Rehashed Verificationism

Antony Flew, before his conversion to theism, wrote an article in which he argued that religious assertions such as “God loves his creatures” are in fact meaningless, because there is nothing that could happen that would cause the believer to deny the assertion. But if there is no state of affairs that would warrant a denial of the assertion, this must be because there is no state of affairs that is excluded by the statement. But every assertion excludes its contradiction; hence, the original statement must not actually be asserting anything, and is therefore meaningless.

This is, of course, plainly absurd. It is absurd even if we grant, for the sake of argument, that there is nothing that could happen that would cause the believer to deny the statement. This is evident simply from the fact that the argument proves too much: innumerable examples can be given of this kind that are plainly quite meaningful:

“It is possible that the sun will not rise tomorrow.” Now, some people might deny that this is possible, based for instance on prior experience. But there are also many people (e.g. Hume) who would maintain that we can never definitely rule out possibilities such as the sun’s not rising tomorrow. Clearly this does not make the statement any less meaningful as proposed by people of the latter sort compared to the former.

“Some human being stepped on this patch of ground exactly 10,000 years ago.” We could conceive of evidence that might rule this out in certain specific cases, but in most cases it is simply not possible to know. Thus, nothing that happens could rule out the statement. Again, this does not prevent it from having a perfectly clear meaning.

And so on and so forth. Some people who believe in conspiracy theories such as that the moon landing was faked, or 9/11 was an inside job, also fit Flew’s description quite well. Does this mean that it is meaningless for them to say that the moon landing was faked?

An interesting thing about Flew’s position is that, if true, it would devastate many assertions made by his (at the time) fellow unbelievers. Bart Ehrman, for instance, basically argues that there is no event that could happen such that it would be rational to ascribe it to supernatural causes rather than natural ones. According to Flew’s argument, Ehrman’s assertion that miracles don’t happen is therefore meaningless.

At the most fundamental level, the argument is obviously false inasmuch as it is based principally on the fact that any assertion excludes its contradiction. On this level, there is evidently one and only one thing that would warrant the denial that God loves his creatures; namely, God’s not loving his creatures. But Flew would obviously not have accepted this, which makes me believe that, if pressed, his argument would ultimately have reduced to the rather tired verificationist claim that an assertion is meaningful only if it could be theoretically disproven by empirical evidence. And this goes back to the problem discussed in the prior posts, namely the completely baseless assumption that the physically observable is all there is.

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Probability and Evidence, Part III

To wrap up the previous two posts, I have a few thoughts on the common invocation of the principle that “extraordinary claims require extraordinary evidence.” We have already seen that this principle doesn’t do what its common proponents would like it to do, for the reason that extraordinary claims constitute extraordinary evidence. However, there is a further problem. Normally, when people invoke this principle, they mean by “extraordinary claims” the types of claims that are associated with religion, e.g. that immaterial beings such as God or angels exist, or that certain miraculous events have occurred, or some such thing (which is English for res).

However, in virtue of what does the claim that, say, immaterial beings exist count as “extraordinary”? Why isn’t the claim that material beings exist also extraordinary? The fact that we experience material beings cannot be invoked to answer this question, since this fact only indicates that there is a (very) high posterior probability that material things exist. But the objector wants to say that it is a priori improbable that immaterial beings exist. It seems to me that no possible reason can be given for thinking that the prior probability of material beings is any higher than the prior probability of immaterial beings.

What about the fact that we don’t seem to experience immaterial beings? In fact, this does not, in general, render their existence any less probable, since the absence of sensation of immaterial things is just what we would expect–on either hypothesis. In other words, the fact that I don’t see an angel in front of me does not render the probability of its existence one bit less, since my not seeing it fits equally well with its existence and nonexistence.

Thus, someone who wants to maintain that it is highly improbable (and thus an “extraordinary claim”) that immaterial beings exist must also maintain that it is highly improbable (with respect to prior probability) that material beings exist, and that it is only with respect to posterior probability that their existence is probable. But this commits one to the view that it is highly improbable a priori that anything at all exists. This seems rather problematic. At the very least, there seems to be no reason that can be given for believing it.

Someone could also try to avoid this problem by saying that there is, in fact, evidence that immaterial beings, at least rational ones, do not exist; namely, that we would expect them to reveal themselves in some way if they did. But this is exactly what most religions claim has happened, and what witnesses of alleged miracles claim has happened. Since the people who deny the existence of immaterial beings are generally the same ones who reject claims of miraculous happenings as a priori improbable, they are trapped in a vicious circle. For if it is not improbable a priori that immaterial beings exist, then that they should interact with the visible world, and hence that miracles should happen, is also not improbable a priori, and the evidence needed to confirm miracles is not extraordinary, since they are not especially unexpected. Thus, the probability of immaterial beings cannot be rendered low by their alleged lack of interaction with the world. It is either low a priori, or it is not low at all. And if it is low a priori, then so is the probability of anything existing at all, which seems absurd.

What it comes down to, then, is that the skeptic wants to say that it is a priori improbable that anything exists which is not subject to empirical observation. But no possible reason can be given why this might be true. I might as well say that it is a priori improbable that anything exists outside of my field of vision. Remember, we are speaking about prior probabilities, probabilities before consideration of evidence. Thus, the fact that there is plenty of evidence that things exist outside my field of vision does not render the comparison invalid; what reason can be given for denying it before considering this evidence? Furthermore, there is plenty of posterior evidence that increases the posterior probability of unobservable things existing. For instance, there is the fact that even many observable things have escaped human observation for most of the world’s history. Many other reasons could be given.

In short, the claim of the skeptic that it is somehow “extraordinary” to posit the existence of immaterial beings functionally amounts to nothing more than a kind of solipsism, in which one selects a mostly arbitrary set of beings–say, what I can see right now–and asserts that it is highly improbable that any other beings exist. Hardly convincing.

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Probability and Evidence, Part II

I didn’t realize until I came to WordPress to write this post that my last post was more than a week ago! I had originally intended to write this last Friday or Saturday. All future statements about forthcoming blog posts should be taken in the same general vein as the Scriptural statement “Behold, I am coming soon.”

Hume states in his Enquiry that no testimony is sufficient to establish a miracle as fact, unless the testimony is such that its falsehood would be more miraculous than the miracle in question. This could be interpreted in various ways, but in order to be a true statement it must mean something like this: that given a choice between two mutually exclusive choices (e.g. the falsehood of certain testimony or the occurrence of an alleged miracle), the rational thing to do is to side with the more probable choice. It’s almost tautalogical in a way; the more probable is more probable than the less probable (which, by the way, reminds of a brand of shampoo that once advertised itself as costing “less than the more expensive brands”).

Now, Hume evidently intends this principle to show that it is irrational to accept the occurrence of any alleged miracle. The idea, presumably, is that testimony is never so strong that it its falsehood would be less probable than supposed miraculous occurrences.

I bring this up because the flaw in Hume’s argument is directly pertinent to the question I asked at the end of the last post. Specifically, Hume’s application of his principle seems plausible on the surface because there is a tendency to consider only the prior probability when judging the probability of, for example, the falsehood of a certain statement. Clearly, if we simply consider in general all the claims that people make, the prior probability of a given claim being false is relatively high. It is less than one-half, since people say more true things than false things, but it is higher than, say, 0.1 percent, which is still much more than the prior probability of, say, water turning to wine. And so the principle implies that someone’s claim that water turned to wine cannot be accepted because it is more probable that the claim is false than that the event actually occurred.

The problem with this, of course, is the consideration of prior probabilities only. By this reasoning, no testimony could ever be accepted if the event being described had a low prior probability. If I read in the newspaper that John Smith won the lottery last week, I could reason to myself that I should conclude rather that the newspaper is in error than that Smith in fact won the lottery, since the chance of Smith winning the lottery is considerably lower than the chance of any given statement in a newspaper being in error. But no one does this, and it is evident that it would be a mistake to do so. The reason that it is a mistake is the one just stated, although this may not be obvious at first. So what does the right analysis look like?

When judging a claim, the right question to ask is not what is the simple probability of the event claimed, but what is the probability of the event given the particular evidence for the event. Even when people realize this fact, they tend to not see (or to ignore) the additional fact that the claim itself constitutes evidence for the event. This error frequently arises when people want to raise doubts about things like the historicity of Scripture; that is, they imply that the baseline assumption is that the events narrated are not historical, and that outside evidence must be accumulated that outweighs the assumption before the events can rationally be accepted as historical. People say things like this (to make up an example): “There is no historical evidence that Caesar Augustus put out a decree of enrollment.” But the truth of the matter is that the Gospel of Luke is itself historical evidence that Caesar Augustus put out a decree of enrollment. How strong evidence it constitutes would need to be considered, of course, but one cannot simply ignore, as people tend to, the fact that it does constitute evidence.

What is most crucial for the original question about extraordinary claims, however, is that not only do claims of events constitute evidence for the events, but also, in general, claims of less probable events constitute stronger evidence. In other words, extraordinary claims are extraordinary evidence. To use the example I gave in the last post, the claimed event of a person flipping a coin and getting eight heads in a row does indeed require stronger evidence than the claim of getting three heads in a row; but the claim itself is stronger evidence. Similarly, the reason the newspaper can be believed when it states that John Smith won the lottery is that, although the average probability of a generic statement in the newspaper being erroneous is greater than the probability of Smith’s winning the lottery, nevertheless the probability of the paper’s claim that Smith won the lottery being erroneous is less than the probability of Smith’s winning the lottery.

This principle might seem counterintuitive, but it is demonstrably true. In particular cases, it can be demonstrated empirically, at least in theory. Given sufficient quantities of newspaper accounts, the claim in the previous paragraph could be shown simply by counting and fact-checking. In general, one reason for the truth of the principle can be seen from Bayes’ Theorem. This theorem relates the conditional and the prior probability of a given event, and is (in one form) as follows: The probability of A, given B, equals the probability of B, given A, times the (prior) probability of A, divided by the (prior) probability of B. Among other things, this theorem is used by many e-mail spam filters to calculate the probability that a particular e-mail is spam, given that it contains the words that it does. In our case, the theorem works like this: The probability that a given event occurred, given someone’s claim that it did, equals the probability of the person’s making the claim, given that the event occurred, times the prior probability of the event occurring, divided by the prior probability of the person’s making the claim. But–and this is crucial–the prior probability of the person’s making the claim is less for less probable events. Now, this prior probability forms the denominator of the fraction, and therefore as it decreases the overall fraction (the probabilty of the event, given the claim of it) increases. The overall change will depend on how the other values change as well, of course, but this is sufficient to show that claims of less probable things constitute stronger evidence; namely, because claims of less probable things have lower prior probabilities. For example, it is less probable that I would claim to have flipped eight heads in a row than three heads in a row (we can ignore here the fact that I might find the latter too unremarkable to bother stating it in the first place), simply because it is less likely to have happened. Thus, when I do make the claim, it provides stronger evidence. It is important to note that there cannot be a simple direct proportion, since that would make all claims equally likely; the exact relation varies from case to case and needs to be judged from other factors.

The point that claims of less probable things have a lower prior probability is also empirically evident. For instance, it is much more common to hear someone say that they recently bought a new car than to hear someone say they recently bought a new pet dragon. The fact that we tend to believe the former and not the latter does not show that the latter is not stronger evidence, as I claimed above; rather, it shows that the overall judgment, which takes into account the low prior probability of someone buying a pet dragon, yields a lower probability.

Does any of this make any sense?

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