A Puzzle About Knowledge
I want to discuss one of the oldest problems in philosophy, not aiming to solve it but with a view to articulating its difficulty. It has a claim to shaping the entire history of Western philosophy, refusing to go away. I mean the problem of a priori knowledge or, as we are apt to say, knowledge by means of pure reason. It is not generally supposed that a posteriori knowledge presents the same problem, though it may present parallel problems. It is supposed that we know about particulars by perceiving them: we have a faculty of perception and it enables us to acquire information about particular things located in space and time. It is not thought impossible to gain such knowledge (putting skepticism aside), because perception makes it possible. It is often maintained that perception works causally, so that perceptual knowledge is simply an effect of external particulars operating on us. This is no doubt oversimplified and not very explanatory, but at least we have a sketch of how empirical knowledge is possible. A further assumption is that we can’t gain knowledge of particulars except by perception (this is the core of empiricism)—in particular, pure reason cannot provide knowledge of particulars. That certainly seems true, but its truth is not as transparent as one might wish. Why is it that reason cannot supply us with knowledge of particulars, if it can supply us with other types of knowledge? Why are we limited to our senses in gaining knowledge of particulars—what is it about particulars that demands such a route to knowledge? Couldn’t we have innate knowledge of particulars, though we have none as things actually stand? Couldn’t we be suddenly blessed with a more direct way of finding out about them? These questions are reasonable enough, but the possibilities they envisage seem remote to the point of non-existence: we must know about particulars by perception and not by our rational faculty alone. Why that is remains obscure, but it does seem that particulars are necessarily known by perceptual means. Just as it is thought that we can’t know about abstract objects except by means of our reason, so it is thought that we can’t know about concrete objects except by means of our senses. In any case, that is not the question I wish to discuss, which is the nature and possibility of a priori knowledge: what kind of knowledge is this, what is its origin, and is it really possible?
We can take Plato’s treatment of Socrates and the slave boy in the Meno as our paradigm example: the boy is brought by judicious questioning from Socrates to discover Pythagoras’ theorem. On the face of it he relies on his own inner resources in coming to have this knowledge—he doesn’t perceive a whole lot of triangles and then infers the truth of the theorem. So it appears that his gaze is directed inward—at his concepts perhaps. His concepts guide him to the truth not his senses. Does he perceive these concepts with a special inward-directed sense? No, but he has access to them somehow: his knowledge of his concepts leads him to knowledge of the properties of triangles, which are not concepts. So we might suggest that a priori knowledge derives from concepts: we move from truths about concepts to truths about the things they are concepts of. This is by now a very familiar line of thought, but it raises a tricky question: must the conceptual knowledge be gained by looking inwards or can we obtain it by examining someone else’s concepts? What if the slave boy could perceive Socrates’ concepts, or know about them by empirical inference—could he use this as a basis for knowledge of Pythagoras’ theorem? The suggestion does not seem absurd, though admittedly farfetched: surely we could in principle know about the content of another person’s concepts and use this knowledge to infer analytic truths concerning those concepts. This would not be so different from using Socrates’ verbal testimony in order to come to know the theorem—the slave boy could have just been told outright what the theorem is, thereby coming to know it. So is it that such knowledge can be obtained by looking outwards, though it is generally not so obtained? But here an interesting point arises: if the boy had come to know the theorem this way, his knowledge would have been quite different from what it is when he comes to see it for himself. We want to say that he really knows it in the latter case, but only takes it on trust in the former case. He understands it, grasps it, and has insight into its truth. So it is the wayhe knows it that makes the difference—by consulting his own concepts. And doing so in that special way we use when engaged in a priori inquiry (not by looking at our own brain, say). The knowledge has a special meaning for the boy: it strikes him in a certain way. So what is this way—what kind of knowledge is it exactly? When we know something a priori what precisely is our state of mind—what specific type of knowledge do we possess?
Here Plato came up with a brilliant idea: it is a form of memory knowledge. This is his recollection theory of a priori knowledge—the doctrine of anamnesis. There is nothing like remembering an earlier experience for searing it into your mind—say, what you were thinking and feeling on a certain day 10 years ago (see M. Proust). Compare this with forgetting what happened and being told about it by someone else: you might well come to know the past by means of such testimony, but it is nothing like remembering it yourself “from the inside”. You really know it then, and it would be dreadful if all your memories were erased and replaced by current testimony from other people. Memory knowledge has a special force and vivacity. Thus when Plato says that the slave boy is recollecting what he knew in a previous life he is attributing to the boy a special kind of knowledge that is not at all like hearing it from Socrates right now. We might call this the memory knowledge theory of a priori knowledge: all such knowledge is a kind of memory knowledge—though not of events in this life, but events in a previous life. Problem solved! A posteriori knowledge is newly acquired knowledge courtesy of the senses, while a priori knowledge consists of recollections of knowledge gained in a previous life. We know what recollection is, and recollection is what enables us to have a priori knowledge. There is only one slight snag: we have to believe in a previous life during which we originally acquired the knowledge in question. We have to believe in something like reincarnation (or an eternal disembodied soul). An enthusiast of Plato’s recollection theory might urge that we have here a proof of reincarnation, since no other theory can do justice to the nature of a priori knowledge; and we have the bonus that we can reasonably expect to be reincarnated ourselves. Still, the intellectually pusillanimous among us might balk at such an extravagant theory, wondering how a priori knowledge could have such momentous consequences. Did the slave boy really exist before he was born stuffed with mathematical and other a priori knowledge? Does he now really recollect what he knew then?
Perhaps we can take the sting out of the theory by updating it. Isn’t genetic transmission a bit like memory? If your parents possessed an item of knowledge genetically, which they pass on to you, isn’t it as if you are recalling what they already knew? Not phenomenologically perhaps, but at least in the sense that a piece of knowledge is being recovered from the past—from a past life in which it was explicitly known. Thus instead of recollection we could postulate genetic transmission—a form of information storage that can be accessed at a later date. Not memory but the DNA. True, recovering such information doesn’t feel much like memory, but this provides a theory of the origin of the knowledge in question, given that it cannot derive from the senses. It doesn’t have the poetry of Plato’s theory, or its power to provide a unique flavor to a priori knowledge, but it does give us an origin story. Socrates was accessing the slave boy’s genes, in effect. The trouble with this theory, which it shares with the recollection theory, is that it is regressive: for how was the first piece of a priori knowledge acquired? It couldn’t be the result of genetic transmission or of recollection. At some point someone had to gain the knowledge in question ab initio—it couldn’t come from a previous life or from antecedently existing genes. So there is no real explanation of the origin of a priori knowledge—no account of how it arose in the first place. How did the slave boy in his previous life come to know Pythagoras’ theorem? Not by recollecting it from a previous life, on pain of infinite regress. How did the first human come to know the theorem? Not by genetic transmission from a previous knower of it. Both theories really leave us exactly where we were, without any account of the origin of a priori knowledge. We are left saying, “We just have it” or “It just pops into our mind”.
The problem is exacerbated by the fact that this kind of knowledge concerns things external to the mind not psychological matters. It is not like introspective knowledge. Pythagoras’ theorem is about triangles not ideas of triangles. How can we know objective facts by looking inside ourselves? How can we discover truths about objectively existing universals by consulting our inner psychological states? Thus a priori knowledge is puzzling, even paradoxical, and seemingly impossible. The theory of anamnesis, though ingenious, does nothing to resolve this puzzle, merely burying it; and the same is true of the genetic theory. And invoking universals, as in the theory of forms, just accentuates the difficulty, suggesting the existence of a perceptual relation that is false to the facts. We don’t see universals. A priori knowledge remains a mystery–far more so than a posteriori knowledge. It is knowledge we gain by directing our attention inward, but we have no model of how it works—no explanatory framework. The same knowledge cannot be acquired in any other way, but that fact too is mysterious. The slave boy appears to perform a miraculous feat, conjuring his geometrical knowledge from nowhere, but the same feat is performed by every normal human. Even allowing for recollection of a previous life is inadequate to explain it. It seems to well up from nowhere, unlike a posteriori knowledge, which pours in from outside.C
 Russell maintained in The Problems of Philosophy that we have “acquaintance with universals”, analogous to our perceptual acquaintance with particulars, but he gave no account of the nature of this alleged acquaintance, and it is hard to see how the analogy can be sustained (ditto for Godel’s remarks on “intuition”). Clearly we have a faculty of a priori knowledge, but how it works remains as mysterious today as it was in Plato’s time.
 The desire to give reductive accounts of the a priori, such as those proposed by the positivists, is therefore perfectly understandable, if hopelessly implausible. I think Plato’s anamnesis theory is the best theory ever proposed for dealing with the problem, but it runs into insurmountable difficulties. One difficulty I don’t mention in the text is that it is curious that these memories from a previous life show no tendency to degrade and disappear, like ordinary memories. They might even persist unaltered across multiple lifetimes without ever being evoked, if there is no occasion to bring them to light. In addition, we don’t normally react to acquiring a new piece of a prioriknowledge by saying, “Oh yes, I remember that!” I should also note that a priori knowledge brings with it modal knowledge to the effect that the known proposition is a necessary truth. This introduces another layer of epistemic perplexity into the picture. Really the whole thing is utterly baffling. And let’s not forget that a priori knowledge and a posteriori knowledge interpenetrate in our cognitive lives, with the perplexities of the former bleeding into the latter (logic, for example).