Saturday, May 27, 2006

Is Quantum Indeterminacy Necessary for Free Will?

OK, I'm back from vacation and well-rested.

Writing-wise, I'm currently finishing an epistemology paper on inferential justification and skepticism. Reading-wise, I'm wrapping up Trenton Merricks' interesting book Objects and Persons, in which he defends the interesting thesis that conscious organisms are the only macrophysical objects there are. On his view, things like chairs, statues, brains, etc. don't exist. Instead, what we have is matter arranged chairwise, statuewise, brainwise, etc. Since all the causal work is done by the microphysical constituents of such 'objects', Merricks' argues that they are ontologically redundant and thus are best eliminated from ontology. But human beings cannot be eliminated, he argues, because we exercise causal powers that are not simply a function of our microphysical constituents.

What I'd like to talk about right now, however, is a tangential argument that occurs on pp. 155-159 of his book. It concerns the relation of quantum indeterminacy (QI) and libertarian free will (LF).

In the first place, it is uncontroversial that QI is not sufficient for LF. Acts that are free in the libertarian sense must be suitably under the deliberate control of the free agent, but the brute statistical randomness of microphysical processes according to QI is not tantamount to deliberate control.

In the second place, however, it has seemed to many that QI (or some other sort of physical indeterminacy) might be necessary for LF. After all, if QI were false and physical determinism were true, then how could any of our acts be free in the libertarian sense? Though he is a believer in LF, Merricks disagrees. He asks us to consider the following two arguments:
  1. Humans have no choice about the following truth: every action a human performs is entailed by what the distant past was like and the nature of the laws of nature.
  2. Humans have no choice about what the distant past was like or the nature of the laws of nature.
  3. Therefore, humans have no choice about what actions they perform.

  4. Humans have no choice about the following truth: every action a human performs supervenes on what the agent's constituent atoms do or are like.
  5. Humans have no choice about what their constituent atoms do or are like.
  6. Therefore, humans have no choice about what actions they perform.
Both arguments have the same structure, so if one is valid, then both are. The first argument is a popular argument for incompatibilism (famously dubbed the 'consequence argument' by Van Inwagen). Defenders of LF typically endorse the validity of the first argument but deny its soundness by rejecting (1). What Merricks points out that is that they also have to deny one or more of the premises of the second argument:
For if determinism precludes human freedom, then so does bottom-up metaphysics. So, given incompatibilism, human freedom requires (at least) one of the following two things. A person has some choice about what her atoms do or are like (the denial of [5]). Some of a person's actions fail to be fixed, one way or another, by atomic behaviour or features (the denial of [4]). If we have either, quantum indeterminacy ... is not needed for freedom. If we have neither, quantum indeterminacy ... won't help. As a result, quantum indeterminacy ... turns out to be irrelevant to human freedom.
I think Merricks is right. Affirming QI doesn't help the defender of LF as long as one affirms a 'bottom-up' metaphysics - one in which the mental is merely a supervenient epiphenomenon of the physical or microphysical. LF requires top-down causation in which the free agent exercises causal power that is not merely the vector-sum of his or her physical or microphysical constituents. In other words, LF requires that one deny the causal closure of the (micro)physical. But once one denies that, then whether QI is true or not at the (micro)physical level becomes irrelevant to LF because the causality exercised by free agents lies outside the scope of (micro)physical causation whether deterministic or indeterministic.

Sunday, May 21, 2006

Currently On Vacation

Just a quick post to update readers. I'm currently on post-semester vacation with my wife in North Carolina. We'll be arriving back in Vegas on May 23. So if I'm a bit slow in approving comments it's because my Internet access is intermittent. Relaxation is the priority right now.


Wednesday, May 03, 2006

Philosophical Action Figures!

This is funny. (HT: Victor Reppert)

Tuesday, May 02, 2006

On Traversing an Actually Infinite Past

In comments on an earlier thread, both Ocham and Brandon express perplexity over my defense of the impossibility of traversing an actually infinite past. Before responding, I must first elaborate a bit on the potential / actual infinite distinction. The distinction goes back to Aristotle and is pivotal in his response to Zeno's paradoxes. Basically, what it amounts to is this.

A potential infinite is a collection or quantity that can increase without bound but is always actually finite. For example, I can begin counting 1, 2, 3, ... and keep going, but I'll never reach an 'infinitieth' number. At every point I am at some finite number. Similarly, I can take a line segment and divide it, thus yielding two line segments. I can then divide it again (3), and again (4), and so forth. At every point what I have is an actually finite number of line segments. The notion of a potential infinite is the one involved in the mathematical notion of a limit. Thus, we say, for example, the limit of 1/x as x approaches infinity (i.e., increases without bound) is zero. We don't evaluate the limit by setting x equal to infinity - 1 over infinity is undefined - but by imagining the value of x getting larger and larger, indefinitely. In sum then a potentially infinite collection or quantity is indefinitely large, but always actually finite.

An actual infinite (of a given order of magnitude), by contrast, is a collection or quantity that has a proper subset of equal magnitude as the parent set. Since Cantor, the standard way to determine whether two (denumerable) sets are equal in magnitude is to place them in 1-1 correspondence with each other. Thus, the set of natural numbers {1, 2, 3, ...} is an actually infinite set because it has a proper subset (a set containing only, but not all, members of the parent set) that can be put into 1-1 correspondence with it. For example, the set of even numbers {2, 4, 6, ...} is a proper subset of the set of natural numbers, and both sets can be mapped on to each other without remainder. Thus, 1 maps onto 2, 2 onto 4, 3 onto 6, etc. The important point to note here is that an actually infinite collection is given all at once - it doesn't start out as a finite collection and then, by finite addition, become actually infinite. No, we posit actually infinite collections as infinite from the get-go. Thus, we refer to the set of natural numbers, or the set of prime numbers, and so forth, as completed totalities.

Now, one way of developing the kalam cosmological argument is as follows:
  1. If there is no beginning to time (a first moment), then an actually infinite number of events has elapsed prior to now.
  2. It is impossible for an actually infinite number of events to elapse.
  3. Therefore, there is a beginning to time.
The rationale for the first premise is that no beginning to time means that before every state of world is another, different state. If only a finite number of events has elapsed, then there would be a state without a prior state. There would be a first state of the world, and a first event. By hypothesis, however, there is no first event; hence, the number of elapsed events must be infinite, not finite.

The rationale for the second premise is simply the idea that one can't turn a potentially infinite magnitude into an actually infinite magnitude by finite addition. This seems obvious: I can keep counting till the cows come home and beyond, count faster and faster and faster, but I'll never arrive at an infinitieth number. At every point in the process, the quantity is finite.

Now, Brandon objects:
If every traversal requires a beginning and an end, and an infinite past has no beginning, this is a problem only if we already assume that traversal of an infinite past would require traversal of infinite days. But on the infinite past view, every day in the past is finitely distant from the present; it's just that for every finitely distant day there's a day that is more distant. Thus this is true: For every day in the past, traversal of the days from that day to today is traversal of a finite number of days. The fact that there are infinite such days doesn't change this. This is true just as much as it is true that the fact that every integer is a finite distant from 1 is not affected by the fact that there are infinite integers.
The crucial assumption of this argument is this:

(A) Every day in an infinite past is finitely distant from the present.

The problem with this assumption is that it conflates the distinction between potential and actual infinites and thereby fails to take the idea of an actually infinite past seriously. (A) is clearly true when we're talking about a potential infinite. We start at the present and run through the time series in reverse, moving farther and farther into the past. Nevertheless, at any point we stop at, we're only a finite remove from the present. But if the distance from past event E to the present is actually finite, then we haven't yet captured the idea of an actually infinite past.

Similarly, the notion of ever larger integers being still a finite remove from 1 is that of a potential infinite, of a magnitude increasing without bound, not of an actual infinite.

The problem with an actually infinite past is that it requires us to posit the impossible, some event in the past that is at an actually infinite remove from the present. The proper analogy is not one of starting in the present and then receding ever further into the past, but of something like trying to count up from negative infinity to zero. It can't be done. And that's the point.

Monday, May 01, 2006

On the Possibility of an Omniscient Being

Is it possible for there to be an omniscient being? Patrick Grim doesn't think so. Before looking at his arguments directly (which I'll save for a later post), I think it would be helpful to take a step back and reflect a bit on what omniscience could be.

First, omniscience is supposed to be a kind of upper limit case of knowledge and understanding. The implication is that knowledge is something that can come in varying degrees. Off the top of my head, there seem to be at least five dimensions along which knowledge can vary:
  1. Breadth: One can know more or less. When we learn, our knowledge grows in extent. When we forget, our knowledge lessens in extent.
  2. Depth: We can understand something more or less well. In a glance, a chessmaster understands more about the position on the chess board than a novice grasps after studying the position minutely for half an hour. A measure of depth is the ability to appreciate the logical consequences of what one knows. One who is adept at math sees the implications of theorem; one who is just beginning doesn't.
  3. Security: We can be more or less justified in our knowledge. Some knowledge is very secure (e.g., 2+2=4), and some is much more tenuous (e.g., string theory is correct).
  4. Transparency: Sometimes we not only know, but we know that we know. Fido, on the other hand, may know where the bone is buried, but he doesn't know that he knows. We can sometimes attain a higher-order perspective on our knowledge. Animals can't.
  5. Fragility: We can lose knowledge, either through failure of memory, trauma (amnesia), disease (Alzheimer's), and so forth. Some people are better at retention than others.
This is not necessarily an exhaustive list, but it should be enough to help us understand omniscience by contrast. To a first approximation, therefore, I want to suggest that we think about omniscience as a state of knowledge that is absolutely maximal in breadth, in depth, in security, in transparency, and in lack of fragility. An omniscient being knows all there is to know about all there is and knows it without any shade of doubt or distortion.

Second, human knowledge and understanding reaches transparency (we become conscious of it) only by becoming abstract. That is to say, we can focus attention on a particular proposition only by regarding it against a tacit, unarticulated background. For example, it is in relation to an empirical background that I can pick out a particular object, say, one of my cats. If there were no discernable distinction between the cat and everything else, I'd never notice it. This gives rise to a distinction between knowledge by acquaintance, the inarticulate familiarity we have with persons, places, and things, and knowledge by description, the articulate but abstract formulations of propositions about persons, places, and things.

But for an omniscient being this would presumably not be the case. Such a being has knowledge that is perfect in breadth, depth, transparency, etc. So it cannot be abstract. Abstractions always leave something out. What this means is that such a being doesn't know how many hairs are on my cat Tiffany by knowing a proposition like Tiffany has exactly 546,234 hairs. Rather, that being knows how many hairs are on my cat by knowing the hairs on the cat. In other words, the knowledge by description / knowledge by acquaintance distinction breaks down for an omniscient being. Such a being doesn't know by means of abstract propositions about reality. Rather, such a being knows reality, directly.

If this is right, then it's inaccurate to describe omniscience as knowledge of all and only true propositions, since such knowledge is not mediated by abstractions as it is for us. Rather, we should say that an omniscient being knows the truthmakers of all true propositions.

Incidentally, this fits the theistic picture of God and creation perfectly. God knows all (real) possibilities through his immediate and thorough acquaintance with his own power and nature. He knows all actualities through his immediate and thorough acquaintance with himself and with his own activity of creating and sustaining.

The remaining question, now, is whether this conception of omniscience can meet the kinds of objections posed by Patrick Grim. Stay tuned.