In a recent book review of Maudlin’s *The Metaphysics within Physics*, Mauricio Suarez (*Stud Hist Phil Mod Phys* **40** (2009): 273-276) proposes an alternative argument against the Humean position Maudlin calls “physical statism” based on objective chance. *Physical statism* asserts that the physical state of the world completely determines all the facts, or, conversely, that all facts supervene on the physical state of the world. Together with *separability*, according to which the physical state of the world supervenes on the Humean mosaic, it entails *Humean supervenience*, which contends that all facts supervene on the Humean mosaic.

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# Category Archives: My half-baked ideas

## Objective chance and anti-Humeanism

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## Is a holographic map discontinuous?

When Leonard Susskind recently visited UCSD and gave a talk here, he strongly advocated the holographic principle. According to this principle, roughly, the physics in an (n+1)-dimensional space can be mapped, without loss, onto an n-dimensional space. The idea seems to be that this principle asserts a sort of equivalence between the physics in an (n+1)-dimensional space and that of an n-dimensional one. Let’s call a map of the physics of an (n+1)-dimensional space onto the physics of an n-dimensional space, which satisfies the holographic principle, a *holographic map*.

Now, interestingly, Susskind also said that such a map was necessarily discontinuous. This seemed intuitive enough (unlike other things he said), but when I tried to find a mathematical theorem that would *establish* a precisified version of the statement that all holographic maps are discontinuous, I quickly realized that this is less straightforward than I thought. I asked a local mathematician at UCSD, Justin Roberts, who explained some of what follows to me.

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## What was Newton’s philosophizing good for?

This week, I met with the media liaison at my campus and we discussed my research project and ways to explain and motivate it to a general public. Inevitably, she wanted to know what the sort of “philosophizing” that Nick and I are undertaking in our ACLS sponsored project was good for. When I explained to her, among other things, reflecting on the conceptual and metaphysical foundations of a physical theory may lead to progress in the science itself. For instance, I elaborated that both Newton and Einstein achieved great progress because they were engaging in serious–one might say philosophical–reflection of fundamental principles and concepts such as space and time. She liked that, but it was way too abstract. Sure, Newton unified celestial mechanics and terrestrial physics and was able to reproduce, from few basic assumptions, Kepler’s and Galileo’s laws. And sure, this led to a greater understanding of these matters. But she wasn’t satisfied. She wanted to know whether either Newton’s or Einstein’s philosophizing led to anything **tangible**, something to which everybody could relate to. I told her that Newton’s laws allowed for the prediction of the motion of celestial bodies (even though Ptolemy and Copernicus could do that too), as well as the calculation of the trajectories of projectiles (and thus helped the military to determine the angle at which they had to put their cannons, etc, but she didn’t really like that). The GPS systems now so common in our cars, I continued, relied on computations based on both special and general relativity, which in turn both depended on Einstein’s “philosophizing”. That was obviously the sort of things she wanted to hear.

So I ask you, dear reader, do you know of any great examples of how Newton’s or Einstein’s (or anybody else’s–I also told her about Maxwell) philosophizing led, quite directly, to tangible results? If so, I (and probably many readers) would love to hear them!

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## Help wanted: wave function realism

One often hears claims to the effect that the non-separability in quantum mechanics or hidden-variables interpretations of quantum mechanics such as Bohmian mechanics entail, or at least strongly suggest, some form of wave-function realism. (There’s no such entailment, to be sure, but a suggestion). It seems fairly clear how an argument like that would go, intuitively, but I have never seen one worked out carefully. Does anybody know of a helpful source which explicates and discusses this argument? Any “locus classicus” for such an argument?

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## Physical possibility

In physics in general, and in general relativity (GR) in particular, the mathematical apparatus of a theory is generally too liberal in the sense that it admits models of the theory which are not considered physically reasonable (or “physically possible” in a narrower sense). In GR, for instance, many spacetimes which satisfy the Einstein equations are not considered relevant in that they violate some allegedly obvious additional “conditions of physical reasonableness”. In electrodymanics, retarded solutions are admitted as physically sensible solutions, but not their advanced counterparts. Although space invaders are strictly speaking possible in Newtonian physics, they are routinely declared “unphysical”. And so on and so forth. But what is it exactly that underwrites these judgments?

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## Structure: A Handout

I followed up a bit on my earlier post concerning the characterization of “structure.” Since I am now teaching a graduate seminar on structure in philosophy, mathematics, and physics, I actually read through a number of graduate textbooks in mathematics to figure out how it is defined in various branches of mathematics. And I produced a handout, summarizing the result. Continue reading

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## Laws vs. initial conditions

Sometimes one finds inspiration in reading old articles, as it happened to me when I read Larry Sklar’s “Comments on Malament”, from the PSA 1984, Vol 2, 106-110. In this short paper, Sklar takes consistency constraints that arise in spacetimes with closed timelike curves (CTCs) to indicate that the principled distinction–a “distinction at the very root of the notion of physical possibility and necessity” (108)–between initial conditions and laws breaks down:

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## What is structure?

“Structure” follows me in my dreams these days: my paper on spacetime structuralism has just appeared, I am preparing to teach a graduate seminar on structure in mathematics, philosophy, and physics, and I have been asked to referee two articles on structural realism in the last two weeks. The question that haunts me most is the issue of *defining* what structure is. Many authors simply behave as if it were entirely clear what it is. Well, it isn’t–at least not to me.

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