1.  The Traditional Analysis of the Concept of Knowledge

Person A knows that p

means the same as

(1)  A believes that p,
(2)  It is true that p, and
(3)  A is justified in believing that p.

        How might one arrive at this analysis?  One standard way of attempting to construct analyses involves searching for all necessary conditions, and then seeing whether the combination of all of the necessary conditions will provide one with a sufficient condition.  If it does, then one may very well have arrived at an analysis of the concept in question.

        To understand this technique, one needs to understand the distinction between necessary conditions and sufficient conditions.  This can be explained as follows:

Suppose that if p is true, then q must also be true.  Then the truth of p suffices to ensure that q is also true, and philosophers say that p is a sufficient condition for q.

Suppose, on the other hand, that if p is not true, then q cannot be true either.  Then the truth of p is necessary if q is to be true, and philosophers say that p is a necessary condition for q.

        he definitions of "sufficient condition" and "necessary condition" can, equivalently, be put as follows:

(1)  "A is a sufficient condition for B" means the same as "A logically entails B".

(2)  "A is a necessary condition for B" means the same as "B logically entails A".

        How, then, might the above, traditional analysis of the concept of knowledge have been arrived at?  One natural way is by searching for necessary conditions of person A's knowing that p - that is, for conditions that must be satisfied if A is to know that p - and then conjoining all of the necessary conditions so discovered in the hope that the conjunction of those necessary conditions, taken together, will be a sufficient condition for A's knowing that p - that is, will be a condition that logically suffices to ensure that A knows that p.

Illustrations:  (i)  If Bruce is the brother of John, what more specific things must be the case?  (ii)  If Mary knows that there is a cat on the mat, what more specific things must be the case?
 

2.  Gettier's Counterexamples to the Traditional Analysis

        Gettier offers two counterexamples to the traditional analysis of the concept of knowledge:

(1)  Smith, Jones, and the person with ten coins in his pocket who will get the job.

Basic structure:  Smith has strong evidence for the conjunctive proposition that Jones will get the job and Jones has ten coins in his pocket.  Smith concludes that the person who will get the job has ten coins in his pocket.  The latter belief turns out to be true, but not because Jones gets the job:  for the job goes to Smith, who happens also to have ten coins in his pocket.  So Smith's belief that the person who will get the job has ten coins in his pocket appears to be both true and justified, but the claim is that one would not regard it as a case of knowing.

        Why is the belief a justified one?  The idea here is that if you're justified in believing p, and p logically entails q, then you're potentially justified in believing q.  And if, in addition, you do believe q, and believe q because you know that p logically entails q, then you are actually justified in believing q.

        This transmission of justification via the relation of logical entailment seems intuitively plausible.  But one can also offer an argument for it, if one can connect up justification with probability in a certain sort of way - namely, if it is true that if the proposition that B is at least as likely to be true as the proposition that A, relative to your evidence, then you are at least as justified in believing B as in believing A.

        The inference here is via existential generalization, where existential generalization is an inference of the following logical form:

                                     a is F
                Therefore:  There is something that is F.

        Or, to use standard logical notation:

                                Fa
            Therefore:  (Ex)Fx.

(2)  Either Jones owns a Ford, or Brown is in Barcelona.

Basic structure:  Smith has strong evidence that Jones owns a Ford, and, as a result, comes to believe that either Jones owns a Ford, or Brown is in Barcelona.  (Smith has no evidence concerning the whereabouts of Brown.)  It turns out, contrary to Smith's strong evidence, that Jones no longer owns a Ford.  Brown, however, just happens to be in Barcelona.  So Smith's belief that either Jones owns a Ford, or Brown is in Barcelona, is in fact true.  Moreover, since that disjunctive belief follows deductively from something that Smith does have strong evidence for - namely, the proposition that Jones owns a Ford - it would seem that Smith also has strong evidence for the belief that either Jones owns a Ford or else Brown is in Barcelona.  But, it is claimed, though this belief is true and justified, it is not a case of knowledge.

        In this case, the inference is via disjunctive addition, where disjunctive addition is any inference of the following logical form:

                            p
    Therefore:        p or q

        Or, to use standard logical notation:

                            p
    Therefore:       p v q
 

 3.  Possible Reactions to the Gettier Counterexamples

(1)  One possible reaction is to conclude that clauses (1) though (3) in the above analysis of the concept of knowledge need to be supplemented by a fourth clause;

(2)  A second possibility is that what is required is not supplementation by a fourth clause, but a stronger version of clause (3) - and probably also of clause (1).

3.1 The Strengthening Strategy

(1*)  A is completely certain, subjectively, that p is the case.

        Rozeboom then wants to maintain that the belief in question will then have to be justified if one is to have a case of knowledge.  So (3) needs to be replaced by something like:

(3*)  A is justified in being completely certain that p is the case.

        Next, Rozeboom suggests that a person, A, is not justified in being completely certain about the truth of p on the basis of some body of evidence, E, unless, given E, p couldn't possibly be false.  But if this is right, then, in the first of Gettier's examples, Smith would not be justified in being completely certain that Jones would get the job, for the evidence that Smith had was perfectly compatible with Jones's not getting the job - as in fact turned out to be the case.  As a consequence, neither would Smith have been justified in being completely certain that someone with ten coins in his pocket would get the job.  So given Rozeboom's amended analysis of the concept of knowledge, Smith didn't know that someone with ten coins in his pocket would get the job.

Question:  What is one to say about this handling of the Gettier problem?

        There are, I think, two main issues that need to be considered.  The first concerns the question of how much knowledge it turns out that we have, given Rozeboom's analysis of the concept of knowledge.  For it certainly looks as if the scope of our knowledge is going to be, at the very least, very restricted.  First, the evidence one has concerning the occurrence of past events is always, it would seem, compatible with those events' not having taken place, so it would seem to follow that one never has any knowledge of the past.  Secondly, if one's beliefs about the external world are, as many philosophers have held, inferential beliefs based upon knowledge of one's sensory experiences, then neither will one have any knowledge of the external world, on Rozeboom's account of knowledge, since one's sensory evidence does not entail the existence of any external state of affairs.

        Rozeboom, however, is well aware of this consequence.  Indeed, he is inclined to think that, given the account of knowledge that he has defended, no one ever knows anything.  He contends, however, that there is not really anything unsettling in that conclusion.  In support of that, he cites our everyday use of words like "spherical".  Such words may be useful, even if there is no object that is strictly spherical in shape:  what we are doing is using a term of things that approximate to being perfectly spherical.  And this is, he suggests, what we are also doing when we speak about knowing various things: we are referring to cognitive states that approximate, to differing degrees, to the impossible ideal of knowledge.

        If Rozeboom is right, then one might try to argue - as Rozeboom does (First edition of The Theory of Knowledge, page 183) - that the project of attempting to get an analysis of the concept of knowledge that includes just those cases that one normally classifies as knowledge, and leaves out cases that one does not normally so classify, is a rather dubious undertaking: the difference is only a matter of differing approximations to an ideal, along a continuous scale, and the precise place that one draws the line along that scale can hardly have much significance.

        One of Rozeboom's main conclusions, accordingly, is that the project of offering an analysis of the concept of knowledge is best set aside, so that attention can be devoted to the important issues in epistemology.   As he says at the conclusion of his article:

"With problems of 'How strongly should X believe p?' lying dark and unfathomed before us, we stand to profit from continued epistemological preoccupation with the nature of 'knowledge' to just about the same extent as would psychology from a return to study of the 'soul'."  (First edition of Pojman's anthology, page 184)

3.2  Possible Supplementation Strategies

(1)  The "No False Intermediate Conclusion" strategy;

(2)  The "No Undermining Evidence" strategy.  This strategy comes in four different versions:

(a)  No potential undermining evidence at all;
(b)  No potential undermining evidence whose denial one is actually employing;
(c)  No potential undermining evidence that one is justified in believing not to exist;
(d)  No potential undermining evidence of a certain, difficult to specify sort.

Comments

        Version (a) is mentioned, but rejected by Gilbert Harman because of an argument that he offers in the middle of column 2 on page 164.  Version (b) appears to be just an alternative description of Approach 1 - the "No False Intermediate Conclusion" approach.  Version (c) appears to be the approach advanced by Lehrer and Paxson, while version (d) is the one favored by Harman.

(3)  The "Causal Connection" strategy;

(4)  The "Inference to the Best Explanation" strategy;

(5)  The "Discrimination and Counterfactuals" strategy;

(6)  The "Knowledge as Tracking" strategy.

4.  Crucial Test Cases

(1)  Gettier-style cases.

(2)  Broken causal chain type cases.  The perception of an external object versus laser photograph case mentioned by Goldman.

(3)  Cases of undermining via potential evidence that one does not actually possess.  Gilbert Harman's two cases involving Tom Grabit:  In both cases the mother is lying, but in one case convincingly, and the other not.  Is Harman's view of the two cases plausible?

Comment

        Lehrer and Paxson certainly seem to disagree with Harman's claim about the first Tom Grabit case, since they say on page 155, column 1, that one's knowledge is not undermined in the case where Tom's mother is a pathological liar.

(4)  Non-discriminability cases.  Barns versus papiermaché, barn facade, facsimile cases.

5.  Consideration of Supplementation Strategies

(1)  The "No False Intermediate Conclusion" strategy;

(2)  The "No False Relevant Beliefs" strategy;

(3)  The "Causal Connection" strategy;

(4)  The "No Undermining Evidence" strategy;

(5)  The "Discrimination and Counterfactuals" strategy;

(6)  The "Knowledge as Tracking" strategy;

(7)  The "Inference to the Best Explanation" strategy.

5.1.  The "No False Intermediate Conclusions" Approach

(1)  The reasoning that the person uses to justify the belief in question is totally free of any false intermediate conclusions;

(2)  Either the reasoning is totally free of false intermediate conclusions, or else any false conclusions that were involved could have been dispensed with, and the person in question knows that they could have been dispensed with.

        Which version one will judge preferable depends upon what view one takes of examples like the 30/30/30 for, 10 against, voting case.  If one agrees that one has knowledge in such cases, one will conclude that the account of knowledge that results from (1) will be too narrow - excluding some cases of genuine knowledge.

        If one can get a version that doesn't suffer from the defect of being excessively narrow, what about the problem of being excessively broad - that is, of counting as cases of knowledge cases where one does not know?  One thing that is crucial to this latter question are the Tom Grabit type of cases.  More importantly, however, there is an objection that shows that this first approach does not provide a satisfactory solution to the problem raised by Gettier, since although this approach handles the cases advanced by Gettier, any Gettier-style counterexample can be transformed into a related counterexample that, though it does not involve any false intermediate conclusion, is not a case of knowledge.

5.1.1  A Decisive Objection to the "No False Intermediate Conclusions" Approach

(1)  John knows that e.

(2)  John knows that e provides good support for p.

(3)   John believes that p, and he does so because of (1) and (2)

(4)  John knows that p entails p or q.

(5)  John believes that p or q, and he does so because of (3) and (4).

        John's belief that p or q is presumably justified, since it is entailed by another belief - the belief that p - that is justified.  The belief that p or q is also true, by hypothesis.  But it isn't a case of knowledge, even though it is a justified true belief.

        The "no false intermediate beliefs" approach blocks this counterexample, since there is an intermediate belief - p - which is false.  But there is a closely related counterexample which is equally strong, and which is not blocked by the "no false intermediate beliefs" analysis.  The basic idea is that one could arrive at the belief that p or q by a different, and more unusual route, but one which involves perfectly sound reasoning, and which does not go through any false intermediate beliefs.  Thus, let e, p, and q be defined as before, but assume that John arrives at the belief that p or q by the following route:

(1)  John knows that e.

(2)  John knows that e entails e or q.

(3)  John believes that e or q, and he does so because of (1) and (2).

(4)  John knows that it is a theorem of probability theory that if the probability of B given A is equal to k, then the probability of B or C given A or C must be equal to or greater than k.

(5)  John concludes that if e provides good support for p, then e or q provides good support for p or q, and he does so because of (4).

(6)  John knows that e provides good support for p.

(7)  John concludes that e or q provides good support for p or q, and he does so because of (5) and (6).

(8)  John believes that p or q, and he does so because of (3) and (7).

        John's belief that p or q is surely justified.  For given that, by hypothesis, he knows that e, and that he knows that e provides good support for p, he would be justified in believing that p, if he did so.  But then, given that, in view of (3), he knows that e or q, it follows from (5), together with the fact that he would be justified in believing that p, that he must be justified in believing that p or q.  So we have a case of a justified, true, belief that is not a case of knowledge.  But this justified true belief has not been arrived at by any inferences that go through false beliefs.  So the "no false intermediate beliefs" analysis of knowledge fails in the face of this modified Gettier counterexample.

5.2  The "No False or Irrational Relevant Beliefs" Approach

        The argument goes as follows.  Suppose that John believes that p or q, but does not believe that p.  Suppose further that John's belief that p or q is based solely upon the reasoning set out in the preceding subsection.  Thus John does not believe that p or q because of independent evidence for its being the case that q, or because q is intrinsically likely to be true.  The situation is therefore one where John's belief that p or q cannot be justified unless the belief that p is justified.  But doesn't this mean that John has an irrational set of beliefs if he accepts the proposition that p or q, but rejects the proposition that p, given that the former belief cannot be justified unless the latter belief is justified?

        If this is right, then John can avoid irrationality, while believing that p or q only by also believing that p.  Consequently, though John does not arrive at the belief that p or q by reasoning that makes use of the false belief that p, the latter belief is necessary if John's belief that p or q is not to be part of an irrational set of beliefs.  Hence, if one holds that a justified true belief, B, cannot be a case of knowledge if either (1) B is part of a complex of beliefs that is irrational, or (2) there is some false belief in the absence of which B would be part of a complex of beliefs that would be irrational, or (3) the justification for B involves a false belief, the case described above will not be a case of knowledge.

5.3  The "Causal Connection" Strategy

(a)  The evidence that justifies the belief in question;

(b)  The state of affairs in the world that makes the belief in question true.

And what is the right sort of connection?  Goldman's answer is:  Certain sorts of causal connections.
Illustration.  In the "Either Jones owns a Ford or Brown is in Barcelona" example, what makes this sentence true is that Brown is, as a matter of fact, and unbeknownst to Smith, in Barcelona, whereas what makes it reasonable for Smith to believe that the sentence is true is evidence that makes it likely that Jones owns a Ford, and these two states of affairs are not causally connected in any relevant way.  Similarly, consider the broken-causal-chain sort of case.  If the causal chain were not broken, then what makes it true that there is a piece of chalk on the table would be the cause of one's evidence that there is a piece of chalk on the table.

        What is the right sort of causal connection?  Goldman suggests that there are two crucial patterns:

Pattern 1:  The state of affairs that makes the belief in question true is a cause of the evidence that one has in support of the belief.

Pattern 2:  The state of affairs that makes the belief true and the evidence that makes the belief reasonable have a common cause.

The basic idea is that pattern 1 applies in the case of perceptual knowledge and memory knowledge, whereas pattern 2 applies in the case of knowledge of future events.

5.3.1  Criticisms of the "Causal Connection" Strategy

(1)  Even where pattern 1 obtains, one may still not have knowledge.  Illustration:  The modified chalk case, where the laser light operates only if a sensor detects the presence of a piece of chalk.  Or compare the - rather more controversial - barn case.

(2)  Neither pattern 1 nor pattern 2 seems to provide an account of one's knowledge of laws of nature - both causal laws and non-causal laws.  For it doesn't seem to be true either that the state of affairs that makes it the case that something is a law causes the evidence that we have for the existence of the law, or that the former state of affairs and the evidence have a common cause.

        It is, in part, this problem that leads Goldman to appeal to the idea that one can combine causal connections with logical connections, and view the combination as still classifiable as a causal connection.  And it is also this problem that leads Harman to advocate replacing references to causal connections by references to what he calls "inferences to the best explanation".

(3)  As both Goldman and Harman point out, it looks as if the causal connections thesis concerning knowledge can be derived from an account that doesn't refer to causal connections, along the following lines:

 Consider something that one cannot directly observe.  How can one have knowledge of the existence of such a thing?  Philosophers who accept a foundationalist view of knowledge would argue that one can have such knowledge only if the entity is connected with things of which one can have direct knowledge.  But I think that this claim can be replaced with a less contentious claim, as follows.  Suppose that one has inferential knowledge of object S that is based upon knowledge of T, and where one's knowledge of T is either inferential or noninferential.  Then isn't it plausible to think that such inferentially-based knowledge is possible only if there is some sort of connection between object S and object T  But if so, what forms can such connections take?  A natural answer, I suggest, is that the connections must be either causal or nomological (that is, a matter of laws, and possibly non-causal laws of co-existence.)  Illustrations:  Principle of inference to a common cause.  Case of two properties that are always found together - such as, perhaps, one unit of negative charge, and a certain mass.

        But if it is in virtue of such connections that things not directly observable are knowable, then isn't it plausible that one can have such knowledge only when one knows that the relevant causal or nomological connections exist?  If so, one has the following thesis:

                Thesis Concerning Inferential Knowledge

One can have inferential knowledge of some entity, S, only if the knowledge is based upon the knowledge that S is connected, either causally or via laws of nature, with some entity T of which one can have knowledge, either inferential or noninferential.

        The point here is not restricted, however, to the case of knowledge.  Thus, consider some object about which one cannot have noninferentially justified beliefs.  How can one have any justified beliefs about such an object?  Isn't it plausible that one can have justified beliefs about it only if it is connected with things concerning which one can have justified beliefs - either inferentially justified beliefs or noninferentially justified beliefs?  But if so, what forms can such connections take?  The natural answer, once again, is that the connections must be either causal or nomological.

        But if it is in virtue of such connections that one can have justified beliefs about things about which one cannot have noninferentially justified beliefs, then isn't it plausible that one can have such justified beliefs only when one is justified in believing that the relevant causal or nomological connections exist?  If so, one has the following thesis:

                Thesis Concerning Inferentially Justified Beliefs

One can have inferentially justified beliefs about some entity, S, only if one arrives at the belief in question on the basis of a justified belief that S is connected, either causally or via laws of nature, with some entity T about which one can have justified beliefs - either inferentially justified beliefs or noninferentially justified beliefs.

(1)  Assume Mary knows that p, and that her knowledge is inferential, rather than direct.

(2)  If Mary has inferential knowledge that p, then Mary's belief that p is inferentially justified.

(3)  Given the above Thesis Concerning Inferentially Justified Beliefs, it follows that Mary cannot be inferentially justified in believing that p unless she arrives at that belief on the basis of a belief that the state of affairs that makes p true is connected, either causally, or via laws of nature, with some state of affairs concerning which she can have justified beliefs - either inferentially justified beliefs or noninferentially justified beliefs.

(4)  But if Mary's belief that p is justified on the basis of a belief that certain states of affairs are connected, either causally, or via laws of nature, with the state of affairs that makes p true, then the latter belief is an intermediate conclusion in the process of reasoning that she uses to arrive at the belief that p.

(5)  The first response to the Gettier counterexamples:  Mary knows that p if and only if she has a justified, true belief that p, and her justification does not go through any false intermediate conclusions.

(6)  It follows from (4) and (5) that Mary's belief that certain states of affairs are connected, either causally, or via laws of nature, with the state of affairs that makes p true, being an intermediate conclusion, must itself be true.

(7)  And so it follows that if Mary is to have inferential knowledge that p, certain relevant states of affairs must be connected, either causally, or via laws of nature, with the state of affairs that makes p true.

        In short, the thesis that inferential knowledge presupposes the existence of causal or nomological connections is a derived thesis - following from the "no false intermediate conclusions" approach together with the above thesis concerning inferentially justified belief.

        A minor comment:  Notice that the argument just set out does not make the assumption that the inferences involved are "inferences to the best explanation".  For in some cases, a belief will be justified not because it is the best explanation of something else, but because it is a likely effect.  (Consider, for example, the justification of one's belief that the sun will rise tomorrow.)

5.4 The "No Undermining Evidence" Approaches

(a)  No potential undermining evidence at all;
(b)  No potential undermining evidence whose denial one is actually employing;
(c)  No potential undermining evidence that one is justified in believing not to exist;
(d)  No potential undermining evidence of a certain, difficult to specify sort.

Comments

(1)  Version (a) is mentioned, but rejected by Gilbert Harman because of an argument that he offers in the middle of column 2 on page 164.  Version (b) appears to be just an alternative description of Approach 1 - the "No False Intermediate Conclusion" approach.  Version (c) appears to be the approach advanced by Lehrer and Paxson, while version (d) is the one favored by Harman.

(2)  One will want to move from the first type of approach - the "no false intermediate beliefs approach - to this third type of approach only if one agrees that in at least some of the Tom Grabit style cases one's knowledge is undermined by the evidence that one does not possess.  Of the four variations on this general approach mentioned above, one is equivalent to the "no false intermediate conclusions" approach.  Of the three approaches that aren't, which one should be adopted depends upon the what view should be taken of various Tom Grabit type cases.

(3)  Is Gilbert Harman right about the untenability of the view that one knows only if no undermining evidence at all exists?  (Harman's argument is based upon considering a proposition of the form k or not-h, where k is some true, but antecedently very improbable proposition, and not-h is the denial of the justified true belief whose status as knowledge is being considered.)

A Possible Objection to Harman

        Suppose I think that I have excellent reason for thinking that h is true.  If I suddenly am presented with evidence that k or not-h is true, but where the evidence in question is not in itself evidence against the truth of h, does the fact that k is antecedently very improbable give me grounds for concluding that it is not likely to be true?  Why am I not justified in concluding that, given that I have excellent reason for believing h, that k, though antecedently improbable, must also be true, since I have just learned that it is likely that k or not-h is true?

(4)  Notice the following, apparent peculiarity of the Lehrer/Paxson view:  Evidence which is not undermining becomes undermining if one is completely justified in believing the denial of that evidence.  Thus, consider the Tom Grabit case.  If one simply doesn't know whether Tom's mother has said that Tom didn't do it, then the fact that she has said this does not, according to Lehrer and Paxson (page 155, column 1) undermine the claim that one knows that Tom stole the book.  But if one is completely justified in believing that she did not say this, then the fact that she did say it defeats one's justification for believing that Tom stole the book.  Surely this is a crazy combination of views.  (The last sentence of the third paragraph in the first column on page 155 suggests that Lehrer and Paxson are muddling together (a) being completely justified in believing that e is false and (b) making use of the assumption that e is false in the reasoning that supports the belief whose status as knowledge is being considered.)

(5)  Is Gilbert Harman right about the two Tom Grabit cases that he discusses?  If he is, one is confronted with the problem of saying exactly what it is that constitutes the difference - a problem that Harman himself does not attempt to grapple with.

(6)  One way of trying to capture the idea that evidence that one doesn't possess, and that would, if one had it, render the belief in question improbable, sometimes undermines one's knowledge claim, and sometimes doesn't is by employing the idea of "total evidence".  Thus, if the belief that p is justified on the basis of the belief that q, then e is undermining evidence if and only if (1) given both q and e, the belief that p would no longer be justified, and (2) given t, where t is the total evidence that is actual - and where t thus contains both q and e - p would no longer be justified.  In short, e must not only undercut one's justification, but it must do so even when conjoined with the rest of the totality of evidence.  (Notice, however, that the line that is drawn in this way does not agree with the one that Harman wants to draw between the two Tom Grabit cases.  For if the relevant test is the effect of total evidence, then in neither of the Tom Grabit cases that he discusses will it be true that one does not know, since in both of those cases the proposition that Tom's mother is lying will be part of the total evidence.)

(7)  Can a claim to knowledge ever be undermined by evidence (a) that one does not possess, and (b) whose denial one does not have to assume in justifying the belief in question?

        The idea behind this question is that if one thinks that one's knowledge claim is undermined in some Tom Grabit-style cases, perhaps the explanation is that if one is to be justified in believing that Tom Grabit stole the book, one must be justified in believing either (a) that there is no evidence that would render the belief in question unreasonable when conjoined with the evidence that one has, or - perhaps more plausibly - (b) that the belief would not be unreasonable given the totality of the evidence that one might have.

5.5  The "Discrimination and Counterfactuals" Strategy

        When, then, does one have knowledge according to this fourth approach?  What is required in addition to justified, true belief?  The answer is that one needs to ask whether, if the situation had been different in certain ways - such that the belief in question would have been false - one would have noticed the difference, and would, as a consequence, not have had the belief in question.

        What one has to consider, then, is whether certain counterfactuals are true or false.  What is a counterfactual?  Basically, it's an if-then statement which implies that the antecedent, the "if" clause is false, and which makes an assertion about how the world would have been different if - contrary to fact - the "if" clause had been true.

Illustration:  Consider some salt that's not in water, and a piece of chalk that's not in water.  One can ask what would happen if each were now in water.  And the answer is that if the salt were in water, it would be dissolving, whereas the piece of chalk would not be dissolving.

        What determines whether a given counterfactual is true or false?  That's a complicated question, and a variety of answers - some of them quite different - have been offered.  But one traditional answer is that what counterfactuals are true is generally a matter of what causal laws there are.  On this view, what makes it the case that if a certain piece of salt were in water, it would be dissolving is, first, that salt has a certain molecular structure, and secondly, that there are laws that entail that anything with such a molecular structure will dissolve when in water.

        Returning to this fourth strategy for supplementing the traditional account of the concept of knowledge, the idea is that one has to consider possible ways in which the situation might have been different and such that the belief in question would have been false, and then ask, of each, whether one would then have noticed the difference, and, as a consequence, not have acquired the belief in question.  To illustrate, consider Henry and the barn.  Instead of a barn, there could have been a mere facade.  If so, it would have been false that Henry was seeing a barn.  Would Henry have noticed the difference?  If the answer is that he would not, then, according to this "discrimination and counterfactuals" approach, Henry did not know that he was seeing a barn.  For the following counterfactual, rather than being true, would have been false:

"If it had been, not a barn, but a facsimile, then Henry would not have believed that there was a barn there"

(1)  One problem with this approach, at least as stated to this point, is that it would seem that it might always be the case that there is some way in which the situation could have been different which is such that one couldn't have detected the difference - one could have been hallucinating, or been a brain in a vat, or confronted with a holographic image, or a facsimile, etc.  So it would seem that if ordinary knowledge claims are to be preserved, one has to restrict in some way the range of alternatives that are taken into account when one considers how things might have been different. Not all logical possibilities can be considered, nor even all possibilities that are compatible with the laws of nature that there are in this world.  (Being a brain in a vat certainly seems to be a possibility that is allowed by the laws of nature.)  So we're confronted with the problem of a range of cases that differ only marginally from nearby cases, but which connect up radically different situations: e.g., lots of facsimiles in Henry's immediate vicinity versus a facsimile off on a planet orbiting around a star in a distant galaxy.  Where is the line to be drawn, and in virtue of what underlying principle?!

(2)  Secondly, there is the fact that, rather than there being something approximating to general agreement that Henry does not know in the barn-case, at least quite a fair proportion of people hold that Henry does know that he is seeing a barn.

(3)  The latter intuition connects up, moreover, with a picture of knowledge that seems fairly appealing.  According to this picture, there are only three sorts of facts that are relevant to the question whether Sandra has knowledge of some object A.  First, there are facts about Sandra's internal states - what beliefs she has, what processes of reasoning she goes through, etc.  Secondly, there are facts about the objects of her beliefs.  Thirdly, there are facts about the connections - causal and nomological - between the objects of her beliefs and her internal states.  Once these three things are fixed, it seems natural to think that it is also fixed whether Sandra does or does not know in the case in question, and that how the rest of the world is - that is, the world aside from her internal states, the objects of her beliefs, and the connections between the two - does not affect things one way or the other.  Such further facts can neither make it the case that she has knowledge, nor make it the case that she does not.

(4)  The final, and, I believe, the most fundamental comment that I have to make regarding this approach to the analysis of the concept of knowledge is that if the basic claim involved in it is true, then it seems to me it is true because it follows from the second account - that is, from the approach that appeals to the idea of undermining evidence that one does not possess.

5.6  The "Knowledge as Tracking" Strategy

        What is meant by "belief that tracks truth"?  First, a belief cannot track truth unless the belief is true.  But this by itself is not enough.  It must also be the case that - and here's the counterfactual element - that if the proposition in question had not been true, then the person in question would not have believed it.

        So, though this is not quite the view that Nozick himself advances, one might put forward the following proposed analysis:

Mary knows that p

means the same as

(1)  Mary believes that p;
(2)  It is true that p;
(3)  Mary is justified in believing that p;
(4)  If p had not been true, then Mary would not have believed that p.

The clause added - clause (4) - formulates the tracking condition, and it is that clause that is intended to deal with problematic cases, especially the Gettier-type cases.

        Consider, then, a Gettier case.  In view of clause (4), one has to ask, for example, whether Smith would have believed that either Jones owns a Ford or Brown is in Barcelona if that proposition, rather than being true, had been false.  That proposition could have been false in various ways, of course, but the idea here is to imagine the world being changed in some minimal way.  Perhaps Brown leaves Barcelona a little earlier, so that he isn't in Barcelona at the time in question.  If that had been the case, would Smith still have believed that either Jones owns a Ford or Brown is in Barcelona?  The answer, surely, is that he would have - since his belief is based upon evidence concerning Jones owning a Ford, and there is no reason why that would be affected by Brown's leaving Barcelona a bit earlier.  So Smith's belief that either Jones owns a Ford or Brown is in Barcelona does not track the truth of that proposition.  He would still have believed that, even if it had been false.

Comment

        This is an interesting account of the concept of knowledge, but it has at least one consequence that seems rather counterintuitive - namely, it entails that falsity of what has been called the "closure condition" for knowledge.

                The Closure Condition for Knowledge

The closure condition can be formulated as follows.  Suppose:
 

(1)  Mary knows that p;
(2)  p entails - that is, logically necessitates - q;
(3)  Mary knows that p entails q;
(4)  Mary comes to believe that q because she believes both that p, and that p entails q.
 

Then:  (5)  Mary knows that q.

        Why does the knowledge-as-tracking account entail that the closure condition upon knowledge is false?  Consider, first, the question of whether one can know, given the tracking account of knowledge, that one is not a brain in a vat.  The problem is that even if one has a justified, true, belief that one is not a brain in a vat, the tracking condition will not be satisfied.  For the question is: "If the proposition that one is not a brain in a vat were not true - so that one was in fact a brain in a vat - would one then not believe that one was not a brain in a vat.  And the answer is that, by hypothesis, all of one's experiences and apparent memories would be just as they are now, and so one would still believe that one was not a brain in a vat.  So the belief that one is not a brain in a vat would not track truth in the way required by condition (4).  So on the tracking account, one does not know that one is not a brain in a vat.

        Secondly, consider whether Mary can know that she is now seeing a table in front of her.  Let us assume that she believes that there is, and that that belief is both true and justified.  The question is then whether her belief tracks truth.  So one has to ask whether the following counterfactual is true:

"If Mary had not been seeing a table in front of her, then she would not have believed that there was a table in front of her."

        So the situation is as follows:

Mary knows that she is seeing a table in front of her.

Mary does not know that she is not a brain in a vat who is not really seeing a table.

But if Mary is seeing table, then it follows necessarily that she is not a brain in a vat who is not really seeing a table.  The conclusion that she can know that the former is the case while not knowing that the latter is the case - together with appropriate additional assumptions - means that the closure condition is not satisfied by the knowledge-as-tracking account.

5.7  The "Inference to the Best Explanation" Strategy

        It is also possible to combine Harman's inference to the best explanation account of inference with the second approach - that is, the "no undermining evidence" view.  This is what Harman himself wants to do, since he thinks that in at least some Tom Grabit-type cases one fails to have knowledge because of the existence of undermining evidence that one is not aware of.

6.  Summing Up:  An Overview of the Alternative Supplementation Strategies

Thesis 1:  Knowledge = Justified belief, plus the truth of relevant beliefs.

(The idea here is that while it is not just the truth of p that is relevant in determining whether one's justified belief that p is a case of knowledge, the relevant truths are restricted to propositions that one believes.)

Thesis 2:  In determining whether a justified true belief is a case of knowledge, the truth of propositions that one does not believe may also be relevant.

Thesis 3:  The right sorts of causal connections are also crucial to whether a given justified true belief is a case of knowledge.

Thesis 4:  The truth-values of relevant counterfactual statements are also crucial to whether a given justified true belief is a case of knowledge.

7.  Interrelations Between the Above Four Theses

                Thesis Concerning Inferentially Justified Beliefs

One can have inferentially justified beliefs about some entity, S, only if one arrives at the belief in question on the basis of a justified belief that S is connected, either causally or via laws of nature, with some entity T about which one can have justified beliefs - either inferentially justified beliefs or noninferentially justified beliefs.

                The Undermining Evidence Criterion

The cases where the inability to perceptually discriminate matters are those cases where evidence concerning one's inability to discriminate would be undermining evidence.

        If this is right, then, first of all, Theses 3 and 4 are less basic than Theses 1 and 2 respectively, and secondly, there would therefore seem to be no reason not to base an analysis of the concept of knowledge upon either Thesis 1, or Thesis 2, rather than upon either Thesis 3 or Thesis 4.

        This line of thought leaves one with the question of whether to accept Thesis 2.  If, as I have suggested, there is no general agreement concerning the Tom Grabit-style cases that are needed to support Thesis 2, it seems to me preferable simply to go with Thesis 1, rather than Thesis 2, on grounds of simplicity.  For I would think that one should accept a more complex account only if there are clear cut reasons for doing so.

8.  A New Alternative?

Person A knows that p

means the same as

(1)  A believes that p,
(2)  It is true that p,
(3)  A is justified in believing that p, and
(4)  Any non-deductive inferences that A makes are based upon true premises concerning causal or nomological connections between states of affairs.

        There is a second reason for preferring this account to the "causal connection" analysis of knowledge.  For the latter has difficulty handling the case where the causal connection is an unusual one - for example, the case mentioned earlier where the presence of a piece of chalk causes a laser to produce a holographic image of a piece of chalk.  The "causal connection" approach needs to appeal, at this point, to some idea of "standard" causal connections.  But on the approach just suggested, there is no difficulty.  As long as one's reasoning employs justified, true  beliefs about causal connections, one will have knowledge, regardless of the unusual character of the causal connections in question.

9.  Further Discussion of the "Discrimination and Counterfactuals" Strategy

        In the Henry and the barn case, it is assumed that Henry is well acquainted with barns.  Suppose that is not so.  Indeed, suppose that, though it has been explained to Henry both what a building is, and what a movie set, building facade is like, Henry, having lived an unusually sheltered life, has been exposed to neither.  Henry is now exposed to his first building - a barn.  Does Henry know that it is a building, rather than a movie set, building facade?

        It seems to me very plausible to say that he does not, on the grounds that he has no basis for believing that his present visual experiences are more likely to be caused by a building than by a backless facsimile.  If this is right, then, in the original Henry case, it would seem that a crucial piece of evidence that justifies Henry in believing that he is seeing a barn is the evidence that barns are much more numerous than movie sets - or at least, in his part of the world.

        But even if evidence for the belief that barns are more frequent than barn facades in his part of the world is not crucial, it is certainly true that he would not be justified in believing that he was seeing a barn, and so would not know that he was, if he had the evidence concerning the low frequency of barns, as compared with facsimiles, in his vicinity.  It therefore follows that if the third approach to the analysis of knowledge were correct, and one could fail to know because of undermining evidence that one did not possess, then one would be able to explain why Henry doesn't know in the original barn case by appealing to the fact that most of the relevant objects in his immediate environment are not barns, but mere facsimiles - a fact that, were he to know it, would undermine his justification for believing that what he now sees is a barn.

        In addition to providing an explanation, this account would have the further virtue that it will answer the question - that the fourth approach on its own apparently cannot answer - of where the line is to be drawn.  Evidence of the existence of facsimiles on another planet will generally not be such that, when combined with the evidence one has concerning the relative frequency of barns versus facsimiles here one earth, one's justification for believing that one is seeing a barn will be undermined.  In short, the line is drawn on the basis of the question: "Precisely what sort of evidence would be undermining evidence?"

        The derivation of the fourth approach to the analysis of the concept of knowledge from third approach depends, then, upon the following basic assumption:

                The Undermining Evidence Criterion

The cases where the inability to perceptually discriminate matters are those cases where evidence concerning one's inability to discriminate would be undermining evidence.

        My conclusion, accordingly, is that the fourth approach appears to be less fundamental than the third approach, and, if so, that it owes whatever plausibility it has to any plausibility that the third approach has.  This, in turn, means that if the Tom Grabit cases turn out not to be acceptable counterexamples to the traditional analysis of knowledge, then the fourth approach, as well as the third, seems likely to fall by the wayside.