02turtleubirrAs I sit here regarding the eighty student essays I have to grade over the course of the next few days– essays that I’ve already had in hand for too long –I naturally cast about for ways to procrastinate. Having completed my posts on Meillassoux’s argument against correlationism (here, here, and here), and having, over the last few days, had an intense, though very productive, discussion with Mikhail surrounding these and related issues (here, here, here, and here), I find myself wondering just how damaging Meillassoux’s argument is. Does Meillassoux’s argument really land a fatal blow to correlationism? I think that depends.

If we are to understand Meillassoux’s argument from ancestrality and against correlationism, it is necessary to understand why he focuses on time. To do this, we need to recall a bit about Kant and how Kant solved the problems of space and time in the Critique of Pure Reason. That is, we have to look at what Kant actually says about the nature of time. If Meillassoux chooses to stake his claim for realism on the issue of time, then this is because primary qualities, qualities that are said to be “in the thing itself” and not dependent on us, are generally understood to be mathematical properties. All that I can know of mathematical properties, the story goes, are those aspects of these properties that can be mathematized. Thus, as Descartes said, “this class of things [primary qualities] appears to include corporeal nature in general, together with its extension; the shape of extended things; their quantity, that is, their size and number; as well as the place where they exist, the time through which they endure, and the like” (Discourse on Method and Meditations on First Philosophy, Hackett, Fourth Edition, 61). What are we speaking of when we speak of the mathematical properties of an object if not the spatio-temporal properties of the object? Meillassoux, of course, wants a much broader domain of primary qualities than shape, size, mass, duration, etc., so as to make room for new properties discovered in science. The point is that when he speaks of primary qualities he is basically speaking of spatial and temporal properties that are subject to mathematical representation. The claim isn’t that the property is a number, but rather that it has a mathematizable structure discoverable through measurement, experiment, observation, etc.

read on!

nebulaTraditionally– that is prior to Kant and the critical revolution –these properties were understood as being in the object itself. Unlike the taste of my wine as bitter or sweet and which arises only in the relation of my wine to my taste buds and neurology, objects have their primary qualities quite regardless of any relation to us. For example, an atom has such and such an atomic weight. It might very well be true that we use arbitrary measuring systems to get at this weight, but what is measured is not in the object as a result of how the object relates to me, nor is it arbitrary. So the realist story about primary qualities change.

One of Kant’s major revolutions was to show that time and space are not primary qualities, but exist only in relation to the subject of science. Where previous philosophers and scientists thought of time and space as being real and independent of humans, Kant argued that time and space only exist for humans and do not belong to things themselves. Newton, for example, believed in the existence of absolute space. The claim that space and time are not real, but rather exist only in relation to us might strike one as very peculiar. After all, the evidence of our lived bodies and our five senses seems to indicate with certainty that that things are side by side, at a distance from one another, that one event follows another, that the future is not here and the past is gone, etc. However, Kant gives a very compelling set of epistemological arguments and observations for the consideration that space and time are for-us and not in things themselves. These arguments revolve around mathematics.

Kant observes that my knowledge of all objects that exist independent of me must be received through my sensibility a posteriori. The key feature of empirical sensibility is that I cannot know, a priori and with certainty, what qualities an object will have, but must rather go to the object to find this out. For example, while I might be warranted in thinking that my cumbers are likely to have sprouted because of when I planted them, I could not know that they had sprouted until, just now, I stepped outside to take a look at my garden. Additionally, it is just as possible that my cucumbers might never sprout, such that the fact they sprouted this year does not provide certainty that they must sprout next year. Such is the nature of contingent truths, under which empirical objects fall.

Now, if space and time were properties of things in-themselves, or were things that exist independently of me, then we would have to learn the properties of space and time through experience. But all things being equal, if space and time are learned from experience, then how is it that I am able to arrive at a knowledge of necessary relations structuring space and time or underlying mathematics (geometry being the math of space, arithmetic the math of time)? As we just saw, I cannot know the empirical properties of an object a priori, but must rather discover these properties through receptivity. I have to see that my friend Tom is wearing a purple shirt because no contradiction is involved in the other possibility of Tom not wearing a purple shirt. Yet in the case of maths, matters are entirely different. First, I know all sorts of things about space and time a priori or independent of directly experiencing them. Second, mathematical truths are necessary rather than contingent. Where the color of an apple is a contingent truth that could be otherwise without involving any logical contradiction, the sum of the angles of a quadrilateral are not contingent, but rather belong to the essential structure of the quadrilateral. Finally, third, mathematical truths are universal, which is to say that they hold for all times and places. The angles of that quadrilateral will add up to 360 degrees and, fortunately, I do not have to travel to the other side of the universe in order to discover this, but can know it a priori and with certainty by virtue of the properties of space.

Yet how, Kant asks in his best David Lynch Quizat Haderach voice, can this be if space and time are properties of things-in-themselves? If space and time are properties of things-in-themselves I must learn them through sensation. But I can know nothing of the things that populate experience in terms of necessity, universality, and certainly not a priori. Were it the case that my knowledge that the sum of the angles of a quadilateral were based on observation, nothing would warrant me in supposing that quadrilaterals tomorrow or on the other side of the universe will have angles that add up to 360 degrees because sensation presents me with nothing but contingent relations. Yet it is absurd to suggest that mathematical truths are contingent in this way. Therefore it follows that we do not arrive at knowledge of these types of relations empirically or through sensation.

Kant’s solution to this problem is famous: “…[T]he pure form of sensible intuition in general is to be encountered in the mind a priori, wherein all of the manifold of appearances is intuited in certain relations (Critique of Pure Reason, A20/B34). I call this the “turtle hypothesis”. Just as a turtle does not find his home in the external world, but rather carries it about on his back, time and space are not, according to Kant, in the things-themselves, but rather reside in our minds. Although this thesis might initially appear strange and outlandish, it is an elegant solution to a host of problems. First, it explains how phenomena of the world can be mathematical. Because all of our relations to the world are structured by the mind in terms of the pure forms of time and space belonging to our minds, it follows that these sensations will have the mathematical properties belonging to space and time. It is for this reason, second, that we can know many things about space and time a priori. Because our mind is structured in terms of space and time, we are able to contemplate temporal and spatial relations independent of a direct empirical experience of particular objects. Finally, third, this explains why mathematics is not simply a custom belonging to a particular group of people like using chopsticks or not cutting one’s whiskers, but is rather intersubjectively universal. Because our minds are structured in the same way, we are able to independently arrive at the same mathematical conclusions. This is truly a beautiful and elegant solution to a whole host of philosophical riddles about mathematics and the mathematical nature of physical reality.

Kant tells us that the realist about space and time must respond to two riddles:

Those… who assert the absolute reality of space and time, whether they assume it to be subsisting or only inhering, must themselves come into conflict with the principles of experience [i.e., the transcendental conditions of experience]. For if they decide in favor of the first (which is generally the position of the mathematical investigators of nature), then they must assume two eternal and infinite self-subsisting non-entities (space and time), which exist (yet without there being anything real) only in order to comprehend everything real within themselves. If they adopt the second position (as do some metaphysicians of nature), and hold space and time to be relations of appearances (next to or successive to one another) that are abstracted from experience though confusedly represented in this abstraction, then they must dispute the validity or at least the apodictic certainty of a priori mathematical doctrines in regard to real things (e.g., in space), since this certainty does not occur a posteriori, and on this view the a priori concepts of space and time are only creatures of the imagination, the origin of which must be really sought in experience, out of whose abstracted relations imagination has made something that, to be sure, contains what is general in them, but that cannot occur without the restriction that nature has attached to them. (A39-40/B56-57)

The first problem Kant alludes to is that of the metaphysical problem of the reality of space and time. What does it mean to say that space and time are real things? Newton had caused a firestorm when he asserted the reality of absolute space. After all, what could it possibly mean to say that something like space or time, that are not material objects (this claim has become disputable today) and that give us no sensations could possibly be real? This, I think, is a deep metaphysical question. The second problem is the problem of learning. Given that all mathematical truths are necessary and universal truths, given that it is possible to know these truths independent of any experience, how could I possibly arrive at a knowledge of such necessity a posteriori? What would warrant the certitude that triangles on the other side of the universe are the same as triangles on this side of the universe? If mathematical reasoning is synthetic rather than analytic as Kant supposes, then I am able to expand my mathematical knowledge simply through thought. Yet if maths are a posteriori this would not seem possible.

Kant is able to elegantly solve both of these problems in one fell swoop by concluding that space and time are not things-in-themselves or in things-in-themselves, but are rather in the mind. This conclusion, of course, comes at a price. As Kant sums up,

We have therefore wanted to say that all our intuition is nothing but the representation of appearance; that the things that we intuit are not in themselves what we intuit them to be, nor are their relations so constituted in themselves as they appear to us; and that if we remove our own subject or even only the subjective constitution of the senses in general, then all the constitution, all relations of objects in space and time, indeed space and time themselves would disappear, and as appearances they cannot exist in themselves, but only in us. What may be the case with objects in themselves abstracted from all this receptivity of our sensibility remains entirely unknown to us. We are acquainted with nothing except our way of perceiving them, which is peculiar to us, and which therefore does not necessarily pertain to every being, though to be sure pertains to every human being. (A42/B59)

In other words, if we are to side with Kant’s solution, then the price we must pay is that we can never have any knowledge of whether things-in-themselves have the spatial and temporal properties of our experience of appearances, because we cannot get out of our minds to know whether things themselves are this way. Indeed, Kant vacillates here, stating in the first part of the quoted passage that things in-themselves aren’t as we intuit them to be, while, in the the second part of the passage, merely expressing a limit to our knowledge or that we cannot know whether they are like we intuit them. In other words, the sacrifice required by Kant’s elegant gesture consists in a shift from the thesis that the universe is spatial and temporal to the thesis that the universe appears spatial and temporal. This seems like a rather minor sacrifice to make given the epistemological security that this move is able to accomplish.

Why, then, in his critique of correlationism through the argument from ancestrality does Meillassoux fix on time rather than space? The answer to this question, somewhat ironically, has to do with the temporal qualities of space. When we talk about space, what we are talking about– at least before Einsteinian relativity and quantum mechanics –are entities that are simultaneous with one another. Consequently, the fact that I am not currently observing my living room poses no special problems for the Kantian for were I to walk into my living room it would be structured according to the pure form of spatial intuition belonging to my mind. In other words, the counter-factual is sufficient to save the day. Meillassoux addresses this point in his response to correlationist rejoinders (cf. Meillassoux III).

With the advent of science’s ability to make ancestral statements about the universe discussing times that precede or are anterior to both life and humans, matters become significantly complicated. We can very well see how, by Kant’s lights, it makes perfect sense to suggest that the laws of Einsteinian relativity were operative in the time of early homo sapiens (assuming relativity is consistent with Kant), for the structuring forms of givenness or time and space were operative at this time. Yet how are we to make sense of claims that predate any life or consciousness. Let us repeat what Kant says since there is a tendency to fly fast and loose with Kant’s claims among correlationists: …[T]he things that we intuit are not in themselves what we intuit them to be, nor are their relations so constituted in themselves as they appear to us; and that if we remove our own subject or even only the subjective constitution of the senses in general, then all the constitution, all relations of objects in space and time, indeed space and time themselves would disappear, and as appearances they cannot exist in themselves, but only in us (ibid). Whether we take the strong (things-in-themselves are not like we intuit them) or the soft (we do not know whether things-in-themselves are like we intuit them) reading of Kant’s claims about time, we run into significant problems with respect to Kant’s thesis as it leads us inevitably to skepticism about these ancestral claims.

In other words, Kant’s thesis about time as a pure form of intuition that does not belong to things-in-themselves necessarily entails that claims about the ancestral must be dogmatic and therefore empty of any claim to the status of knowledge. If this is so, then it is because an ancestral claim is a temporal claim about things-in-themselves, not time for consciousness. It presupposes a time anterior to consciousness. As a result, the correlationist must reject the thesis that humans evolved or that we can meaningfully talk about a time prior to humans because things-in-themselves are not, for the correlationist, structured in terms of time. This is the point that Husserl when he remarks that, “[t]he existence of nature cannot be the condition for the existence of consciousness since Nature itself turns out to be a correlate of consciousness: Nature is only in being constituted in regular concatenations of consciousness” (Ideas I, 116). Aye, the correlationist gives us stellar grounds for the universality, necessity, and a priori knowledge we know to belong to our mathematics. He is able to explain why being has the mathematical structure discovered by thought. But only so long as we talk within the framework of the existence of human beings. Whenever we stray from this framework, to a time anterior to the existence of life our humans, all of this breaks down because we cannot intelligibly talk about a time belonging to things themselves. As a result, the consistent correlationist must reject the theory of evolution, the big bang, and, as follows from Husserl’s remark, neurology as well. This seems like a rather high price to pay.

Setting aside the issue of the metaphysical status of time or what it would mean to say that time and space exist, it seems to me that the most attractive and compelling features of Kant’s thesis is its ability to account for both how we are able to arrive at mathematical knowledge through thought alone, yet in such a way that the objects of our universe themselves have mathematical properties. As Kant famously says,

Up to now it has been assumed that all our cognition must conform to the objects; but all attempts to find out something about them a priori through concepts that would extend our cognition have, on this presupposition, come to nothing. Hence let us once try whether we do not get farther with the problems of metaphysics by assuming that the objects must conform to our cognition, which would agree better with the requested possibility of an a priori cognition of them, which is to establish something about objects before they are given to us. (Bxvi)

Kant here, I think, hit on a deep and profound metaphysical and epistemological riddle. We don’t expect the world to conform to a story or a novel (entities produced through thought), yet somehow the world does conform to the mathematical truths we discover in thought. How can this be? Kant provides one of the most convincing solutions to be found. Yet is it true that Kant provides us with the only viable solution to this profound problem? Can we not find a solution that both preserves Kant’s deep insight into the a priori status of mathematics (our ability to establish something about objects prior to them being given to us), while simultaneously being able to assert that mathematical properties belong to objects as they are in-themselves regardless of whether or not humans exist? It would seem that the theory of evolution, coupled with the thought of Whitehead and Deleuze provides us with precisely such an alternative. Unfortunately, Kant labored in a philosophical period that began from the premise of fully formed or actualized subjects regarding or contemplating the world. Under this model, knowledge was either analytic, a priori, and innate, or knowledge was empirical and received through sensibility. Empirical knowledge, of course, lacked the claws of necessity. Moreover, everyone is agreed that mathematical knowledge is a priori (though Kant disputes that it is analytic), while they were unable to explain how objects could also be mathematical, how we could know certain mathematical properties prior to the object being given, without an untenable appeal to God as co-ordinator between a priori mathematical knowledge and the structure of the world. In this context, where subject and object, mind and world, agent and environment, are abstractly opposed to one another and the question is one of how object migrates into the mind as an adequate representation, Kant’s solution is the best solution in town.

The theory of evolution offers an alternative to this line of thought. From an evolutionary standpoint, our ability to know something of objects prior to them being given has to do with the fact that our minds evolved in a universe with a mathematical structure. That is, evolutionary theory gives us the possibility of an ontogenetic account of our cognitive structures. Just as my bone structure, my cells, my digestive system, etc., is fitted to a particular environment that has a specific range of pressure, heat, gravity, light, etc., so too could our cognition have evolved in a way that was fitted to the mathematical structure of the world. It is precisely such a theory of cognition that Whitehead and Deleuze offer in their respective genetic ontologies. Whitehead describes the subject as a “superject”. To describe the subject as a “superject” is to describe it as the result or product of the process by which it is formed and the manner in which it internalizes its relations to the rest of the world. Likewise, Deleuze, in his account of individuation, understands individuation not as the question of the criteria by which one entity is distinguished from another, but rather as the genesis of an individual from what he calls a “transcendental field” or its relations to the world about it. In each of these cases we’re presented with a genesis of cognition and certain structures of thought that both allows us to maintain a realist theory of spatial and temporal properties belonging to things-themselves and an account of how something like a priori knowledge or knowledge prior to and even independent of givenness is possible. These mathematical structures of cognition, resulting from evolution, could be very simple and minimal. All that would be required are a few minimal or rudimentary structures upon which more complex forms of mathematics could be built. In this way, we wouldn’t have to make the sharp sacrifice of Kant’s Copernican revolution.