Aspects of the A Priori

It is now fifty years since I first tried to define a priori knowledge. I wrote a long paper on the subject in 1975 that was abbreviated to appear in the Proceedings of the Aristotelian Society in 1976 (“A Priori and A PosterioriKnowledge”). The basic idea was that a posteriori knowledge is knowledge caused by the subject matter of the corresponding belief, while a priori knowledge is defined as knowledge not so caused. The definition was extensionally adequate, I argued, but it lacked a positive account of what a priori knowledge is. It was too spare. It didn’t shed much light. Now I propose to fill that gap by bringing in some further apparatus—I want to spice the theory up, give it some substance.[1] I shall do this by describing certain aspects of the a priori that characterize its nature—specify what kind of epistemic kind it is. The aim is not so much stating necessary and sufficient conditions (though it will be that too) as conceptually illuminating elements or facets—the shape of the fact, what it means to be known a priori.

It is best to start by fixing the nature of a posteriori knowledge; then we can define a priori knowledge by way of contrast (we could in principle do it the other way about). Perceptual knowledge is the paradigm or paragon: this is knowledge by means of primitive sense experience. It is distinctive of such knowledge that it is perspicuous in the sense that we know how we have it when we have it; it is not a mystery to us why we know basic facts about perceived objects, precisely because we are consciously aware that it is based on sense experience. The object is perceptually presented in consciousness as being a certain way, as it might be purple and hexagonal; we are not guessing at its color and shape—this is given in experience. The situation is unlike blindsight or subliminal perception or extrasensory perception; we don’t just have a hunch that a purple hexagon is before us. We know it, perceive it to be so. We can have merely conjectural knowledge, but in the primary cases the knowledge is perspicuously possessed. Conscious sense experience delivers the knowledge, whole and intact; we don’t have to make a stab at it hoping for the best. Thus, such knowledge has two distinctive features: it is perspicuous and it is experiential—evident and sensation-based. The former makes it (primary) knowledge; the latter makes it a posteriori. The question then is how a priori knowledge is both like this and also different, so that it is clearly a case of knowledge and also sharply distinguished from a posteriori knowledge. For it cannot fail to count as knowledge according to the definition we are seeking, and it cannot differ only in degree from a posteriori knowledge: we can’t have a merely expressive theory of it or a conventionalist theory, and we can’t fail to register its sui generis status by making it just a special case of a posteriori knowledge. Our theory must be unequivocally cognitive and yet sharply contrastive—these are our “conditions of adequacy”. The two conditions clearly pull in different directions.

First, I want to say that my old theory survives in the present picture: a priori knowledge is not causally dependent on the subject matter of the corresponding belief—a priori facts don’t cause a priori beliefs. Abstract objects, meanings, and logical relations don’t cause us to have beliefs about them—no energy emanates from them. They are not like the objects of vision or touch. We are not dealing with material objects in space that send out particles and waves that interact with our senses. The interesting question, having accepted that, is whether the knowledge is perspicuous in the defined sense: is it a mystery to the knower that he knows? Is it like blindsight or subliminal perception? Clearly not: the knower is convinced that his belief is on the right track, not unsure and hesitant. If anything, he is even more certain than in the perceptual case, because of the absence of a priori hallucinations—you are never under the illusion that 7 is even, say, or that brothers are female. Thus, these cases of knowledge are cases of well-grounded primary knowledge, solid as a rock—not inferential and conjectural. How, then, do they differ from perceptual knowledge? The answer is that they are not sensation-based: we don’t have sensations of numbers and logical relations that trigger belief. We can then add that a priori knowledge is evident but non-perceptual—perspicuous and well-grounded but not in the senses. It is genuine knowledge but it isn’t perceptual knowledge. The subject isn’t surprised to find himself with such knowledge, but not because he perceives its objects with his senses. We can then say that a prioriknowledge is non-causal and non-perceptual, whereas a posteriori knowledge is both.

But now we reach the pith of the problem: do we know how we know in the a priori case? Can we cite anything analogous to the occurrence of sense experience? Evidently not: we just know, but not in virtue of anything we can put our finger on or spy with our little eye. We know “by intuition”. This is the puzzle of the a priori. We can say that it seems to us that such-and-such is the case, but we can’t find a sensation that constitutes this seeming—it is seeming without sensing. We perceive the truth, but we don’t perceive it. So, we can add to our inventory of aspects of the a priori the fact that a priori knowledge is shrouded in mystery: it isn’t mysterious to the knower that he knows, but it is mysterious how he knows. Sensation is what precludes mystery in the perceptual case, but sensation doesn’t exist in the a priori case. Let us then characterize the a priori as non-causal, non-perceptual, and non-intelligible—though it is cognitive, perspicuous, and epistemically solid. Suppose we were to invert our procedure and begin by defining the a priori; and suppose we were attracted by linguistic theories of the a priori (supposing these to be intelligibly stated). Then we could say that a prioriknowledge is knowledge that arises from the introspection of meanings (or some such), this construed as non-perceptual (no sensations of meaning). Proceeding to the a posteriori, we could then stipulate that such knowledge is knowledge not arising from such linguistic introspection, leaving it open how it does arise. That might well be extensionally correct, but it would be unsatisfactory, given that we have no real account of so-called introspection of meanings (not to mention the inadequacy of the linguistic theory as a general theory of the a priori). The definitions aren’t wrong exactly, just obscure, incomplete. Starting with the a posteriori, however, we come to appreciate a distinctive mark of the a priori—that it lacks theoretical transparency. That is part of what it is—conceptually, constitutively. A priori knowledge differs from a posteriori knowledge in being unclear—puzzling, peculiar. It has the epistemic virtues proper to real knowledge, but it lacks theoretical openness–it is, in a word, mysterious. What makes it non-mysterious that the knower knows is itself mysterious. I know quite well that I know that “larger than” is transitive—this is not a mystery to me—but it is mysterious to me what makes it non-mysterious. All I can find to say is that it seems to me that “larger than” is transitive—but not because it looks or feels transitive. This is part of what marks the a priori off from the a posteriori. The lack of mystery is mysterious: I know quite well that I know (I am certain of it) but I don’t know how I know—beyond the lame “It seems to me”. It is a mysterious kind of seeming, so a priori knowledge rests on a mysterious kind of seeming, unlike a posteriori knowledge. I have no problem with that philosophically, being habituated to mystery, but it is worth pointing it out as an aspect of the phenomenon in question.

We have accomplished our goal, i.e., to specify the distinctive marks of the a priori. We now know how it differs from the a posteriori and what its internal features are. We weren’t trying to explain its possibility, only to capture its essence, which includes its appearance to us. It isn’t about the causal order, or the world of sensation, or the (more or less) intelligible world (roughly, the mechanical world); it’s about something else entirely. What exactly, we find it hard to say, so we use words like “intuition” and “apprehension”. Very crudely, we could say that the a priori concerns the unintelligible part of epistemology—that is what distinguishes it from the a posteriori. Yet it is knowledge in good standing. It exists, and is sharply different from a posterioriknowledge, but we don’t really grasp its nature.[2]

[1] I have been influenced by Michael Ayers’ discussion of knowledge and the a priori in Locke (1991). I have adopted some of his terminology and general epistemological perspective. When I first wrote about a priori knowledge fifty years ago there was very little interest in the topic, though a good deal of interest in necessity and mathematical knowledge; things have changed since. My own interest in it goes back to reading Leibniz as a student.

[2] We are inclined to say that the faculty of a priori knowledge involves a type of “seeing’, but all we have are vague analogies to ocular seeing. The concept seems inclusive enough to include both, but it is hard to find any literal parallel. We could accordingly define the a priori as a faculty of non-literal seeing: that hits if off nicely, but it wallows in metaphor. I can see that “larger than” is transitive, but my eyes don’t come into it.

Aesthetic Tennis

As Wimbledon builds towards its climax, the question on everyone’s mind is “Who is the most aesthetic player in the world?” We all have our views, some more informed and sensitive than others. I will wade into these shark-infested waters, in which one’s credibility is totally on the line. Like, totally. I think we can all agree—I should hope so—that Wimbledon is the most aesthetic tournament, distantly followed by Roland Garros, with the Australian and American Open trailing far behind. The English do some things right (not many, perhaps, but some). But which player wins the Aesthetic Open? I don’t just mean among today’s active players but of all time. Some will certainly anoint Roger Federer and one can see why: his elegance, lightness, polish, poise. Roger was a joy to behold, despite his somewhat fragile backhand (vide Rafael Nadal). Nadal himself had a certain bullish beauty, with his grunts and topspin and shapely legs (I have seen them close to). I wouldn’t dismiss Nadal as among the top beauties of the game. Djokovic also has a strong claim among his devotees (I am among them): his is the beauty of the well-oiled machine, the BMW of the tennis world. Andy Murray? Well, he has the rugged elegance of a Scottish racing horse (if there is such a thing)—big, sturdy, solid as a rock, a bit temperamental. But none of these worthy works of art come close to the player I would anoint—and you know who I am talking about. Carlos Alcaraz of course! He is by far the best player to watch in the history of the game, is he not? The feet, the hands, the speed, the ball control. The brutal bullet of the backhand, so accurate, so stinging; the sudden explosion of the forehand as it leaves the opponent gasping; the delicate devastating drop shot, carving languidly through the air. For Alcaraz the ball is his paintbrush, the racket his violin bow. Every rally is a work of art; when he misses you feel deprived, disappointed. I particularly admire the foot work on his two-handed backhand—so perfectly placed, balanced, alive. He doesn’t hit, he sculpts; he drills it, or knifes it, wherever his heart desires. Now Jannik Sinner is a fantastic player, also aesthetically formidable: he has complete consistency, total control, phenomenal foot speed. I would respect the opinion of anyone who pronounced him the world’s aesthetic Number One: he is like a gazelle in flight equipped with a devastating right hook. He is clearly a great art-work of the tennis court. But he doesn’t quite have Alcaraz’s breathtaking flair; he doesn’t surprise like Alcaraz. Alcaraz loves to create; Sinner likes to get the ball in. As one beaten player remarked, “Sinner is like a wall who hits every ball back at 100mph”. Alcaraz is like an elastic medium that treats the ball (and his opponent) as a plaything—he decides what he is going to do with it. He alters the laws of tennis ball motion. This is why his play is described as magical not mechanical. Sure, he takes risks, but he often defies the laws of nature. He serves with calm confidence, so you don’t feel nervous on his service games; he isn’t going to get the wobbles. He enjoys the spectacle as well as the win. He is clearly the most popular tennis player in the world to watch—he is a happening, in the Sixties sense. You want him to win and he obliges; you want beauty to emerge victorious. In addition, he is a spectacularly nice guy, always smiling, never angry. He is only twenty-two and already master of the art of tennis. So, in my opinion, with my credibility on the line, I submit Carlos Alcaraz as my choice of the most aesthetically pleasing tennis player of all time.[1]

[1] I have said nothing of the women’s game: am I then a tennis aesthetic sexist? Mmm, no. I have my views here too, and they are not heterodox. I nominate Iga Swiatek as the best aesthetically, because of her foot speed and ball control; but I want to put in a special mention for Emma Raducanu for her general elegance and variety. I do have to admit that for me the men are more beautiful than the women in tennis, beautiful as the latter undoubtedly are.

Interests

What am I not interested in and don’t enjoy? And what am I somewhat interested in but can do without?

I am not interested in politics—in fact I am repulsed by it—but I follow it closely for purely utilitarian reasons. I find it intellectually dismal if not abysmal. I am not interested in business or the stock market or “technology”. I am not interested in medicine and illness (though my son is a doctor). I don’t like Frank Sinatra. I’m not into dancing (though I used to be in my teenage mod days). I don’t care much for travel, though I’ve done a fair amount of it—too much effort, not enough reward. I’m not a keen gardener. I don’t like rap music. I can’t stand bad people.

I have a range of secondary interests, but not obsessions. I am interested in clothes and fashion, especially shoes. I have always been interested in humor, though a lot of it leaves me cold. I am interested in food and cooking and like to invent dishes (not easy). I’m very fond of nature, mainly animals. I like cars and motorbikes. I like Persian rugs. I collect guitars. Stamp collecting has its appeal. I like knives but not guns. I admire trees, but I’m not afraid to cut them down. I quite like swimming, but I don’t love it. Diving I enjoy more. Interior decoration is only mildly interesting to me. I can do without vases of flowers. I like cutlery and crockery. I favor an orderly fridge. I like nice people, but there are not too many of them. I find television worth watching, but selectively. I’m not a big opera fan, though I have seen many operas and enjoyed them (I prefer ballet).

Is there a pattern here? Are there many people with the same set of interests and antipathies?

Me at 75

I thought I’d sum up where I am today.

Intellectually, I see myself as a philosopher, scientist, and novelist–in that order. I see these as separate, though overlapping in places.

Athletically, I am mainly a tennis player, a table tennis player, a skateboarder, a knife thrower, and a motorcyclist. I have been other things in the past, depending on the time in my life. Most recently, I was mainly into watersports—kayaking, surfing, windsurfing, skimboarding, bit of kiteboarding. Earlier at school it was gymnastics and pole vaulting. I still do some discus and Frisby occasionally.

Musically, I see myself these days as a singer, drummer, guitarist, harmonica player, and songwriter.

I do none of these things for a living, so they are not “work”. On the other hand, they are not “hobbies”—I take them too seriously for that. I am always trying to improve, so I practice regularly. I suppose the word “vocation” fits—“a strong feeling of suitability for a particular career or occupation” (OED). In close possible worlds they might have been my job. I just read a long article about Ringo Starr in the New York Times in which he said about being a drummer: “I love to hit the buggers”. That is my attitude towards all these activities, though I admit that actual hitting can’t be beat. Am I a philosophical hitter man?

I recommend making such a list to my readers.