The early modern period saw a great interest in trying to give an explanation of space. Probably the most famous are those of Descartes (a continuum of physical extension or body), of Newton (presentation in the immobile divine sensorium), and of Leibniz (a system of relations between substances), and of partisans on different sides of the dispute, but there are quite a few attempts to look at the topic in a different way. One interesting one that has not been looked at in any detail is that Catharine Trotter Cockburn, who is unusual in that she is a rationalist with a strong Lockean influence.
Cockburn's suggestion for understanding space starts with Locke in a place that you might not expect. In the Essay (Book III, Chapter VI, Section 12), Locke has an argument for angels: "in all the visible corporeal world, we see no chasms or gaps" so that "we shall find everywhere that the several species are linked together, and differ but in almost insensible degrees", so we have reason to think there are probably numerous kinds of minds more perfect than our own:
And when we consider the infinite power and wisdom of the Maker, we have reason to think that it is suitable to the magnificent harmony of the universe, and the great design and infinite goodness of the Architect, that the species of creatures should also, by gentle degrees, ascend upward from us toward his infinite perfection, as we see they gradually descend from us downwards: which if it be probable, we have reason then to be persuaded that there are far more species of creatures above us than there are beneath; we being, in degrees of perfection, much more remote from the infinite being of GOD than we are from the lowest state of being, and that which approaches nearest to nothing. And yet of all those distinct species, for the reasons above said, we have no clear distinct ideas.
Cockburn takes the underlying idea of a "great chain of beings" (her phrase) and adapts it in a different direction. We have reason to think there are bodies, i.e., material substances, and minds, i.e., immaterial substances, and there are obvious obstacles (as noted by Descartes and others) to reducing one to the other. But this is quite a sharp division -- there appears to be a chasm between senseless material substance and intelligent immaterial substance, and if we do not find chasms in nature, then we would expect some spectrum of gradation between them -- which would have to be something like each. This is Cockburn's suggestion for the nature of space: "an immaterial unintelligent substance, the place of bodies, and of spirits, having some of the properties of both" (p. 97). However, as with Locke's gradation argument, Cockburn's gradation argument on its own gets us something for which we don't have a clear idea.
Obviously a major concern with understanding this proposal is what Cockburn means by 'substance' and, unsurprisingly given the rest of her argument, what she has in mind is a Lockean notion of substance as an unknown something to which qualities may be attributed; as Locke says (Essay Book II, Chapter XXIII, Section 2):
The idea then we have, to which we give the general name substance, being nothing but the supposed, but unknown, support of those qualities we find existing, which we imagine cannot subsist sine re substante, without something to support them, we call that support substantia; which, according to the true import of the word, is, in plain English, standing under or upholding.
This is, Locke says, an "obscure and relative" idea; we know that there has to be something to which we are attributing the qualities, but as we only know of this something indirectly, by knowing that we can attribute these qualities to it but can't just be the qualities themselves, it is a we-know-not-what. It's this that Cockburn has in mind. That might seem very weak, but in fact one of her concerns is to deny the view that space is nothing at all, or else just something in the mind; on the contrary, she argues, space is real and has qualities attributable to it. We don't know much more about it than this, but the qualities it does have would make it fit right into the gap between mind and body, as a real thing that is not material (and thus not a body) and yet not intelligent (and thus not a mind).
To argue this she needs more than just the argument from gradation, because a very common position historically is that any immaterial substance would ipso facto be an intelligent substance. (Of course, historically, most of the people who held this had a much more robust conception of substance than Locke does.) Cockburn thinks that the standard (broadly Cartesian) arguments that all thinking substances are immaterial are probably right, although like Locke she holds that we can't rule out that God could create thinking matter, but she denies that immateriality implies thinking. This makes sense given the Lockean conception of substance: immateriality just tells you the kind of qualities not attributable to the unknown something that is mind (it's not a shape, it has no length, it has no resistance, etc.); nothing requires that this implies that the only qualities that can be attributed to an immaterial substance are cogitative.
On the basis of this, Cockburn is inclined to be skeptical of the common view at the time that space is infinite -- the only infinity that could be relevant is a negative infinity of having no bounds, and this seems to be the sort of thing that only applies to things that are abstract (number, mathematical extension, etc.), not something that can be attributed to a "real actual complete existence" (p. 105). What leads people to call space infinite, Cockburn thinks, is that it is indefinite -- we don't know what could be setting bounds to space itself. But this is a claim about what we can conceive, not about space:
As I cannot conclude space to be nothing, because we know not what it is, neither can I conclude it to be infinite, because we are ignorant what can set bounds to it. May there not be many ways of setting bounds to space, that we know nothing of? It may be bounded by its own nature, or by the will of God, or by some kind of beings, that we are not acquainted with. (p. 105)
Thus, since there may be things that can bound space, and negative infinity seems only to apply to abstract objects like number, not real particular existences, she thinks we have no reason to call space infinite. She notes, though, with some amusement, how much out of our depth we are in discussing it, given that some people have claimed that space is nothing, others that it is infinite, and yet others that it is divine; it is certainly a remarkable thing that some have argued that it is not real and others that it is supremely so!
[Catharine Trotter Cockburn, Philosophical Writings, Sheridan, ed. Broadview (Peterborough, ON: 2006).]
Various Links of Interest
* Sabine Hossenfielder, Hawking temperature of black holes measured in fluid analogue, explains an interesting example of experiment-through-analogy.
* Edward Conze: A Study in Contradiction, at "Jayarava's Raves"
* Catarina Dutilh Novaes has an interview on the radio program, "The Philosopher's Zone", on mathematical proof and beauty.
* James V. Schall, Understanding Law with Thomas Aquinas
* Dan Hitchens, Ex-FBI agents to help investigate Cardinals on abuse and corruption. Something like this is certainly necessary; it has to be done properly, but something like it is needed. There were some people claiming that this would be in violation of article 80 of Universi Dominici Gregis; but this is obviously absurd -- the relevant section only addresses people involved in papal elections, and only prevents them from actions that suggest that civil authorities have the right to exercise some kind of veto in papal elections, so it is not even remotely relevant. Nor, contrary to some reporting elsewhere, does the explicitly stated plan seem to be to try to influence papal elections to begin with: the planned report is supposed to be on voting members of the College in general. But if this does manage to get off the ground, I suppose we can expect some bishops trying to claim it is a canonical violation. I would prefer something with more oversight than this seems likely to have, though.
* David Oderberg, Opting Out: Conscience and Cooperation in a Pluralistic Society
Jules Verne, Family without a Name
Jean-Luc Marion, Being Given
Catharine Trotter Cockburn, Philosophical Writings
Lloyd Humberstone, Philosophical Applications of Modal Logic
Jules Verne, In Search of the Castaways