A number of my posts have looked at the tight connection between rationality and probability. One of the pioneers of this kind of work was Frank Plumpton Ramsey, who made major contributions to mathematics, economics, psychology, and philosophy before passing away at the young age of 26. Ramsey was also a friend of the influential and enigmatic philosopher Wittgenstein, and helped both to translate Wittgenstein’s Tractatus Logico-Philosophicus into English and to convince Wittgenstein to return to philosophy after he had abandoned it.
Ramsey’s work is actually quite readable, and I encourage anyone who is interested in the topics I discuss in this blog to read some of his work. In particular, Truth and Probability is a foundational and fairly accessible essay. However, for this post I thought I would just give you a taste of Ramsey by looking at one of his very short papers, Knowledge.
I couldn’t find a good link to the paper online, but it is short enough that I will do this post as an annotation. The paper begins
I have always said that a belief was knowledge if it was (i) true, (ii) certain, (iii) obtained by a reliable process. But the word ‘process’ is very unsatisfactory; we can call inference a process, but even then unreliable seems to refer only to a fallacious method not to a false premiss as it is supposed to do.
The traditional account of knowledge going back to the ancient Greeks is that knowledge is justified true belief. This is very similar to Ramsey’s starting point above, except he replaces belief with certain and justified with obtained by a reliable process. We might want to say that the latter of these two are not so different, and that the only way a belief can be justified is if it is formed by a reliable process. This actually seems right to me.
Furthermore, we might want to say that I believe something only when I am certain of it. I am less sure what to think here, since I often say “I believe” something when I am not certain of it, e.g. I might only be very confident. Sometimes (I try to do it often and when appropriate) I actually try to qualify my belief in a Bayesian way by attaching a particular number to it. For example, my credence that I am writing this between 11am and 12am is 0.95 (I haven’t looked at a clock in a while but I vaguely remember when I started writing). At this point we are not exactly sure what Ramsey means by “certain”, whether it corresponds to a probability of 1, or whether it is “close enough” to 1, whatever that may mean. He addresses this a little later in the paper.
Ramsey is then concerned about the use of the word “process,” for it doesn’t seem to specify clearly what part of inquiry we are talking about. His example is that if we take (deductive) inference we might call that a process. If we carry out the process of deductive inference we can certainly come to false beliefs—if we start with false premises. However, the method itself does not seem unreliable—that is, if we start with true premises it must lead to true conclusions. Do we include the premises of a particular deductive inference in the process? Thus, to speak of inference as a process is unclear—is it reliable or not? We need to sharpen up the notion of process.
Can we say that a memory is obtained by a reliable process? I think perhaps we can if we mean the causal process connecting what happens with my remembering it. We might then say, a belief obtained by a reliable process must be caused by what are not beliefs in a way or with accompaniments that can be more or less relied on to give true beliefs, and if in this train of causation occur other intermediary beliefs these must all be true ones.
We often think that remembering can give us information. Can it give us knowledge? If so, then according to the definition remembering would have to be a reliable process. What exactly is the process of remembering? At some level, there is some causal process going on. An apple falls from a tree. Light bounces off the apple and hits my retina, causing a series of changes in my brain. When I remember the apple falling, there is a direct causal link back to the actual apple falling. In this was, there is a causal process connecting what happens with my remembering it.
With this example up and running, Ramsey gives a sketch of what we might mean by a belief obtained by a reliable process. The belief must be caused by things that are not beliefs — for example, the actual apple falling from the actual tree, the light bouncing off the apple, etc. — and any parts of this process that are beliefs must also be true. For example, before I remember the apple falling I might when I actually see that apple fall think “there is an apple falling”. This is part of the process of remembering (we might imagine) and it is a belief, but since it itself is true and formed by a reliable process we are okay.
E.g. ‘Is telepathy knowledge?’ may mean: (a) Taking it there is such a process, can it be relied on to create true beliefs in the telapathee (within some limits, e.g. when what is believed is about the telapathee’s thoughts)? or (b) Supposing we are agnostic, does the feeling of being telepathed to guarantee truth? Ditto for female intuition, impressions of character, etc. Perhaps we should say not (iii) obtained by a reliable process, but (iii) formed in a reliable way.
(a) is asking that, supposing we know there is a process of telepathy, is it reliable? Instead, (b) is asking if we don’t know there is such a process, does our mere feeling that someone is communicating to us telepathically give us true beliefs. In the first case we have an actual method we are trying to evaluate. In the second, we have merely a feeling the cause of which we are uncertain.
We say ‘I know’, however, whenever we are certain, without reflecting on reliability. But if we did reflect then we should remain certain if, and only if, we thought our way reliable. (Supposing us to know it; if not, taking it merely as described it would be the same, e.g. God put it into my mind: a supposedly reliable process.) For to think the way reliable is simply to formulate in a variable hypothetical the habit of following the way.
In the words of one of the professors for whom I TAed, certainty is cheap. Merely being certain does not guarantee that the belief is good. However, Ramsey thinks that when we actually sit down and reflect on our beliefs, we should only keep our certainty if we thought the way in which we formed the belief was reliable. The initial “I know” is sort of at the beginning of our reflection, at which point we haven’t yet actually put much thought into our belief. As we reflect on it, we can correct our level of certainty if need be.
The last line is a little unclear to me, but I think it might have something to do with the following. In order for the way in which my belief is formed to be reliable, I would have to imagine how the belief would have been formed had the world been different. For example, in the earlier case with the apple falling from the tree, it is clear that the way in which my belief is formed in sensitive to whether or not the apple in fact falls. I can run the hypothetical in both case—the apple falling and the apple not falling—and in both cases if I have a particular habit of following the way (sight, in this example) then the way is reliable. In other words, you want your beliefs to be correlated with the world. I think this is a super helpful way of thinking about belief formation.
One more thing. Russell says in his Problems of Philosophy that there is no doubt that we are sometimes mistaken, so that all our knowledge is infected with some degree of doubt. Moore used to deny this, saying of course it was self-contradictory, which is mere pedantry and ignoration of the kind of knowledge meant.
Russell and Moore were two influential philosophers of Ramsey’s time. This comment is pointing to a disagreement they had about whether or now we can be skeptical of our own beliefs. What Ramsey writes next explains this in more detail.
But substantially the point is this: we cannot without self-contradiction say p and q and r and … and one of the p, q, r … is false. (N.B–We know what we know, otherwise there would not be a contradiction). But we can be nearly certain that one is false and yet nearly certain of each; but p, q, r are then infected with doubt. But Moore is right in saying that not necessarily all are so infected; but if we exempt some, we shall probably become fairly clear that one of the exempted is probably wrong, and so on.
So the problem is suppose we believe a bunch of things, but we also believe that at least one is false. This would of course be a contradiction. This is Moore’s point from the previous paragraph. However, as Ramsey says, this reflects “ignoration” of the kind of knowledge meant. If we give up absolute certainty in each of the things we believe and instead replace it with a high degree of certainty, then the apparent paradox is resolved. However, this does of course means that we have some minor degree of doubt in each proposition. The last line is about a regress if we start excluding a few as beyond doubt and then become certain that at least one of the ones we excluded is false. The solution seems to be that we should keep track of our uncertainty, and that in fact everything is infected with at least some small degree of doubt. Far from being a problem, though, this seems like good epistemic hygiene.
As I mentioned this is a very short little paper of Ramsey’s. However, his longer papers reward reading.