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Can we infer whether all of physical reality began to exist? Several novel results are offered suggesting a negative verdict. First, a common strategy for defending a cosmic beginning involves showing that individual beginningless…
Discussions surrounding the nature of the infinite in mathematics have been underway for two millennia. Mathematicians, philosophers, and theologians have all taken part. The basic question has been whether the infinite exists only in…
Inflationary Cosmology makes the universe ``eternal" and provides for recurrent universe creation, ad infinitum -- making it also plausible to assume that ``our" Big Bang was also preceeded by others, etc.. However, GR tells us that in the…
There is some evidence that the Universe is presently undergoing accelerating expansion. This has restored some credit to the scenarios with a non-vanishing cosmological constant. From the point of view of a theory of fundamental…
Despite the success of modern physics in formulating mathematical theories that can predict the outcome of experiments, we have made remarkably little progress towards answering the most fundamental question of: why is there a universe at…
In this paper we analyze the definition of quantum superpositions within orthodox Quantum Mechanics (QM) and their relation to physical reality. We will begin by discussing how the metaphysical presuppositions imposed by Bohr on the…
There is a problem with the foundations of classical mathematics, and potentially even with the foundations of computer science, that mathematicians have by-and-large ignored. This essay is a call for practicing mathematicians who have been…
Nature abhors an infinity. The limits of general relativity are often signaled by infinities: infinite curvature as in the center of a black hole, the infinite energy of the singular big bang. We might be inclined to add an infinite…
I give a pedagogical explanation of what it is about quantization that makes general relativity go from being a nearly perfect classical theory to a very problematic quantum one. I also explain why some quantization of gravity is…
Much has been discussed in the philosophy of science about how we should understand the scientific enterprise. On the one hand, scientific realists believe that empirically adequate theories can be supplemented by interpretations that can…
Cosmology today is confronted with several seemingly insoluble puzzles and strange, inexplicable coincidences. But a careful re-examination of the Cosmological principle and the Weyl postulate, foundational elements in this subject,…
The extravagances of quantum mechanics never fail to enrich daily the debate around natural philosophy. Entanglement, non-locality, collapse, many worlds, many minds, and subjectivism have challenged generations of thinkers. Its approach…
A complete model of the universe needs at least three parts: (1) a complete set of physical variables and dynamical laws for them, (2) the correct solution of the dynamical laws, and (3) the connection with conscious experience. In quantum…
We argue by using Godel's incompletness theorems in logic that platonism is the best metaphysics for science. This is based on the fact that a natural law in a platonic metaphysics represents a timeless order in the motion of matter, while…
The expansion of our universe, when followed backward in time, implies that it emerged from a phase of huge density, the big bang. These stages are so extreme that classical general relativity combined with matter theories is not able to…
The way Leibniz applied his philosophy to mathematics has been the subject of longstanding debates. A key piece of evidence is his letter to Masson on bodies. We offer an interpretation of this often misunderstood text, dealing with the…
The aim of this essay is to propose a conception of mathematics that is fully consonant with naturalism. By that I mean the hypothesis that everything that exists is part of the natural world, which makes up a unitary whole.
It is argued that the traditional "realist" methodology of physics, according to which human concepts, laws and theories can grasp the essence of reality, is incompatible with the most fruitful interpretation of quantum formalism. The proof…
When one takes into account gravitation, the measurement of space and time cannot be carried out with infinite accuracy. When quantum mechanics is reformulated taking into account this lack of accuracy, the resolution of the measurement…
The Planck scale is usually believed to be an unpassable wall. Putting a cutoff there and thinking of it as a quantized spacetime entity shows that. However, this is exactly the cause of many problems in quantum gravity. The cosmological…