Scepticism and Knowing That One Knows

Canadian Journal of Philosophy

Scepticism and Knowing That One KnowsAuthor(s): Michael HallSource: Canadian Journal of Philosophy, Vol. 6, No. 4 (Dec., 1976), pp. 655-663Published by: Canadian Journal of PhilosophyStable URL: http://www.jstor.org/stable/40230654 .

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CANADIAN JOURNAL OF PHILOSOPHY Volume VI, Number 4, December 1976

Scepticism and

Knowing That One Knows

MICHAEL HALL, Ohio State University at Newark

I

One way of developing a sceptical position is to take some hypothesis (H) which entails the sceptical thesis (T) that nothing is known, and argue that since H is not known to be false, T cannot be known to be false either. That is, since H is not known to be false, it is not known that anything is known. One may then argue convincingly that no one knows anything at all (T) on the grounds that it is not known that anything is known is virtually equivalent to nothing is known (sc. that knowing is virtually equivalent to knowing that one knows). Take, for example, the Cartesian sceptical hypothesis that there is an evil demon systematically deceiving everyone all of the time about everything. Instead of arguing that the hypothesis is true and that there actually is such a creature, it is much more plausible to suggest that no one knows for certain that there is not, so that in this sense it is possible that there is. What follows is not that no one knows anything, but that it is not known that anything is known. By the virtual equivalence principle, though, this reduces to the radical sceptical thesis, T.

The advantage of this procedure is obvious. It meets the challenge that T could never be known to be true. It would be self-refuting to argue that T must be true since H is true. The argument could be used against itself. For if T really were true, no H could be known to be true, and the proposed demonstration would have to be considered incorrigibly unsound. More to the point though, if T were true, then T could not be known to be true. That is why the sceptic is debarred from making even that claim. So he avails himself of this way out. Without so much as suggesting that his hypothesis is known to be true, he points out, in a non-dogmatic fashion, merely that it is not known to

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be false. This may amount to no more than an appeal to the broad fact that human beings are ignorant of many things relevant to what they claim to know. I n effect, the more outlandish the suggestion, the more plausible it is to argue that no one has ever thought of it before and that no one knows at all for certain that it is false. It follows thatT is not known to be false, and therefore, according to the virtual equivalence principle, that T is true and nothing at all is known. No knowledge claims are made.

Let 'Kp' stand for 'It is known that p' ('p' = a prepositional variable). T = - (Ep) (Kp) (using 'E' for the existential quantifier). Now suppose that H is some sceptical hypothesis, i.e.

(1) H entails -(Ep) (Kp)

and also that

(2) -K-H

i.e. that H is not known to be false. (1) and (2) together imply

(3) -K(Ep) (Kp)

i.e. that it is not known that anything is known. From (3), by the virtual equivalence principle, we get

(4) -(Ep) (Kp)

the sceptical thesis, T.

There are two epistemic rules of inference involved here. The one governing the move from (1) and (2) to (3),

R1 If p entails q, and -K-p, then -K-q

and the virtual equivalence principle justifying the inference from (3) to (4)

R2 (Ep) (Kp) is virtually equivalent to K(Ep) (Kp)

It might be tempting to dismiss this sceptical argument by rejecting these inference rules. But they express some effective intuitions about knowledge - not perhaps the knowledge of individual human beings as expressed by what they claim, but the body of human knowledge and what is known in some systematic sense, e.g. in science. At any

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Scepticism and Knowing

rate, they seem to apply in some disciplines and areas (maybe the most rigorous), and it is therefore going to be a lively question whether this form of scepticism crops up there.

What I want to bring out is that this sceptical strategem is inconsistent. It is almost an exact model of an indefensible piece of reasoning.

The argument, (1) - (4), is designed to get around the problem of the primitive indefensibility of radical scepticism. Arguing that T must be true, since H is true, is indefensible. For T implies that there could not be any grounds for claiming to know it is true. It is for this reason that (2) is adopted. It is a switch from claiming (dogmatically) that any sceptical hypothesis is known to be true, a switch that is made to save consistency. It is important to see this as a fall-back maneuver, a retreat from claiming to know that H, and consequently that T, is true. For though it is conceded that there is no straightforward proof of T (-(Ep) (Kp)), there is nevertheless supposed to be a way of establishing (3) -

K(Ep) (Kp), from (1) and (2), and of deriving T, i.e. (4), after all, by R2, the virtual equivalence principle. But this final step is inconsistent with the rationale behind the strategy, that even through it is impossible to argue directly that T is true, it is defensible to argue for (3) -K(Ep) (Kp). Obviously, this strategy is going to be consistent only if R2 is false and invalid, that is, only if the sceptical thesis, -(Ep) (Kp), is not virtually equivalent to (3) -K(Ep) (Kp) - in which case, the inference from (3) to (4) fails. In short, the rule (R2) which is supposed to give this argument a sceptical twist at the end makes the opening move (2) untenable to begin with.

Let us take a closer look at this. One of the things implied by the virtual equivalence principle is that whatever justifies the assertion that such and such is known must also be sufficient to justify the assertion that it is known that such and such is known.1 Likewise, whatever it is that justifies the claim that it is not known that such and such is known justifies the claim that it is not known simpliciter. Now apply this to the present case. We already know what would count as a complete justification - a direct proof - of the sceptical thesis. Show that some H is true, and it follows that T must be true. Show, for instance, that there is an evil demon systematically deceiving everyone about everything, and it follows that no one could possibly know anything to be true. But the philosophical sceptic cannot meet this demand for a conclusive, demonstrative proof. So he falls back to arguing merely that T is not known to be false, and that it is an open question whether it is true, on the minimal grounds that some sceptical hypotheses are not known for a fact to be false. (Very often

1 Vide J. Hintikka, Knowledge and Belief (Ithaca, Cornell U. P., 1962) p.111

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this takes the form of claiming that there are reasonable grounds for believing, albeit not for claiming to know, that T is true). Now this is a philosophical hedge against making any claims to know anything, to make radical scepticism defensible. But it is just the sort of hedging that is disallowed by R2. If one is not in a position to argue directly that T is true, one cannot be in a position, according to that rule, to argue that T is not known to be false. If there were grounds for claiming that it is not known that T is false, R2 says that they would suffice to justify the claim that T is true; but we already know that there is no argument to justify that claim. This way out of the sceptic's difficulty is thus no escape at all. It presupposes that arguing for (3) -K(Ep) (Kp) is a way out of the inconsistency that comes up in trying to argue directly for -(Ep) (Kp), and surely this is incompatible in some sense with the conclusion that these two propositions are virtually equivalent, i.e. that (3) virtually implies (4).

This tactic is subtly deceptive, because it is defensible, and is quite plausible in many cases, to argue in this way (via R1) that (3) is true, and that it is not known that anything is known. This might be a plausible view to take of present-day natural science, not that nothing at all is known, but only that the fact that anything is known is itself not perfectly certain and finally settled. Such a view is plausible, though, because it has no sceptical implications; i.e. it does not entail that nothing at all is known. If it did, it could not be established in this way, by appealing to the uncertain character of our knowledge claims themselves. For then the conclusion of this line of reasoning could be used against the initial supposition to show that it too is not certain, so that the argument becomes vain and futile. What prevents self- refutation here is precisely not taking the ordinary and plausible judgment that no knowledge claim is itself perfectly certain as being virtually equivalent to the philosophical thesis that nothing at all is perfectly certain. In short, you cannot argue this way and accept the virtual equivalence principle too. If you do buy this line of argument, you are committed to rejecting its (apparent) sceptical implications. On the other hand, if you accept R2 in order to preserve the sceptical implications of the claim (3) that it is not known that anything is known, you deprive yourself of the only plausible line of reasoning in support of your view. For then arguing for (3) must be as self-refuting as arguing directly for (T).

This result is somewhat counter-intuitive. Someone might object: "Maybe claiming to know that T is true is self-refuting. Still, couldn't one suppose it is true, think it is true, merely believe it is true, and so go around declaring that it is true (as the philosophical sceptic does). After all, T might be true. The state of affairs in which no one knows anything is possible. It may even be probable. Hence, it should be at least defensible, and may even be reasonable, to suppose thatT is true

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- short of claiming to know it for certain. Just because a radical sceptical argument cannot be made out as a deductive proof it does not follow that it cannot be made out in terms of probability. Why not think of T simply as a more or less probable thing to believe about human beings and the status of the claims they make about the world in science and in everyday life?"

This is an attempt to implement the very strategy under consideration. Such talk about grounds for believing or merely supposing that T is true (short of claiming to have knowledge) is patently a hedge against any claims to know that it is true. It is a concession to the fact that T cannot be proved at all. It is what I have been alluding to as a "fall-back" maneuver. T cannot be defended as a strong knowledge claim; but it is supposed that the defence of it can be picked up by falling back to claiming merely that there are grounds for believing that it is true. The strategy is adopted with the conviction that these grounds, whatever they may be, can never be conclusive, and that the belief will never be fully justified. Now just what can be expected from such a defence of scepticism?

Isn't someone who is committed merely to believing that T is true (on these philosophical grounds) committed thereby to supposing that it is not known to be false? It would hardly be reasonable to suppose that T is true if it were known to be false (sc. it would not be a defensible philosophical position). So merely believing that nothing is known virtually implies that it is not known that anything is known. And now we have the same situation as before and the same argument applies. This way of talking about merely believing that T is true is a hedge against claiming to know that it is true, but now we can see that it is specifically a hedge by way of claiming that it is not known to be false. It is hedging against T in this sense that is incompatible with R2. How could supposing that T is not known to be false get around the difficulty of giving a direct deductive argument that T is true, if the one virtually implies the other? Once started down this detour around arguing conclusively in favor of T, the sceptic can reach the conclusion that T is not known to be false, -K(Ep) (Kp), but from there he has no access back to T, -(Ep) (Kp).

II

Here are some illustrations of this strategy: the first, from a recent defence of scepticism by Peter linger.2 The author opens with the following gambit:

2 P. linger, "A Defense of Skepticism", in Philosophical Review, Vol.80 (1971) pp.198-219

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Michael Hall

...I will not argue that nobody knows anything about anything. ..The somewhat less radical thesis which I will defend is this one: every human being knows, at best, hardly anything to be so...On this skeptical thesis, no one will know the thesis to be true. But this is all right. For I only want to argue that it may be reasonable for us to suppose the thesis to be true, not that we should ever know it to be true.

These are the "reasonable" considerations. A proposition is known only if it is certain. But it is certain only if it is absolutely certain, meaning by that only if it is more certain than anything else or at least only if nothing is more certain than it is. Thus, unless a proposition is at least as certain as anything, it cannot be known. So this is Unger's sceptical hypothesis: no proposition is absolutely certain in this sense. For any proposition you take, you can always find another which is more certain than it is. Here, H does entail T, provided that knowledge does involve certainty, and that 'certain' can be defined as an absolute term. Then if it is true that no proposition is flat-out certain, then nothing is known. The only question is: can H be determined to be true and is this argument sound? Naturally, it is self-refuting to argue that nothing is known since no proposition is certain (one could not be certain that no proposition is certain). Instead, Unger argues that H is not known to be false (-K-H). It is not clear, he says, that any proposition is certain. We should be advised to suspend judgment on the matter. This cautious position, we are even told, recommends itself quite generally.3 The sceptical hypothesis 'deserves, if not our acceptance, at least the suspension of our judgment/ What follows from this? Not that T is true and that nothing is known, but only that it too 'deserves, if not our acceptance, at least the suspension of our judgment/4 That is we should admit at least that it is not certain and that it is not known that anything is known. To give this weak assertion a sceptical twist, Unger has to interpret it in such a way that it virtually implies that it is not the case that anything is known. It is clear, though, that he is in no position to make such a connection, as the strategy behind his argument is the counter-example to the rule of inference involved (R2).

Unger's formulation of the argument makes this last step appear unnecessary. To a philosopher who accepts that knowing involves certainty (like G.E. Moore) Unger says that he would have nothing left to say in defence of scepticism. But unless 'suspension of judgment' on T is taken to indicate that hardly anything at all is known (by R2), he will not even have ruled out Naive Realism. A philosopher like Moore

3 Ibid, pp.212-213

4 Ibid, p.216

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would still be free to insist that he knows - really knows - various things, in spite of the fact that in some sense or other he ought to suspend judgment on the truth of T. All he would have to do to make this plausible is reject R2 and the virtual implication from it is not known that T is false to nothing at all is known. He could say for instance: "I really do know that there are at least three misprints in a certain book. I just looked and saw them. Maybe I am not in a position to say definitely that I or anyone else knows that I know that, since no one knows what the correct analysis of knowledge is. Still, I really think that I do know that." Ironically, in hearing this objection, Unger must hear an echo of his own beliefs, since in effect he is already committed to rejecting R2 and accepting this epistemological move in defence of Realism. For his whole sceptical strategy is that it may be reasonable to believe that T is true (in the sense that it is not definitely known to be false) but not reasonable to be arguing that it definitely is true and that nothing at all is known. Having rejected R2 on methodological grounds in this way, he has to concede that his main contention is itself in suspense, and nothing but a pseudo-sceptical thesis, since it does not, and cannot (barring inconsistency), imply that people do not know various things. All he has brought out is that some knowledge claims themselves may not be known for certain to be true. Without R2 to give this a sceptical twist, however, it has no bearing at all on whether anyone knows anything at all.

Here is another example of this strategem from a recent defence of scepticism by Keith Lehrer.5

The form of scepticism I wish to avow is more radical than traditional sceptics have been wont to defend... I wish to consider a stronger form of scepticism, to wit, that we do not know anything. Some qualification is necessary. ..The form of scepticism that concerns me does not embody the thesis that we know that we do not know anything. That thesis is obviously self-refuting. Rather, the contention is that no one knows anything, not even that no one knows anything...scepticism entails that, just as the sceptic does not know that we do not know anything, so we do not know that we do know anything, and, moreover, that we do not know anything.

The familiar strategy is unfolding. (1) It is definitely being claimed that T is true and that nothing is known. But (2) it is conceded that claiming to know that would be self-refuting. So (3) the qualification is introduced that the sceptic must not be understood as claiming to know anything, but only as claiming not to know anything (including, among other things, that T is false). It is precisely this qualification of,

5 K. Lehrer, "Why Not Scepticism?", in Philosophical Studies (1971) pp. 283-298.

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and restraint on, the sceptic's position, consistently adhered to, which deprives him in the end of any access back to T and the claim that no one knows anything.

Though the sceptic is claiming not to know anything, he means to argue for his view, and he has a stake in developing some sceptical hypotheses. Here is Lehrer's:6

...There are a group of creatures in another galaxy, call them Googols, whose intellectual capacity is 10100 that of men, and who amuse themselves by sending out a peculiar kind of wave that affects our brain in such a way that our beliefs about the world are mostly incorrect... If you are inclined to wonder why the Googols do not know anything, it is because there is another group of men, call them Googolplexes, whose intellectual capacity is 10100 that of the Googols, and who amuse themselves by sending out a peculiar wave that affects the brains of Googols in such a way that... I think you can see how the story goes from here. I shall refer to this hypothesis as the sceptical hypothesis...

All right, but is there any reason for thinking that this hypothesis is true? Lehrer comments:7

...Dogmatists affirm that the beliefs of common sense are innocent until proven guilty, but why, the sceptic might inquire, should his hypothesis not receive comparable treatment before the bar of evidence? Why not regard the sceptical hypothesis as innocent until proven guilty...

In other words, we ought to suspend judgment on H in this case. Regarding it as innocent means accepting that it is not known to be false. This is a constant refrain in the sequel and Lehrer's main contention. To establish that something is known, an argument has to be given showing that the various sceptical hypotheses are false. But they are not known to be false (or, they cannot be known to be false -

this is not clear), and as a result, no one really knows anything.

...We are not completely justified in rejecting the sceptical hypothesis, and thus we are not completely justified in believing the others [the dogmatic beliefs]. We do not know that the sceptical hypothesis is false, and thus we do not know that anything else is true. That is the agnoiology that sustains scepticism.8

6 Ibid, p.292

7 Ibid, p.292

8 Ibid, p.297

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What follows from the premise here that we do not know that the sceptical hypothesis is false (-K-H) is not that we do not know anything else, as Lehrer declares, but only that we do not know that we do know anything (-K-T). Lehrer could go on to infer that T is true and that nothing is known at all, only if -K-T virtually implies that T is true, according to the virtual equivalence principle (R2). Unfortunately, the 'qualified' sceptical position he is maintaining is exactly a qualification of this epistemic principle. One cannot fall back from arguing directly that T is true (via arguing that some sceptical hypothesis is true) and argue that T is not known to be false (via arguing that H is not known to be false), and then turn around and conclude that T is true and that nothing at all is known by appeal to that principle. Such a position must be untenable for anyone who accepts that knowing and knowing that one knows are virtually equivalent. Arguing that it is not known that anything is known cannot be a way out of, or a solution to, any of the problems that come up in arguing directly for the truth of T - unless R2 is false and invalid. In which case, Lehrer's claim that we do not know anything cannot be justified on the grounds that some sceptical hypotheses are not known to be false.

It is hard to think of a better reason for adopting this principle. It blocks at once the development of a whole new generation of neo- Cartesian, pseudo-sceptical arguments.

July 1975

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Scepticism and Knowing That One Knows