1 All references to the Meditations and to other of Descartes’ writings are from The Philosophical Works of Descartes, trans. Elizabeth S. Haldane and G.R.T. Ross (London: Cambridge University Press 1967).

2 B. Williams, Descartes: The Project of Pure Enquiry (Hassocks: The Harvester Press 1978), especially 193-206

3 Ali Kazmi has indicated to me, in conversation, that he holds a similar view. We disagree, however, over the fundamental question of how to handle the difficulty that the weaker sort of certainty faces (see sections IV-V, and especially my remarks on Williams).

4 Even epistemic certainty needs to be time-relativized. For, a person may know at t what she doesn't know at a later time. Perhaps this is not possible if she has followed the rules for the direction of the mind at both times (see n. 5) and has not suffered a calamity in the interim. I am happy to drop the relativity for this case.

5 Throughout I will be assuming that it is possible for Descartes to achieve a state of mind—by following the rules for the direction of the mind (see Rules for the Direction of the Mind, HR I 1-77)—which is such that when one is in it, one achieves the best intellectual results of which one is capable. It is, I think, uncontroversial that Descartes thinks that such a state is attainable. With this assumption in place, we avoid facing the sort of objection that seeks to capitalize on such features as relative incompetence (because of fatigue, etc.), relative inattention and the like. The objections remaining will concern what is clearly of interest: the limitations, if any, of right reason.

6 Janet Broughton, ‘Skepticism and the Cartesian Circle,’ The Canadian Journal of Philosophy 14 (1984) 593-616

7 Broughton does not, of course, say that Descartes is explicit about this in the First Meditation. Rather, she claims that we may infer that this is so from the way Descartes proceeds in the Third Meditation proof that a non-deceiving God exists.

8 Mis-seeing is possible for Descartes. As I point out below, he is able to doubt even those propositions which he has intuited.

9 It might be thought that epistemically certain propositions are such as to ‘indicate’ especially clearly, consequent propositions. Perhaps so; but there is no sense at all in supposing that they do so to a psychological entity (like Descartes) any more dearly than do propositions that are merely psychologically certain for such an entity. Given this, there can at least be nothing, so far as inference itself goes, on whose basis such an entity could distinguish inference from epistemically certain premisses from inference from psychologically certain premisses.

10 In Principles of Philosophy—see HR I 203-302 (selections).

11 It is also true that in the Rules Descartes states that ‘deduction … cannot be erroneous when performed by an understanding that is in the least degree rational’ (Rule II, HR I 4-5). There can, I think, be little doubt that this remark is secured by the final results of the Meditations (or the Principles). It cannot be affirmed at the First Meditation stage. Indeed, in the passage immediately following in the Rules, Descartes extols the virtues of the certainty of Arithmetic and Geometry—a certainty that he explicitly calls into question in the early Meditations.

12 Two points: one terminological, one substantive. First: I will use ‘compute’ quite generally to denote the process of going through a proposition to determine whether it is true. To compute a proposition then is to submit it to whatever is the correct procedure for determining its truth. For ‘2+3=5,’ for example, the relevant procedure is addition. For complex geometrical theorems it is demonstration from axioms. In many cases however, we will not be able to specify the ‘procedure’ any more specifically than: thinking the proposition through.

Second: I have just said that Descartes actually computes 2+3 to get 5; and I will soon attempt to make much of the gap between affirming that 2+3 yields 5 upon computing it and affirming that 2+3=5 when there has been no computation. But is it plausible to insist on such a gap here? Doesn't one ‘compute’ the sum in thinking 2+3? Or, to put the point as Descartes might have: doesn't one immediately intuit that 2+3=5 when one thinks 2+3?

Well, so far as the text goes, it is perfectly clear that Descartes can doubt that 2+3=5 when he hasn’t ‘direct[ed his] attention’ to it. But to doubt it he must think it; think it, therefore, without ‘directing his attention’ to it. I submit that we can make sense of this distinction (viz., between thinking, and directing one’s attention to, a proposition) only if we take it as marking the difference-in the present case, and in general-between thinking a proposition with, and thinking a proposition without, computing it.

But, forget for a moment about what Descartes can or cannot do. Imagine that the example had been 6723+3480 rather than 2+3. We have a clear sense that we can think 6723+3480 without computing it, and that we can suppose at that point that a prior computation of it had gone wrong. Equally though, we are unable, when computing that sum, to doubt any step of it.

Now, I claim that the fact that the thinking/computing distinction is well motivated in the case of 6723 + 3480 makes it plausible to suppose that Descartes selects the simpler sum for shock value alone. Certainly, it is more plausible to think that 2 + 3 is relevantly like 6723 + 3480 than to think it differs from the latter in some principled way. (I submit [though I shall not argue the point here] that it would not be possible to distinguish relevantly between the sums in terms of a further distinction between ‘simple’ and ‘complex’ computations. Nor is the intuition/ deduction distinction likely to be of use. Can’t we, after practice at least, intuit the sum of 6723 and 3480?)

13 It might be objected here that if it is indeed true that every application of Descartes’ procedure (addition, in the case discussed) is impugnable, then the distinction I have been urging on his behalf, between impugning particular applications of a procedure and impugning the procedure itself, is just idle. For surely, if every application of a procedure is impugnable, then the procedure is itself impugned. And if that is so, there is no reason to think that the procedure could yield any knowledge at all.

This objection misses the mark. To see this, notice that I did not say that every possible application of addition is impugnable. On the contrary, it is actually possible, at least in principle, for Descartes not only to know, but also to secure a knowledge that 2+3-5. For, since he is able to raise a doubt against ‘2+3=5’ only when he is not actually adding 2 and 3, then should he continually focus his attention on (i.e., continually compute) 2+3, he will never be able to doubt the result he gets (viz., 5). In that case, that 2+3=5 would ever be immune to his psychological doubt; and hence, he would ever know that 2+3=5.

The full significance of this point will emerge in later sections. Here, however, it should suffice to note that the objection misses the possibility that some application by Descartes of a procedure for determining whether a proposition is trueactually, some series of applications-could be, as a matter of fact, unimpugnable. Of course, given that it is not Descartes’ entire project to come to know that 2+3=5, continually focusing on 2+3 would be pointless for him. That would not, however, be because he couldn’t come to a secure knowledge, by so doing, that 2+3=5.

14 Descartes tells us that atheists may ‘know clearly that the three angles of a triangle are equal to two right angles’ (Reply to Obj. II, HR II 39). However, ‘such knowledge on his part cannot constitute true science’ (HR II 39), exactly because atheists do not know that a non-deceptive God exists. How atheists can know anything if the main argument of the Meditations is circular in the way described at the outset escapes me. On my interpretation, however, these two passages make perfectly good sense together. In particular, since even atheists can come to be psychologically certain of, e.g., the above geometrical proposition, they can (momentarily) know it. Even so, that knowledge cannot constitute true science because the atheists’ belief that the proposition is true is ever subject to metaphysical doubt when the proofs by whose contemplation the knowledge is made possible are absent from their minds. (Atheists, of course, precisely reject the only proof which can fell metaphysical doubt forever in a single rendition-though I have yet to explain exactly how the proof accomplishes this.) Thus the atheists’ knowledge is ephemeral, and not suitable as a foundation for science.

15 Broughton, following Gewirth and others, argues for the same point. But her argument, presupposing the legitimacy of epistemic doubt, is different from the one I offer below.

16 In fact, there are two ways in which Descartes may reinstate his title to affirm a proposition against which he has succeeded in raising metaphysical doubt. Either he may, as we saw earlier, compute the proposition again, or he may refute the only reason he has come up with for doubting it (viz., that God might have caused him to miscompute it) by proving that a non-deceiving God exists.

17 As I shall argue immediately below, Descartes is now in a position to see that such a being is not really possible But it might be objected that if I am right that Descartes must see whether a putative reason for doubting a proposition represents a possible state of affirs before he can count the reason as impugning the proposition, then this (general deceiver) hypothesis (and, it should be added, the deceiving God hypothesis) should never have been permitted to count as impugning any proposition in the first place.

In a sense this objection is correct. It is simply impossible, however, for Descartes to have done everything at once. He might, perhaps, have started by discovering (via the cogito, presumably) the significance of psychological indubitability, then proceeded to the proof that a non-deceiving God exists, and only then attempted to raise-unsuccessfully-the hypothesis that a being other than God might be causing him to miscompute propositions. But there are pretty clear expositional (not to mention dramatic) reasons for him to have proceeded in the way he actually did.

Perhaps the best way to think of this is to imagine Descartes, in the First Meditation, as provisionally accepting the demon hypothesis-clearly the model for our general deceiver hypothesis-as a genuine reason for doubting propositions. For all he can see at that point, it does represent a way in which he could be going wrong in affirming propositions as true. And then, as the Meditations proceed, we may think of him precisely as exploring the question of whether that hypothesis is really possible, and discovering in the Third Meditation that it is not.

18 I am not suggesting that Descartes must be able to see in detail how a reason would falsify a proposition. But he must at least be able to see that it could.

19 Williams, 205

20 It might be thought that, for Williams, systematic doubt is not successfully raisable (i.e., that it fails to be a genuine doubt) after the Third Meditation proofsthough that fact is itself something of which Descartes could assure himself only by going (again) through those proofs. Since I do not have the space to present Williams’ interpretation in detail, I can only give a rough indication of the correct response here.

For one thing, Williams speaks of the theist answering systematic doubt by rehearsing the proof that God exists. But it would be strange to suppose that a doubt unsuccessfully raised-a spurious doubt-needs answering. (On my proposal, no doubt gets answered).

More fundamental, however, is this. Williams’ entire treatment of the circularity charge rests on his claim that Descartes may adopt an acceptance rule for propositions. Such a rule is supposed to allow Descartes to accept as objects of ongoing beliefs, propositions of which he has been psychologically certain. I claim, however, that such an acceptance rule needs justification, precisely because of the time limitations of psychological certainty. Now, Williams strongly suggests that no such justification is possible. He says, rather, that the rule ‘is [simply] a minimal structural condition of getting on at all’ (206). But he offers no account for why Descartes may help himself to this condition. It can’t be, for example, that Descartes may adopt the rule because, without it, he would be unable to attain secure knowledge (and hence, in that sense would be unable to ‘get on’)-for systematic doubt is intended precisely to challenge the possibility of attaining secure knowledge. Accepting the rule on those grounds then would certainly not be to answer systematic doubt. Indeed, it is possible to view systematic doubt as exactly challenging Descartes’ adopting of the acceptance rule. If that is right though, one may not suppose that one may now affirm as true, propositions that one was able to affirm, until that challenge has been met. That is just to say, however, that one must view systematic doubt as impugning-though not, of course, irreparably-rights earlier achieved to affirm particular propositions as true.

21 It is of course not the case, on my interpretation, that Descartes’ right to affirm that God exists lapses when he is not directing his attention to the Third Meditation proof. On the contrary, that right is exactly as secure as his right to affirm any other proposition of which he has been psychologically certain. My point here has been simply that a general security cannot be achieved at the price of Descartes’ needing continually to be psychologically certain of any particular proposition.