Answering the Skeptic: Part Two

What is Knowledge?

Let’s begin with the obvious. Suppose that the brain-in-a-vat hypothesis given in the previous post were true. In that case, a great many of our beliefs about the external world would be false, and this, without needing skeptical argument, would be sufficient for our lack of knowledge on these matters. So falsehood is a disqualifying condition for knowledge, and what is just the same thing, truth is a necessary condition. But, what is almost as obvious, truth is not sufficient for knowledge either. There are as many truths as there are falsehoods, perhaps even an infinite number of each, whereas the knowledge of such beings as yourself and I are partial and finite. Moreover, it is beings like you and I to whom that knowledge belongs, and thus is essential to knowledge that it be possessed by a knower. So we need some further condition which constrains knowledge in these respects, and it is customary to take this extra condition to be belief.

Still, our definition is not nearly sharp enough. For consider that our skeptical hypothesis (“a possible state of affairs that is both consistent with the evidence we have, and is inconsistent with our usual hypothesis based on that evidence”) manages to cast knowledge into doubt even if we insist that our beliefs about the external world are true. Such hypotheses may be laughable, yet it seems their mere possibility is enough to challenge our knowledge claims. And so we need to add to our definition a third condition, one which, even if it does not confute the skeptic, shows why skeptical arguments are effective.  

The traditional proposal, dating all the way back to Plato in the 4th Century BC1, is that our third condition is justification. One motivation for this condition is the idea that if one knows, the connection between one’s belief and the truth of it is somehow more secure than in the case where one merely has true belief. Knowledge is steadfast, and so assertions of knowledge are more trustworthy than assertions of truth alone. Another motivation is that to say that one knows is to commit oneself to being able to show that their beliefs are true. Such ‘showing’ is quite naturally identified with the verbal practice of justifying oneself, and so our new theory of knowledge as justified true belief (hereafter JTB) is an obvious development. Indeed, it remained the orthodoxy for two millennia.

Or so it is commonly supposed. In reality, there was no such widespread consensus on the concept of knowledge, and different philosophers tended to pursue a conception of knowledge based upon their own metaphysics. What is true is that the most prominent analytic accounts of knowledge from the first half of the twentieth century each gave a very similar breakdown of knowledge to the JTB theory, and so it came as somewhat of a watershed when Edmund Gettier published his 1963 criticism of such theories. Gettier exploits the fact that the justification for a belief need not entail the truth of that belief, a subtlety which allows that knowledge on the JTB theory can be a matter of luck, where the justification for some reason or other fails to connect one’s belief to the truth. Here is an example2:

“Knowledge” is sometimes defined as “true belief”, but this definition is too wide. If you look at a clock which you believe to be going, but which in fact has stopped, and you happen to look at it at a moment when it is right, you will acquire a true belief as to the time of day, but you cannot be correctly said to have knowledge.

The example comes from Bertrand Russell, and though the target of it is the view that knowledge is merely true belief, it works just as well for the JTB theory. We would surely grant that the appearance of the clock is sufficient for justifying a belief as to the time, and so it looks as though all three conditions are met. Yet, intuitively, this is not knowledge.

Various proposals have been put forward to accommodate Gettier-style examples – that we should shore up the justification condition or replace it, that we should add some fourth ‘Gettier’ condition, that we should abandon the search for necessary and sufficient conditions in favor of a ‘family resemblance’ between cases of knowledge, or, what may or may not be the same thing, that we should recognize knowledge as inherently unanalyzable and thus a theoretically primitive notion3. Rather than adjudicate between these options, I’ll sketch the kind of theory of knowledge I tend to think in terms of, leaving the specifics to a later post. The theory I have in mind is called ‘Reliabilism’.

Reliabilism would have us replace the justification condition. In short, it is the view that knowledge is true belief produced by a means that is reliable in the circumstances. Of course, much rides on the phrase “in the circumstances”, and it is this which allows a treatment of Gettier cases. Taking Russell’s example above it is this qualification which explains why the passerby lacks knowledge, for although the clock is ordinarily a reliable time-keeper, obviously once it has stopped it is no longer reliable. It also explains the intuition that led us to the justification condition in the first place – when one claims knowledge, one is claiming that their beliefs originate in a reliable process, and providing justification is a verbal demonstration of the impeccable heredity of a belief.

Yet, despite the similarities between Reliabilism and the JTB account, Reliabilism heralds a serious wind-change for epistemology. Whereas the traditional JTB account requires that the security of one’s belief be transparent (or accessible) to the knower, Reliabilism allows that we can have knowledge without access to facts concerning the reliability of our beliefs. The philosophical terminology that goes with this distinction labels the former construal of the justification condition as ‘internal’ and the latter as ‘external’, corresponding to the relation that each describes relative to the human mind. Hence accounts such as the JTB theory are known as ‘internalist’, and accounts such as Reliabilism are known as ‘externalist’.

This conception of knowledge appears to me to be roughly correct. So in the next post I’ll concern myself with applying it to the problems raised by skepticism, showing both where we can resist the skeptic’s arguments, and what is right about them.

1 His Theaetetus dialogue.
2 Bertrand Russell, Human Knowledge: Its Scope and Limits (1948), p. 91. It is odd that Russell’s example should have been overlooked, despite it’s publication fifteen years prior to Gettier’s paper. It’s also odd that Gettier’s paper is held in such esteem when one of it’s principle targets, A.J. Ayer’s view in The Problem of Knowledge, is misrepresented. Ayer is much closer to the Reliabilist accounts in his conception of knowledge as “having the right to be sure” than he is to internalist JTB theories. It has been said that Gettier’s paper at once set the agenda for future work in epistemology and created a myth about the subject’s past. I can’t help but agree.
3 In whatever philosophical theory you like, there will be unanalyzable terms, since breaking down concepts into their component parts is not a process which can continue forever. In the end we must rest our theory on such notions, and so if the theory is to be illuminating as a whole, the unanalyzables at the bottom of it had better be concepts we intuitively grasp. Those who think we do have an intuitive grasp of knowledge seek to analyze other epistemic concepts in terms of it.

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10 thoughts on “Answering the Skeptic: Part Two

  1. christopherolah says:

    It’s strikes me that this `Reliabilism’ is a rather utilitarian theory. Such a definition may work in day to day life and satisfy Gettier’s problems, but is still unsatisfying (knowledge seems like a claim to something more absolute than what you propose). Personally, I’d prefer to strengthen the justified aspect of JTB, requiring proof with the same rigour as I would in math. This would, clearly, lend to a skeptical argument.

  2. TaiChi says:

    You could be right, Christopherolah – perhaps knowledge really does require certain proof. But to agree with you I’d need an indication of the why you feel that this is so: I don’t share your intuition, and seeing that it leads to skepticism, I’m not inclined to suppose it unless it becomes obvious to me that I have to.

    • christopherolah says:

      It’s hard to argue about a definition of something without relying on intuition, since we have nothing to base arguments off of. We can’t just extend the definition from common use because, like most words in the English language, it’s ambiguous.

      Our first option is make a definition that attempts to approach the common parlance in a precise way. I perceive this to be Reliabilism. While there’s substantial deviation, I believe that your definition would satisfy the majority of usage.

      This doesn’t make it the best.

      One of the most interesting questions in epistemology is the claim to certainty. For convenience, we would like a verb that asserts a personal but non-subjective certainty regarding a claim. By this I mean:

      Personal: One person being certain is not enough to make another certain.
      Example: A person experiences a color that no one has seen before and can not be recreated. They are certain that it exists, but no one else can be.

      Non-subjective: One person can’t just decide to be certain. There are objective qualifications for it.

      Certain: There can be no questioning.

      In the philosophic tradition, this word has been `know.’ To distinguish it from normal usage I will write Know when I mean this and know when I mean the Reliabilism definition. For a more formal definition of Know, I will provide the definition:

      A Knows B iff A can prove that B is true. ie, B is a proven true belief.

      I speculate that this might have been the intention behind JTB: A justification that is not a proof is not a valid justification. One can’t just choose anything as their justification!

      I’d also note that Reliabilism can be reconciled with my definition if we select the correct context.

      … So that’s my 2 cents. I eagerly await your comments. I think I’ll make this into a post, once I’ve expanded this a bit more. And try to construct some math-like proofs regarding basic metaphysical claims.

  3. TaiChi says:

    Hmm. As I understand it, the point of a philosophical theory of knowledge is to analyze the widespread and everyday concept. I’m not sure what purpose there would be in analyzing some special philosophical term that goes by the same name, and I’m not even sure I find the idea coherent – where does the special philosophical term come from, if not from an analysis of the everyday concept? And if that is where it comes from, doesn’t that belie your suggestion that the theory of knowledge isn’t properly concerned with our workaday ‘knowledge’?

    It seems to me that what you have is not a theory of knowledge, but a stipulation of a new term, called “Knows”, for which you have some special purpose in mind. That’s perfectly fine, and it may take us somewhere interesting, but I don’t see any to revise my own views to accommodate that. I’ll be interested what you have in mind, if you do post it.

    One last thing: a proof may be good grounds for certainty, but having a proof and being confident that it is a proof are two different things. If you want your definition to capture subjective certainty, you’ll have to add something.

    • christopherolah says:

      >Hmm. As I understand it, the point of a philosophical theory of knowledge is to analyze the widespread and everyday concept.

      Many people fail to distinguish between opinion and knowledge. That’s not a reason to discard the latter…

      > I’m not sure what purpose there would be in analyzing some special philosophical term that goes by the same name,

      I’d perceived it to be fairly common, though that may be a function of my philosophical ignorance. Regardless, why should we pursue it? The knowledge of Reliabilism is useful (as I said before, utilitarian knowledge) but can make no claim to `perfect truth.’

      Perhaps this is fundamentally a difference in aescthetic between us?

      > and I’m not even sure I find the idea coherent – where does the special philosophical term come from, if not from an analysis of the everyday concept?

      “But though all our knowledge begins with experience, it does not follow that it all arises out of experience.” — Kant, _Critique of Pure Reason_

      Just because the idea of Knowledge begins with knowledge does not mean the idea of Knowledge can not arise. It’s an idealisation of it, I suppose.

      >And if that is where it comes from, doesn’t that belie your suggestion that the theory of knowledge isn’t properly concerned with our workaday ‘knowledge’?

      That seems to me like saying that because the idea of a triangle comes from the imperfect ones we see in phenomena, mathematicians should study imperfect ones rather than the idealised concept.

      > It seems to me that what you have is not a theory of knowledge, but a stipulation of a new term, called “Knows”, for which you have some special purpose in mind. That’s perfectly fine, and it may take us somewhere interesting, but I don’t see any to revise my own views to accommodate that.

      Once again, I think that the difference is that of aesthetic. We both know what the other means and the others argument, but we simply do not like the definition of knowledge.

      > One last thing: a proof may be good grounds for certainty, but having a proof and being confident that it is a proof are two different things. If you want your definition to capture subjective certainty, you’ll have to add something.

      An excellent point, but I’m not sure they’re as different as you think. Mathematicians have already thought a great deal about this and constructed methods of verifying proofs. Rigour, formal proofs… proof-checkers.

      One has axioms and constructs proofs from there. Given ZF, would you question that 2+2=4 ?

      One can do philosophy in the same way, I believe…

  4. TaiChi says:

    “Many people fail to distinguish between opinion and knowledge. That’s not a reason to discard the latter…”

    Sure, but isn’t the meaning of words one case where convention and truth coincide? Does it make sense to suppose that everyone understands a word a certain way, but that they are wrong? I don’t think that’s possible, so I take the folk seriously in this matter.

    “The knowledge of Reliabilism is useful (as I said before, utilitarian knowledge) but can make no claim to `perfect truth.’”

    Why not? Are you saying that you don’t think it’s true? (I’m afraid you’ll find me hardheaded when it comes to pragmatist and relativist locutions).

    “That seems to me like saying that because the idea of a triangle comes from the imperfect ones we see in phenomena, mathematicians should study imperfect ones rather than the idealised concept.”

    I don’t find these cases analogous – the ideal triangle is approximated by real world exemplars, whereas your Knowledge is something yet different from knowledge. For example, the Reliabilist allows that animals and children can have knowledge. They don’t need to know how they know, all they need is a true belief formed by reliable processes. But if these can be cases of knowledge, then it is not merely the case that knowledge is like Knowledge, only with less justification, but that these are entirely different concepts.

    “Once again, I think that the difference is that of aesthetic. We both know what the other means and the others argument, but we simply do not like the definition of knowledge.”

    We have different purposes; we want to analyze different things. From my point of view, and I think yours, there are a couple of senses of knowledge in play, and each of us is dealing with the sense that interests us. So we needn’t disagree with each other’s definitions. I’m fully prepared to recognize your Knowledge, though I have doubts about its usefulness.

    “An excellent point, but I’m not sure they’re as different as you think. Mathematicians have already thought a great deal about this and constructed methods of verifying proofs.”

    Suppose I have in my hand a mathematics textbook (I have resolved to address my ignorance of mathematics). You ask for a proof of the Pythagorean Theorem. I’ve never heard of it, but I look up the index, flick to the page, and read out the proof uncertainly. You are satisfied: I have proven to you the Pythagorean Theorem. But you wish to maintain superiority over me, so you tell me that the proof is flawed. I believe you, and my uncertainty about the Pythagorean Theorem remains.

  5. christopherolah says:

    > Does it make sense to suppose that everyone understands a word a certain way, but that they are wrong?

    I never said that it was wrong, merely that it wasn’t a reason to discard the other definition.

    > We have different purposes; we want to analyze different things. From my point of view, and I think yours, there are a couple of senses of knowledge in play, and each of us is dealing with the sense that interests us. So we needn’t disagree with each other’s definitions. I’m fully prepared to recognize your Knowledge, though I have doubts about its usefulness.

    Well put.

    > Suppose I have in my hand a mathematics textbook (I have resolved to address my ignorance of mathematics). You ask for a proof of the Pythagorean Theorem. I’ve never heard of it, but I look up the index, flick to the page, and read out the proof uncertainly. You are satisfied: I have proven to you the Pythagorean Theorem. But you wish to maintain superiority over me, so you tell me that the proof is flawed. I believe you, and my uncertainty about the Pythagorean Theorem remains.

    I think that you need to differentiate between having the formalisation of a proof and a proof. I could train a parrot to say “two plus two equals four” and one might say, “the parrot knows that two plus two equals four.” But it does not follow from the parrot’s statement that it knows that two plus two equals four but rather it that it knows the modern, English formalisation of it.

    One only has a proof if they understand it. Since it is a proof, if they understand it, they know it is a proof and will be convinced.

    As to the Pythagorean theorem. To be true, one must add the condition “in a Euclidean Space.” What is a Euclidean space, you ask? Well, one of the requirements of being Euclidean is that the Pythagorean theorem is true (sometimes an equivalent statement is used in the definition instead…). So the Pythagorean theorem is true by definition: a tautology.

    What is an example of a clearly non-Euclidean space? The surface of a sphere! Try drawing triangles on the surface of a sphere and it will become clear that the Pythagorean theorem does not hold.

    So the real question is: is a plane in real life Euclidean? While it is the inspiration of Euclidean spaces, it is not it self Euclidean thanks to Relativity. On Earth, it is essentially Euclidean though…

    This is, of course, the rigorous way of looking at it. It is normally `proved’ by using equivalent properties that are naively granted. You may enjoy the visual proofs at Wikipedia.

  6. TaiChi says:

    One only has a proof if they understand it. Since it is a proof, if they understand it, they know it is a proof and will be convinced.”

    I still don’t think it’s true that someone only has a proof if they can understand it. If you like, you take that as a suggestion that you add redundancy to your definition to make sure that others understand it as it should be understood. There’s no point in quibbling over semantics.

    “As to the Pythagorean theorem. To be true, one must add the condition “in a Euclidean Space.” “

    I’m aware of this, but I wonder whether you’ve thought through the consequences. For centuries space was thought to be Euclidean, the Pythagorean theorem was thought to be a necessary truth, and surely a great number of people believed that they had a proof of the theorem. But you and I know, with hindsight, they were wrong – qualifications needed to be added to the Theorem for it to retain its necessity. All that suggests that having what one understands to be a proof is not sufficient guarantee of its truth. Such a guarantee is not to be had.

  7. christopherolah says:

    > For centuries space was thought to be Euclidean, the Pythagorean theorem was thought to be a necessary truth, and surely a great number of people believed that they had a proof of the theorem.

    Rigour is a recent innovation. It requires that all statements are essentially analytic from our premises and axioms; they’re tautologies.

    The only things that remain unproven are the axioms. “If you don’t accept that there’s an empty set, we can’t help you…”

  8. TaiChi says:

    “The only things that remain unproven are the axioms.”

    Exactly. You have no guarantee of a proof.

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