On 4/5/99, in response to an earlier discussion, I wrote:

What I want to be sure I understand is what X really says. (We can tackle its truth or falsity after that.) Could someone please post a statement of what this assertion is, which Mr. W. denies and which Mr. S. (apparently in the company of [Leo] Strauss) affirms?

To this, Mr. S. replied on 4/7/99 in part as follows:

Your question here is a good one because I think we are much in need of a good formulation of this question if we hope to make any progress in answering it. As far as I can tell, in the simplest form, the question is whether knowledge is possible--or even simpler, what is knowledge?

Mr. W., among others, has taken to referring to "weak knowledge," and "strong knowledge," and "absolute proof," and "proof." I suggest that this indicates what the difficulty is. We do not know what knowledge is and so could not recognize it if we came upon it. Now there has also been much discussion of "certainty" and the impossibility of same. I take it that "certain knowledge" is akin to "strong knowledge." And so "common sense" is then "weak knowledge," which is "good enough." But again, it seems to me we are not clear on what certainty is, or about what exactly is weak about common sense.

As far as I have been able to tell the argument is something like this. Human beings have perceptions. This no one denies. A perception is of an appearance. An appearance is of some thing. But there is no perception of any thing, but only of appearances. "Weak knowledge" then is perception of appearances and reasoning about appearances--descriptions of them and how they change and most importantly speculations about what the appearances are appearances of. This "knowledge" is weak because it can never be compared to that which the appearances are appearances of. There is no perception of the things themselves by themselves. Perception of the things themselves, if it were possible, would be "strong knowledge," would be certainty.

My response to this is that "weak knowledge" is not knowledge at all but opinion or belief. Thus to call it knowledge, even qualified by "weak," obscures what is at stake. It allows us to have our cake and eat it too -- to say we cannot know the truth but can nevertheless have knowledge. And what is at stake of course is nihilism. For if we can never see "behind" the appearances then we can never know whether nihilism is not true for we can only have faith. If this is so, then natural right and philosophy are impossible--unless one is willing to give to social science and natural science the role formly given to political philosophy, namely the inquiry into ethics and politics. But we have seen that neither natural nor social science can provide us with ethics.

Two weeks later I finally responded as follows:

I have wanted to reply to this post since I read it, but I have known that any reply would take a while to write and I haven't wanted to invest the time. I think I have a little time right now, so I will give it a stab.

Mr. S. has given us a brief account of what knowledge is, or at any rate what it might be. I want to offer an account of my own. I don't know how different it is from Mr. S.'s -- that is, I think we see slightly different sides of the problem, but our answers may be consistent with each other.

To start with, the question as Mr. S. poses it is "What is knowledge?" I will consider this more or less synonymous with the question, "What do we mean when we say we know something?" And I think the shortest possible answer is that we mean a number of different things, although they may have a common core. But on the surface, at least, our usage is not altogether consistent.

I want to distinguish at least two uses of the words "know" and "knowledge". I propose to distinguish these with numbers -- they should be subscripts, but e-mail has its limitations and one of them is the inability to display subscripts. So I propose to use the words "know1" and "know2". These are conjugated the way you expect: I know1, you know1, he or she knows1, ..., I knew1, you knew1, ..., and likewise for know2. That which one knows1 is called knowledge1; that which one knows2 is called knowledge2. And so on.

Now, I think the most basic use of the word "know" -- what I will call "know1" -- is as a kind of synonym for "be aware of" or "perceive". This means that knowledge1 is much the same thing as awareness. Using the most common metaphor there is for knowledge1, one could say that to know1 is (so to speak) the same as to see. I know1 something is true when I see it: with my own eyes, or with my other senses, or with my mind's eye. Therefore, I know1 that it is sunny outside right now; I know1 that my neck itches and that it feels better now that I have scratched it; I know1 that I exist; and I know1 that it is impossible for the same statement to be both true and false about the same objects at the same time in the same way. All of these are things that I just perceive directly.

There would be no need to use the word "know" in any other sense if there were not problems with knowledge1. But there are. Sometimes I can see things directly that turn out not to be so. I see someone in the distance; I perceive directly that it is my brother, so I can say I know1 it is he; then this someone gets closer and I see I was wrong. Or I can say to myself as I write this, "I just know1 Mr. S. will agree with everything I say in this post (or disagree, of course)," because I have a picture in my mind -- which I perceive directly -- of reading Mr. S.'s reply telling me how brilliant I am (or how totally I've missed the point, as the case may be). But none of this has any bearing on what Mr. S. is really going to say.

I called this a problem. Why? Well, here is the difference between "knowing" and perceiving, which is why the sense know1 is not enough to exhaust the meaning of the word "know". Because when we see something, we readily admit that we could be wrong; we see mirages in the desert and think they are water. But the core notion behind "knowledge" is, I think, not only that we see things, but that we really see them as they really are. This is where we get additions on to the basic component of direct perception -- components like saying that "knowledge" is not just belief, but true belief, or maybe justified true belief. (The addition of "true" covers seeing things as they really are; the addition of "justified" covers really seeing them, so we know exactly why and how things are as they are.)

Please notice that I have not said anything here about a definition; I think most of the time we use words like "knowing" and "knowledge" without worrying about precise definitions. It's just as well, too, because we have to turn to philosophers for defintions of this sort of thing, and philosophers often don't agree. And while they are arguing, the rest of us still need to be able to use the words. So instead we proceed on hunches, vague notions, and intuitions. Then afterwards, philosophers come along to clear things up, either by showing us the reality of which our hunches made us only dimly aware (Plato) or by showing us exactly when and in what circumstances we use certain locutions (Wittgenstein).

So we have a hunch that "knowing" should somehow mean really seeing things as they really are, and we realize that knowing1 allows for too many errors. This is where we get a second usage, knowing2. What I mean by knowing2 is this:

We say we know2 something when we assert it to be the case in the context of dispute. That is, we say we have knowledge2, and not merely belief or perception, when we think we can prove or definitely establish something to a person who questions it or denies it. And the way we establish that we know2 something is by connecting it to something else.

So for example, if my wife loses her keys this morning and asks for my help in finding them, I may try to think where she could have left them. I might say, "Well, I know2 you must have had them when you came home, because otherwise you couldn't have started your car. Therefore they are either still in the car, or in the house, or between the two -- but in any event I know2 they can't be at the office." Notice that I don't know1 this, because I can't see the keys; but I know2 it, because I have connected the question of where her keys are to some other facts about how she travels home from work and about how cars function.

If someone asks me about some result in mathematics, my knowledge of it is likely to be knowledge2 and not knowledge1: in a few cases, maybe I will see the result obviously in my mind's eye; but most of the time I have to follow the proof which derives the result from something else which is already known2. Then that result is derived from another, and so on back to the axioms. In each case, a result is related to something else (ultimately to the axioms) to justify it.

Notice that I am being quite general about what it means to connect one statement to another: there are many examples of this, but I think they all fall under the rubric of knowledge2. Proving a theorem from axioms is one sort of knowledge2. Citing passages from Scripture or an acknowledged authority is another sort of knowledge2. Consulting alternative accounts of a thing to see whether there are any contradictions or discrepancies is another sort. And basic day-to-day inferences of the most banal kind -- like in my example of the car keys, above -- are another sort. All these are things that we think we "know" because we know2 them; we can stand up and assert them in spite of any dispute, because we have connected them with something else.

This also means, by the way, that when Mr. S. says he

>makes [his] argument in the form of quotes from and commentaries on >other people rather than in [his] own name

and when Mr. Y.  tries to make a point by citing innumerable other sources and scholars whom I have never read, they are both aiming at knowledge2. They are both using a tactic that involves establishing one statement by connecting it with others. On the other hand, when Mr. W. says of certain things that he thinks we can know them but he can't imagine proving them, I think he is talking about knowledge1.

In fact, there are some things that we can know1 without knowing2 them. Descartes tried to offer a proof -- that is, knowledge2 -- of his own existence. But from the point of view of knowledge1, the question is silly -- no-one could seriously doubt his own existence. The Law of Contradiction -- that A and not-A cannot both be true -- is something that we all know1, but I doubt we could know2 it: that would mean relating it to something else less questionable (for example, proving it from something more basic), and what could there be? This law is, itself, the foundation of all proof; it is the least questionable thing there is, to which other things get related to justify them. Asking for a way to know2 it apart from just knowing1 it would be pretty strange.

This question all started from an earlier question -- namely, whether there is any sort of knowledge that can be simply known, without presuppositions or starting places that are taken on faith. I now think it is possible to answer this question fairly easily:

• All knowledge1 is known1 directly, without presuppositions or starting points. But some of the things we know1 are nonetheless false.
• All knowledge2 requires something else to lean on, so it is impossible to find a piece of knowledge2 that we know2 directly. All knowledge2 requires presuppositions. In order to know2 those presuppositions, we must have pre-presuppositions. In order to avoid an infinite regress, we must finally come to things that we accept somehow without knowing2 them. (Of course, we might know1 them.)

There's the answer, as far as it goes. In these terms, I think the original question can be rephrased, "Is there a kind of knowledge that we could call 'knowledge3' which gives us the best of both worlds? Is there a knowledge3 which is self-sufficient (like knowledge1) and also able to stand up in an argument (like knowledge2)?"

I don't see how there can be. Proof, certainty -- these are the things we have with knowledge2, not knowledge1. But knowledge2 is concerned with proof to other people, or with certainty in the face of doubt and dispute. Even when we are only reasoning things out for ourselves, we use the canons of proof that have been developed in order to convince others so that we can convince ourselves; since we know that knowledge1 is fallible, then for our own sakes we picture a question to ourselves as if there were someone else there whom we had to convince, so that we can marshal our proofs to establish that yes, we really do have knowledge2 and not merely knowledge1.

But other people do not see with our eyes. Therefore, nothing that can be convincing to others -- and this is the meaning of words like "certainty" -- nothing that has the compelling features of knowledge2 can possibly have the immediacy of knowledge1. When we gain certainty, we lose immediacy; the price of proof is a reliance on other things which have not themselves been proven. We can jettison proof and return to knowledge1, where the things that we know1 are known1 immediately -- but then we have fewer filters against error and self-delusion.

Then what was [Leo] Strauss talking about when he said, as Mr. S. reminded us, that ...

"We cannot exert our understanding without from time to time understanding something of importance; and this act of understanding may be accompanied by the awareness of our understanding, by noesis noeseos, and this is so high, so pure, so noble an experience that Aristotle could ascribe it to his God." (LAM, p.8)

This sounds like knowledge1 to me. Strauss says "awareness" of understanding -- and awareness is a synonym for knowledge1. He does not say "proof" or "certainty". The reference to God is a little unsettling, because it is hard to imagine knowledge1, with all its imperfections, as something that a man would want to ascribe to God. But then, after all, Strauss himself does not ascribe it to God; he just says that Aristotle did. So there is no reason to suppose that Strauss himself meant anything else in this passage than knowledge1.

It remains to wonder about Aristotle. Did he mean the same thing as Strauss -- did he just mean knowledge1? It's hard to say; Strauss doesn't give the reference, and I don't know Aristotle enough to recognize it. I can only guess, though, that when God and knowledge show up in the same sentence, we are probably not taking about any kind of human knowledge, be it knowledge1 or knowledge2. If knowledge3 is the kind of knowledge that Aristotle's God has, it is reasonable to wonder whether it is, in that form, even accessible to humans at all. There are mystics who use the word "know" to describe the way they perceive the Whole; their perception sounds a little like knowledge1, but as I am no mystic I can't judge how closely this fits. Aristotle might be an unlikely candidate for the label "mystic", but plenty of people have applied it to his teacher Plato, and there may have been connections between their thoughts that are not apparent in their writings.

I'd like to think this clarifies the question a little, but I wouldn't swear to it; I hope at least that I haven't made things worse.