1. A miracle consists in either violating a law of nature or not.
2. If a miracle consists in violating a law of nature, then it is an impossible event.
   1. A miracle consists in violating a law of nature.
   2. A law of nature is by definition a true, universal generalization of all events that occur.
      Therefore,
   3. If a miracle consists in violating a law of nature, then it is impossible for it to correspond to any event that has occurred.
3. If a miracle does not consist in violating a law of nature, then it is a natural event (and thereby not a miracle).
   1. A miracle does not consist in violating a law of nature.
   2. Any event that does not consist in violating a law of nature is a natural event.
   3. A natural event is not a miracle.
      Therefore,
   4. If a miracle does not consist in violating a law of nature, then it is a natural event (and thereby not a miracle).

   Therefore,

4. A miracle is either an impossible event or a natural event (and thereby not a miracle).

The above argument intrigued me because the first premise is an instance of the law of excluded middle, and it isn’t terribly difficult to draw anti-miraculous conclusions from both horns. Given the sort of sub-arguments I have provided for each alternative, it seems that the possibility of miracles looks grim.

Of course, in philosophy everything depends on how you define your terms. The obvious strategy for the defender of miracles is to tweak the definition of a miracle or a law of nature (or both). I’m willing to allow the definition of a law of nature as an exceptionless description of the natural world (or some variation on that theme). However, I don’t think that it is correct to define a miracle as an exception to the laws of nature. Rather, I think that a miracle should be defined in terms of divine agency. This would mean (roughly) that a miracle is an event that is brought about by the unmediated actions of a divine being. This definition of a miracle is consistent with the laws of nature being unexceptional, and it provides a nice way to distinguish natural events from miraculous ones.

One of the most eloquent writers who explained this was C. S. Lewis, in his book Miracles, which I will quote at length because it is so good.

If the laws of Nature are necessary truths, no miracle can break them: but then no miracle needs to break them. It is with them as with the laws of arithmetic. If I put six pennies into a drawer on Monday and six more on Tuesday, the laws decree that —other things being equal—I shall find twelve pennies there on Wednesday. But if the drawer has been robbed I may in fact find only two. Something will have been broken (the lock of the drawer or the laws of England) but the laws of arithmetic will not have been broken. The new situation created by the thief will illustrate the laws of arithmetic just as well as the original situation. But if God comes to work miracles, He comes “like a thief in the night.” Miracle is, from the point of view of the scientist, a form of doctoring, tampering, (if you like) cheating. It introduces a new factor into the situation, namely a supernatural force, which the scientist had not reckoned on. He calculated what will happen, or what must have happened on a past occasion, in the belief that the situation, at that point of space and time, is or was A. But if supernatural force has been added, then the situation really is or was AB. And no one knows better than the scientist that AB cannot yield the same result as A. The necessary truth of the laws, far from making it impossible that miracles should occur, makes it certain that if the Supernatural is operating they must occur. [...skipping a bit...]

It is therefore inaccurate to define a miracle as something that breaks the laws of Nature. It doesn’t. If I knock out my pipe I alter the position of a great many atoms: in the long run, and to an infinitesimal degree, of all the atoms there are. Nature digests or assimilates this event with perfect ease and harmonises it in a twinkling with all other events. It is one more bit of raw material for the laws to apply to, and they apply. I have simply thrown one event into the general cataract of events and it finds itself at home there and conforms to all other events. If God annihilates or creates or deflects a unit of matter He has created a new situation at that point. Immediately all Nature domiciles this new situation, makes it at home in her realm, adapts all events to it. It finds itself conforming to the laws. [...skipping a bit...] The divine art of miracle is not an art of suspending the pattern to which events conform but of feeding new events into that pattern. It does not violate the law’s proviso, “If A, then B”: it says, “But this time instead of A, A2,” and Nature, speaking through all her laws, replies, “Then B2″ and naturalises the immigrant, as she well knows how. She is an accomplished hostess.

1. An essential feature of internalism is that it makes a subject’s actual or potential awareness of some justification-contributor a necessary condition for the justification of any belief held by that subject.
2. The awareness required by internalism is either strong awareness or weak awareness.
3. If the awareness required by internalism is strong awareness, then internalism has vicious regress problems leading to radical skepticism.
4. If the awareness required by internalism is weak awareness, then internalism is vulnerable to the Subject’s Perspective Objection (SPO), in which case internalism loses its main motivation for imposing the awareness requirement.
5. If internalism either leads to radical skepticism or loses its main motivation for imposing the weak awareness requirement (i.e. avoiding the SPO), then we should not endorse internalism.
6. Therefore, we should not endorse internalism.

Before criticizing the argument, I’d like to explain how Bergmann intends for us to take these premises and why he thinks they are true. In a follow-up post (or posts), I’ll try to unpack what I think is wrong with this dilemma.

The first claim follows from accepting the awareness requirement discussed above. Since Bergmann takes internalism’s only adequate motivation to be its response to the SPO, he believes that all internalists will accept this premise. Notice that this claim places on internalists the requirement of being aware of some “justification-contributor.” What Bergmann means by a “justification-contributor” isn’t perspicuous, but it seems that what he means could refer to either another justified belief or some justified belief-forming process.

The second premise in Bergmann’s dilemma recognizes that internalists can attempt to satisfy the awareness requirement with either strong or weak awareness. Bergmann defines strong awareness as (actually or potentially) involving the epistemic agent to conceive of the justification-contributor that is the object of awareness as being in some way relevant to the justification or truth of the belief. Weak awareness, on the other hand, does not involve (actually or potentially) conceiving of the justification-contributor that is the object of awareness as being in some way relevant to the justification or truth of the belief. Presumably, Bergmann understands the internalist who accepts weak awareness to claim that being actually or potentially aware of some features of one’s justification-contributors is necessary for a belief to be justified, but one need not be aware (potentially or actually) of all the relevant justification-contributors of the belief in order to be justified in holding that belief.

The third and fourth premises provide the implications for accepting weak or strong awareness. In the third premise, Bergmann states that strong awareness would lead internalists to accept a vicious regress that would result in radical skepticism. To see Bergmann’s support for this premise, recall his account of the internalist’s awareness requirement. The two conditions that must be met to satisfy the awareness requirement are that there is something (X) that contributes to the justification of a belief, and that one is aware of X. To see how the vicious regress is generated, consider how (on Bergmann’s analysis) an internalist who requires one to have actual strong awareness would explain that a person S’s belief B is justified. According to the awareness requirement, in order for B to be justified, S must have a further justified belief with respect to something (let’s call it X1) that shows that S is aware of the relevant justification-contributor for B. In other words, S must believe that

P1: X1 is in some way relevant to the appropriateness of holding B.

A little reflection will show that in order for S to take P1 to be justified, S would need to hold a further justified belief about the justification-contributor (X2) with respect to P1. So, for S to be justified in believing P1, S is required to believe

P2: X2 is in some way relevant to the appropriateness of believing that ‘X1 is in some way relevant to the appropriateness of holding B.’

Of course, internalists who accept a strong awareness requirement will need to have a further justified belief (potentially or actually) concerning the justification-contributor (X3) with respect to P2. From here it is clear to see how the infinite regress ensues. Bergmann believes that the regress is vicious for two reasons. First, the regress would require an epistemic agent to have an infinite number of beliefs in order to have any justified beliefs. Second, the regress increases the complexity of beliefs, which after a few iterations makes the requisite beliefs too complex for any human mind to understand. For both of these reasons, requiring strong awareness for justified beliefs implies that no human possesses a justified belief. The result is that strong awareness leads to radical skepticism.

The fourth premise considers the implications of accepting weak awareness. Since weak awareness does not require the subject to be aware of all the relevant justification-contributors in order for one to be justified in holding a belief, the internalist can take this route to avoid the vicious regress that follows from accepting strong awareness. Bergmann sees that the problem with accepting weak awareness to be that it makes internalists vulnerable to the SPO (see this post by Ian for some discussion of the SPO). As Bergmann defines weak awareness, to be justified in holding a belief one does not need to be aware of all of the justification-contributors that are relevant to the belief in question. Even though the vicious regress can be avoided with weak awareness, it is unable to provide internalists with a response that adequately responds to the SPO. Since some of the relevant justification-contributors do not need to be conceived as relevant to the justification by the epistemic agent, from the subject’s perspective, the truth of the belief appears to be an accident. This means that the internalist is vulnerable to the charge of the SPO, which Bergmann has isolated as the internalist’s only adequate motivation for endorsing internalism. Given that weak awareness does not effectively answer the SPO, it follows that by endorsing weak awareness the internalist has not significantly improved his position over externalism.

The fifth premise claims that if internalism leads to radical skepticism or fails to satisfy the SPO, then internalism should not be endorsed. The first disjunct can be supported by realizing the severity of the radical skepticism that follows from adopting strong awareness. The regress specified in the third premise entails that nobody possesses any justified beliefs. Consequently, one could not even be justified in believing that one has no justified beliefs. In other words, internalists who accept the strong awareness requirement and see that it leads to radical skepticism would have to admit that they are not even justified in believing that radical skepticism is true. As Bergmann notes, adopting such a position would be self-defeating because it would require one to place confidence in a position that one believes there is no justification for holding. If internalists accept weak awareness instead, then Bergmann claims that they are not satisfying the SPO. Since weak awareness does not require epistemic agents to be aware of all the justification-contributors of a belief in order for it to be justified, then it does no better at satisfying the SPO than having no awareness requirement at all. Bergmann asks, “So why is weak awareness better than no awareness at all?” And he answers, “Without a good answer to that question, the weak awareness requirement is not adequately motivated.”

The next match is with the Lakers for the Western Conference title. This is going to be fun. Especially since my friend who has cable is a Lakers fan.

By the way, I’m still way behind on my school work right now. I’m leaving town soon to spend some time in Texas before the wedding, and I still have some wedding plans to settle. Needless to say, I probably won’t be doing any serious blogging until I get back from the honeymoon. Of course, there are other contributors to this blog, so you might check in occasionally to see if they’ve posted anything interesting.

Think of a cloud — just one cloud, and around it a clear blue sky. Seen from the ground, the cloud may seem to have a sharp boundary. Not so. The cloud is a swarm of water droplets. At the outskirts of the cloud, the density of the droplets falls off. Eventually they are so few and far between that we may hesitate to say that the outlying droplets are still part of the cloud at all; perhaps we might better say only that they are near the cloud. But the transition is gradual. Many surfaces are equally good candidates to be the boundary of the cloud. Therefore many aggregates of droplets, some more inclusive and some less inclusive (and some inclusive in different ways than others), are equally good candidates to be the cloud. Since they have equal claim, how can we say that the cloud is one of these aggregates rather than another? But if all of them count as clouds, then we have many clouds rather than one. And if none of them count, each one being ruled out because of the competition from the others, then we have no cloud. How is it, then, that we have just one cloud? And yet we do.

The article, then, shows the paradox with the following set of claims:

1. There are several distinct sets of water droplets s_k such that for each such set, it is not clear whether the water droplets in s_k form a cloud.
2. There is a cloud in the sky.
3. There is at most one cloud in the sky.
4. For each set s_k, there is an object o_k that the water droplets in s_k compose.
5. If the water droplets in s_i compose o_i, and the objects in s_j compose o_j, and the sets s_i and s_k are not identical, then the objects o_i and o_j are not identical.
6. If o_i is a cloud in the sky, and o_j is a cloud in the sky, and oi is not identical with o_j, then there are two clouds in the sky.
7. If any of these sets s_i are such that its members compose a cloud, then for any other set s_j, if its members compose an object o_j, then o_j is a cloud.
8. Any cloud is composed of a set of water droplets.

I have to admit, I’ve always been sympathetic to rejecting claim (2).