Russell and the Stopped Clock

Many philosophers today appear to regard Russell’s example of the stopped clock as the really hard Gettier counterexample, the one to beat — or believe that it can be tweaked slightly to defeat most current solutions. In the last post I sought to counter this view by describing my own truthmaker solution and showing that it defuses this example in the same way as the others. Here I want to say a little bit more about this example in the context of Russell’s writing on epistemology.

The first thing that needs repeating is that Russell himself did not put up the stopped clock example as a Gettier counterexample — i.e. he did not see it as an example of a justified true belief that yet wasn’t knowledge. Rather he saw it as an example of a true belief that yet wasn’t knowledge because the proper justification was here lacking. Here is the full quote from Human Knowledge: Its Scope and Limits, pp. 170—1.

It is clear that knowledge is a sub-class of true beliefs: every case of knowledge is a case of true belief, but not vice versa. It is very easy to give examples of true beliefs that are not knowledge. There is the man who looks at a clock which is not going, though he thinks it is, and who happens to look at it at the moment when it is right; this man acquires a true belief as to the time of day, but cannot be said to have knowledge. There is the man who believes, truly, that the last name of the Prime Minister in 1906 began with a B, but who believes this because he thinks that Balfour was Prime Minister then, whereas in fact it was Campbell-Bannerman. There is the lucky optimist who, having bought a ticket for a lottery, has an unshakeable conviction that he will win, and, being lucky, does win. Such instances can be multiplied indefinitely, and show that you cannot claim to have known merely because you turned out to be right.

If you have a true belief just from dumb luck you do not have knowledge: knowledge requires that you have come by your belief legitimately, as the result of honest toil. That was Russell’s point. But Gettier went further: his idea was that you could have acquired the belief as the result of toil and yet still have been merely lucky that it was true, because its truth wasn’t guaranteed by the evidence that you obtained and that provided you your justification. But would Russell have agreed with this? Or would he have thought that this was a pseudo-problem, generated by a false view of how beliefs are justified? I think, the latter.

First let us note that, for Russell, it is, in the first instance, beliefs that are true or false, and that sentences only become true or false derivatively in expressing beliefs. Also — and most importantly — beliefs are far richer for Russell than simple sentential reports. One can have beliefs without language; Russell notes that many animals have beliefs, but no language. But even for us: beliefs may go far beyond what we are able to express, or ever actually express. As he says: ‘the belief is richer in detail and context than the sentence, which picks out only certain salient features’.

You say “I shall see him soon”, but you think “I shall see him smiling, but looking older, friendly, but shy, with his hair untidy and his shoes muddy” — and so on, through the endless variety of details of which you may be only half aware.

Given this, I think we can see that Russell would have had very little patience with Gettier’s first counterexample, about Smith and his belief that the man who will get the job has six coins in his pocket. For Russell, the content of this belief fixes the referent as Jones, because it is Jones who Smith believes will get the job. Thus, since it is Smith who ends up getting the job, Smith’s belief is simply false. It is irrelevant that Smith happens to have six coins in his own pocket — that is just dumb luck — what matters is that Smith’s belief was a belief about Jones. Thus, for Russell, this would be merely a case of a false belief — and not knowledge simply because it is false.

What Gettier did — his trick, as it were — was to make beliefs thin: delimited by the content of a proposition. But then there was a second trick: the believed proposition was expressed in words (as though the belief was merely a string of words in Smith’s head) and thus was capable of implying other sentences and of being treated as separate from Smith’s intentions — in fact capable of being ambiguous as to its referent. Thus, in the proposition the man who will get the job has six coins in his pocket, Gettier can construe the referent of the descriptive term the man who will the job as whomever is picked out by that description, as a matter of objective fact. And that man is Smith himself, since, unbeknownst to himself, he will get the job.

But the two steps that Gettier takes are steps that Russell explicitly warned against. Beliefs are thick, for Russell, and it is they that are true or false. And it is also they that have evidential support. There is no reason to believe that the evidential support for a thick belief will descend to a proposition believed in Gettier’s thin sense — because so much content is removed. Thus, for Russell, Gettier’s target proposition the man who will get the job has six coins in his pocket has no evidential support if the descriptive phrase the man who will get the job does not specifically refer to Jones. It is void.
For Russell, Gettier’s first counterexample would simply be a mistake in analysis.

But in fact the second counterexample would fail for similar, though not exactly the same, reasons.

By treating Jones’s belief (remember that was Brown owns a Ford) as a proposition in a thin sense — one that has the structure of a sentence — Gettier is able to use the elementary Propositional Calculus to form another proposition that will be true if that original proposition is true (remember: that new proposition is Either Brown owns a Ford or he is in Brest-Litovsk). If Jones is going to believe this disjunctive proposition it would be because he has additional beliefs about the truth functional character of the inclusive disjunction and the validity of the rule of Addition (Or-Introduction). His evidence that Brown owns a Ford would not be enough, alone, for him to believe the disjunction. But the situation is even worse than this.

Truth functional implications apply to propositions in logical derivations — not to beliefs. It isn’t the Belief-Functional Calculus. From the belief Brown owns a Ford Jones could not move to the disjunctive proposition but only to the more complex conditional proposition

If Brown owns a Ford then either Brown owns a Ford or he is in Brest-Litovsk.

With his beliefs about truth-functionality, Jones could well believe this conditional. He should. But one cannot say, on Jones’s behalf, that since Jones believes Brown owns a Ford he must then believe that either Brown owns a Ford or Brown is in Brest-Litovsk. Because Jones should protest: Only if my belief is true will that disjunction be guaranteed to be true; if it is false there is no such guarantee, and my evidence must then be misleading; and my believing something to be true does not mean that it is true. So I do not, as a matter of fact, believe the disjunction: my belief in this case is void. (This argument seems to me to be very similar to an argument that John Broome has given in Ratio — but I don’t have the reference available.)

In other words Jones should believe

  1. If p is true then p or q is true for all q,

but there is no good reason for him to believe

2.    If I believe p then I must believe p or q for all q.

One can see this perhaps more clearly if we note that Jones, believing p, may give up p when it is pointed out to him that it implies some other proposition r.

The upshot is that there is no reason to suppose that Jones should believe Gettier’s disjunctive proposition. And I think — though of course one cannot be sure — that this is what Russell would say about the example. For Russell evidence and belief are fused together rather like parts of a single organic process. The evidence once received is turned into the belief; the thickness of the belief is a function of the thickness of the evidence. The belief is a mental state in a rich sense, more resembling, in its complexity, a painting than it resembles a thin proposition. This suggests that evidence need not be transferable — from a belief to a proposition that is logically implied by it (in Gettier’s sense). And if it is not transferable then Gettier’s disjunction need have no evidential support. In the case of the stopped clock I think Russell would say that merely glancing at a clock does not give you sufficient evidence to believe that it is accurate. (But I emphasise that with respect to Russell, I am speculating as to what he would say to Gettier.)

It is this transferability of evidence that does the heavy lifting in Gettier’s argument and opens up the gap between a justified true belief and knowledge. Once we allow it we must find a way to close it again. This is where the truthmaker account comes in. By insisting that the state of affairs that is the truthmaker be the same as the state of affairs that the evidence is evidence of, the gap is closed.

It is worth noting that, in Human Knowledge, Russell describes a truthmaker theory. I think that most students of philosophy do not understand this — almost certainly because they have never been taught it. They might be aware that Russell outlines something resembling a truthmaker account in the Lectures on Logical Atomism, from 1918. But there seems to be a general idea that this is something he gave up. He didn’t. In his works of the 1940’s — An Enquiry into Meaning and Truth and Human Knowledge — he holds to it. It is true that Russell doesn’t use the word ‘truthmaker’ but he does certainly speak of facts making beliefs and sentences true. Thus he says

In like manner we want a description of the fact or facts which, if they exist, make a belief true. Such fact or facts I call the “verifier” of the belief. (p. 166)

So a verifier is a truthmaker. The whole theory of truthmakers is just the development and continuation of the view initiated by Russell and Wittgenstein before and during WWI. It is a great shame — and a lost opportunity that lasted for nearly a full century — that this view was not taken up and developed as it needed to be. And even today the theory is treated as something odd and unfashionable — as though philosophers were peacocks that can only stand to be seen in the latest dress!


Postscript for bibliophiles.

The copy of Human Knowledge that I have is a first edition — I bought the book second hand many years ago. It comes from the library of T. D. Kellaway, who was Professor of Pathology at Cambridge University. But what is particularly interesting is that the dust jacket of the book is printed on the back of a WWII map — since paper was still in short supply in Britain through the 1940s and rationing was still firmly in place. Images below.


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