Friday, December 22, 2006

Foreknowledge, Free Will, and "The Modal Fallacy"

In his Internet Encyclopedia of Philosophy article entitled "Foreknowledge and Free Will," Norman Swartz defends the view that divine foreknowledge is compatible with human free will and contends that arguments for incompatibilism inevitably commit a certain modal fallacy. I think he's wrong on both counts, but I want to focus here just on the second claim.

First, I need to clarify that 'free will' is to be understood in the libertarian (indeterminist) sense and that 'divine foreknowledge' is to be understood as the view that God from the beginning infallibly knew of every possible state of affairs S and of every moment of time T, either that S will obtain at T or that S will not obtain at T.

Now, what is this "modal fallacy" that Swartz makes so much of? Basically, it's the inference from "Necessarily, if p then q" to "If p then, necessarily, q." In other words,
Nec(If p then q)
∴ If then Nec(q)
This is indeed a modal fallacy. That p entails q and that p happens to be true, does not imply that q is necessarily true, i.e., true in all possible worlds. The relevance of this fallacy to the foreknowledge-free will debate lies in the thought that the incompatibilist argues as follows:
  1. Necessarily, if God knows that S will obtain at T, then S will obtain at T.
  2. God knows that S will obtain at T.
  3. Therefore, necessarily, S will obtain at T.
And, indeed, if the incompatibilist were limited to arguing in this fashion, Swartz's charge that she must commit a modal fallacy would be right on target. But to suppose that the incompatibilist is limited to arguing in this fashion is quite uncharitable. For one thing, the incompatibilist doesn't need to show that S's obtaining at T is logically necessary, but only that it must be causally necessary (or unpreventable) if foreknown by God. The following argument, in other words, is - if sound - sufficient to establish the incompatibilist thesis, and it does not commit the modal fallacy identified by Swartz:
  1. Necessarily, if God knows that S will obtain at T, then S will obtain at T.
  2. Unpreventably, God knows that S will obtain at T.
  3. Therefore, unpreventably, S will obtain at T.
Premise (4) follows from the thesis of divine foreknowledge (understood in the sense defined above) together with God's essential omniscience (i.e., the claim that God knows all and only truths in all possible worlds in which God exists). Premise (5) follows from the supposition of divine fore-knowledge (i.e., that God knew in the past that S was going to obtain at T) together with the plausible claim that the past cannot be altered. From these (6) seems to follow. I should mention, though, that many scholars have challenged premise (5) claiming that God's past noetic states are not unpreventable "hard facts" but rather "soft facts" that depend for their content on what happens in the future. I think this objection is misguided, but I'll set that aside. My point here is simply that incompatibilist arguments need not commit the modal fallacy described by Swartz.

One last point. We have seen, the incompatibilist can avoid the modal fallacy by invoking in the conclusion a weaker type of necessity than logical necessity. The important point is that there are different modes of necessity, and these are distinguished by their scope. Logical necessity has as its scope all logically possible worlds. Physical necessity has as its scope all logically possible worlds with the same physical laws as ours. Temporal necessity has as its scope all logically possible worlds having the same history up to some specified point. Note that types of necessity other than logical necessity add further qualifications or restrictions of scope. One can always validity infer from a broader scope to a narrow scope contained in the broader one. Thus, if something is logically necessary, then it is also physically necessary. But one cannot legitimately infer from a narrower scope to a broader one. This is the problem with the so-called modal fallacy. In the premise
Nec(If p then q)
the type of necessity that pertains to q is not the type of necessity indicated by the operator "Nec()" but a necessity of a narrower sort because the antecedent "if p" adds a further qualification. Thus, the necessity pertaining to q is what we might call p-necessity, which has as its scope all logically possible worlds in which p is true. From this we can validly infer
If p then p-Nec(q)
but not
If p then Nec(q)
for the latter involves moving from a narrower scope to a broader one.

Wednesday, December 20, 2006

Bart Ehrman on History and Miracles

I'm just about finished listening to an audio CD lecture series entitled "The Historical Jesus" by Bart Ehrman. It's an interesting series by a scholar who, I gather, represents more-or-less a mainstream position in biblical scholarship. In other words, Ehrman is neither an out-and-out debunker of orthodox Christianity nor an out-and-out advocate and apologist. Rather, he styles himself as a professional "historian" and limits himself to what he thinks can be established with reasonable historical certainty. The result is that Ehrman accepts much of the New Testament account of the life of Jesus, but also rejects significant parts of the account.

As for the miracles attributed to Jesus, Ehrman neither affirms nor denies them. Rather, he invokes a kind of "historian's privilege", arguing that as a historian he cannot, in principle, affirm that a miracle, any miracle, has occurred in the past. Here's where I was most disappointed with Ehrman, because his a priori justification of this agnostic stance rests on what stikes me as a transparently fallacious argument. Here, in a nutshell, is his case:
  1. It is the job of the professional historian to determine what probably happened in the past.
  2. Miracles are, by definition, improbable.
  3. Therefore, the professional historian cannot as such affirm that a miracle has occurred.
The problem with this argument is the Ehrman conflates prior probabilities with posterior probabilities. The sense in which miracles are definitionally "improbable" according to premise 2 has to do with their having a low prior probability. In other words, miracles are not the sort of things that, given our usual background assumptions about the world, could be predicted in advance. Instead, we would expect under normal conditions that miracles would not happen. But the sense in which it is the job of the historian to determine what "probably" happened according to premise 1 has to do with posterior probabilities, that is, with the probability of a given reconstruction of events in the light of all of the available historical evidence. Since the relevant sense of "probability" shifts from premise 1 to premise 2, Ehrman's argument commits the fallacy of equivocation, and is therefore invalid.

Let me put my point more precisely with the help of Bayes' Theorem, which is provably true given the standard axioms of probability theory and widely used in philosophy of science as a model for evaluating the degree of support given to a hypothesis by new evidence.
  • Let B=a set of background assumptions
  • Let M=the hypothesis that a given miracle has occurred (say, the resurrection of Jesus)
  • Let E=the totality of historical data in addition to B that bear on M
  • Let PrB(X)=the prior epistemic probability that X is true in the light of B
  • Let PrB(X|Y)=the posterior epistemic probability in the light of B that X is true given that Y is true.
In these terms, Bayes' Theorem states that

PrB(M|E) = [PrB(E|M) × PrB(M)] / PrB(E)

With Ehrman, let's suppose that the prior probability of a miracle is very small, i.e., PrB(M) is close to, but not equal to zero.It is possible in principle that we could have good enough evidence to raise the posterior probability of the miracle to greater than 0.5? Sure. All we need, in this scenario, is for the value of

PrB(E|M) / PrB(E)

to be sufficiently high. PrB(E|M) represents the predictiveness of the miracle hypothesis. What are the odds that we would have the evidence we do if the miracle hypothesis were true? In general, it is not hard to get this probability as close to 1 as we please by choosing a suitably elaborated miracle hypothesis. The more crucial factor is PrB(E). This represents the surprisingness of the evidence. To get a high value for PrB(M|E) we need PrB(E) to be as low as possible. Thus, the more surprising the evidence, the better. Using another result or probability theory, we can say that

PrB(E) = [PrB(E|M) × PrB(M)] + [PrB(E|~M) × PrB(~M)],

where ~M stands for the complement of M, i.e., all of the ways in which M could fail to be true. Presumably, PrB(~M) is going to be fairly high (close to 1), whereas PrB(M) is going to be fairly low (close to 0). Now the value of PrB(E|M) must be less than or equal to one, and since that times a very low number is a very low number, the left hand part of the sum will generally be very low. What matters, then, if we are to have a low value for PrB(E), is that PrB(E|~M) be very small, sufficiently small to more than overcome the large value for PrB(~M). In other words, the predictiveness of the miracle hypothesis must be much higher than the predictiveness of any hypothesis not involving a miracle.

In sum then, Ehrman is wrong. A historian can in principle be warranted in believing that a miracle has occurred.

Wednesday, December 13, 2006

Socrates Meets Elton John

This is quite an entertaining dialogue (HT: Victor Reppert). It makes a good point about the concept of tolerance, namely, that to be tolerant of something is not to accept it, but to graciously put up with it while rejecting it.

Another important issue that comes up near the end is that of discrimination. What, exactly, is wrong with it? The dialogue ends short of answering that question, and I hope the "to be continued" promisory note is delivered on. Offhand, I would say that there is nothing morally wrong with discrimination per se. It only becomes morally wrong when either (a) one's reason for discriminating is immoral in the first place (e.g., a group of terrorists is deciding who to behead next), or (b) the criteria or grounds used to discriminate are insufficient to justify differential behavior toward different people (e.g., an employer rejects a job candidate simply because of racial reasons when race is irrelevant to the job in question).

To see that discrimination, even racial or gender descrimination, are not invariably wrong, consider a movie producer casting for the title role in a serious drama on the life of Martin Luther King, Jr. Suppose that the best actor to apply for role is white and female. Would the producer be justified in giving the role to a black male instead? Of course, I would think. The nature of the role demands an actor who can convincingly play a black male. Since race and gender are relevant in this case, discrimination on such a basis would be justified.