On knowledge and belief

We are finite knowers. This is a platitude. But it easy to lose sight of what the platitude means. Part of what it means is that we do not know everything; that the amount of things we know is finite — perhaps in the mathematical sense of the term, but certainly, and more importantly, in the sense that there is a limit to what we know. There is a limit to what we know that is not also the limit of the knowable. What we know falls short of what there is to be known. Expressed positively: we always have more to learn.

This first aspect of our finitude as knowers is closely related to a second aspect: our fallibility. We may believe we know p and yet fail to know it, perhaps because p is false, or perhaps for some other reason. It may seem, on the face of it, that this second type of finitude is independent of the first type; that there is a finitude in terms of scope and another, separate, finitude in terms of fallibility. For it may seem that the following two are at least intelligible scenarios:

  • A knower whose knowledge is limited in scope, but who is infallible. The traditional example would be the stoic sage, who assents to only those thoughts that he can be absolutely certain about.
  • A knower whose purported knowledge is unlimited in scope, such that no further enquiry is possible, but who is nevertheless fallible. This being is godlike in the sense of being able to grasp the entire richness of a world at once, but fails to be godlike in that they may be wrong about whether the world they grasp is the same as the world that is real.

There are, however, good reasons to doubt the intelligibility of both of these scenarios. Infallible knowledge of the type to stoic sage is said to have seems to be possible, if at all, only for isolated items of experience that have no implications beyond the mere having of the experience. We might hope to infallibly know that we seem to see a mug, but not that we see a mug or that there actually is a mug. But our grasp of such isolated items depends on our prior grasp of the full-blooded kind of experience that can be either veridical or misleading. If one divorces the supposedly infallible elements of our experience from the fallible ones, the infallible elements lose their content and are no longer candidates for assent or truth. (This theme is discussed in my earlier post, Kantian and Cartesian scepticism.) To make the same point in a different way, consider what it takes for something to be an item of knowledge. A necessary condition of this is surely integration with the rest of our knowledge; where integration involves relations of fitting or failing to fit that have epistemic importance. But the items that the sage might know infallibly are such that they cannot be undermined by other items that he might come to know. Hence, these items do not stand in relations of fitting and failing to fit to each other, and therefore they are not truly items of knowledge at all.

What about the second scenario? Let us first zoom in on the fact that knowledge is essentially self-conscious. To be a knower is to be aware of oneself as a knower; it is, among other things, to be responsible for one’s beliefs and to be (at least a little) confident about (at least some of) one’s beliefs. To self-consciously be a finite knower is to be aware of one’s finitude as a knower. Now one can only be self-conscious of one’s finitude in the second sense of fallibility if one is also self-conscious of one’s finitude in the first sense of always having more to learn; for to be self-conscious of one’s fallibility is to be aware that one might need to revise one’s beliefs; and this requires the awareness that new items of knowledge might emerge that may fail to fit one’s current beliefs. Conversely, to be aware that enquiry is not over, that new items of knowledge may appear, implies that one is aware of one’s fallibility. Here we see why the second scenario at the very least does not make sense from the inside. For we are asked to imagine a being for whom enquiry is at an end, but who is nevertheless fallible. This can never be anyone’s self-conscious conception of themselves. (Whether it might be a true third-person description of someone is something we will touch on below.)

The previous paragraph has also revealed to us a third aspect of our finitude as knowers, one which is again not truly different from the other two but forms an indissoluble whole with them: temporality. To be a finite knower is to be engaged in a project of enquiry that unfolds in time and is teleologically oriented towards knowledge.

The crucial Kantian insight… well. I suppose there is a tendency in all of us who have been impressed by Kant to talk about the crucial Kantian insight, as if there were only one of them, and to then present a rather wide variety of insights as the single core idea from which all of Kant’s critical philosophy emerges. And yet perhaps we are not entirely wrong to do so. For perhaps all these insights are at bottom the same insight. Anyway, one of those crucial Kantian insights, one that has as much right to be called the Kantian insight as any other, is that we must not understand the finite knower as an imperfect version of an infinite knower, but that we must — that we can only — understand the finite knower from the finite perspective of the finite knower themselves. To be a finite knower is not to have a limited amount of that which God has an unlimited amount of. Our only purchase on the concept of knowledge is that which we can glean from our self-understanding; and this means that any conception of knowledge — or of belief, justification, and so forth — we can have is essentially one from the finite perspective.

(And this is one of the reasons why we can’t make sense of the idea suggested in the second scenario, the idea of someone who has a finished belief system, who has no further opportunities for revision, but who is nevertheless wrong. To cast the claim that we can’t make sense of this as a dubious ‘coherentist’ claim that leads to ‘relativism’ and cannot be accepted by anyone who cares about ‘correspondence with reality’ is to fail to see the point.)

It is easy to miss the Kantian insight when we focus on the first aspect of finitude, which in fact seems to invite our thinking of finitude as a sort of subset of infinity: God has all the knowledge, we only have some of it. It is perhaps also easy to miss it when we focus on the second aspect; for we might perhaps talk about degrees of certainty and then claim that we finite knowers just have less certainty than God — less than God has, yes, but nevertheless the same kind of stuff. (This can’t be right, though. God cannot be certain in any sense of the word that is even putatively applicable to us.) But it’s much easier to keep the critical insight in focus if we consider the third aspect of finitude: temporality. For the idea that knowledge is the teleological end point of a temporal process of enquiry simply has no equivalent in the realm of the divine. And so it is useful to emphasise, again and again, that knowledge, belief, justification, evidence, and so on, always need to be understood against the background on an unfolding process of finite enquiry.

Conversely, we may expect any epistemology that does not take the Kantian insight on board to neglect the temporal aspects of knowledge and to conceive of the central epistemological notions apart from the process of enquiry. And this is precisely what happens in mainstream epistemology. In order to develop our insights, we will now look at the famous JTB analysis of knowledge. (At the end of our post, we will also make some remarks about Bayesian epistemology.)

S knows that p if and only if (1) S believes that p; (2) S is justified in believing that p; and (3) p is true. There are many facets of this analysis that are worth commenting on. One is the essentially third-person nature of the knowledge ascription. Another is the idea that belief is in some sense a component of knowledge; that knowing p and merely believing p share a common factor, which is the belief. I will return to both of these. But for now I want to focus on the fact that time makes no appearance in this analysis; that knowledge, belief and justification are presented as static states of affairs, apparently unconnected to a past and a future, or at least not essentially so connected.

Presumably a belief is justified if and only if one has good reasons for holding it — if one has those reasons right now, at the moment one holds the belief. But this misses out on a crucial dimension of our epistemic responsibility. Suppose that one believes p, say, that medicine X is a cure for disease Y. Suppose further that one bases this belief on all the available medical evidence; that the evidence is indeed overwhelmingly in favour of the truth of p; and that p is true. Is this enough to conclude that one is epistemically responsible in believing that p? Not at all. For one’s belief in p to be epistemically responsible, one also has to have certain commitments for the future. One must be committed to changing one’s belief if contrary evidence comes in; perhaps one must even have a willingness to seek out such evidence if there are plausible sources of it. We should never say of someone: “he is epistemically responsible in believing that p and whatever further evidence comes in, no matter how negative for p, he will keep believing that p.” Such a person is precisely not epistemically responsible.

But isn’t it the case that this person would be perfectly justified now and would simply lose that justification if and when this further evidence turns up? Or isn’t it perhaps the case that while the person is justified in their belief, they lack something else, perhaps responsiveness? Insofar as this is a merely terminological quibble, not much hinges on how we answer these questions. I take it that ‘justification’ has usually been used as the name for the ‘being epistemically responsible’ element of enquiry; but of course one can make a different terminological choice. What is not a quibble and not a matter of choice is the importance of keeping the temporal dimension of enquiry in view. To use justification as a term that can be evaluated at an isolated instant is to run a grave risk of failing to do precisely that.

The point becomes even clearer when we turn to the ‘belief’ component of the JTB analysis. Consider the following statement: “I believe that p but I will give up this belief ten seconds from now without any reason.” This speaker does not believe that p, not, at least, in the full-blooded sense of the term. Or consider: “I believe that p and whatever new evidence comes in, I will continue to believe that p.” This speaker also does not believe that p in the full-blooded sense of the term. Perhaps they are fanatically attached to p, but this locution precisely indicates that with regard to p, they have given up the quest for knowledge. So a belief is not to be thought of as a static state, but rather as a stage in the ongoing process of rational enquiry.

This is not to say that there are no contexts in which beliefs can come loose from the process of enquiry. We understand perfectly well what someone means who says: “Right now I believe that Rosemary truly loves me, but I know that the doubts will come back and that tomorrow I will no longer believe it.” But here we have a special use of the verb believe, what I think James Conant would call a self-alienated use of the verb. (See The Logical Alien, pp. 700-730 and thereabouts, where Conant discusses disjunctivism and Sellars’s and McDowell’s tie shops.) It is intelligible enough, but only as a special, derived, degenerated form of the normal kind of believing. It requires the speaker to take a step back from their beliefs, to regard themselves almost from a third-person perspective; it requires them to acknowledge that they do not believe in the full sense of the word.

One objection to what I said above about belief and justification is that the two stories were altogether too similar. If justification requires us to be responsible actors in the quest for knowledge; and if belief also requires us to be responsible actors in the quest for knowledge; then I might seem to be committed to the claim that there is no such thing as an unjustified belief. Well, yes! An unjustified belief is defective; not just defective in some external sense, but defective as a belief. As an analogy, consider a broken chair. Is a broken chair still a chair? There is a sense in which it is, but also a sense in which it is not. Since a chair is something that can be used for sitting on, and since a broken chair cannot be so used, it is no longer quite a chair. Of course we can still call it a chair, given our usual practices of making and using chairs-in-the-full-sense. It’s the same with beliefs. An unjustified belief is a belief in an attenuated sense, which can still be called a belief because it is similar in certain relevant respects to full-blooded beliefs. But while it makes sense to imagine people all of whose beliefs are justified, it makes no sense to imagine people all of whose beliefs are unjustified — such people would not be recognisable as epistemic agents. (They would therefore not be people either.)

This brings us to the second interesting aspect of the JTB analysis: its third-person nature. Of course the analysis is formulated in a third-person idiom; but that might be thought to be a mere artefact of representation, merely a way to indicate generality. However, the analysis is also third-person in a more fundamental way. It requires us to think about epistemic states in a way that cannot be done in the first-person. To state that knowledge is justified true belief is to contrast knowledge with other types of belief: unjustified beliefs and false beliefs. But one cannot say: “I believe that p and p is false.” And one also cannot say, if one is using the verb ‘to believe’ in the full-blooded, non-self-alienated sense: “I believe that p and I am not justified in believing that p“. To say one of these things is to become entrapped in Moorean paradoxes. This is certainly curious: why would the analysis of knowledge depend on assertions that are never intelligible from a first-person perspective? And there’s another puzzle. Given that we can never assert such Moorean sentences, is there any difference of meaning between the first-person assertions “I believe p” and “I know p“?

Take the sentence: “I believe p but I do not know p.” This sentence is not obviously paradoxical. We say such things all the time; e.g., when we say “I believe there’s still some alcohol-free beer in the fridge, but I don’t know for sure.” But if we just plug JTB into the above sentence, it seems that anyone who claims to believe but not know something, is someone who claims this: “I believe p and either p is false or I am not justified in believing that p“. This would be a Moorean paradox. It is also clearly not what someone who asserts that they believe but do not know p is asserting. So what are they asserting?

To understand this, let us look at the third interesting aspect of the JTB analysis. I can state it in three roughly equivalent ways: (1) it analyses knowledge in terms of belief, rather than the other way around; (2) it takes an item of knowledge to be a belief to which something optional has been added; (3) it claims that an episode of knowing that p and an episode of merely believing that p have a common factor, namely, the belief that p. Now we have already seen a reason to be suspicious of (2). A justified true belief is not like a small red car; a car that, in addition, has some properties that are in no way essential to cars. Something is only a belief in the full sense of the term if it is justified; if it is taken up into a process of enquiry for which arriving at truth is a criterion of success. So a justified true belief, knowledge, is not one among many kinds of beliefs; it is the central kind. All other kinds of belief are defective kinds. And so it is, contra (1), knowledge rather than belief that is the fundamental concept. And, contra (3), an episode of knowing and an episode of merely believing do not have as common factor a belief; rather, an episode of merely believing is a defective episode of knowing, it is something that would be an episode of knowing if only it didn’t have the defects that it has. (The theory propounded here is exactly analogous to disjunctivism about perception.)

Given this analysis, what is the point of saying “I believe p” rather than “I know p“? To say that one believes p is to keep some distance from one’s positive cognitive attitude towards p. I am not talking about merely acknowledging fallibility here. One can say that one knows p even if one believes that one is fallible about p. I know (I do not merely believe) that there is a mug of tea on my desk; but of course I could be mistaken about it. However, I seem to be in as good a position as I can be to assert that there is a mug of tea on my desk. There are no further plausible avenues for enquiry; there is no need for further enquiry; with respect to this little fact, the search for knowledge is effectively over. In other words, I have a positive cognitive attitude towards there being a mug of tea on my desk and I fully identify with that attitude.

It is crucial for the search for knowledge that one can also take up a positive cognitive attitude without fully identifying with it. This is what we express with the verb believe. I believe that cold nuclear fusion is impossible, but I’m willing to seriously consider experiments done by competent scientists. I believe that there is still milk in the fridge, but I do plan to check before I go to the shops. I believe that everything I write in this blog post is true, but I’m eager to hear counterarguments.

When I say that I believe p, I say that I have that positive cognitive attitude towards p that I would express by the phrase “I know pif I were to fully identify with it. When I say (or imply) that I believe but do not know p, I am not committing a Moorean paradox; rather, I am stating that although I do have a positive cognitive attitude towards p, I do not fully identify with that positive cognitive attitude.

There is, then, a kind of self-alienation in the very nature of a finite knower. To be an enquirer requires us to be, first, the person who is taking up the positive attitudes (which makes it true to say that I have these beliefs); to be, second, the person who takes a step back from the current state of the enquiry to critically compare it with the ultimate goal of unified knowledge and to thereby not fully identify with the current state; and, finally, to be the person who unifies the other two persons into the one unified cognitive agent that we must be. (There is perhaps something not merely superficially Hegelian about this scheme.) This tripartite nature of the knower is what allows us to intelligibly say “I believe p but I do not know p.” The first I is the I that believes; the second I is the I that does not identify with the belief; and the third moment, the moment of unity, allows the references of the two I’s to nevertheless be the same. (One could also phrase this in temporal terms — we are at the same time the I of the present, the I of the future, and the unity of the two.)

Thus we see again that a belief that is not embraced as knowledge is defective as a belief. It is a belief that is not fully believed; it is believed, but only partially, only provisionally; not in the full-blooded sense of the verb.

We can return to the analysis we made earlier of the speaker of the following sentence: “Right now I believe that Rosemary truly loves me, but I know that the doubts will come back and that tomorrow I will no longer believe it.” When we first analysed it, we said that the speaker was self-alienated. We can now see that the speaker is actually doubly self-alienated. For the speaker is not only alienated from the first I, the I that has beliefs; but also from the second I, the I that distances itself from their current beliefs by looking forward to the results of further enquiry. This is a kind of self-alienation that is no longer proper to the project of enquiry, but that entails a failure in the carrying out of that project; it is alienation from one’s own nature as a finite knower.

This blog post is already far too long. Nevertheless, as a coda, I want to make a few remarks about Bayesian epistemology. Does the Bayesian not have an attractive alternative to my analysis of the difference between belief and knowledge? For the Bayesian, with her degrees of belief, can say that to know p is to have P(p)=1; while to believe p is to have 0.5 < P(p). Thus, to say that one believes p but does not know p is simply to state that one has 0.5 < P(p) < 1. No complicated story about self-alienation is needed.

In effect, where I say that a mere belief is a less-than-full identification with a fully positive cognitive attitude, such a Bayesian says that a mere belief is full identification with a less-than-fully positive cognitive attitude. But this means that the Bayesian cannot get the crucial fact into view that there is something defective about mere belief; that the goal of belief is knowledge, and that belief that falls short of that goal calls out for further enquiry.

Consider the Bayesian attitude towards having the fully positive attitude of P(p)=1. Given Bayesian updating, the cognitive attitude expressed by such a formula is not responsive to further evidence; and for this reason, many Bayesians hold it to be irrational to ever take up such a fully positive cognitive attitude. Thus, knowledge is no longer the goal of rational enquiry, but something to be avoided! This is not a surprising insight about knowledge; it is the unfortunate result of confusing a claim to knowledge with an embrace of fanaticism.

One option for the Bayesian is to relax her criterion for self-ascription of knowledge; perhaps to, who knows, having a degree of belief higher then 0.9. But apart from being arbitrary, such a proposal also fails to address the fundamental problem, which is that the Bayesian conception of rationality simply does not incorporate a teleological relation to knowledge. What is rational for the Bayesian is to update according to the updating rules and accept the degrees of belief that follow. There is no sense in which particular degrees of belief are better than others; there is, in particular, no rule of rationality that requires us to seek high degrees of belief. This may look like a benefit. The Bayesian looks only at the evidence! If the evidence fails to allow for high degrees of belief, so be it! Long live science!

But this means that the Bayesian will not be able to see anything wrong with the cognitive situation in which all our beliefs about things that matter to us either continually hover around the value of 0.5, maximal uncertainty, or fluctuate wildly through time. In fact, however, such a situation would entail a complete breakdown of rationality — a situation of utter inductive scepticism, in which enquiry would not be so much as possible. One problem with the Bayesian scheme is that it promises to provide us with rational cognitive attitudes no matter what evidence will be incoming. Whereas the truth of the matter is that in a sufficiently chaotic world, taking up rational cognitive attitudes is impossible.

We can make substantially the same point by looking at identification and self-alienation. According to my account, the defectiveness of having mere beliefs is evident from the first-person point of view by a lack of full identification; one has positive cognitive attitudes with which one cannot fully identify, and which are therefore not in the full sense the attitudes that they ought to be. There is a tension, a defect, and it calls out for resolution through further enquiry. According to the kind of Bayesian we are considering, mere beliefs are identifications with attitudes that are not entirely positive. There’s no tension in that. Having a mere belief is like being luke-warm about a book, or liking-but-not-loving a certain dish. There is nothing about mere belief that calls for further enquiry. And to represent belief in such a way is surely to misrepresent the nature of finite knowers. It is to fail to grasp the fact that finite knowers are essentially embarked on a project.

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