The Euclidean Geometry objection
In the Transcendental Aesthetic, a fairly important passage in the Critique of Pure Reason; Kant asserts that space and time are pure forms of intuition; that is, pre-experiential modes of perceiving reality; so, to talk about time and space like they are things in the world is to confuse what it is to experience the world. Space and time (treated in identical ways); are the ways in which we presuppose the organisation of phenomenal experience. WHen I read this I found this a very very powerful case, I still do, but I also find it very very troubling…because of what we may call the Euclidean geometry objection.
The Euclidean geometry objection goes something like this; Kant’s conception of space and time is such that we have a priori platitudes and ideas about the nature of space and time; time, for example, is one-dimensional, one-way. Space, is an infinite, vast domain, boundless in scope, and indivisible. To say that space is indivisible means that we cannot think of ‘two spaces’, but we think of space itself as a singular, unified concept. We can only break space down in terms of talking about regions of the same space; but there is no such thing as a discreteness of space where there exist two such domains which are the same that we may call space. Space, is the huge infinite vastness that we understand all objects persisting within, and wherein we use relational terms to understand objects (such as, ‘this can is to the left of me’).
There are various problems with this; firstly; is it conceptually absurd to think of space as nondiscrete? It doesn’t offend the imagination, or our very mode of cognition (as Kant would have you believe), if we thought of a discrete and multiplicity of ‘spatial domains’? This sounds like a very weird thing I can argue against Kant about, but…Narnia. Narnia is a world where children go into a cupboard and enter a completely different region, a different set of relations and spatial co-ordinates, almost entirely discrete. I wonder what the status of things like logical possible worlds, or physical alternate dimensions would lie…forget even if they are possible, just think of their conceivability, and we have already struck a arrow into the heart of the argument.
The actual ‘Euclidean’ geometry objection is that, well, Kant’s intuitions about the world are Newtonian, and thus, Euclidean. Kant’s intuitions about space stongly obey the Third and Fifth Postulates of Euclid; the latter of which is deemed false by 19thC geometric notions. The fifth postulate goes something like this; if we have two tangents parallel to each other; they will never meet. Well; we may deny this because we may deny that the tangent is perfectly straight, or that it goes on ad infinitum. We can talk about lines which are elliptical (Riemannian) or hyperbolic. Kant’s so-called a priori necessity claims about space are, by the hand of modern mathematicians and physicists (so I hear…), simply false.
I can imagine a certain philosopher of science colleague of mine saying “metaphysics must be naturalised!”, and “science is what is certain and stops being philosophy!”. It is highly offensive to the scientifically learned philosopher (which isn’t me) to even think of trying to do some physics, or science generally, a priori. I think this is a caricature of Kant, if we dare accuse him of this.
Kant was trying to take his hand in the Leibniz-Clarke dispute about the nature of space; Kant was also a big admirer of Newton, and, like Hume before him, wanted a philosophy of the kind of greatness that Newton had with his laws of motions. Kant’s conception of biology was, perhaps surprisingly, also influenced by Newton; the phrase ‘Newtonian Biology’ refers to the notion that there are mechanistic processes underlying the natural phenomenon of organic life.
I ask this question: can we have intuitions about science? Or, must we make our beliefs fit the empirical data; the latter claim sounds obviously correct…but is it really? We may find that a fundamental part of our everyday discourse and talk is completely false over a scientific explanation; should we then dispel of our beliefs that are pretheoretic? We may say some phenomenon like the reflex arc is non-voluntary, and this may eliminate our intuitions about how we behave when we act in reflex. But how far does the rabbit hole go? How much of our everyday intuitions must we abandon in the name of scientific authority?
What about intuitions in mathematics? what are the status of, say, our intuitions about propositions, the notion of infinity, the notion of space and time itself, truth? Of what is our source by which we appeal to make an analysis; what is it, that we use to understand those building blocks of reality that constitute the abstract, and the concrete?
Michael (and Destre)