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According to mathematical constructivism, a mathematical object can exist only if there is a way to compute (or "construct") it; so, what is non-computable is non-constructive. In the example of the quantum model, whose Fock states are…
In this article, the weakest possible theorem providing a foundation for the Hilbert space formalism of quantum theory is stated. The necessary postulates are formulated, and the mathematics is spelt out in detail. It is argued that, from…
According to the Integrated Information Theory of Consciousness, consciousness is a fundamental observer-independent property of physical systems, and the measure Phi of integrated information is identical to the quantity or level of…
The rather unintuitive nature of quantum theory has led numerous people to develop sets of (physically motivated) principles that can be used to derive quantum mechanics from the ground up, in order to better understand where the structure…
Did Leibniz exploit infinitesimals and infinities `a la rigueur, or only as shorthand for quantified propositions that refer to ordinary Archimedean magnitudes? Chapter 5 in (Ishiguro 1990) is a defense of the latter position, which she…
We reconsider briefly the relation between "physical quantity" and "physical reality in the light of recent interpretations of Quantum Mechanics. We argue, that these interpretations are conditioned from the epistemological relation between…
Do scientific theories limit human knowledge? In other words, are there physical variables hidden by essence forever? We argue for negative answers and illustrate our point on chaotic classical dynamical systems. We emphasize parallels with…
We use fast-growing finite and infinite sequences of natural numbers and more complicated constructs to define models of hypercomputation and interpret non-arithmetic predicates, with the strongest extensions reaching full second order…
In this paper we consider the observables describing fundamental spatiotemporal properties and relations in the context of Quantum Gravity (QG). As we will show, in both Loop Quantum Gravity and in String Theory, these observables are…
Leibniz entertained various conceptions of infinitesimals, considering them sometimes as ideal things and other times as fictions. But in both cases, he compares infinitesimals favorably to imaginary roots. We agree with the majority of…
A remarkable feature of quantum theory is that particles with identical intrinsic properties must be treated as indistinguishable if the theory is to give valid predictions. In the quantum formalism, indistinguishability is expressed via…
We present a general formalism with the aim of describing the situation of an entity, how it is, how it reacts to experiments, how we can make statistics with it, and how it changes under the influence of the rest of the universe. Therefore…
When the physics is wrong, physics-informed machine learning becomes physics-misinformed machine learning. A powerful black-box model should not be able to conceal misconceived physics. We propose two criteria that can be used to assert…
This work demonstrates that a complete description of the interaction of matter and all forces, gravitational and non-gravitational, can in fact be realized within a quantum affine algebraic framework. Using the affine group formalism, we…
A strongly deterministic theory of physics is one that permits exactly one possible history of the universe. In the words of Penrose (1989), ''it is not just a matter of the future being determined by the past; the entire history of the…
The predictions that quantum theory makes about the outcomes of measurements are generally probabilistic. This has raised the question whether quantum theory can be considered complete, or whether there could exist alternative theories that…
The indeterministic outcome of a measurement of an individual quantum is certified by the impossibility of the simultaneous, definite, deterministic pre-existence of all conceivable observables from physical conditions of that quantum…
Quantum mechanics led to spectacular technological developments, discovery of new constituents of matter and new materials. However there is still no consensus on its interpretation and limitations. Some scientists and scientific writers…
I propose a novel interpretation of quantum theory, which I will call Environmental Determinacy-based (EnDQT). In contrast to the well-known interpretations of quantum theory, EnDQT has the benefit of not adding non-local,…
Some relations between physics and finitary and infinitary mathematics are explored in the context of a many-minds interpretation of quantum theory. The analogy between mathematical ``existence'' and physical ``existence'' is considered…