Metaphysics of Richard Healey

University of Arizona


Is there a vacuum in nature? This is a question which preoccupied natural philosophers for millennia. Great thinkers including Democritus and Newton maintained the existence of a vacuum, while Aristotle, Descartes and Leibniz argued strongly that there was not, and perhaps could not be, any such thing. A casual glance at the literature of contemporary physics may leave the impression that scientific progress has produced a definitive positive answer, so that the philosophers' debates are now of only historical interest. Not only is the attainment of high vacua a multimillion dollar industry, but almost every text and research paper in theoretical high energy or condensed matter physics or cosmology includes multiple references to the vacuum and its often surprising properties. And yet we have it on the authority of no less a scientist than Einstein himself that his general theory of relativity vindicates Descartes' conclusion that there could be no vacuum since the idea of space without matter is unintelligible! Does this mean that there is after all no scientific consensus on this issue, and that the ancient philosophical debate should simply be resumed with renewed vigor? I shall argue that it does not. The progress of physics has given rise to such a proliferation of different (though related) uses of the word 'vacuum' as to irretrievably alter the terms of that debate. Rather than asking whether there is a vacuum in nature, one should ask how well what counts as the vacuum in some physical theory represents reality. This in turn splits up into a semantic question (What aspect of which model counts as the vacuum in this theory?) and an empirical question (How strong is the evidence that nature is faithfully represented by this aspect of the model?) I shall focus mainly on the prior, semantic question here.

While it is often unclear whether contemporary physicists are talking about the same thing as their illustrious predecessors, there are times when they are clearly not talking about the same thing as each other. But this rarely leads to confusion because the role of the term 'vacuum' is sensitive to its context of use in such a way as to effectively eliminate ambiguities in its intended reference. Arguably, the progress of science has led to increased knowledge about the nature of so-called natural kinds such as water or gold, while the terms 'water','gold' referred to the very same things throughout this progress. But 'vacuum' is not a natural kind term: while constrained by a rough root meaning, and guided in its development by certain vague principles, neither its intended referent nor its precise semantic role has remained fixed as physics has progressed.

One significant change in semantic role is particularly worth noting. In contemporary theoretical physics, the term 'vacuum' is typically used to refer not to something in the physical world, but rather to a feature of a theoretical model irrespective of its relation to the physical world. Since this is not a straightforward referential use, it poses no substantive question as to whether the vacuum 'exists'. The term 'vacuum' is here used to describe an element of physical theory rather than an element of reality, so one might take it to be part of a physical metalanguage, and in that sense a term of metaphysics. I would therefore hope that the present investigation into the metaphysics of emptiness is just the sort of study of the language of science of which even a positivist like Carnap would have approved.

Intuitively, a vacuum is what is left when all matter (invisible as well as visible) is removed from a region. This goes along with an intuitive idea of what counts as matter, and what counts as a region. Thus, when a long tube full of mercury is inverted above a vessel of mercury, the level of mercury in the tube may be seen to fall to a level no higher than about 98 centimeters above the surface of the mercury in the vessel. Historically, those disputing the existence of a vacuum took it that the part of the tube higher than 98 centimeters above the level of the mercury in the vessel contains a vacuum just in case it contains neither residual mercury nor any other subtle form of matter. Thus one reason today to doubt that there is a true vacuum in the tube is the presence there of a small amount of mercury vapor. Now the ancient atomists would have argued that at any time there is indeed a vacuum in the tube above the level of the liquid mercury, namely that region not then occupied by any atoms (of mercury, or of anything else). For they took it that all matter is composed of atoms, in the spaces between which is the void. On this conception, there is even a vacuum in the lower part of the tube, in between the atoms of liquid mercury.

Aristotle, of course, rejected this conception. He maintained on the contrary that the world is completely filled with continuously divisible matter. On this view, as the mercury level drops in the tube, its place is taken by some more subtle form of invisible matter. Aristotle based his denial of the existence of a vacuum on his theories of place and of motion.

Here is one Aristotelian argument against the possibility of a vacuum. For Aristotle, every distinct real object exists somewhere--i.e. in some place: therefore there are places. But what is a place? According to Aristotle, the place of an object is the boundary of its closest containing object: he accepts the implication that the universe as a whole is not in any place. Now if there were a vacuum in some container, then two small solid spheres inserted into that container would occupy the same place, since the inner wall of the container would constitute the boundary of the closest containing object of each. But this leads to the absurd conclusion that two distinct objects could be in the same place at the same time. Hence there can be no vacuum.

Aristotle maintained that if left to itself each element would naturally move to its natural place (earth downward, fire upward, for example). This ascribes distinct powers, not to distinct regions of some kind of absolute space, but to distinct places. He also argued that since the speed with which such motion occurs is inversely proportional to the density of the medium through which the moving object passes, the existence of a vacuum would have the absurd consequence that an object moving through it would move infinitely fast.

Descartes' own formulation of the law of inertia committed him to rejecting this last conclusion, but he too denied the possibility of a vacuum, this time because it was inconsistent with his conception of matter. Since he took it that to be material just was to be extended, the concept of a vacuum--something that was extended but empty of matter--was simply incoherent. Of course, his denial of a vacuum then meant that the law of inertia lacked any possible application!

It is with Newton that the law of inertia first becomes integrated into an explanatorily powerful mechanics, and it is no coincidence that Newton accepted the possibility of a vacuum. For him, absolute space exists over and above any material objects which may be located in it, and any region in which there are no such objects therefore constitutes a vacuum. Indeed, in unpublished writings Newton even entertains the possibility that material objects themselves are nothing but regions of space endowed with impenetrability. On this view, space is the fundamental entity, and a vacuum is simply any region of space not endowed with the characteristics that would render it material.

Leibniz famously rejected any such absolute space, and his conception of a vacuum was accordingly rather different. As a relationist, he believed that space was not an object at all, but simply a system of relations among material objects. On his conception, a vacuum would exist just in case the spatial relations between existing bodies were such that it was possible that some body should bear certain specific spatial relations to existing bodies, even though no actual body did so. Unlike Aristotle and Descartes, therefore, Leibniz found room for the notion of a vacuum in his system. But he then appealed to the alleged empirical impossibility of producing one in support of his denial that there actually is any vacuum in nature.

This rapid historical survey already makes clear that whether one accepts that there is a vacuum in nature depends critically on how one understands the notions of matter, space and emptiness. The development of physics since Newton has brought with it transformations in all three of these concepts.

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