Certainty

Edward Feser on Naturalism

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Edward Feser, discussing David Hart on natural law, says, “For Darwinian naturalism, as Hart points out, gives us a view of the mind on which it floats entirely free of truth.  Any belief or argument whatsoever could seem absolutely indubitable even if it were completely wrong, if this were conducive to survival.” He takes this as an argument against Darwinian naturalism, which means that he thinks the claim, “Any belief or argument etc.” is either false or implausible.

It is not entirely clear why he thinks this, given that either he agrees, or at least does not disagree, with the biological theory of evolution. However, it may be that, holding that the intellect is immaterial, he believes that it is not subject to the process of natural selection. But this cannot be true. It is evident that whatever the exact relationship between the mind and the body, there is certainly some relationship, and the null hypothesis is basically always false. Consequently, whether or not the intellect is immaterial, there will be bodily causes that influence a person’s tendency to be certain or uncertain about things, with the result that the claim, “Any belief or argument whatsoever could seem absolutely indubitable etc.”, will surely have at least some truth.

It is also clearly true from experience. For example, in Muslim societies, most of the population are extremely convinced that Islam is true, even though this is completely wrong, but very conducive to survival, since even in the present day the death penalty continues to be used against apostates from Islam.

Obviously Islam has not existed long enough for natural selection to have much effect here, however, so in fact this particular case is probably part of a more general situation where agreeing with the people around is “conducive to survival”, both in the literal sense, and in the sense of producing economic and social advantages.

Nor does this imply that the mind “floats entirely free of truth”, since in most cases wrong beliefs about the world are harmful, and true beliefs helpful. If there is a pit of spikes in front of me and I believe that there is not, this is not conducive to survival at all. It does imply that the mind is not perfect and that there is a need to reflect on its work and frequently correct it. The possibility of self-reflection provides possibilities for progress in truth, even given the existence of such mental flaws.

100%

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Given that probability is a formalization of subjective degree of belief, it would reasonable to consider absolute subjective certainty to correspond to a probability of 100%. Likewise, being absolutely certain that something is false would correspond to assigning it a probability of 0%.

According to Bayes’ theorem, if something has a probability of 100%, that must remain unchanged no matter what evidence is observed, as long as that evidence has a finite probability of being observed. If the probability of the evidence being observed is 0%, then Bayes’ formula results in a division by zero. This happens because a probability of 0% should mean that it is impossible for this evidence to come up, and indicates that one was simply wrong to claim that there was no chance of this, and a different probability should have been assigned.

The fact that logical consistency requires a probability of 100% to remain permanently fixed, no matter what happens, implies that it is generally a bad idea to claim such certainty, even in cases where you have absolute objective certainty such as mathematical demonstration. Thus in the previously cited anecdote about prime numbers, if SquallMage claimed to be absolutely certain that 51 was a prime number, he should never admit that it is not, not even after dividing it by 3 and getting 17. Instead, he should claim that there is a mistake in the derivation showing that it is not prime. Since this is absurd, it follows that in fact he should never have assigned a 100% probability to the claim that the number was prime. And since there was subjectively probably not much difference between 41 and 51 for him at the time, with respect to the claim, neither should he have claimed a 100% probability that 41 was prime.

Absolute Subjective Certainty

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Any conclusion at which one arrives after a long process of reasoning will have a possibility of error, just as I said about mathematical arguments. Consequently if we want to find some absolute subjective certainty, it will need to be something either without a process, or with a minimal one; something very basic.

First principles such as the principle of non-contradiction and the like are one possibility.

Another would be immediate apprehensions such as “I exist”, “I am thinking”, “I am awake”, and so on.

Still another would be facts of immediate experience such as “I am currently working on a blog post.”

We might come to a different result depending on whether or not we include the content of the assertion as well as the mode of apprehension. If the mode of apprehension is considered alone, “I exist,” cannot be said to have such absolute certitude if it is possible for someone to be certain in exactly the same way of the claim, “I do not exist,” and it seems to me that this might be possible. This is even more likely to be possible in the case of the claim about being awake; a waking person can believe that he is asleep and dreaming.

If we include the content of the assertion, this kind of certitude is not fully distinct from objective certitude, and there will surely be at least a few cases such as the claim about existence. Thus someone who believes that he exists, cannot fail to exist, not so much because of the certainty of his belief, but because having a belief includes existing.

External facts of immediate experience, such as the fact that I am currently writing this blog post, or that there is a computer on the table in front of me, are not infallible even including both the content and the condition of my certainty, since we are often wrong about such things, e.g. “I know my glasses were there on the table, I just saw them,” but they were not.

Overall the situation is not entirely clear. Absolute subjective certainty, including the content of the assertion as well as the mode, is possible, as in the case of the claim about existence, but it is not clear that it is possible if the content is not included. In any case, whether or not the content is included, such certainty could only refer to immediate apprehensions, and at most only to a few such apprehensions.

One other case which is sometimes proposed is the case of faith in divine revelation. Thus the Catechism of the Catholic Church states, “Faith is certain. It is more certain than all human knowledge because it is founded on the very word of God who cannot lie.” It seems likely that in reality this refers to objective certitude: one who believes something revealed by God cannot be wrong, because God does not reveal things that are false. Such an objective certitude would not imply absolute subjective certitude, for the same reasons that mathematical demonstration does not imply such a subjective certitude. However, some believe that the Catechism refers to an absolute subjective certitude. I will consider this idea in another post.

Absolute Certainty

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If I say that I am certain of something, this can mean that I personally do not have any doubt that it is true. Naturally, this does not ensure that the thing is in fact true. The fact that I do not doubt it, does not prevent it from being false, and people are frequently sure of such things.

But asserting that I am certain can also imply that the thing cannot fail to be true. As discussed in the previous post, this could mean that the thing cannot fail to be true on account of the objective nature of my conviction, or on account of its subjective nature.

As an example of the objective nature of the conviction, someone can say that he has a demonstrative argument for a conclusion, based on first principles. Given this kind of conviction, the thing cannot fail to be true, because something that actually follows from first principles will always be true. Thus I can prove in this way that 13 is a prime number. The objective nature of the conviction here is mathematical knowledge, and given that I have mathematical knowledge of a thing, the thing will always be true.

However, it would be either rare or impossible to have a subjective apprehension of my own knowledge such that I infallibly recognize my own possession of mathematical knowledge, and therefore can judge about the truth of the conclusion infallibly. I consider my knowledge and say, “This is a valid mathematical demonstration,” but my apprehension of this fact is not itself infallible. This was illustrated earlier with the example of a mathematician claiming that there is a flaw in a proof. If my apprehension of the fact that something is a demonstration is infallible, then I will know through this infallible knowledge that his claim is mistaken. But this does not happen in reality, and thus my knowledge is not subjectively infallible, not even when I have a valid mathematical demonstration for some conclusion.

To be continued…