Interpreting Quantum Probability

I have been reading more about the philosophical interpretations of probability and how this topic relates to the interpretation of quantum mechanics (QM). If we assume hidden-variable theories don’t work, some notion of probability is at the core of QM.

I had previously read this SEP article on the interpretation of probability. It provides a good overview of the history of the issue among philosophers, and reveals a wide variety of ideas under past and present consideration. Among physicists, however, debate on interpreting probability seems to center broadly on two conceptions: a frequency interpretation and a Bayesian interpretation.

I thought this recent post at physics musings was a good one on this topic, and I also benefited from the links (including the one to this John Baez page). Then, a recent post at Quantum Quandaries provided a link to this paper by Marcus Appleby. In it Appleby argues persuasively for the Bayesian conception and considers the implications for interpreting QM.

The frequentist conception appeals because it is intended to be objective. If we could repeat an experiment an infinite number of times we would empirically fill out the probability distribution of outcomes. The problem is we can’t do this. The Bayesian interpretation is epistemic: it shows how, given one’s prior assumption about a probability distribution, a measurement outcome serves to improve it. Appleby argues that an epistemic conception is unavoidable. He shows the problems with frequentist conceptions which try to provide an interpretation in situations with finite ensembles; here, one attempts to focus only on a pragmatically relevant finite subset of outcomes. However, this choice of subset is influenced by the context of the situation and the biases of the chooser and thus reintroduces the subjective element.

Appleby discusses the propensity interpretation of QM, which places the probability as an objective property of the system being measured. He suspects this idea usually underlies the adoption of a frequentist perspective. Propensity can, however, be made consistent with the Bayesian conception, if one gives up the idea that propensity is a directly observable property.

Appleby next discusses attempts to formulate an objective version of the Bayesian conception. Can the prior probability distribution be objectively grounded? No, because as some point you have an initial assumption which is not empirical. You cannot derive a probability from a non-probabilistic empirical fact.

Now, getting back to what it all means for our worldview: since probabilities are irreducible to objective facts, and quantum mechanics describes reality, does this mean we have to give up the idea that there is an objective real world out there? Is it true, a la most summaries of the Copenhagen interpretation, that QM only describes the content of our knowledge?

In turning to this question in the last section of his paper, Appleby surprised me by bringing up the problem of qualia from the domain of the philosophy of mind. Qualia (arguably) are irreducibility first-person phenomena which do not fit into a mechanistic view of the world. A fully objective realist view of the world has no place for qualia. And yet, Appleby says, you would say the same thing about real probability or propensity, since these are irretrievably “contaminated” by subjectivity. For him, this points to the need to give up the fully objective realism and accept that we need to find a fuller extension or development of a Copenhagen-style interpretation.

Not mentioned in this 2-year old paper is the Relational Interpretation of Quantum Mechanics (RQM), which can be thought of as such a generalization and extension of Copenhagen. This interpretation seems to fit best with the Bayesian interpretation of probability. For some more recent discussion of RQM follow some of the links in the physics musings post above and also see the recent posts in this thread at PhysicsForums.

Two Metaphysical Birds with One Stone

This paper “had me” at the title: Composition as Causation. The author is István Aranyosi (thanks due to Online Papers in Philosophy, maintained by Jonathan Ichikawa). A brief summary follows below.

Aranyosi reviews two paradigmatic ways of developing a mereology. One includes an axiom known as the principle of extensionality (or “uniqueness of composition” in David Lewis’ formulation). This says that if x and y share all their proper parts, then they are identical. According to some philosophers it can be further understood to mean that the totality of parts is identical to the composed individual -- composition as identity.

Others have developed an ontological view Aranyosi calls “constitution theory”. By these accounts, constitution is not identity, but an irreflexive and asymmetric relation. However, such theorists need a different composition relation. The problem is that it has been difficult to develop an alternative model to fill out the idea that an individual is “more than the sum of its parts”.

Yet we should develop such a model since composition as identity conflicts with a strong intuition that the relation of x’s comprising y should be asymmetric. In addition to satisfying this intuition, Aranyosi lists the other criteria a constitution theory would need. The relation posed should be able to relate the same parts in the same fashion to distinct individuals at the same spatiotemporal location (e.g. the statue and the lump of clay with which it materially coincides). Also, the relation should be such as to relate the same parts to different individuals at different times (the lump of clay after smashing the statue). Finally and importantly, it should be such as to allow the same individual to be composed of distinct collections of parts at different times, or in different worlds (the cat which loses its tail is still the same individual). Composition as identity satisfies none of these criteria.

In thinking about these criteria, Aranyosi proposes that the notion of causality as composition may be able to satisfy them. First, like composition, causation is intuitively asymmetric. Second, in considering the criterion of the relation of the same parts to different individuals at the same spatiotemporal location: causes can have multiple effects at the same location. Next, for the criterion of relating the same parts in the same fashion to distinct individuals at different times or worlds: the same causes can be causes for distinct things. Finally, the criterion that the relation allow of distinct collections of parts to compose the same individual: the same effect can be brought about by distinct causes at different times.

Aranyosi considers some issues with this proposal. Part/whole relations are considered simultaneous while causality is temporal (but there may not be any problem with the idea of simultaneous causation). He also discusses how this fits with event vs. object ontologies, and discusses possible problems stemming from how causation fits in with laws of nature and counterfactual analysis. He further discusses the conflict between causation as part of contingent laws of nature vs. the traditional view of merelogical relations as metaphysically necessary. Aranyosi doesn’t present this paper as providing a complete and convincing account of composition as causation, but suggests it is a fruitful starting point for further work.

I like this idea of connecting composition with causality, and recall that I had already come across it in Gregg Rosenberg’s metaphysical system (discussed in posts here and here). In Rosenberg’s theory of causality the receptive properties proposed to help explain real causation were also connective properties which bound natural individuals together into causal nexii at various levels in nature.

What Physicalism Can't Allow

A couple of posts ago I said “…an account of genuine ontological emergence…must fail, given an assumption of physicalism.” Fortuitously, this issue was explored in depth in a paper posted by Terry Horgan in the last week of the recent Online Philosophy Conference entitled Materialism: Matters of Definition, Defense, and Deconstruction. There was also an interesting commentary on the paper by Thomas W. Polger. Of the several related topics explored in Horgan’s paper, one crucial issue was whether necessary “inter-level” metaphysical relations which go beyond physics are allowed or not for the materialist. (Please note that “materialism” and “physicalism” refer to the same thing – the older term has been ‘winning out’ in recent times it seems).

In the first part of his paper, Horgan sets out to take the pre-theoretic conception of materialism which he thinks most people share and create a rigorous definition.

I’m going to summarize the first parts of his formulation quickly, so please refer to the paper for the real thing. His effort is in the spirit of ideas from David Lewis and Frank Jackson, among others. Horgan utilizes “physically possible worlds”, which are possible worlds which have the same physical laws and entities as the actual world (“worlds” here mean maximal propositions: the actual world instantiates a possible world). Then to help screen out physically possible worlds that have superfluous non-physical stuff, he utilizes also uses the notion of a “minimal physical duplicate” of a world, which duplicates a world’s physical stuff but contains nothing beyond whatever is needed for it to be a physical duplicate. His definition of materialism then says that the actual world is such a minimal physical duplicate of itself, and for any 2 physically possible worlds, their minimal duplicates are identical. So, the actual world has no extra non-physical stuff; further, all physically possible worlds (which like the actual one lack superfluous non-physical stuff) must be the same in all respects.

[UPDATE/CORRECTION - JAN 26,2007: A helpful e-mail correspondent has pointed out a couple of problems in the the last two sentences of my summary above. First, where I say "for any 2 physically possible worlds, their minimal duplicates are identical" -- this will only be true only if the worlds selected are alike in all physical detail, not just laws and types of entities (Horgan's text doesn't say this, but it is implied) Then my last sentence has two mistakes: I should not have said all physically possible worlds must be the same in all respects; further, while the definition specifies that the actual world doesn't have superflous stuff (since it is a minimal duplicate of itself), there is no attempt here to rule out superfluous stuff at all physically possible worlds. I apologize for the errors.]

Horgan further adds a loophole-closer ruling out worlds having more than one spatio-temporal regions within them which are physically identical but otherwise differ.

So far this is somewhat familiar territory, but Horgan next explores one of the thorniest and most interesting aspects of defining physicalism.

Even the formulation given above isn’t enough to meet our pre-theoretic concept of materialism, says Horgan, and he adds a final part to his formulation. He worries that someone could propose a necessary metaphysical supervenience connection between certain high level non-physical properties and low level physical properties where such connection is brute and could not be derived from other facts. Such a “strong emergentist” proposal is not ruled out by the modal appeal to minimal physical-duplicate worlds in the definition (the necessary connections would exist in all worlds).

So he adds another clause to his formulation of materialism which says: “there are no brute inter-level relations of metaphysical necessitation linking physical particulars or properties to non-physical particulars or properties.”

Polger wonders if this clause amounts to “throwing out the baby with the bathwater.” Horgan is led to the clause by considering some examples of strong emergence which seem obviously unacceptable to the physicalist. These include G.E. Moore’s meta-ethical position that “intrinsic goodness” necessarily supervenes on the physical; and, of course the example of immaterial Cartesian minds brutely and necessarily emerging when a human brain is formed. Polger says: “is it generally true that being a relata of a metaphysically fundamental necessitation relation disqualifies a property from being physically acceptable? I don’t think so.” He then lists some examples which he thinks would be OK. These include: causal relata; the whole individual’s relations to its parts; identity relations between higher level and lower level concepts (water and H2O). Polger argues that just because some examples of brute metaphysical relations are not compatible with physicalism doesn’t mean they all are.

Polger concludes that the extra clause goes too far. He concedes it would remain an interesting and important question which metaphysical relations are physically “kosher” and which are not, and how we decide this. Further he says it remains a particularly difficult problem to see how phenomenal consciousness will be made to fit into the picture. “But it should be clear enough that we need not answer that question by consulting physics alone…Why think that physics itself could be the source of not only the basic entities and properties but also the source of all ontological relations?”

Well, I think that most materialists/physicalists do think physics itself is (or will be) adequate and therefore Horgan is right to include his additional clause. I find Polger’s objection to be very interesting because, apart from serious metaphysicians themselves, one never sees advocates of materialism conceding that it is an inadequate metaphysics without explicitly adding relations (or entities) which go beyond current or contemplated physics. While scholars continue to debate competing theories of causality and ontology, most folks appear to assume one can be a materialist without troubling too much about these difficult topics.

There is a good deal more to Horgan’s paper (also Polger’s response) than what I have discussed here; the heart of the paper concerns how one can go about defending materialism as defined, and what are the prospects for success. This focuses on finding “kosher” or materialist-friendly ways to conceptualize the phenomena in the world which we describe using non-physical vocabulary. He notes how difficult this is especially when it comes to phenomenal concepts, and concludes that philosophers have yet to successfully defend materialism by providing adequate accounts of these concepts.