The Duality at the Heart of Physics

I’m speaking of the measurement problem or paradox in quantum physics. One the one hand we have the continuous deterministic dynamical evolution of the wave function (in Schrödinger’s formulation of quantum mechanics), and on the other we have the discontinuous process of measurement which “collapses” the wave function into a definite state. What, if anything, does quantum physics mean for the nature of reality?

Interpretations of this problem historically have tended to devalue the ontological status of one or the other side of this duality. Some versions of the Copenhagen interpretation treated the wave function as a mere calculation framework which shouldn’t be accorded the status of something real. Over recent times, variants of the many-worlds hypothesis have become more popular: these emphasize the reality of the well-behaved wave function, and dismiss our perception of the everyday classical world as either a limited or illusory view of true reality. As I wrote in (the last part of) this post, more careful analysis of Neils Bohr’s own views tend to show he understood that the two quantum processes were irreducibly interdependent.

My own view is that quantum measurements are the events which make up the concrete fabric of our world. The wave function also exists, however, and can be considered the space of abstract possibilities which provide the raw material for the actualization of each event. While we can only observe "inter-measurement" phenomena associated with the wave function (e.g. entanglement) in carefully constructed laboratory situations, it comprehensively enters into our everyday world as well.

In fact, each larger system in nature is an extended event complex which continually self-implements measurements as interactions with the environment. Each set of measurements gives rise to a new possibility space which is raw material for further events.

Notes on Plantinga's Modal Realism

Here are some brief notes on Plantinga’s system of modal realism. I have not found this to be easy territory. Sources: Essays in the Metaphysics of Modality, and Christopher Menzels’s SEP article on Actualism.

In place of possible worlds we have a full set of abstract maximal states of affairs. These “worlds”, along with the concrete world we know, are all part of existence. The difference between an abstract maximal state of affairs and our everyday world is that ours happens to be the maximal state of affairs which “obtains” -- this obtaining is analogous to a propostion being true. Note: in some of Plantinga’s writings, he says our world is the actual world, and the abstract ones are not actual, yet they exist. It’s easy for “those of us at home” to be confused when the words ‘actual’ and ‘exists’ are divorced! But leaving this aside, it is a primitive fact that one world – ours—is picked out as the concrete world. Lewis was extremely critical of this aspect – in his system actual is a merely indexical term: the actual world is the world I happen to be in, but otherwise the worlds exist on even-handed terms relative to each other.

Another key aspect for Plantinga is that for any object/individual there exists an individual essence. This is unlike Lewis’ counterpart theory, where I have counterparts in other worlds, and there is no dogma saying precisely when it is that the counterpart’s properties differ enough from mine that it is no longer worthy of being called my counterpart. The postulate of individual essences also seems a brute primitive. It serves to replace possible individuals in modal statements with something ‘actual’. But it’s not an actual individual – it is an (platonic) essence. The notion of individual essence seems to me a way to avoid the question of what it is which makes a bundle of properties an individual. (Some technical objections to this part of the system are also summarized in Menzel’s article.)

Plantinga takes seriously that we need to have truthmakers for modal truths (which I like). He also thinks there are should be no non-existent objects or mere possibilia as truthmakers, so everything needs to be explained via things which exist. To make it work, he needs a panoply of abstract entities to cover all the angles. I don’t have a problem with this in and of itself, since I am open-minded regarding the existence of abstract objects. The 2 issues I have are those mentioned above: first, the way our world gets picked out of the set of abstract worlds is a primitive; and the postulate of individual essences (as distinct from individuals themselves) is another feature I find somewhat gratuitous.

Platonism on Tap at Maverick Philosopher

Posts on the subject are underway at Bill Vallicella's active and interesting blog (see here and here). Good group of commenters as well.

Driven to Abstraction

Plato just won’t go away.

I’ve been thinking about whether the truthmakers for modal truths could involve abstract possible worlds, but this requires backing up a bit in order to consider the status of abstract objects in general.

Defining what it is to be "abstract" is not trivial. Lewis made this point in On the Plurality of Worlds. His breakdown of several ways to approach the question is followed by Gideon Rosen in this brief SEP article on Abstract Objects. The most often used methods are to define abstract objects in terms of what they are not, and then work out the idea using examples. Abstract objects are neither physical nor mental – usually they are thought of as unchanging and causally inert (the potential role of abstract objects in a theory of causation is something to come back to, however). Numbers and universals (“redness”, “roundness”) are paradigm examples.

This SEP article on Platonism in Metaphysics, by Mark Balaguer, summarizes the state of abstract objects in modern metaphysics. He surveys the landscape by seeing how the main candidates for abstract object status (mathematical objects, properties, propositions, possible worlds) fare under Platonism and its main rivals (nominalism, immanent realism, conceptualism). It’s an exceptionally reader friendly article, and was a helpful review for me.

One item I thought was interesting is that, according to Balaguer, the strongest argument for Platonism is a truthmaker argument. The things denoted in literally true statements (“3 is prime”) must exist as abstract objects in order to make the statement true. Alternative accounts of how these statements work or attempts to deny their truth all have problems and objections.

Of course, Platonism has strong objections. Balaguer singles out the epistemological issue as the biggest problem: if abstract objects are non-physical (and exist outside of space-time) how can we have knowledge about them? Different accounts have been proposed regarding how this can work; objections have been lodged, and the debate continues.

There is a running “meta-theme” here which I’ve been thinking about as I’ve tried to survey different topics in metaphysics (ontology, causality, modality). These metaphysical questions are difficult, and simple solutions obviously don’t work or the debates would have ended long ago. What this means to me is that the common presumption that something like physicalist monism should be the “default” metaphysical position is unfounded. More “extravagant” metaphysical systems need to be weighed in the quest to find a better mousetrap for explaining how the world works.