A brief history of space

If Stephen Hawking could write A Brief History of Time, I can surely write a brief history of space. Indeed, I’ll one-up Hawking and make my monograph actually, and not just putatively, brief.

At first glance in our little history of space, we can follow a trajectory from Democritus and Plato’s view of space as a container, to a view of space as a relation between things rather than a container (Leibniz), and finally to a view of space as a purely subjective construct – a way of organizing the world rather than a thing in the world (Kant – and I’ll welcome comments from expert readers like the ever-helpful STEVE MORRIS on the extent to which this continues into Einstein and modern physics).

Democritus and Plato both saw space as a receptacle but in quite different ways. Democritus (5th century BC) famously said, “Nothing exists except atoms and empty space.” This sense of space as a universal void is perhaps still the most common sense of the term. In Timaeus, Plato specifically calls space “a receptacle,” but he seems to mean it in a more local sense, as that which houses a series of shapes. In a weird way, space is matter to Plato, per his example of gold. You see now a pyramid of gold, then a cube of gold, then a sphere of gold. The gold is the receptacle space inhabited by the succession of different shapes. Idiosyncratic maybe, but more of that later.

As we move toward what I perhaps simplistically call the Leibniz position, space is not a receptacle at all – not the local matter that houses shapes nor the void. It is rather a relation between things, and it has no existence other than as a relation between things. Then onto Kant, and space as purely a subjective way of organizing the world. It seems at this point that we’ve come a long way from Plato, but the canny Greek has a way of coming back (nb. Alfred North Whitehead’s comment that all of Western philosophy is “a series of footnotes to Plato”).

I’ll step back to Plato by way of a convenient half-way point – Boethius (late 5th/early 6th century, on the cusp between classical and post-classical culture, roughly 1000 years after Plato and 1500 before us). To quote my fine former post on Boethius, who wrote The Consolation of Philosophy while in prison pondering his forthcoming execution, “The relationship between the ever-changing course of Fate and the stable simplicity of Providence is like that between reasoning and understanding … or between the moving circle and the still point in the middle.”

That image of the circle, of seeing reality from two points of view – the still point in the middle and the moving point along the perimeter – can be applied to both time and space. Here, it more directly applies to time. From the point of view of eternity (the still point in the middle), all things are simultaneous. From the temporal point of view (moving along the perimeter), we see reality in its aspect of “always becoming,” as philosophers have called it.

To extrapolate, from the eternal point of view, time does not exist; similarly, from the infinite point of view, space does not exist. Rather, space only exists where that dynamical relation between things exists – distance and extension only make sense within the scope of finite reality.

So is Boethius the great Hegelian synthesizer who can push the dialectic between Plato and Kant forward (thesis – antithesis – synthesis)? Or is the double vision of Boethius merely an indicator of his historical moment, one foot dancing with the wine-bibbing Greek and the other tiptoeing toward the finicky Prussian? Is he just a midway point toward our more accurate modern view?

No, the midpoint reading won’t do. On some level, Plato anticipated the whole circus. Or, to further twist the metaphor, we have circled back to Plato. In the Timaeus, Plato, like Boethius, has a double view, though it plays out a little differently. In Plato, there are two primary levels of reality (which can be further subdivided, as in the myth of the cave): “that which always is and has no becoming” and “that which is always becoming and never is.” The realm of eternal, unchanging ideals (being) is the subject of rational knowledge, whereas the visible world of the senses (reality in its aspect of “always becoming”) is the subject of empirical knowledge. Plato notably privileges the rational side, but he at least here grants the empirical its purview. And this turns out to be crucial to our present argument.

If we focus the history of ideas on the world of becoming – the physical world, we might call it – we can, to recap, follow a movement from space as a container to space as a relation between things  and finally to Kant’s purely subjective construct.

But if we look at the other realm in Plato, the realm of being, the intellectual realm of the unchanging ideals, rather than the realm of becoming, we see that he had already recognized space as an imaginary construct.

He quite explicitly says that the concept of “space” does not apply in the intellectual realm, but is only needed to accommodate the dynamics in the realm of becoming.

Indeed, some time after introducing those two realms (the realm of being and the realm of becoming), he refers back to the two natures corresponding to the two realms: “one … was a pattern intelligible and always the same; and the second was only the imitation of the pattern, generated and visible.” Then he adds: “Now a third must be revealed … the receptacle, and in a manner the nurse, of all generation,” insofar it enables all the processes of generation or becoming to happen.

The “receptacle,” whether you call it space or matter, is only introduced as a way of explaining processes in the realm of becoming.  But the realm of becoming for Plato is the realm of more-or-less degraded knock-offs from the realm of being. When reality is seen in it most true and stable aspect, the ontologically prior realm of being, space (or matter) does not exist.

Now, one could argue that the spaceless, timeless, immaterial zone of true reality (prior to all the knock-offs in the realm of becoming) in Plato is not truly subjective as in Kant, that Plato imagines this reality as objective reality. To which I say, maybe. I’m not sure how truly significant that distinction is. I don’t think Plato would call it objective in the modern sense of objective (which implies physical, spatial reality). All Plato postulates is that the spaceless, timeless realm of pure being, pure forms, is the true base of reality. That he treats it as an intellectual realm as opposed to the sensible is clear – so does that imply that it IS subjective, as in Kant? I’m not sure but, back to Alfred North Whitehead: we are quibbling about footnotes here. Face it, everyone (especially angst-ridden academics seeking tenure) wants to find the next ground-breaking idea, but it’s still hard to beat the old Greeks. See my other fine post on Aristotle, Wittgenstein, and Identity Politics if you don’t believe me.

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A Defense of Plato

Dear MT,

Per your comparisons, I don’t think Plato is as eager as Nietzsche or Kierkegaard (or perhaps MT) to separate men into two groups and condemn the ignorant masses. Plato’s myth of the cave is more about PROCESS than about passing judgment on the ignorant. It’s sort of like a rational correlative to the Buddhist process of enlightenment. We ALL resist the truth when it first dazzles us and we’re used to shadows. Plato’s myth is about the process we ALL have to go through if we want to achieve enlightenment. And yes, some are not strong enough, some have to turn back. But for Plato I think all rational beings have the capacity if they can find the fortitude. And he quite explicitly says that the enlightened ones should go back and help those who are still in the cave. In this sense he’s more Buddhist and less condescending than Nietzsche and Kierkegaard (especially Nietzsche in my estimation). In this process-orientation, Plato is actually not far from Aristotle’s notion of entelechy, where all things strive unconsciously toward their ideal destination, like the acorn strives toward becoming the oak. In fact, the wedge between Plato and Aristotle is somewhat forced. They have different emphases, yes, but they share a lot of fundamentals. Aristotle learned his Plato well.

In metaphysics, I think your resistance to Plato is a resistance to a straw man version of Plato – as if his formal world is like the Christian God with the beard who sits somewhere in physical space. I find it hard to believe Plato would be so naïve. He is just saying, in the cave and elsewhere, that there is an intellectual reality, a kind of Jungian collective unconscious, which is a hidden prerequisite to all the contingent truths we find in our everyday (transitory) reality. Whether we realize it or not (and most of us don’t), the contingent truths we structure our daily lives by would not be intelligible were they not undergirded by that collective unconsciousness, that conceptual substrate of deeper truths. And the deeper we dig, the closer we get to eternal truths and the more deeply we understand the prerequisites of our surface knowledge.

So you’re right that your idea of a perfect car may not match my idea of a perfect car, but were it not for some abstract concept of perfection implicitly acknowledged by both of us, neither of us could have ANY idea of a perfect car. The concept of perfection is a presupposed premise of your idea and my idea. So now we can talk about a concept of perfection that, albeit abstract, is a necessary prerequisite to our contingent and various concrete ideas. Now we can ponder things at a deeper level, and delve dialectically deeper into the roots of our own consciousness. That’s what Plato is all about.

Re politics, of course Plato’s politics does sort men, but the sorting is not as damning as in Nietzsche. He just says that few men will find their way out of the cave and stay out, and those should be our leaders. And he is undemocratic in the sense that he seems to believe that order requires hierarchy – a practical consideration more than an existential judgment about master and slave races a la Nietzsche. We moderns tend to dismiss hierarchy as a prerequisite to political order, but go back just to the late 18th-century Enlightenment and you will still find strong and intelligent voices (e.g., Edmund Burke, Samuel Johnson) arguing that without hierarchy is chaos. So I don’t agree with Plato here, but I’ll give him a pass on politics. (From what I hear, Rebecca Newberger Goldstein’s new book, Plato at the Googleplex, presses Plato harder on the human implications of his politics, but I haven’t had a chance to read it yet.) Anyway, as I’ve said, I don’t think politics is the most compelling branch of his philosophy, but I still agree with Bertrand Russell’s mentor, Alfred North Whitehead, that “Western philosophy is a series of footnotes to Plato.”

And with due respect to Nietzsche’s wit, I think Plato would be the more amiable drinking companion.