Quantum Ontology without Speculation

Existing proposals concerning the ontology of quantum mechanics (QM) either involve speculation that goes beyond the scientific evidence or abandon realism about large parts of QM. This paper proposes a way out of this dilemma, by showing that QM as it is formulated in standard textbooks allows for a much more substantive ontological commitment than is usually acknowledged. For this purpose, I defend a non-fundamentalist approach to ontology, which is then applied to various aspects of QM. In particular, I will defend realism about spin, which has been viewed as a particularly hard case for the ontology of QM

The relevance of ontological commitments

In this introductory note, I describe my particular view of the notion of ontological commitments as honest and pragmatic working hypotheses that assume the existence (out there) of certain entities represented by the symbols in our theory. I argue that this is not naive, in the sense that it does not entail the belief that the hypotheses could ever be proved to be true (or false), but it is nevertheless justified by the success and predictive power of the theory that contains the concepts assumed to exist. I also claim that the ontological commitments one holds (even if tacitly so) have a great influence on what kind of science is produced, how it is used, and how it is understood. Not only I justify this claim, but I also propose a sketch of a possible falsification of it. As a natural conclusion, I defend the importance of identifying, clarifying and making explicit one's ontological commitments if fruitful scientific discussions are to be had. Finally, I compare my point of view with that of some philosophers and scientists who have put forward similar notions.Comment: Submitted for peer-revie

The ontology of number

What is a number? Answering this will answer questions about its philosophical foundations - rational numbers, the complex numbers, imaginary numbers. If we are to write or talk about something, it is helpful to know whether it exists, how it exists, and why it exists, just from a common-sense point of view [Quine, 1948, p. 6]. Generally, there does not seem to be any disagreement among mathematicians, scientists, and logicians about numbers existing in some way, but currently, in the mainstream arena only definitions, descriptions of properties, and effects are presented as evidence. Enough historical description of numbers in history provides an empirical basis of number, although a case can be made that numbers do not exist by themselves empirically. Correspondingly, numbers exist as abstractions. All the while, though, these "descriptions" beg the question of what numbers are ontologically. Advocates for numbers being the ultimate reality have the problem of wrestling with the nature of reality. I start on the road to discovering the ontology of number by looking at where people have talked about numbers as already existing: history. Of course, we need to know not only what ontology is but the problems of identifying one, leading to the selection between metaphysics and provisional approaches. While we seem to be dimensionally limited, at least we can identify a more suitable bootstrapping ontology than mere definitions, leading us to the unity of opposites. The rest of the paper details how this is done and modifies Peano's Postulates

The Divine Action Project, 1988–2003

This article explores the state of the art in theories of special divine action by means of a study of the Divine Action Project (DAP) co-sponsored by the Vatican Observatory and the Center for Theology and the Natural Sciences in Berkeley. The basic aim is to introduce the DAP and to summarize its results, especially as these were compiled in the final “capstone” meeting of the DAP, and drawing on the published output of the project where possible. The subsidiary aim is to evaluate criticisms of theories of special divine action developed within the DAP.ye

Misleading signposts along the de Broglie-Bohm road to quantum mechanics

Eighty years after de Broglie's, and a little more than half a century after Bohm's seminal papers, the de Broglie--Bohm theory (a.k.a. Bohmian mechanics), which is presumably the simplest theory which explains the orthodox quantum mechanics formalism, has reached an exemplary state of conceptual clarity and mathematical integrity. No other theory of quantum mechanics comes even close. Yet anyone curious enough to walk this road to quantum mechanics is soon being confused by many misleading signposts that have been put up, and not just by its detractors, but unfortunately enough also by some of its proponents. This paper outlines a road map to help navigate ones way.Comment: Dedicated to Jeffrey Bub on occasion of his 65th birthday. Accepted for publication in Foundations of Physics. A "slip of pen" in the bibliography has been corrected -- thanks go to Oliver Passon for catching it

The utterly prosaic connection between physics and mathematics

Eugene Wigner famously argued for the "unreasonable effectiveness of mathematics" for describing physics and other natural sciences in his 1960 essay. That essay has now led to some 55 years of (sometimes anguished) soul searching --- responses range from "So what? Why do you think we developed mathematics in the first place?", through to extremely speculative ruminations on the existence of the universe (multiverse) as a purely mathematical entity --- the Mathematical Universe Hypothesis. In the current essay I will steer an utterly prosaic middle course: Much of the mathematics we develop is informed by physics questions we are tying to solve; and those physics questions for which the most utilitarian mathematics has successfully been developed are typically those where the best physics progress has been made.Comment: 12 pages. Minor edits on an essay written for the 2015 FQXi essay contest: "Trick or truth: The mysterious connection between physics and mathematics

Primitive ontology and quantum state in the GRW matter density theory

The paper explains in what sense the GRW matter density theory (GRWm) is a primitive ontology theory of quantum mechanics and why, thus conceived, the standard objections against the GRW formalism do not apply to GRWm. We consider the different options for conceiving the quantum state in GRWm and argue that dispositionalism is the most attractive one.Comment: arXiv admin note: text overlap with arXiv:quant-ph/0603027 by other author

Thoughts, Things, and Theories

We to critique the following question: can we have reasonable certainty that the terms in speculative or empirical theories correspond meaningfully to things in the ontological structure of the world, or are they only convenient fictions useful for predicting phenomena? We first justify this question as meaningful, and capable of admitting a meaningful answer. We then analyze question itself with examples from physics and biology. We conclude that we can be reasonably certain that the terms in an empirical theory have some degree of ontological significance, provided that they are directly related to phenomenal experiences. We also suggest that the advance of science can be aided through this understanding. Finally we use these conclusions to analyze the existence of the mind and certain physical structures