Gettier Counterexamples and the Causal Theory

Gettier Counterexamples

In 1963, Edmund L.Gettier III published a paper of just three pages which purports to demolish the classical or JTB analysis. His demolition job, very widely taken to be successful, involves considering the following two examples:

Case 1: Smith and Jones have applied for a particular job. Smith has strong evidence for the following conjunctive proposition:

[d] Jones is the man who will get the job, and Jones has ten coins in his pocket.

Smith’s evidence for [d] might be that the president of the company assured him that Jones would in the end be selected, and that he, Smith, had counted the coins in Jones’s pocket ten minutes ago. Proposition [d] entails:

[e] The man who will get the job has ten coins in his pocket.

Let’s suppose, says Gettier, that Smith sees the entailment from [d] to [e], and accepts [e] on the grounds of [d], for which he has strong evidence. In this case, Smith is clearly justified in believing that [e] is true.

    But then we’re to imagine that he, Smith, and not Jones, gets the job. And, unbeknownst to Smith, he himself has ten coins in his pocket. Proposition [e] is then true, although the proposition from which he inferred it, [d], is false. In other words, [e] is true, Smith believes [e], and Smith is justified in believing [e]. But, says Gettier, we don’t want to say that Smith knows that [e] is true, because [e] is true in virtue of the number of coins in his pocket, which Smith has no idea of! Smith got lucky. If he hadn’t had ten coins in his pocket, the proposition wouldn’t have been true at all. (Notice that no sceptical problem is being raised, since everything we have said, however, is compatible with the idea that if Jones had got the job, we would have granted Smith that he knew Jones would get the job).

Case 2: Suppose Smith has strong evidence for the following proposition:

[f] Jones owns a Ford.

Smith’s evidence might be that Jones has at all times in the past within Smith’s memory owned a car, and always a Ford, and that Jones has just offered Smith a ride while driving a Ford. Let’s imagine now that Smith has another friend, Brown, of whose whereabouts he is totally ignorant. Smith selects three place-names quite at random, and constructs the following three propositions:

[g] Either Jones owns a Ford, or Brown is in Boston,

[h] Either Jones owns a Ford, or Brown is in Barcelona,

[i] Either Jones owns a Ford, or Brown is in Brest-Litovsk.

Each of these propositions is entailed by [f], since any proposition entails the disjunction of itself and any other proposition (‘p’ entails ‘p or q’). Imagine that Smith realizes that each of the disjunctions he has constructed are entailed by [f], and proceeds to accept [g], [h] and [i] on the basis of [f]. Smith has correctly inferred [g], [h] and [i] from a proposition for which he has strong evidence, and he is therefore justified in believing each of these three propositions. But, of course, he has no idea where Brown is.

Imagine now that Jones does not own a Ford, but is driving a rented one, and secondly that Brown is, by pure coincidence, in Barcelona. We now have a situation in which [h] is true, Smith believes [h], and is justified in believing [h]. But still Smith doesn’t know that [h] is true. Gettier’s conclusion is that justified true belief is insufficient for knowledge.

Is Justification Necessary?

Is justification even necessary for knowledge? That is, if one knows that p, must one at least be justified in believing that p? Consider the following kind of case. D.H.Lawrence wrote a story called ‘The Rocking-Horse Winner’, in which a young boy who had a rocking-horse could predict the outcome of horse races. By riding his rocking-horse while thinking about the race to about to happen, he could accurately predict which horse would win that race. This is, of course, an unlikely scenario. But it’s at least imaginable. And in such a scenario it would be understandable to say of this boy that he knew which horse would win, even though he had no justification for believing that it would do so. So, on the one hand, we might well come to say of him: "We’ve no idea how he does it, but somehow or other he does know which horse will win the race". On the other hand, this would be an example of knowledge without justification, since the only reason the boy can cite why he’s confident that his next prediction will be correct is his own past run of successes. But a past run of successes only gives you a good reason to think that you’ll be successful in future if you have reason to think that the past run won’t give out on you. And the rocking-horse winner has no such reason.

If this line of argument is correct, we have to dilute the justification condition.

The Causal Theory of Knowledge

Many responses to Gettier counterexamples rely on some diagnosis of what’s gone wrong in those cases, an explanation of why they don’t count as knowledge. One popular general diagnosis is that in these cases, the fact that the person’s belief was true is just luck. As we might say in a revealing phrase: for all Smith knew the man who did get the job (i.e. Smith himself) did not have ten coins in his pocket. So we might think that for genuine knowledge and not just fortunately true belief luck ought to be ruled out, and there ought to be an appropriate connection between the fact that p and the believer’s belief that p.

One thought in the immediate aftermath of Gettier was that this connection might be causal. Perhaps there ought to be a causal connection between the fact that makes p true and X’s belief that p.

The suggestion might be, at a first try, that a third condition:

[iii’] The fact that p caused X’s belief that p,

should replace the justification condition. Such an analysis adverts essentially to the way that beliefs are acquired, their pedigree, as it were.

How does the addition of this causal condition (or the replacement of the justification condition by this causal condition) affect the cases raised in the Gettier counterexamples? In the first example, Smith’s belief in the proposition (e) The man who will get the job has ten coins in his pocket, is based on his belief in proposition (d) Jones is the man who will get the job, and Jones has ten coins in his pocket. But (d) is false, for it’s, he, Smith, who will get the job. Nevertheless the causal requirement requires that Smith’s belief in the proposition (e) should be caused by the fact that the man who will get the job has ten coins in his pocket. But it isn’t.

With the second example, Case II, where Smith believes that (h) Either Jones owns a Ford, or Brown is in Barcelona, his belief is caused by neither disjunct of the proposition. That is, it isn’t caused by the fact that Jones owns a Ford (since this isn’t a fact at all), and it isn’t caused by the fact that Brown is in Barcelona, (since although this is a fact, Smith just picked it out of the air without suspecting that it was, and since it doesn’t cause his belief anyway). So the causal condition does seem to give the right judgment in these cases, it shows us why they aren’t cases of knowledge.

Goldman’s Version of the Causal Theory

Alvin Goldman, once the main defender of the causal theory, formulated it as follows:

X knows that p iff the fact that p is causally connected in an ‘appropriate’ way with X’s believing p.

(The above formulation obviously includes the idea that p is true (‘the fact that p’) and that X believes that p. It strongly suggests, contrary to Goldman’s own remark that he wants to add the causal condition to the traditional analysis, that Goldman is in fact replacing the justification condition by the causal condition).

When asked to spell out the idea of an ‘appropriate’ causal connection, Goldman thinks we can do no better than give examples, like the following:

(1) Perception: our ordinary concept of e.g. sight, seems to include a causal requirement. If the relevant causal process is absent, if the object allegedly seen plays no causal role in the formation of the perceiver’s belief, we withdraw the assertion that X saw that so-and-so. [The hologram example, Goldman, p.359].

(2) Memory: S remembers p at time t2 only if S’s believing p at an earlier time t1 is a cause of her believing p at t2.

To these, we can add knowledge-producing (or knowledge-transmitting) ‘mechanisms’ like inference and testimony. By leaving the list of appropriate causal connections open Goldman admits that we can allow for the discovery that, e.g. extra-sensory perception might be a knowledge-producing mechanism. So our ideas about exactly which processes of belief-formation are trustworthy enough to yield knowledge are allowed room to change.

Some Replies to Some Objections

Goldman’s formulation of the causal theory does seem to deal, or at least to help deal, with some of the most prominent objections.

(1) Can the theory cope with knowledge of the future? People do ordinarily claim to know things like that I will raise my arm in the next ten minutes, or that some students will turn up for some future theory of knowledge lecture. But how can the facts in question be said to cause one’s beliefs in each of these things? (Arguably, those facts don’t even obtain yet (at the time of speaking)). Are we forced to conclude, along with the sceptic, that knowledge of the future is impossible? Goldman is aware of the problem. Indeed, this is exactly why he uses the above formulation. "The analysis" he says, "requires that there be a causal connection between p and X’s belief, not necessarily that p be a cause of X’s belief. p and X’s belief of p can also be causally connected in a way that yields knowledge if both p and X’s belief of p have a common cause." (Goldman op cit., p.364).

An example he uses to illustrate this is as follows. Mrs. Black intends to go downtown on Monday. On Sunday, she tells Mrs. Green of her intention. Hearing Mrs. Black say she will go downtown, and having good reason to believe that Mrs. Black is a reliable sort of person who rarely says what she doesn’t mean, Mrs. Green infers that Mrs. Black really does intend to go downtown on Monday, and from this she concludes that Mrs. Black will do so. Now suppose that Mrs. Black fulfills her intention by going downtown on Monday. Can Mrs. Green be said to have known that she would do so? This is surely a reasonable candidate for knowledge about the future. It’s just the sort of case where, after the event, Mrs. Green would be likely to say that she knew that Mrs. Black would go downtown on Monday, and not just that she believed it. And it’s the kind of case where we ordinarily would allow that she did know this.

Mrs. Black’s going downtown on Monday obviously can’t be said to be the cause of Mrs. Green’s belief the previous day. Nevertheless there is a common cause of Mrs. Black’s going downtown on Monday and Mrs. Green’s belief that Mrs. Black would go downtown, viz., Mrs. Black’s intending (on Sunday) to go downtown the next day. (See the diagram on p.365 of Goldman’s article). If we agree with Goldman that "if a chain of inferences is ‘added’ to a causal chain, then the entire chain is causal" (p.362), then we can agree that Mrs. Green’s belief is causally connected to Mrs. Black’s visit.

(2) How can there be such a thing as knowledge of universal truths? A universal truth is of the form ‘for all x, ...’. Jonathan Dancy expresses this objection by saying: "My belief that all men are mortal is caused, but not by the fact that all men are mortal; if any facts cause it they are the facts that this man, that man, etc., have died" (Introduction to Contemporary Epistemology, p.34).

Suppose that John, Jane, Susan, Eric, etc., each die. And suppose that I come to believe that John, Jane, Susan, Eric, etc., etc., were mortal (by seeing that they’ve died). I then infer from these singular beliefs that all humans are mortal via an inductive inference, which presumably can be (to some degree) warranted. Since each of the singular beliefs is causally related to the singular facts about each person’s mortality, those singular facts are causally related to my belief that all humans are mortal. Moreover, since the universal fact that all humans are mortal is logically related to each of these particular facts which are its instances (it is because all humans are mortal that John, Jane, etc. died), this universal fact is causally related to my belief that all humans are mortal. Hence, on the causal theory we can make sense of the claim that I know that all humans are mortal. Again, this depends on our accepting Goldman’s assumption that "causal chains with admixtures of logical connections are causal chains" (p.368).

(3) Can facts really stand in causal relations? Arguably, only events or agents can cause things to happen. Goldman simply declares his intention to speak of facts as causes (p.360, note 6), but does nothing to legitimate such talk. (Note, however, that even Dancy, who raises this objection, doesn’t put a lot of weight on it. In fact he gives his very own counterexample to it (p.34)). The question is, if we say:

X happened because of the fact that F,

is this just elliptical for some statement of the form:

X happened because the event E occurred?

The underlying problem here is whether states, rather than just events can be causes. It’s a deep metaphysical question which can’t be resolved here. We just ought to note that we do talk of facts as being causes.

(4) A further problem, not strictly within our scope at the moment, but worth mentioning, is: How can the causal approach cope with the case of mathematical knowledge? Even epistemological sceptics usually allow that we can have knowledge of this kind. Are we forced to attribute causal powers to seemingly inert abstract mathematical objects (like numbers)?

Here, Goldman wimps out. He says that he believes the traditional (JTB) analysis to be "adequate for knowledge of nonempirical truths" (p.357). This suggests that his theory is one where empirical knowledge is given an entirely different treatment from nonempirical knowledge.

Gettier Counterexamples to the Causal Theory?: Deviant Causal Chains

Goldman’s version of the causal theory of knowledge is more demanding than the JTB analysis in certain respects, but less demanding in others. It might or might not require that our subject should be justified in believing that p. It definitely does require that ‘the appropriate kind’ of causal connection should exist between the fact that p and X’s belief that p. Why? Why wouldn’t just any causal connection suffice?

To require only that there be some causal connection would open the theory up to modified Gettier counterexamples, like the following sort of case:

Steve is in Japan. He is at a newsstand. Suddenly, a newspaper falls off the rack. Steve sees the headline. It reads, "Earthquake hits Japan." Steve now believes that an earthquake has just hit Japan. Steve’s belief is justified because he saw the headline. What’s more, it is actually the case that an Earthquake just hit Japan. Thus, Steve’s belief is true. However, the newspaper Steve read is actually 30 years old. But, Steve’s belief that an earthquake just occurred is caused by this earthquake, since the paper’s falling from the rack was caused by an earth tremor resulting from the earthquake.

Such examples put pressure on the Causal theorist to elaborate the requirement that the fact that p must cause the belief that p. The Causal theorist will have to say that the fact must cause the belief in the right sort of way. But what sort(s) of ways are acceptable? How can one rule out deviant causal chains? These questions might make us suppose that the causal theory of knowledge hasn’t taken seriously enough the idea that what knowledge must rule out is luck. A causal connection between a fact and a belief that that fact obtains can quite well be forged as a result of chance. To capture the content of our concept of knowledge, a different kind of connection between the fact and the belief is required.

The Space of Reasons and the Space of Causes

The Causal theory of knowledge is part of a family of theories that have been proposed in recent years as a result of the ‘naturalistic’ turn in philosophy. It has taken its place alongside causal theories of perception, memory, and action. We ought not to ignore the possibility of learning something about the Causal theory of knowledge from glancing at these other causal theories.

It has, for example, been suggested that all such theories share a common fault: they all postulate the wrong kind of relationship between the psychological phenomenon (belief, mental representation, memory-image) and the non-psychological condition (fact, state of affairs, etc.). The idea is that the causing of the psychological constituent is neither necessary nor sufficient for the achievement (knowledge, perception, memory) to have taken place.

In the case of the causal theory of knowledge, the objection is that the relationship it postulates between reality and belief is just of the wrong kind. Causality doesn’t have the features necessary to make it the right link between psychology and reality. Causality is a non-normative relationship which holds between natural events (and other things, like objects and facts, perhaps). But, it might be said, what is typically required for cases of knowledge, is that the subject, the person who has the knowledge, must be able to give a reason for the belief in question. Reasons, however, are not causes, since whereas reasons exist within a normative framework (a framework in which questions like ‘How good a reason was it?’ make sense) there is no correlative question ‘How good was the cause of that event?’. The space of causes is descriptive, not prescriptive.

Second, it’s often argued that if a person has a reason to believe that p, he or she must be able to state that reason. No such condition applies to causes: one could quite well be caused to have a belief without one’s knowing anything about the cause in question. This difference gives us an initial glimpse of the dispute between ‘internalists’ and ‘externalists’ in epistemology. Roughly, internalists hold that the relationship between what is known (that p) and the knower’s belief that p is one which must be accessible to the subject. Unless it is accessible, the internalist argues, the subject won’t and shouldn’t count as knowing that p. The externalist, by contrast, proposes to dispense with this condition, insisting that there must be a relationship between the fact and the subject’s belief, but allowing that it might be one which is not within the knower’s ken.