Space, stuff, and God

Look around : where’s space?

We don’t get any featureless, homogeneous receptacle into which we get to drop cars, photons, and even a void. What we get is a world where, when we look around, everything has something in common, even the atoms and void. We can call this common feature “space”.

That said, in calling it common we hit on something that is just as much space as time. The one is just as common as the other.  Sure, all abstractions are somehow timeless (when is cat or red?) and in that sense space qua abstraction is too, but this is an uninteresting point that tells us nothing about space. The abstraction time is just as timeless, though this obviously tells us only a fact about abstractions, not about time.

Aristotle thought that this common thing was finite and ended at a crystalline sphere pock-marked with stars. It was nonsensical and contradictory to speak of what was “outside” of this. For him, this common feature of things interacted to form a spherical structure, and its primary job was to give things location. Location in turn was seen as the defining feature of natural substances: fire jostled its way towards the circumference, earth burrowed its way toward the center, and all the other elements depended on these locations to act and move and give rise to things.

Newton in one sense intensified and absolutized this account and in another sense threw it out. He thought that location was critical to nature, but that no given set of concrete objects could be responsible for it. His solution was to make location the result of an interaction between an abstraction and the concrete world, though he called the abstraction absolute. The conceptual problems with an abstract entity giving rise to a concrete location are, however,  insurmountable – it’s literally like asking how far it is from London Bridge to the Pythagorean theorem. It was certainly a conceptual muddle that proved easy to work with since there’s nothing easier than to imagine London Bridge in Euclidean space, but it was nonsense all the same.

That’s not right. Newton understood what one was committed to in saying that the abstract acted on the concrete, sc. that the abstraction would have to be concretized in an entity that, by definition, would have to transcend the difference between the abstract and concrete. This makes it self-evidently beyond all language (we have no nouns that are beyond the abstract and concrete) beyond conceptualization, and most of all beyond the existence within the very natural universe the being was invoked to explain. Absolute space and time had to be God. The theology in the Principia is more than the last scholium and more than just a hypothesis to account for the initial conditions of the planets. Newton knew very well that absolute space wasn’t some featureless, inert blackboard. In fact, he knew it couldn’t be space. His followers either forgot this or thought it was the musings of a crank.

But we still haven’t quite gotten rid of this idea of abstractions interacting with concrete entities – the axiom that “space tells matter how to move, matter tells space how to bend” suggests the same confusion even while it doesn’t require it. All  that seems to be involved is that the common feature in things allows for divisions that in turn allow for interactions, which is exactly what one would need in order to have physics at all. That said, Newton’s absolute space was not not so much done away by space time as re-defined. The Cartesian grids of action are still integral to the account of what is going on.


  1. William Farris said,

    September 2, 2015 at 6:55 pm

    Classically, abstract objects apparently have no causal relation to anything. Concreta, however, do. Space seems not to be in the set of causal entities, nor is time. Therefore, space is an abstract object on that basis (of being non-causal). And so is time. Thus, space and time are abstract objects that do exist in reality: space-time exists in and of itself. So I think we have at least 2 abstracta that exists outside of minds. More generally, realism has a huge advantage over anti-realism. This opens the possibility that other things in the great platonic pantheon of abstract objects (numbers, properties, propositions, etc.) also have an independent existence now that causality can be shown to be an illegitimate criterion for differentiating abstracta from concreta. Repondez…

  2. September 3, 2015 at 11:55 pm

    Concrete ground inducts abstract potential says Faraday.

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