What we should say to the Skeptic

Nick Bostrom, PhD
(c) 1996
[email protected]
Dept. of Phil., LSE. and Dept. of Math., King's College
Go to Nick Bostrom's Home Page


How can we be justified in believing that the sun will rise tomorrow?

Since it is conceivable that the sun won't rise tomorrow although it has always done so in the past, we cannot hope for justification for the belief that it is strictly speaking absolutely certain that the sun will rise tomorrow. What we are looking for is an explanation of why it is reasonable even to believe with a high degree of confidence that the sun will rise.

A first step towards such an explanation is to point out that, given what we know, the simplest hypothesis is that the sun will not behave differently tomorrow from what it has always done; to assume that it will rise is to assume that nature is regular in this respect.

This is well and good as far as it goes. If many more details were added and the result were generalized to cover other cases too, we might have claimed thereby to have made a contribution to scientific methodology. Had we asked, not for grounds for believing that the sun will rise, but for reasons for believing in the inflationary scenario of cosmological development, for example, then an answer along this line may well be presumed to have satisfied the inquirer. We would explain to him the available evidence, argue why certain objections are invalid or at least not decisive, and implicitly or explicitly appeal to a principle of induction to prove our claim that the we have grounds for believing in the inflation theory and the predictions that can be derived from it when taken together with other pieces of accepted science. However, it is clear that this is not what a philosopher asking why he should believe that the sun will rise tomorrow is out for. To the above explanation he would reply: "Yes, but why should I believe in the principle of induction?".

Here is the "problem of induction": What should we say to that skeptic philosopher?

We might argue with him as follows.

Dogmatist: You should believe in the principle of induction because it is rational to do so.

Skeptic: Why is it rational?

Dogmatist: It is rational per definition. That is simply part of what we mean when we say that someone is rational: that he typically expects that nature is as regular as is compatible with his prior experiences. If you doubt this fact about the use of the word "rational", then I beg you to observe cases where it is used, and you shall see that it is a very natural way of making sense of its usage.

Skeptic: Okay, it might indeed be true that that is how the word "rational" is used. But then again, why should I be rational in that sense?

Dogmatist: Well, of course it is up to you whether you want to be rational or not. In our experience, people that are insufficiently rational have tended to end sadly: they may run out in the street and got run over by a bus, for example. It is rational to suppose that extremely irrational people in the future will have a similar fate, i.e. it follows from observations and the principle of induction that this is a probable outcome. So if you want to avoid accidents, it is rational for you to chose to be rational. If I thought there were a real danger that you would chose to go irrational, I would have added more examples here, making them as vivid as possible, in the hope that you would be sufficiently rational to see that you do not, after all, really believe that it would be good for you to go irrational. But I am certain that this won't happen, for it is as good a psychological prediction as any that you won't ever be convinced that going irrational would be good for you.

Skeptic: So I should be rational because it is rational to believe that being rational will be good for me?

Dogmatist: Correct.

Skeptic: But that argument is of the same form as the following: I should be irrational because it is irrational to believe that being irrational will be good for me! Why is not this argument as good as the former?

Dogmatist: You are getting me wrong. If my saying was an argument at all, it was an argument that you should be rational in the future. The reason I gave for this purported to show that it would be rational for you now to believe that it would be good for you if you were rational in the future. This is (part of) the form of a valid argument: the conclusion is that it would be rational to believe something, which is just a way of saying that good reasons exist for believing it, which, in turn, is to say that it follows logically from known facts together with the principle of induction that the conclusion has a high probability (where "probability" is defined by reference to the principle of induction). If you then go on to ask why an argument of that form (and satisfying certain other requirements) is "good" or "valid", then the answer is that this is simply what we mean by "good argument", -and that can be argued for by a linguistic examination of the way that term is used.

Skeptic: So you claim only to have given (the outline) of a good argument for being rational in the future. I asked why I should be rational now, indeed why I should be convinced by any "good argument" in the first place.

Dogmatist: It is up to you to decide whether you should be convinced by a good argument. It would, as I said, be irrational of you not to; but if you are irrational, then that's what you are and I can't refute a fact.

Skeptic: Shall I take this to mean that you agree that the skeptic cannot be refuted?

Dogmatist: No! The refutation goes as follows: The skeptic is irrational because he don't believe in the principle of induction, and part of what is meant by "being rational" is believing in that principle. This is a refutation because it shows that the criticized position is irrational, and to show that is what is meant by "a refutation".

Skeptic: But what if I persist in being what you call "irrational"? What could you do to convince me that I'm wrong?

Dogmatist: What do you mean by "wrong"? Are you asking a moral question now?

Skeptic: No, I mean: how can you convince a skeptic that skepticism is false.

Dogmatist: What is skepticism?

Skeptic: The doubting that knowledge is possible. -No, sorry; I take that back. That would make skepticism a phenomenon, and a phenomenon cannot be true or false. Instead I define skepticism as the doctrine that knowledge is impossible, at least empirical knowledge. How could you convince me that that doctrine is false?

Dogmatist: I do not claim that I could give a convincing argument, i.e. an argument which is likely to change the mind of someone who initially disbelieves the conclusion (which is that the skepticism is false). Sincere radical skepticism is a clinical condition, and it cannot always be cured by a talk therapy. -I claim only that I can give a good, or valid, argument for my proposition. I have already given you the argument, and the conclusion was that skepticism is irrational, i.e. that we have reason to believe that the doctrine that empirical knowledge is impossible is false. If this argument does not convince you, then that does not show that the argument is not good, but it does show, perhaps, that you are unreasonable.

Skeptic: How can an argument be good if it is unlikely to convince anybody who did not already believe what it purported to show?

Dogmatist: Well, it's like deriving a simple logical truth from axioms which are no more certain than the conclusion. That does not make the derivation fallacious. The reason, however, why I want to call my "derivation" an argument, is that I think that in this case the conclusion is not quite as obvious as the premises. The history of philosophy shows that.

Skeptic: It can't be right because it's too simple. If a problem is indeed solved by this simple reasoning, it can hardly be the same problem that has puzzled great thinkers for over two millennia!

Dogmatist: You are right. What I have given so far is only part of the solution, only part of what I have to say to you. There are two main things that remain to be explained. One is how what I have said can be incorporated into a more general account of knowledge and reasoning. The other is why intelligent people have taken skepticism so seriously. But what I have said so far, contains, I think, the core of the solution to the problem of induction.

I think there are several reasons why skepticism has been taken seriously. It has been seen as a challenge against the view that we can have certain knowledge about matters which go beyond our experience. But, of course, on my account, such certainty cannot be obtained, so even if my solution of the problem of induction is correct, it won't provide us with an explanation of how absolute certainty is obtainable -it isn't.

Another reason is that there are forms of skepticism that have clear merits. I'm talking about moderate skepticism, the doctrine that we should be wary of the frailty of human reasoning and not be too sure about anything, but rather keep an open mind and be prepared to change any beliefs if sufficient reason is provided. -There are also particular skepticisms, concerning questions about God, afterlife, other minds, etc. which might be thought to have some justification. Especially I would like to mention political skepticism, which I define to be the doctrine that it is practically impossible for humans to have any well grounded beliefs about what political actions are likely to have good effects in the long run. This is a very serious form of skepticism; and it might be true, for human society seems to be a chaotic system. I am deeply concerned about this possibility, but it not the same as the thesis that we can't know anything about the external world at all.

Then we have the everyday-skepticism, when we ask for grounds for believing this or that mundane statement. Someone says: "John won't be home in time for dinner today." We might ask: "Why do you think that? I met him this afternoon and he told me he had decided not to go to the club tonight." In this case we might be satisfied if we get the answer: "Yes, I know, but he just called and said that his car broke down." In situations such as this, there is a substantial answer to the query for reasons; a philosopher can be misled to believe that something at least equally substantial is required as an answer to the skeptic.

Finally there might be a neurological mechanism for global doubt. It is known that electrical stimulation of certain parts of the limbic system will cause a feeling that is described as "that everything is unreal". This state of mind is similar to the state of mind of a serious skeptic. Perhaps part of the attention paid to skepticism is an attempt to reconcile such experiences with the rest of our belief system. I think that it would be possible to track down many metaphysical and ethical positions to primitive areas of the brain-

Skeptic: Well, that's for psychologists and scientists! Let's return to philosophy. You said that the terms "justification", "rational", "good argument" etc. were simply defined in such a way as to make skepticism unjustified and irrational?

Dogmatist: I said that such is the way those words are used. I don't claim that they have been explicitly defined, or that there is in general a unique well-defined logistic meaning to every word and sentence.

Skeptic: But the problem as I see it is that, on your account, "justification", "rational" etc. seem to be purely descriptive, just like such words as "table", "electron" etc. But to me it seems clear that they aren't.

Suppose you had made a thorough investigation into the use of the word "justification" and come up with a set of necessary and sufficient conditions for a proposition being justified in a given context. This is, of course, impossible to do in practice; but let's assume, for the sake of argument, it had been done. So we would have a statement of the form "p is 'justified' to the degree d in context c iff q". But this would still leave it open whether p would really be justified to degree d in context c, given q! Just because we use the word "justified" to apply to such cases this does not mean that p would actually be justified: that would still be a question that could be sensibly asked. The point is that our usage of the word "justified" can never guarantee that we are indeed justified. "Justified", "rational" etc. are all normative terms and can never be reduced to a set of necessary and sufficient conditions, because we could always ask whether the concept defined by those conditions would really coincide with true Justification and Rationality.

Dogmatist: It is equally true of a purported set of necessary and sufficient conditions for an object x being a table that we could sensibly ask whether that set really coincide, intentionally or extensionally, with our concept "table". So that is no special problem for my account of rationality.

As for normativity, there are at least two points to be made.

First it should be pointed out that the notion of "rationality" may very well be normative on my account, in the sense that it would apply to ways of thinking which we would do good in seeking to emulate. Just like "speed" is normative for constructors of microprocessors.

Second, I do not rule out that what we mean by the term "rational" may be defined partially to refer to the sort of cognitive actions that would in fact tend to lead us to true beliefs. In that case there might be some sort of necessary connection between rationality and truth, so that it couldn't be the case that the majority of possible rational agents would be very mistaken in most possible circumstances, -or something like that- a weak variant of the so called charity principle, perhaps-

Skeptic: Ah! But in that case, how could we ever know that we were rational? And if you admit we can't, then it seems you have bought my skepticism after all!

Dogmatist: Note first that I did not claim that "rational" was defined that way; I just said that I didn't rule out that possibility. But in any case, there is no reason why we couldn't know that we were being rational, even if "rationality" is thus defined. Remember that knowledge does not imply (absolute) certainty. We cannot be absolutely certain that the sun will rise tomorrow, because it might not. But we know it will.

Let me spell out, roughly, my analysis of knowledge.
S knows that p iff:

(1) S is convinced that p.
(2) S is justified in believing that the probability that p is very high.
(3) p.
(4) S's justification for believing p is of the right sort.

All four conditions can be fulfilled for p="I am rational.", even if the "rationality" is defined to include some guarantee of truth.

Skeptic: What do you mean by condition (4)?

Dogmatist: You are now challenging me to give the last part that is missing in my solution of the problem of induction: to explain how my theory can be incorporated into a broader epistemology. Let me say at once that I haven't worked out more than at most the outlines of such an explanation. To fully explain this, one would in fact need to develop a full-blown theory of knowledge. I don't think that could be done successfully in isolation form cognitive science, neuroscience and related disciplines; and I don't think it would be possible even if one took into account what is known in these areas today. We can begin, of course; but our efforts as armchair philosophers are likely to be fruitless.

What I can hope to achieve by my stumbling explanations is to convince you that the questions you ask are either scientific or else unimportant. I would call a question unimportant if it turns out that what it asks for is a decision between two approximately equally good conceptual frameworks, neither of which is likely to serve any scientific purpose. A debate about such a question is a debate about words. The decision to explicate our previous usage so as to fit one of these conceptual frameworks may have some consequences, but the issue is unimportant compared to the cosmic and metaphysic significance which philosophers have traditionally attached to such questions.

It seems to me that any analysis of the word "knowledge" that assigned to it a meaning according to which it would be impossible to know any ordinary empirical proposition would be highly suspect, to say the least. I think it should rather be viewed as a reductio ad absurdum of the analysis if it had such a consequence. And if the analysis turned out to be correct after all, then we should immediately define a new concept of knowledge and reject the old notion as a useless confusion and try to forget it.

None of this shows that my particular analysis of knowledge is correct, although it suggests that radical skepticism is false. -Now to your question.

I included (4) to allow for intuitions according to which we do not have knowledge in so called Gettier cases.

It has been argued that justified true belief isn't knowledge; for if I hear voices outside my door, I will believe that there is somebody there, and this belief is justified and it may be true too, but it won't count as knowledge if the voices I hear come from a tape recorder, while the people outside my door are silent.

For people whose concept of knowledge is such that I won't know that there is somebody outside my door in this example, I have added clause (4). Suppose that my reasoning occurs in separate steps: First I think "There is a very high probability that I hear voices as if they came from outside my door."; then I think "There is a very high probability that I'm not hallucinating."; and "If voices almost certainly emanate from outside my door, then there is a very high probability that there is somebody there."; and finally "So there is very probably somebody there.". Then we might make clause (4) a little more precise by saying that it means that every step and every premise in the reasoning whereby I justify my belief in p should still be valid given full knowledge of the actual case. This would mean that we would not have to say that I knew that there were somebody outside my door, because one of the step in my justification for that belief (namely "If voices almost certainly emanate from outside my door, then there is a very high probability that there is somebody there.") would be invalid given knowledge of the fact that there was a tape recorder outside my door playing a taped conversation.

One could go on to elaborate this in more detail, but I don't think that is necessary for my purposes... The point is that there is no reason to suppose that a correct analysis of "knowledge" would have to show that it is impossible for us to know that we are rational, even if rationality is defined to be anchored in truth. Such a connection would no more make knowledge impossible than the obvious connection between knowledge itself and truth ("knowing p implies p") need make knowledge impossible.

Skeptic: Well, so you say that we can know that we are rational. We can also know ordinary empirical propositions, although it may always turn out that we were mistaken. So it would make perfect sense to say: "I know the sun will rise tomorrow. Maybe the sun won't rise tomorrow." But that sounds odd to me.

Dogmatist: Yes, it sounds peculiar, but that is only because you normally say "The sun will rise tomorrow." when you wish to indicate that we may take for granted that it will; but we say "Maybe the sun won't rise tomorrow." exactly when we wish to challenge that assumption. I am sure that much more could be said about the nuances of different utterances involving claims to knowledge and possibilities of being mistaken, but I don't think that is essential for my point; which is that skepticism is false.

Skeptic: But why do you assume that there is some "strict sense" of the word "knowledge" over and above what it is commonly used to indicate and convey?

Dogmatist: Because I think that it clarifies matters if one separate different aspects of a word, and call one aspect its "force", another its "logistic meaning", a third its "reference" and so forth. But my argument in no way depends upon that being so. Even if it is a mistake to speculate about language in those terms and concepts, even if we should stick to direct manifestations of use, it still holds true that knowledge of ordinary empirical things is possible! Your skepticism, indeed, presupposes an analysis of the word "knowing" that deviate from its ostensible use. For if we just look at how that word is used, it is evident that we often use it to ascribe knowledge to people, and these ascriptions are often accepted and there is nothing in the plain speech behavior of speakers that would indicate that knowledge of empirical matters is impossible. Therefore I assume the worst-case scenario for my anti-skepticism and admit a semantic theory that distinguishes the "strict sense" of the word "knowledge" from its superficial appearance in our language behavior. You can surely not object to that policy!

Skeptic: Okay, I accept that, but I still think it strange to say that one can be wrong about what one knows.

Dogmatist: One cannot! If S knows that p, then p. He can't be wrong, if he actually knows that p.

Skeptic: But you said earlier that it was no contradiction to say: "I know the sun will rise tomorrow. Maybe the sun won't rise tomorrow.". If the sun doesn't rise tomorrow, then I'm wrong in my claim that I know it will rise. So when I say: "Maybe the sun doesn't rise tomorrow", I thereby imply that I may be wrong. But you just said that I can't be wrong if I actually know that the sun will rise tomorrow. So when I claim that I know that the sun will rise tomorrow, I imply that I can't be wrong about that. Hence the above statement both implies that I can be wrong and that I cannot be wrong. So it is a contradiction.

Dogmatist: No. It is true that when I say "Maybe the sun doesn't rise tomorrow", I thereby imply that I may be wrong when I say that I know that the sun will rise tomorrow. It's no contradiction to say: "p, but I may be wrong to believe that p." The catch is that the sentence "I may be wrong (about p)." can be true even if I am right (about p). When I say "I know that p", I am not saying that I can't possibly be wrong about p.

Now, this sounds as if it contradicts what I said earlier, that S "can't be wrong (about p) if he actually knows that p", but the contradiction is unreal. In the present context, the modal operator "can't" operates on ordered pairs consisting of a proposition and a set of evidence.

"Can't (<¬p, {S' evidence for his belief that p}>)" can be false (and is indeed false if p is the proposition that the sun will rise tomorrow and S (today) is an ordinary mortal).

"Can't (<¬p, {p}>)" is true.

I suspect, however, that in order to get to the root of the confusion, we have distinguish two senses of "knowing".

In one sense of the word, let's call it the "ordinary sense", we commonly know such things as that the sun will rise tomorrow. Knowing, in this sense, does not imply (absolute) certainty. Maybe the sun won't rise tomorrow, and in that case I will be wrong now if I say that I know that the sun will rise tomorrow. But if the sun indeed rises, then I will presumably be right now to claim that I know that the sun will rise tomorrow. -I anticipate that you will object to this that it would imply that I could never know that I now know that the sun will rise tomorrow, at least not until tomorrow morning when I see it rise. But this would be a mistake. I can know now that I now know that the sun will rise tomorrow, for I have sufficient grounds for believing that (and, of course, the sun will rise tomorrow). These sufficient grounds are basically the same as my grounds for my claim that I know that the sun will rise, and these grounds are presumably sufficient (for that is what we mean by "sufficient grounds").

When I said that "knowing" in the ordinary sense does not imply absolute certainty, what I meant was that there is no rational method that would guarantee that one never made a mistake and still permit one to claim to know at lot of things about everyday matters. One can know, and one can know that one knows, but sometimes one will mistakenly believe that one knows when, in fact, one doesn't: even if one is perfectly rational all the time.

But then there is another sense of "knowing", the sophisticated sense. Knowing, in this sense, implies absolute certainty. A perfectly rational being will never be wrong about p when he claims to have sophisticated knowledge of p. It is easy to see that one could never rationally claim to have this sort of knowledge about ordinary empirical propositions. Perhaps one can know that one exists and thinks, and perhaps propositions of logic and mathematics are also possible to know in this sense; but one could not thus know that the sun will rise tomorrow.

What one can have sophisticated knowledge of, however, is a proposition like "The probability that the sun will rise tomorrow, given my evidence, is p." This is to say that, given a box containing "my evidence" and other boxes containing knowledge of what is meant by "probability", "the sun will rise tomorrow", etc., it should in principle be possible to work out the correct probability that the sun will rise tomorrow, given my evidence. I use a fanciful terminology like "box with evidence" to indicate that what goes on here is not a psychological construction; it is just a way of saying something about what "rationality", "probability" etc. means. To be rational means to assign such and such probabilities to those and those propositions (to believe those propositions with such and such levels of confidence). If I am perfectly rational, I will assign the probability 0.997, say, to the proposition that the sun will rise tomorrow. It is possible for me to know that the probability that the sun will rise tomorrow is 0.997, given my evidence. Even if the sun stays down tomorrow, it will remain true that the probability that it would rise, given my present evidence, is 0.997. Sophisticated knowledge implies absolute certainty, albeit certainty about a probabilistic proposition.

Let me be the first to say that this "theory" is not a fruitful one. The only reason why I explain it to you is that I think it reflects certain intuitions that get confused into our other notion of knowledge, what I called "knowledge in the ordinary sense". Such a confusion is, I suggest, the cause of your feeling that it is strange to say that one can be wrong about what one knows. In one sense of the word knowledge one can, in another one can't. Or else your misgivings were caused by the logical mistake about not recognizing that the truthhood of "Can't (p)" is relative to a set of evidence, as I pointed out a minute ago in response to your purported discovery of a contradiction in my doctrine.

Skeptic: Well, I guess you can escape the contradiction, but haven't you subscribed to my skepticism when you admit that there is a sense of "knowledge" -the sophisticated sense, you call it- in which it is impossible to know such things as that the sun will rise tomorrow. For this is the important version of knowledge: we can't really know, we can't be certain that the sun will rise tomorrow! At least you have offered me a draw.

Dogmatist: By no means! It was clear all along that absolute certainty was not to be had about such issues. If that was all you wanted to claim, then there was no need to waste our time: that sort of epistemic limitation has been recognized ever since the dawn of empirical science, and probably before.

Skeptic: But you said yourself that there was a sense of "knowing" in which we can't know that this night will de followed by a morning etc. Why isn't that radical skepticism?

Dogmatist: First of all because that sense is contrived and sophistic; it is not what we usually mean by "knowledge" and it is definitely not what we think about when we become shocked and perplexed in those moments when skepticism presents itself as a serious possibility (when we have that feeling of general unreality or dreamlikeness).

Second because, as I indicated earlier, there are ways of accommodating to the "sophisticated" usage of "knowledge" that will permit us to make essentially the same claims as otherwise, only in a different wording. Instead of saying "I know that this stone will fall if I drop it." we could say "The probability that the stone would fall is very high relative to my evidence, and I have enough experience about this matter to be trusted." -or something like that.

Skeptic: Hmm. -I don't like this talk about probabilities. Is there really a well-defined notion of probability, apart form particular contexts such as statistics and the theory hazardous games? Is general epistemic probability -a unique real between 0 and 1 that is singled out as soon as a proposition and a set of evidence has been specified- is such a notion not merely a myth, nay a lullaby, composed by superficial positivists to soothe and sedate the serious mind that suspects there is something deeply problematic about the idea of knowledge? And must such a palliative not be despised by any philosopher worth his salt?

Dogmatist: It is of course open to serious doubt whether the products of philosophers doing doxastic logic or Chisholm-style epistemology are of any value whatsoever. I would like to suspend my judgment on that point. And a general notion of epistemic probability could turn out to be purely "philosophical" in the worst sense of the word. None of this would make my argument inadequate as a tailored reply to traditional radical skepticism, however. In my view, "general epistemic probability" belongs to the same family of terms as "propositional belief", "(sentential) evidence" and so forth. Whether your use of them is objectionable depends on what you do with them. It is unobjectionable to use them to counter a position (radical skepticism) that is formulated in those very terms. If you give me a version of radical skepticism expressed in purely physicalistic terms, I will explain to you in physicalistic terms why it is false.

Skeptic: I am not sure that "general epistemic probability" is not more obscure than the notion of propositional belief etc. For example, how do you apply it to mathematical reasoning?

Dogmatist: Hitherto I have simplified our discussion by assuming that the object of a belief is a logistic proposition, i.e. the set of truth conditions for an ordinary sentence like "It will rain tomorrow." or "Lambda-hyperons have mass.". This is obviously inadequate when it comes to mathematics, for logical and mathematical theorems all have the same truth conditions, namely the empty condition: they are true whatever the world is like. (At least according to most theories that would allow logistic propositions in the first place.) But of course one can know that 3*4=12 without knowing that 5763*389=2241807 or that ZF is consistent with ¬AC.

There are at least two ways of dealing with this difficulty. One would be to introduce a notion of modes of presentation, and say that, under some modes of presentation, the tautology is trivial, whereas it can be very hard to know presented in another manner. -This essentially brings us back, from the proposition, to the sentence, i.e. the linguistic expression. It might be argued that we could as well have remained by the sentence all along and never bothered to introduce propositions at all.

Another way, which I consider more true to the original intuitions behind the use of "propositions" etc. is to maintain that all tautological expressions have the same meaning, express the same proposition, but then to explain their different epistemic status by maintaining that our grasps of their meanings are imperfect. On this view we should say that anybody who completely understood what is meant by "5763", "389", "*", "=", and "2241807" must necessarily also know that 5763*389=2241807. But such a complete understanding is not required for it to be truly said of someone that he understands those expression; for when we say that, we mean merely that he has a reasonably good grasp of what they stand for. And so it is possible to know the meanings of all numerals and of "*" and "=", and still not know that "5763*389=2241807" is true.

Skeptic: But everyone who knows those meanings should be able, in principle, to verify the sentence "5763*389=2241807" by purely a priori reasoning, shouldn't he?

Dogmatist: Yes, and thereby he would improve his grasp, perhaps, of those meanings. Skeptic: Hmm... So you allow a priori reasoning as a source of knowledge?

Dogmatist: At least it could serve to make implicit knowledge explicit. When I said that a reasonably good grasp of the meaning of a mathematical expression suffices for it to count as knowing its meaning, what I meant was that in order for the meaning "to be known" it has to be known implicitly, but not explicitly, at least not perfectly. And by "implicit knowledge" I mean: knowledge that could in principle be made explicit by a sustained effort of a priori reasoning (where it not for limitations in our working memory etc.) By "explicit knowledge" I mean: knowledge that the subject could normally directly express in sentences, without having to think about the matter for a long time. You see all these notions which I here present are intertwined in such a way that their definitions seem to be circular; and indeed they are. I used the term "explicit knowledge" instead of the more common "declarative knowledge", for example, to avoid appearing as if I were trying to construct a framework for cognitive science. I'm not. The only thing I arguing for here is that to the extent to which these traditional epistemological and semantic notions are fruitful and make sense, to that extent they also submit to an analysis according to which it is perfectly possible to have both empirical and a priori knowledge of most of those things which have normally been supposed to be thus knowable; and that analysis is the right one.

I could go on and give you a story about how mathematics can be useful on this account. It's quite easy: mathematics is useful because it creates channels through which implicit knowledge can be more or less automatically transformed into explicit knowledge.

To see what I'm getting at, think of your mind as a set of propositions, each with a number attached to it. These numbers represent the confidence the subject has that their corresponding propositions are true. The numbers, however, do not quite form a probability distribution, for the subject does not have a completely coherent belief network. By reasoning, the subject can adjust the weights attached to each proposition in such a way that the contradictory tensions in his belief network are reduced. This is the process whereby implicit knowledge is made explicit: this is a priori reasoning. And logic is the study of patterns of such knowledge transformation.

There is much more to be said on this topic, but perhaps we should leave that till tomorrow?

Skeptic: There is one more thing I got to ask you before we depart. Why do you claim that skepticism is false rather that nonsensical, as some would say?

Dogmatist: As I said: to the extent to which the terms "knowledge", "belief", "evidential support" etc. make sense, to that extent is skepticism meaningful and, as I have tried to show, false. But it is obvious that these terms do make sense in many contexts; hence skepticism is false as a thesis about "knowledge" taken in the sense it has in those contexts; and in what other sense could we take it?

When I hold up my hand and say "Here is a hand. I know that there is a hand here", what I am saying is not nonsensical but simply true. That's how I prefer to use the term "nonsensical". If you do not want to use "x is nonsensical" in that way but rather as meaning "there is no point in saying x" or "here x could be thought to say something very substantial but really it's just a matter of words" or "it is peculiar to say x (in this context)" or "do not expect to build an interesting theory upon the fact that x is not false" or "the use of x (here) is misleading for it does not function as it does on other contexts" or something like that, then I would point out that nonsensicality would be a matter of degree, and yes, in those senses both radical skepticism and its negation would be to a certain quite high degree nonsensical. But I avoid the word "nonsense" because it is so blunt and ambiguous. (Every time I hear the word, I see the image of a bulldog.)

Skeptic: Dear friend, I shall consider what you have said. See you tomorrow morning, when the sun rises!

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