every part has a global and instantaneous connection with the whole universe. For this reason the foundation of the world cannot be the part (elementary particles), but the whole, which is therefore logically and ontologically prior to the part, i.e., self-consistent. Consequently, the principle of global intercorrelation elucidates and validates some of the oldest philosophical problems and intuitions about the unity or self-consistency of the world. An example in this sense is the bootstrap theory of American physicist Geoffrey Chew, which presents such striking similarities to the metaphysical system of Leibniz's Monadology that the two intertwine and mirror each other, like twin souls, to the extent that it could be stated that if Chew’s bootstrap theory represents the explanatory physical level of Leibniz’s metaphysics, then, analogously, Leibniz’s Monadology represents the explanatory metaphysical level of Chew’s physics.
The scientific paradigm which I rely upon in the framework of this article is quantum mechanics, whose “cognitive revolution” consisted of replacing the classical principle of separability with the principle of nonseparability or global intercorrelation. According to this intercorrelation, highlighted at the subatomic level, the part cannot be separated from the whole, because every part has a global and instantaneous connection with the whole universe. For this reason the foundation of the world cannot be the part (elementary particles), but the whole, which is therefore logically and ontologically prior to the part, i.e., self-consistent. Consequently, the principle of global intercorrelation elucidates and validates some of the oldest philosophical problems and intuitions about the unity or self-consistency of the world. An example in this sense is the bootstrap theory of American physicist Geoffrey Chew, which presents such striking similarities to the metaphysical system of Leibniz's Monadology that the two intertwine and mirror each other, like twin souls, to the extent that it could be stated that if Chew’s bootstrap theory represents the explanatory physical level of Leibniz’s metaphysics, then, analogously, Leibniz’s Monadology represents the explanatory metaphysical level of Chew’s physics.
Abstract Despite its extraordinary predictive power, quantum mechanics has been hailed as a paradoxical, self-contradictory theory of nature. How does it question the intelligibility of physical worldview? The wave-particle dualism, the incompatibility of physical quantities, the complementarity between the space-time description and the causal description of phenomena question key-notions of the traditional metaphysics, such as substance and cause, but they also call attention to the vital dialectical contrast between the continuous and the discrete, the infinite and the finite, consciousness and matter, and to the essential relational character of measuring, seeing, and knowing. Does quantum physics also question the Western way of thinking? The aim of this article is to show how quantum monadology not only breathes new life into Leibniz’s and Nicholas of Cusa’s monads, but also echoes Nishida’s ‘dialectical monadology’ and orients our gaze towards a metaphysics of universal harmony, i.e., a metaphysics of the dialectical universal or a metaphysics of indeterminacy.
In this thesis I argue that many problems in the philosophy of science and mathematics (in particular, the unreasonable effectiveness of mathematics in physics) can only be addressed within a broader metaphysical framework which provides a coherent world view. I attempt to develop such a framework and draw out its consequences. The attempt is in two parts: first, I develop a speculative framework based on an analogy to set theory; then I combine elements of the framework with ideas from Leibnizian monadology and consistent histories quantum theory to introduce (what I call) quantum monadology. The two parts focus on different aspects of the problem and should be viewed as stages on the way to a final formulation. The inspiration for the thesis came from Plato’s Timaeus and Wigner’s comments on quantum mechanics. As it turned out, Leibniz’s Monadology became a third key source.
If the paradigm of classical epistemology follows the logic of the part, being tributary to the principle of subject-object separability, in which the subject, that is, the part, is considered separate from the object, that is, the whole, then the new paradigm of the quantum theory has replaced the principle of separability, specific to the logic of the part, with the principle of subject-object nonseparability or global intercorrelation, specific to the logic of the whole. Starting from this principle of quantum nonseparability, I will show that it can be explored and applied in new forms of psychotherapy. I mean here the art of meditation, as the art of the whole, that is, the art of perceiving the world and ourselves in a nondualistic nonanalytical, and nonfragmentary way, in which the subject and the object, the observer and the observed, the part and the whole, are not separated, but interconnected.
Relational ideas for our description of the natural world can be traced to the concept of Anaxagoras on the multiplicity of basic particles, later called “homoiomeroi” by Aristotle, that constitute the Universe and have the same nature as the whole world. Leibniz viewed the Universe as an infinite set of embodied logical essences called monads, which possess inner view, compute their own programs and perform mathematical transformations of their qualities, independently of all other monads. In this paradigm, space appears as a relational order of co-existences and time as a relational order of sequences. The relational paradigm was recognized in physics as a dependence of the spatiotemporal structure and its actualization on the observer. In the foundations of mathematics, the basic logical principles are united with the basic geometrical principles that are generic to the unfolding of internal logic. These principles appear as universal topological structures (“geometric atoms”) shaping the world. The decision-making system performs internal quantum reduction which is described by external observers via the probability function. In biology, individual systems operate as separate relational domains. The wave function superposition is restricted within a single domain and does not expand outside it, which corresponds to the statement of Leibniz that “monads have no windows”.
Metaphysical models by which we understand the fundamental make-up of our universe are all the more plausible when informed by empirically confirmed scientific theory. I have argued that contemporary physics tells us that there are no elementary particles , in any metaphysically serious sense of the word “particle”. Quantum phenomena are not concrete particular entities. The replacement of quantum mechanics by quantum field theory has major consequences for our metaphysics, in that it calls into question the tradition of according categorial priority to particular entities. Instead, categorial priority should be accorded to generic processes. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
The idea that the world is made of particles — little discrete, interacting objects that compose the material bodies of everyday experience — is a durable one. Following the advent of quantum theory, the idea was revised but not abandoned. It remains manifest in the explanatory language of physics, chemistry, and molecular biology. Aside from its durability, there is good reason for the scientific realist to embrace the particle interpretation: such a view can account for the prominent epistemic fact that only limited knowledge of a portion of the material universe is needed in order to make reliable predictions about that portion. Thus, particle interpretations can support an abductive argument from the epistemic facts in favor of a realist reading of physical theory. However, any particle interpretation with this property is untenable. The empirical adequacy of modern particle theories requires adoption of a postulate known as permutation invariance (PI) — the claim that interchanging the role of two particles of the same kind in a dynamical state description results in a description of the identical state. It is the central claim of this essay that PI is incompatible with any particle interpretation strong enough to account for the epistemic facts. This incompatibility extends across all physical theories. To frame and motivate the inconsistency argument, I begin by fixing the relevant notion of particle. To single out those accounts of greatest appeal to the realist, I develop the logically weakest particle ontology that entails the epistemic fact that the world is piecewise predictable, an ontology I call ‘minimal atomism’ (MA). The entire series of scientific conceptions of the particle, from Newton’s mechanically interacting corpuscles to the ‘centers of force’ in classical field theories, all comport with MA. As long as PI is left out, even quantum mechanics can be viewed this way. To assess the impact of PI on this picture, I present a framework for rigorously connecting interpretations to physical theories. In particular, I represent MA as a set of formal conditions on the models of physical theories, the mathematical structures taken to represent states of the world. I also formulate PI — originally introduced as a postulate of non-relativistic quantum mechanics — in theory independent terms. With all of these pieces in hand, I am then able to present a proof of the inconsistency of PI and MA. In the second part of the essay, I survey responses to the inconsistency result open to the scientific realist. The two most plausible approaches involve abandoning particles in one way or another. The first alternative interpretation considered takes the property bearing objects of the world to be regions of space rather than particles. In this view, the properties once attributed to particles in quantum states are attributed instead to one or more regions of space. PI no longer obtains in this case, at least not as a statement about the permutation symmetry of property bearers. Rather, the new interpretation naturally imposes an analogous constraint on quantum states. The second major approach to evading the inconsistency result is to dispense with objects altogether. This is the recommendation of so-called ‘Ontic Structural Realism’ (OSR). The central OSR thesis is that structure rather than entities are the basic ontological components of the world. OSR is intended to embrace the ‘miracle’ argument in favor of scientific realism (it would be a miracle if a scientific theory were predictively successful unless it were also approximately true with regard to its description of reality) while avoiding the pessimistic meta-induction (most predictively successful theories along with their associated ontologies have been overturned, so we should expect the same of our current theories). I demonstrate that one principal motivation for OSR based on the under-determination of interpretations in QM is actually dissolved by the incompatibility result. At the same time, I suggest reasons to think that OSR fares no better with respect to the pessimistic meta-induction than traditional realism does. Thus, while PI and MA may be incompatible, object ontologies remain the best option for the realist.