The New New Math

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Post-blogging the Central: Plantinga and Dennett

The Central APA in Chicago this past weekend seemed fairly empty, although I heard from one of the organizers that registrations this year were about the same as last year. One of the more interesting sessions was in the very last time slot, and had Dennett commenting on Plantinga's "Science and Religion: Where the Conflict Really Lies". Partly what was remarkable about the session was how many people were there. The room was changed at the last minute to accommodate the additional interest, but even so, it was still standing room only. With at least 200 people packed into a small conference room, it was certainly one of the better attended APA events that I have been to.

I had to leave early to make my flight, so I only heard Plantinga's talk. Here I didn't hear much that was new. In the first half Plantinga argued that a committed theist could accept evolution because evolution per se is compatible with theism. This is mainly because the process of natural selection with random variation was said to be consistent with a divine plan which guided what we see as random. I am not sure how much this point of view depends on Plantinga's view that the warrant for theism is basic, but granting that point, I can see the coherence of his position.

The second half of the presentation argued that there is a quasi-religious "naturalism" which is in fact in tension with belief in evolution. Here Plantinga rehearsed his notorious argument that the combination of naturalism and evolution is self-defeating because it undermines the belief in the reliability of our cognitive faculties, and so provides a defeater for these beliefs.

Hearing the argument again drew my attention to one of the steps that seems very problematic. Plantinga's first premise is that P(R/N&E) is low. Here R is the belief that our cognitive faculties are reliable, N is naturalism and E is evolutionary theory. My concern is that even if this probability is low, that is irrelevant to the existence of defeaters. For a basic point about conditionalizing is that we should only conditionalize on our total evidence. Often this is captured by some kind of K meant to encapsulate all our background knowledge. So, even if P(R/N&E) is low, P(R/N&E&K) may be higher, and actually end up being high enough to avoid a defeater for R.

If we ignore total evidence, we can come up with easy defeaters for theism T. For example P(T/S) is low, where S is suffering. But of course theists are not forced to conditionalize on S, but can also include other beliefs from their store of background knowledge.

I am not an expert on the discussion of this argument, so maybe someone has made this objection before. Any comments are welcome, especially by those who saw the rest of the session!

Update: there is now an extended description of the session here.

"Idealization in Science" APA Session

Readers of this blog might be interested in checking out a session this Thursday night, 7:30-10:30pm, at the Central APA on the topic of idealization. The lineup:

Robert Batterman (University of Western Ontario), “Explanatorily Essential Idealizations”

Otávio A. Bueno (University of Miami), “Idealization in Science: An Inferential
Conception”

Christopher Pincock (Purdue University), "How to Avoid Inconsistent Idealizations" (formerly “Idealization and Mathematical Tractability”)

Michael Weisberg (University of Pennsylvania), “Deploying Highly Idealized Models”

I will be defending the contentious claim that idealizations of ocean waves do not involve the assumption that the ocean is infinitely deep ...

Thanks to Omar Mirza (St. Cloud State) for chairing!

Wilson on the Missing Physics

In “Determinism and the Mystery of the Missing Physics” (BJPS Advance Access) Mark Wilson uses the debate about determinism and classical physics to make the more general point about “the unstable gappiness that represents the natural price that classical mechanics must pay to achieve the extraordinary success it achieves on the macroscopic level” (3). Wilson focuses mostly on Norton’s “dome” example and Norton’s conclusion that it shows that classical mechanics is not deterministic. The main objection to this conclusion is that Norton relies on one particular fragment of classical mechanics, and only finds a counterexample to determinism by mistreating what are really “descriptive holes” (10). By contrast, Wilson argues that there are different fragments to classical mechanics: (MP) mass point particle mechanics, (PC) the physics of rigid bodies with perfect constraints (analytic mechanics) and (CM) continuum mechanics. Norton's example naturally lies in (PC). Each fragment has its own descriptive holes which become manifest when we seek to understand the motivation for this or that mathematical technique or assumption at the basis of a treatment of a given system. Typically, a hole in one fragment can be fixed by moving to another fragment, but then that fragment itself has its own holes that prevent a comprehensive treatment. As a result, Wilson concludes that there is no single way the world has to be for “classical mechanics” to be true, and, in particular, there is no answer to the question of whether or not classical mechanics is deterministic.

I think Wilson has noticed something very important about the tendencies of philosophers of science: philosophical positions are typically phrased in terms of how things are quite generally or universally, but our scientific theories, when examined, are often not up to the task of answering such general questions. It seems to me that Wilson opts to resolve this situation by rejecting the philosophical positions as poorly motivated. But another route would be to try to recast the philosophical positions in more specific terms. For example, if, as Wilson argues, descriptive holes are more or less inevitable in these sorts of cases, then a suitably qualified kind of indeterminism cashed out in terms of the existence of these holes can be vindicated. Other debates, like the debate about scientific realism, seem to me to be in need of similar reform, rather than outright rejection.

An Introduction to Carnap's Aufbau

As promised earlier, here is a draft of a survey article on Carnap's Logical Structure of the World or Aufbau. The article will eventually be submitted to Philosophy Compass. Comments welcome, although please bear in mind that it is hard to summarize 80 years of discussion in 6000 words! Update (May 2012): A comment has drawn my attention to the broken link -- the published version is now online here.

Weisberg on Models of Cognitive Labor in Science

Anyone who enjoyed the old cellular automata game of Life will have fun with the Java application that Michael Weisberg has made available on his webpage. Here Weisberg gives a small piece of the broader research project that he has been carrying out with Ryan Muldoon concerning how to understand the division of labor in successful scientific communities. As explained here the approach adopts a landscape approach where regions correspond to research strategies, and where different regions have different levels of epistemic significance. In the model agents then explore these landscapes according to different strategies. A preliminary result is that populations of "mavericks" who deliberately avoid regions explored by others do best. While the significance of this for the original question is not entirely clear, this is certainly an exciting way to investigate the issue!