Three leading ideas will guide us, each independently plausible, and all in line with the virtue epistemology defended in earlier lectures.

First, knowledge is a matter of degree, in various respects. Holmes and Watson may both know something, while Holmes knows it better. Among the things that Holmes knows, moreover, some he knows better than others. This comports with our conception of animal knowledge as apt belief, since aptness of belief admits degrees in three respects: in respect of the competence exercised, in respect of the quality of the conditions, and in respect of how much the correctness of the belief is due to that competence exercised in those conditions. There is also a higher level of knowledge—reflective knowledge, apt belief aptly noted—which imports further gradations.

Prominent among things we hold dear, according to a second leading idea, is the coherence of our minds. When constituted by inter‐belief explanatory relations, such coherence goes with the value of understanding. We want our beliefs to be so integrated as to enable answers for our many and varied whys.

A third idea will also figure eventually: namely, that the evaluation of a particular entity, such as an action or a belief, (p. 114 ) can be importantly relational. In a landscape, or a poem, or a conversation, at a certain point something may fit well or ill, and if the former, it is then relevantly “appropriate,” or perhaps even “required.” The object of evaluation is thus a particular item, but it is evaluated relative to its relevant wider context. And the wider context of evaluation may include possibility space, as when an archer hits the bull's‐eye with a shot that is not only accurate but also “skillful,” with its counterfactual implications. A belief may similarly hit the mark of truth unaided by luck, and may also fit within the believer's wider body of beliefs. And we can then evaluate it as “epistemically justified,” in one or another sense: “competently adroit” perhaps (or reliably based, or counterfactually safe, etc.), or perhaps “rationally justified” (coherently fitting, and held in part on that basis).

Guided by these three ideas, we next consider two seemingly trivial principles, which together hold surprising consequences. Drawing and assessing these will be our main project.

A. Some Consequences of Two Principles

First the principles:

Ascent (principle of epistemic ascent).

If one knows full well that p and considers whether one knows that p, then one must be justified in thinking that one does. ¹

(p. 115 ) Closure (principle of the closure of epistemic justification through justifiedly believed entailment).

If one is fully justified in believing p and in believing that, necessarily, unless it is so that q, it cannot be so that p, then one must also be justified in believing that q.

These principles both concern the conscious contents of a mind at a given time. Ascent, for example, when spelled out more fully, reads thus:

If, at a given time when one knows full well that p, one consciously considers whether one knows that p, then one must also be justified in affirming that one does.

Why should we believe this? Anything one knows full well must be something of which one is sufficiently confident. Suppose that, while consciously confident that p, one also considers, at that same time, whether one not only believes but knows that p. Exactly three options open up: one might say either (a) “No, I don't know that,” or (b) “Who knows whether I know it or not; maybe I do, maybe I don't,” or (c) “Yes, that is something I do know.” One is better off, surely, if able to give the later answers: better off with the second answer than with the first, and better off yet with the third. Answer (a), and even answer (b), would reveal a certain lack of integration in that stretch of consciousness; only answer (c), of the three, entirely avoids disharmony within that consciousness at that time. If one has to give answer (a), or even answer (b), one thereby falls short, and one's belief that p itself falls short. That belief is then not all that it could be. One is not as well (p. 116 ) justified as one might be, epistemically. You are best justified in consciously believing that p at that time if you can answer in the affirmative your own conscious question whether in so believing you thereby know. You are better justified in so believing if able to answer thus affirmatively than if consciously forced to withhold judgment; and you are especially better justified in so believing if able to answer thus affirmatively than if consciously led to deny that you know. ²

(p. 117 ) Suppose the knowledge at issue in the antecedent of Ascent to be knowledge of our coherence‐requiring high quality. A belief would not qualify as a case of such knowledge if enmeshed in a debilitating incoherence—as when one has to accompany one's belief, at that same time, with a conscious denial that it is knowledge, or even with a conscious suspension of judgment. If it is knowledge of that high level that is involved in our principle, then the combination of the two conjuncts in its antecedent requires the truth of its consequent. One does not attain high‐level knowledge, when one consciously wonders whether one does know, unless one is able to say yes. What is more, to say yes arbitrarily would not do. One's belief amounts to reflective knowledge only if one can say that one does know, not just arbitrarily, but with adequate justification.

Our principle of Closure, too, concerns the fully conscious contents of a mind at a given time, so that, when spelled out more fully, it reads like this:

If, at a given time, one consciously believes both that p, and that, necessarily, unless it is so that q it cannot be so that p, then one is fully justified in these two beliefs only if one is also justified in then affirming that q.

Suppose, again, one consciously believes that p, and, at that same time, second, one consciously believes that, by logical necessity, if p then q. Exactly three options open up on the (p. 118 ) proposition that q: either (a) one might deny it, assenting consciously to its very negation, or (b) one might consciously withhold judgment on it, thinking consciously: who knows, maybe it's true, maybe it's false, or (c) one might consciously affirm it. One is better off, surely, if able to give the later answers: better off with the second answer than with the first, and better off yet with the third. Answer (a), and even answer (b), would reveal a certain lack of integration; only answer (c), of the three, avoids disharmony. If one has to give answer (a), or even answer (b), one falls short, and either one's belief that p or one's belief that, necessarily, if p then q, itself falls short. At least one of these beliefs is then not all that it could be. One is not as well justified as one might be, epistemically, in that belief. One is best justified in consciously believing both that p and that, necessarily, if p then q, at that time, only if one can also assent consciously to the proposition that q. One is better justified in so believing, anyhow, if one can thus consciously affirm that q, than if one has to suspend judgment on it, or, worse, consciously deny it.

Suppose the justification at issue in the antecedent of Closure is justification of our coherence‐requiring high quality, so that incoherent beliefs would not be thus justified—as when one believes that p and that, necessarily, if p then q, and yet consciously denies that q, or consciously suspends judgment. If so, if it is justification of that coherence‐requiring level that is involved in our principle, then the combination of the two conjuncts in its antecedent requires the truth of its consequent. One does not attain the epistemic heights required for high‐level conscious justification—both that p and that, necessarily, if p then q—unless one also consciously assents to the proposition that q; and (p. 119 ) one must assent not just arbitrarily but with adequate justification. ³

From these two principles—Ascent and Closure—we may already derive a principle with a substantial role in recent and not‐so‐recent epistemology:

Exclusion (principle of exclusion).

If one knows full well that p and considers whether one knows that p, and one is then fully justified in believing that, necessarily, unless it is so that q one cannot know that p, then one must also be justified in believing that q.

This follows straightforwardly. Via Ascent, the first two conjuncts of the antecedent of Exclusion entail this: that one is justified in believing that one knows that p. And this, in combination with the third conjunct, via Closure in turn yields: that one is justified in believing that q. Putting all this together, we see Exclusion entailed by Ascent and Closure. Of course, our focus is still a single time when someone consciously believes and considers the relevant items. So the knowing, considering, and justified believing that Exclusion concerns is all to take place in a single consciousness at the same time.

Exclusion implies that if one is to know full well that p while consciously believing it, then if one also consciously considers whether one knows that p, while consciously believing with full justification that unless q one cannot possibly know that p, then one must justifiedly believe that q. (p. 120 ) Exclusion thus implies that in order to know full well that p, one must be able to “defend it in the arena of reflection”: one must be able to view oneself as meeting every condition that one recognizes as required in order then to know that p; or, alternatively and to the same effect, one must be able to exclude justifiedly any possibility one consciously recognizes to be incompatible with one's then knowing that p.

Exclusion is a powerful principle in the skeptic's hands, once we are persuaded to grant the following:

Here is something that most of us are fully justified in believing: that no belief can amount to knowledge unless formed in a way that is at least minimally reliable.

This fact in combination with Exclusion entails a “principle of the criterion”:

PC1. If one knows full well that p, while considering whether one knows that p, then one is justified in believing that one's belief that p is formed in a way that is at least minimally reliable.

Given how it has been derived, this we must still view as a principle about the contents of any given consciousness at any given time. Spelled out more fully, PC1 hence claims this: that if one consciously knows full well that p, and at the same time considers whether one knows that p, then one must be justified in believing that one forms one's belief in a way that is at least minimally reliable (that the source of one's belief is at least minimally reliable). Consciously knowing something full well while in the arena of reflection requires that one actively defend one's belief against all entertained possibilities that one consciously takes to be incompatible with one's knowing in so believing.

(p. 121 ) Undeniably there is much that one knows without being aware of it at the time. One still knows a lot when asleep and even when entirely unconscious. And we want our reflections to apply to knowledge generally, not only to the highly restricted domain of what rises to consciousness at any given time. Fortunately, we can broaden our scope with little or no loss in plausibility. We need only focus, not just on someone's conscious beliefs and experiences at the target time, not just on what they actually manage to defend reflectively; we need rather to focus, more generally, on what they would be able to defend, no holds barred, were it cast in the arena, perhaps by a hypothetical skeptic.

It would not do, however, to suppose that someone already knows something just because if they started thinking about how to defend their belief, they would then come up with a fine proof. Someone who guesses the answer to a complex addition problem does not already know the answer just because, given a little time, he could do the sum in his head. If he had not done the sum, if he had just been guessing, then he acquires his knowledge through reflection, and does not know beforehand. In some sense, at some level, if one already knows pre‐reflectively, then the justifying reasoning must already be operative before one enters the arena. When challenged in the arena, one simply reveals the support that one's belief already enjoyed pre‐entry. In order to occupy the desired pre‐reflective position, moreover, one needs already, pre‐reflectively, the wherewithal to defend one's belief if exposed to reflection, and one's belief must already be supported by the structure of reasons constituting that defense‐at‐the‐ready. We are not just interested in the weaker position of someone who would be able to defend the belief, but only because its exposure to reflection would lead (p. 122 ) the subject to new arguments and reasonings that had never occurred to him, and that in any case had played no role in his acquisition or retention of the target belief.

Our most recent reflections in turn induce a second principle of the criterion:

PC2. In order to know full well that p one must be justified in believing (at least implicitly or dispositionally, if not consciously) that one's belief that p is formed in a way that is at least minimally reliable, that it has an at least minimally reliable source (if the proposition that one's source is thus reliable is within one's grasp).

This principle is not restricted to beliefs entertained consciously; it is rather meant to apply more generally to implicit, subconscious, dispositional beliefs, and even to beliefs that one has while asleep or unconscious.

In fact PC1 and PC2 are only two members of a whole family of “principles of the criterion,” whose unifying thread is that they all concern the satisfaction of requirements for various degrees of knowledge. Thus, certain levels of knowledge would be compatible with one's knowing the sources of one's belief to be just minimally reliable, but higher degrees would require knowing them to be quite reliable, or highly reliable, and so on.

B. The Pyrrhonian Problematic

Sometimes a justified belief is justified because supported by reasons; reasons that the believer not only could have but does have. The fact that given time one could think of some good reasons for believing something is not enough to make one justified in so believing. Again, someone who guesses (p. 123 ) on a sum could perhaps do the addition in his head; but, even supposing he could do it, that alone does not justify him in believing his guess before he actually does it. One's rationale for a belief cannot be successful if dependent on some arbitrary or otherwise unjustified component. Justifying beliefs need to be justified in turn. And now we have three possibilities. As we consider the reasons for one's belief, and the reasons, if any, for these reasons, and the reasons, if any, for these in turn, and so on, either (1) some ultimate reasons are justified noninferentially, are justified in some way that does not require the support of some ulterior reasons, or (2) there are no ultimate reasons: further reasons always justify one's reasons, at every level, no matter how remote the level, and these further reasons always go beyond any reason already invoked at earlier levels, or (3) there are no ultimate reasons: further reasons always justify one's reasons, at every level, but these further reasons need not go beyond reasons already invoked at earlier levels.

Possibility (1) corresponds to foundationalism. The foundations are constituted by the ultimate reasons that require no further supporting reasons in their own behalf. Possibility (2) is that of infinitism. Each supporting line of reasons extends infinitely to further reasons, ever‐new reasons for the reasons at each level, no matter how remote that level may be from the justified conclusion. Possibility (3), finally, is that of the circle. One's justifying structure of reasons circles: some reason for a reason at a given level returns us to an earlier level.

C. Is Foundationalism a Myth?

According to conventional wisdom, foundationalism has been historically the option of choice. This, we are told, may (p. 124 ) be seen with special prominence in Aristotle among the ancients, and in Descartes among the moderns. According to this story, it is only with Hegel that persistent reflection on the ancient problematic yields a powerful defense of the circle. It took Hegel's philosophic genius to overcome the foundationalist inertia of the tradition and the immense influence of Descartes. Only Hegel returns to the ancient problematic and reveals the power of its anti‐foundationalist side, and the virtues of circularity.

Among analytic philosophers, it is Sellars who took the lead against foundations, with his attack on the “Myth of the Given.” The attack targets not just a givenism of sensory experience, but a much more general doctrine, one amounting to foundationalism of whatever stripe. Thus, Sellars's attack in “Empiricism and the Philosophy of Mind,” focuses, not on experiential foundations via introspection, but on perceptual foundations via observation. The following is marshaled effectively in his critique of direct realism:

In order to be fully justified, perceptual belief requires background beliefs (assumptions) that in turn require justification.

In accepting the deliverances of one's senses one assumes that they are so constituted, and so adjusted to the relevant environment, that they tend to get it right.

More recently, Laurence BonJour has generalized from Sellars's principle as follows:

No belief B is fully justified simply because it satisfies some condition F such that beliefs satisfying F are probably true. The believer must also be aware, at some level, that B satisfies the condition.

(p. 125 ) This generalization, BonJour's Generalization, sets up a clash of intuitions. On one side are the epistemic internalists, who believe that justification requires justifying beliefs, and that no one can be really justified in a certain belief while unaware of its sources.

Foundationalism and its Myth of the Given were thus attacked famously by Sellars, in a way generalized by BonJour. But the sort of problem raised is not unique to their critique. A main theme of Richard Rorty's attack on foundationalism is the alleged “confusion of causation with justification” that he attributes to Locke and others. Donald Davidson also adds his voice: “As Rorty has put it, ‘nothing counts as justification unless by reference to what we already accept, and there is no way to get outside our beliefs and our language so as to find some test other than coherence.’ About this I am, as you see, in agreement with Rorty.” ⁴ Just how damaging is that line of objection against experiential foundations?

Here intuitions clash. For externalists, a belief is justified by being related appropriately to its subject matter, perhaps causally or counterfactually, or by deriving from a reliable source that yields mostly true beliefs with great reliability. This need not come to the attention of the believer; it need only be in fact true, whether believed or not. On this side are arrayed Goldman, Nozick, Plantinga, and Unger, among others.

Intuitions in this stand‐off have hardened over the years, and each camp tends to regard the other as just missing the point in some crucial respect.

(p. 126 ) Most interesting for us is the fact that BonJour's Generalization (of Sellars's insight) is a member of our family of principles of the criterion. ⁵ So it should be as plausible as the two simple principles from which the family derives: namely, Ascent and Transfer. One reaction to this is to accept the Sellarsian reasoning and reject foundationalism. But if we reject foundationalism, then we are still caught in the Pyrrhonian Problematic. What then is the way out?

Ironically, a way out is opened already by the foundationalist‐in‐chief of the received story, Descartes himself, whose real view of these matters is quite subtle, or so I will argue, and must be approached gradually.

D. Descartes' Way Out

Three commitments are standardly attributed to Descartes, not all of which could be held by anyone of middling intelligence. The first doctrine is a rationalist foundationalism according to which “intuition and deduction are the most secure routes to knowledge, and the mind should admit no others.” On this view, whatever one knows one must either intuit directly, through its immediate clarity and distinctness, or one must prove it deductively, on the basis of ultimate premises each of which is itself intuited as clear and distinct.

(p. 127 ) According to the second commitment, in order to attain really certain knowledge of anything whatsoever, one must first prove that there is a God who is no deceiver. Consider, for just one example, the following passage, from the last sentence of the fourth paragraph of Meditation Three, where, speaking of the “metaphysical” doubt that he has raised, Descartes has this to say: “[I]n order to be able altogether to remove it, I must inquire whether there is a God as soon as the occasion presents itself; and if I find that there is a God, I must also inquire whether he may be a deceiver; for without a knowledge of these two truths I do not see that I can ever be certain of anything.”

Descartes also apparently believes, third and finally, that God's existence and nondeceiving nature must be demonstrated through appropriate reasoning (involving, among other lines of argument, the ontological and the cosmological).

Clearly, these three commitments cannot be combined coherently. But the second and third would be hard to defeat, given their textual support. This puts in doubt the long and widely held belief that Descartes was a foundationalist.

On the other hand, the attribution of foundationalism to Descartes is not just arbitrary. There is textual evidence in its favor, including the passage above. Weightier evidence yet supports attributing to Descartes the second and third commitments, however, so that, if a foundationalist at all, Descartes was no simple or flat‐out foundationalist. His position must be subtle enough to sustain not only the first commitment, under some interpretation, but also the second and the third. Consider a key passage in which Descartes claims epistemic advantage over the atheist: (p. 128 )

The fact that an atheist can be “clearly aware that the three angles of a triangle are equal to two right angles” is something I do not dispute. But I maintain that this awareness of his [cognitionem] is not true knowledge [scientia], since no act of awareness that can be rendered doubtful seems fit to be called knowledge [scientia]. Now since we are supposing that this individual is an atheist, he cannot be certain that he is not being deceived on matters which seem to him to be very evident (as I fully explained). And although this doubt may not occur to him, it can still crop up if someone else raises the point or if he looks into the matter himself. So he will never be free of this doubt until he acknowledges that God exists. ⁶

Here Descartes is not claiming only ex post facto advantage over the atheist. Take the moment when both are clearly and distinctly perceiving the fact that the three angles are equal to two right ones. Even at that very moment, according to Descartes, the atheist is at an epistemic disadvantage.

That, moreover, is not the only passage where Descartes claims or implies the specified sort of advantage. Here is another, from the last paragraph of Meditation Five (and compare also the fourth paragraph from the end of that Meditation):

And so I very clearly recognize that the certainty and truth of all knowledge depends alone on the knowledge of the true God, in so much that, before I knew Him, I could not have a perfect knowledge of any other thing.

(p. 129 ) According to this, cognitio of the true God is required for scientia of anything whatever.

Descartes was well aware of the Pyrrhonian Problematic, as may be seen, for one example, in his “Search for Truth.” Such skepticism suffused his intellectual milieu, and he knew its content and sources. Against this backdrop, a passage from Sextus is revealing:

Let us imagine that some people are looking for gold in a dark room full of treasures. . . . [N]one of them will be persuaded that he has hit upon the gold even if he has in fact hit upon it. In the same way, the crowd of philosophers has come into the world, as into a vast house, in search of truth. But it is reasonable that the man who grasps the truth should doubt whether he has been successful. ⁷

No one is likely to disdain the good fortune of finding gold in the dark. On normal assumptions, one is of course better off for having done so. More admirable yet is getting the gold through one's own efforts, however, where one succeeds through one's own deliberation and planning. Here success is not just luck in the dark; it crowns rather an enlightened pursuit of a desirable goal. In that passage Sextus suggests distinguishing similarly in epistemology. Here again it is more admirable to attain one's worthy objective through one's own thought and efforts than it is to be a passive recipient of brute luck. At a minimum it is better to proceed in the light of an adequate perspective on one's own cognitive doings.

If convinced by this Pyrrhonian thought, Descartes would make just the distinction he does make between cognitio (p. 130 ) and scientia. Cognitio is the attaining of the truth, which can happen through one or more layers of good luck, in the environment, in oneself, and in the adjustment between the two. One might of course attain the truth through luck, by a mere guess that the fair dice will come up seven, and surely this does not yet qualify as cognitio. Cognitio requires at a minimum that one attain the truth by being appropriately constituted, and appropriately situated, to issue reliable judgments on the subject matter. So constituted and situated, one would be right on that question. Here of course are matters of degree: how reliable are one's operative dispositions, one's epistemic competences? Are they infallible? Nearly infallible? Very highly reliable? And so on. This has to do with how easily one might go wrong in thinking as one does through exercising the relevant dispositions, one's faculties or virtues. Cognitio furthermore requires that the correctness of one's belief be attributable to the exercise of such a competence in its appropriate conditions. Cognitio is animal knowledge, or apt belief.

Scientia requires more. It is attained only through an adequate perspective on one's epistemic doings. Only if one can see how it is that one is acquiring or sustaining the belief in question does one attain scientia. What is more, one must see that way as reliable, as one that would tend to lead one aright, not astray. But this is just what is required by our principles of the criterion. According to this family of principles, various levels of knowledge will require various degrees of perceived reliability in the sources of the belief constitutive of the knowledge. In accepting Sextus' Pyrrhonian thought, therefore, Descartes would be accepting the importance of satisfying a principle of the criterion, whereby one must believe one's source to be reliable. How reliable? This will (p. 131 ) depend on how high a level of knowledge is selected in the context.

Suppose Descartes accepts the Pyrrhonian Problematic, and accepts also Sextus' contrast between attainments in the dark and those that are enlightened. In that case he faces this question: is enlightened knowledge possible for us? Can we attain an enlightened perspective on what we believe and on our ways of acquiring and sustaining those beliefs, one that reveals the sufficient reliability of those ways? This, I submit, is what sets up Descartes' epistemological project. He is trying to meet Sextus' demands, to the extent that these are reasonable. Further features peculiar to Descartes' own project derive from his desire not just for reasonable and reliable belief but for absolutely certain and infallible knowledge. However, much of interest in his thought need not be tied to that desire.

In a bare sketch, here is how I see Descartes's epistemic project. First he meditates along, with the kind of epistemic justification and even “certainty” that might be found in an atheist mathematician's reasonings, one deprived of a world view wherein the universe may be seen as epistemically propitious. Descartes' reasoning at that stage can be evaluated, of course, just as can an atheist mathematician's reasoning. Atheist mathematicians will differ in the worth of their mathematical reasonings. Absent an appropriate world view, however, no such reasoning can rise above the level of cognitio. If we persist in such reasoning, nevertheless, enough pieces may eventually come together into a view of ourselves and our place in the universe that is sufficiently comprehensive and coherent to raise us above the level of mere cognitio and into the realm of higher, reflective, (p. 132 ) enlightened knowledge, or scientia. No circle vitiates this project. ⁸

A mere thermometer reaction to one's environment cannot constitute real knowledge, regardless of whether that reaction is causally mediated by experience. It is not enough that one respond to seeing white and round objects in good light with a “belief” or “proto‐belief” that one faces something white and round. Having asked oneself “Do I know that this is white and round?” or “Am I justified in taking this to be white and round?” suppose one has to answer “Definitely not” or even “Who knows? Maybe I do know, maybe I don't; maybe I'm justified, maybe I'm not.” In that case one automatically falls short, one has attained only some lesser epistemic status, and not any “real, or enlightened, or reflective” knowledge. Knowing full well thus requires some awareness of the status of one's belief, some ability to answer that one does know or that one is epistemically justified, and some ability to defend this through the reliability of one's relevant competence exercised in its appropriate conditions. But this leads to a threat of (p. 133 ) circle or regress, a main problematic, perhaps the main problematic of epistemology. Surprisingly, already in Descartes himself, the founder of modern epistemology, ⁹ we find a way beyond it. ¹⁰