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Quantum mechanics poses a challenge to epistemology in terms of what is measurable, what is observable, and realism in general.

But does it pose a challenge to ontology as well? Ontology is the examination of the nature of things, presumably this supposes everything has a unique nature. Wave particle duality shows us that objects can have more than one nature. Is this a challenge to ontology? Does the law of excluded middle apply here or is ontology underpinned by a non classical logic (such as fuzzy logic or Von Neumann and Birkhoff's quantum logic)?

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It poses a challenge to overly-specific notions of ontology, but there aren't many around that are that specific.

Relatively general ontological frameworks like process philosophy (e.g. as promoted by Whitehead) have a sufficiently general notion of what is "actual" that a phenomenon that has both wave-like and particle-like properties (depending on context) is not a serious challenge.

But even substance metaphysics has to deal with stuff like water and sand and sound and light, and so it's usually phrased in a general enough way that it doesn't have at its core the idea of involately particulate matter. Some specific arguments may fall flat, but overall it is so general that ideas e.g. of substance being a combination of form and matter survive with only minor tweaks when one considers that the matter has characteristics best described by quantum mechanics.

In particular, with wave vs particle duality, you just say that the substance is what it is, and you will notice different aspects of its behavior in different conditions.

And, thus, all you have to do to rescue most arguments is to insert an "in the classical regime" and everything goes through as before, albeit with a little less satisfaction about having gotten to the true nature of things.

So, in general: no, not very much. In any particular case: you need to check the details.

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I would like to take the question a bit more general: Does quantum mechanics challenge ontology?

Yes, quantum mechanics is a big challenge to ontology, not only to epistemology.

Even in the mesocosmic domain we do not know what the objects are in itself, as has been emphasized by Kant. Even more in quantum mechanics: We do not have access to quantum mechanical objects alike to our direct access to mesocosmic objects. Broadly speaking, an electron is what satisfies the Dirac equation.

More precisely, in the microscosmic domain one often has to abandon the principle of individuality: When considering electron-electron scattering one cannot say that the electrons before scattering are the same as the electrons after scattering. Not only that microcosmic objects. e.g. bosons, possibly are indistinguishable, they may even lack a permanent individuality. Is a photon before and after virtual pair-creation and annihilation the same photon or a different one?

I do not know whether serious attempts for an ontology of the microcosmos have been made until now.

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Ontology concerns the nature of being itself. What is, what exists, or perhaps what really exists.

This is not the concern of modern science, which is a particular method of epistemology. The classic division came with Newton's statement regarding gravity that he "feigns no hypothesis" as what it really is, a question that bothered the Cartesians. This was a decisive turn from the ontological concerns of metaphysics or "first philosophy."

I believe most scientists tend to be Kantians or pragmatists in this sense, at least officially. Gravity is a set of concepts, a mathematical model that works. We cannot pull off the phenomenological drapery and look behind the concept to see what is really there. Something, we assume. Kant's "noumena" or Locke's "something I know not what." But we can only improve the precision of the models.

Similarly, wave-particle duality are not phenomena that confront us in daily life. They are conceptual products of science, mathematical models. In this case especially, it seems quite obvious to all concerned that "wave" and "particle" are simply convenient nametags applied to "we know not what." Thus, as scientific models, which is what they are, they do not present ontological issues.

However, this is admittedly a somewhat superficial answer. The seemingly endless regress of subatomic physics does have ontological implications, that in my own view tend to support some sort of Kantian or pragmatic compromise, casting doubt on "substance" ontology. And philosophers, unconstrained by scientific prudence, do continue to discuss "ontologies" in relation to scientific concepts, but I'm not familiar with the latest in such matters.

You may want to look at "The Wave Function: Essays on the Metaphysics of Quantum Mechanics" (editors, A. Ney and D.Z. Albert), which does deal with ontology and quantum phenomena. Haven't read it yet, so can't summarize.

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If I define a mammal to be a warm-blooded creature that gives birth to live offspring and has hair, and I define a fish to be a vertebrate that has fins and lives in the ocean, do whales (with their "mammal/fish duality") pose a challenge to ontology? Do whales demonstrate that creatures can have more than one nature?

Or, perhaps, does it just mean that my arbitrary classification scheme, drawn up before I knew about whales, needs to be tweaked a little?

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If ontology is the science of being, we have Heidegger, who in the opening to Being and Time wrote:

Within the framework of the following fundamental elaboration of the question of being we cannot offer a detailed temporal interpretation of the foundations of ancient ontology - especially of scientifically highest and purest stage, that is, in Aristotle.

And

Being is not a genus of beings

But QM is about a genus of beings: elementary particles in their most elemental mode; in this sense it is not about Being in Heideggerian sense, in the sense he uses it in Being and Time; but it might be in sense of being, that Aristotle uses when he is being scientific in the sense we would recognise today, were he our contemporary - he is already a contemporary for Heidegger.

To this end, it might be worth quoting Rovelli on QM:

in spite of 70 years of development ... QM still maintains a remarkable level of obscurity; ... it is difficult to overcome the sense of unease that QM communicates. The troubling aspect of the theory assumes different aspects within different interpretations ...[notwithstanding that] some of these objections may be naive or ill-posed.

Rovelli suggests a comparison with the discovery of SR, where the formalism was more or less discovered (by Lorentz) but the actual physical principle that lay behind the formalism had to await Einsteins contribution - that simultaneity was not absolute, but relative, and which implied the revision of the Newtonian conception of space and time.

According to Rovelli, we again have a formalism but not a properly physical principles for QM.

Many interpretations have been investigated, but none have really achieved the level of consensus that SR did.

It's probably worth emphasising, given that this site is philosophical, that ontology isn't purely orientated to the thing-like things that physics is concerned with - for which the qualifier physical might come in useful, as in physical ontology; for example, one could compare that sense of ontology with what I began with - Heideggerian ontology - which is more concerned with:

The being of this being as it is related to its being

Which has a family resemblence with the Socratic injunction:

gnothi seauton (know thyself)

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