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The Rationality of Skepticism

All the Things That You Don't Know

In my last article, "Oh Yeah, What Do YOU Know?", I presented the closure principle and left you wrestling with a conundrum that results from it.

Recall, according to the closure principle:

Closure
Anybody who knows A and knows "A" entails "B" also knows B. Conversely, anyone who knows "A" entails "B" but doesn't know B doesn't know A, either.

The conundrum results in considering the possibility that you, the reader, aren't actually sitting at a computer as you seem to be, but are really trapped in the Matrix, being deceived to think you're sitting at a computer. The idea is that, because you have no way of ruling out the possibility that you're presently trapped in the Matrix, you don't know that you're not presently trapped in the Matrix. But since you know "I'm sitting at a computer right now" entails "I'm not presently trapped in the Matrix," it follows (according to the closure principle) that you don't know you're sitting at a computer right now.

In fact, if you don't know you're not trapped in the Matrix, it seems that you can't claim to know much of anything, for nearly all of your beliefs can be plugged into the following sort of argument.

Let "NC" stand for any non-controversial claim you might make about the world — for example, the claim that Oxford is in England, the claim that you got dumped at prom in 10^th grade, the claim that Bush loves Yanni, and so on. Also, let M stand for the claim that you're trapped in the Matrix, being deceived with respect to NC. (If NC is the claim that Oxford's in England, then M might be the claim that you're trapped in the Matrix being deceived to believe Oxford's in England, whereas, in reality, not only is Oxford not in England, there's really no such place as England at all.) If M is formulated according to these stipulations, then NC and M are mutually exclusive — the truth of one entails the falsehood of the other.¹ The problem is, almost without exception, no matter what NC stands for, the skeptic can level the following argument against your belief in NC.²

(1) If you know that NC is the case, then you know that M is not the case.
(2) You do not know that M is not the case, since you have no way of ruling out the possibility that you're really trapped in the Matrix, being deceived to think NC is the case.

Therefore,

(3) You don't know that NC is the case.

One Man's Modus Ponens is Another Man's Modus Tollens

So what should we make of this argument? A good place to start is the recognition that its basic form is modus tollens.

In case you've forgotten (or not read "Abduction and the Limits of Science, Part 1"), modus tollens arguments are formally similar to modus ponens arguments. Compare:

Modus Ponens
If P, then Q.
P.
Therefore, Q.

and

Modus Tollens
If P, then Q.
Not Q.
Therefore, not P.³

A modus ponens-style argument with respect to the right interpretation of the drawing would go as follows:

If you're looking at a drawing of a goblet, then you're not looking at silhouettes of angry identical twins showing their teeth at each other before battling to the death over the love of a woman. You are looking at a drawing of a goblet. Therefore, you're not looking at silhouettes of angry identical twins showing their teeth at each other before battling to the death over the love of a woman.

In contrast, a modus tollens-style argument with respect to the same drawing would take this form:

If you're looking at a drawing of a goblet, then you're not looking at silhouettes of angry identical twins showing their teeth at each other before battling to the death over the love of a woman. You are looking at silhouettes of angry identical twins showing their teeth at each other before battling to the death over the love of a woman. Therefore, you're not looking at a drawing of a goblet.

As these examples make clear, one man's modus ponens might be another man's modus tollens. That is, where two parties agree that Q follows from P, you might get deductively valid arguments running in opposite directions.

For one party, it might be completely obvious that P is true. Thus, even though Q seems false, Q must be true too. For the other party, however, it might be completely obvious that Q is false. Thus, even though it seems like P is true, it must be the case that P is false too.

In cases such as these, the real question becomes, which is the more rational? Accepting P (and thereby accepting Q), or rejecting Q (and thereby rejecting P)?

Is Skepticism Rational?

According to the closure principle, if you know that you're sitting at a computer right now, and you know that "I'm sitting at a computer right now" entails "I'm not trapped in the Matrix, being deceived to believe I'm sitting at a computer," then you know that you're not trapped in the Matrix, being deceived to believe you're sitting at a computer.

Both skeptics and anti-skeptics accept the closure principle. Where they differ is in the arguments they run with respect to it. For the skeptic, modus tollens is the way to go. The skeptic thinks it's completely obvious that you don't know you're not in the Matrix, so, in spite of the fact that you appear to know you're sitting at a computer right now, you actually don't. Because you don't know you're not in the Matrix, being systematically deceived about the world, you know next to nothing.

Anti-skeptics, on the other hand, see things the other way around. From their view, the modus ponens argument is correct. You obviously do know you're sitting at a computer right now. (I mean, come on! How could you fail to know a thing like this?) So, in spite of the fact that it's difficult to say exactly how you know you're not in the Matrix, as a matter of fact, you do know you're not in the Matrix. And since you do know you're not in the Matrix, the fact that the Matrix is metaphysically possible doesn't give anyone reason to doubt you know lots of other things as well.

C O F F E E  S H O P

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Who's more rational, the skeptic or the anti-skeptic?

Join the discussion!

So which is the more rational position, then? The skeptical position, according to which you don't know you're not trapped in the Matrix? Or the anti-skeptical position, according to which you do know you're sitting at a computer right now? You probably started this article (or, at least, the one preceding it) assuming that you do know things, and that your sitting at a computer right now is as clear an example of the sorts of things you know as any. But if you're right, then (via the closure principle) you also know you're not trapped in the Matrix. So, has the skeptic given you any reason to change your mind about things? Is rejecting the modus ponens argument in favor of the modus tollens argument the rational way to go?

I'll tackle this question in my next article.⁴

Notes

1. Mutually exclusive, but not jointly exhaustive. Recall that two propositions are mutually exclusive if they can't both be true at the same time — if the truth of one guarantees the falsehood of the other. (Example: The proposition "Blake has more athlete's foot than any man in Dekalb" and the proposition "Phil lives in Dekalb, and he has more athlete's foot than any man in the world" are mutually exclusive; the truth of one guarantees the falsehood of other.) In contrast, two propositions are jointly exhaustive if one of them has to be true — if it's logically impossible that neither of them is true. (Example: The proposition "Blake has more athlete's foot than any man in Dekalb" and the proposition "Blake does not have more athlete's foot than any man in Dekalb" are jointly exhaustive, since it's logically impossible that they're both false.) Back^
2. One exception would be the claim that you exist, since the Matrix couldn't deceive you with respect to this claim. As Descartes famously made clear in his Second Meditation, it's logically impossible that one be deceived about whether or not one exists. If Newman is deceived, then it follows that Newman exists, since one cannot be deceived unless one exists. But this means the proposition "Newman is deceived about his existence" is incoherent. "Newman is deceived" entails that Newman exists. But if Newman exists, then Newman is correct to believe he exists. But if Newman is correct to believe he exists, then Newman isn't deceived about his existence. Since we can generalize from Newman to anybody who believes he or she exists, it follows that it's impossible for one to falsely believe that one exists. Back^
3. Thinking about modus ponens and modus tollens, it's important to keep clear that combining the two in a particular way results in the logically fallacious form of reasoning typically referred to as "affirming the consequent." If Q follows from P and P is the case, you can validly infer (via modus ponens) Q; if Q follows from P and Q isn't the case, you can validly infer (via modus tollens) that P isn't the case either; but if Q follows from P and Q is the case, you can't validly infer P. As usual, a concrete example will make this clear. If you know I'm in Bangkok, you can validly infer that I'm in Thailand; conversely, if you know I'm not in Thailand, you can validly infer that I'm not in Bangkok either; but from the fact that I am in Thailand, you can't validly infer that I'm in Bangkok, for I might be in Chiang Dao, Bahn Non or Khaw Yaay instead. Back^
4. In case you're wondering (and I'm sure you are — who wouldn't be?), I once overheard a fellow complain that a certain ministry ought not sell Elisabeth Elliot products due to Elisabeth Elliot's immodesty. When the guy was asked why he thought Elisabeth Elliot wasn't modest, he said he'd seen a video in which Elliot's long-sleeve blouse didn't completely cover her … wrists. Yeah. Her wrists. Now if that's not scandalous, I don't know what is. Back^