The Architecture of Matter: Galileo to Kant (review)

The place of a body, most philosophers will agree, is a region of space. This region, in the opinion of most, can be divided ad infinitum. We can conceive of each part of this region that it has proper parts of its own — at least two — the sum of which is that part. Does it follow that each part of the body that occupies that region likewise has proper parts? Thomas Holden's Architecture of Matter shows how intractable this question was for modern philosophers.

A few philosophers attempted to retain the Aristotelian conception according to which an undivided body has indefinitely many potential parts, but (given that it is actually undivided) only one actual part. This has the advantage of avoiding the paradoxes thought to be associated with the existence of actually infinite aggregates; in an Aristotelian framework, moreover, it is just another application of the fundamental distinction between the actual and the potential. Physical division, like other natural changes, is merely the actualization of potential. The distinction of actual and potential fared badly in modern philosophy, and in the case of material parts it was rejected by almost everyone.

The contrary doctrine holds that the parts of an undivided body are substances on a par with the whole. Division is not the making but only the separation of parts. This "actual parts doctrine" was by far the more popular, so much so that once the Scholastics had been disposed of, philosophers often no longer bothered to argue for it. But once you have plumped for actual parts, you are faced with a choice. Either you agree that the parts of a body are, like the parts of the region of space occupied by the whole, infinite in number, or you take them to be only finite in number. To choose the first was to take on the paradoxes of the actual infinite; to choose the second required one to show that there are genuine indivisibilia without reverting to a doctrine of potential parts. Kant's Physical monadology (1756) and Boscovich's Theory of natural philosophy (1758) attempt to do so: the "atoms" of their system are in each macroscopic body finite in number, and have no metaphysically distinguishable parts, not even potentially. Holden notes that those atoms end up being quite mysterious: a "force-shell atom" has no intrinsic, but only dispositional, properties (271-72); the substratum is a conceptual blank.

If you reject metaphysical atoms, you are left with infinite divisibility. In addition to the lesser-of-two-evils argument, there was a widely accepted argument according to which the formal divisibility of spatial regions entails the metaphysical divisibility of any body occupying such a region. As Holden notes, you must show not only that physical space — identified with the infinitely divisible extension of Euclidean geometry — has an actual infinity of parts, but also that whatever occupies this space must therefore also have an actual infinity of parts. A few philosophers asked whether physical space really is accurately described as consisting in infinitely divisible extension. Most did not. The occupation of space by bodies then seemed to yield a compelling argument for their having infinitely many actual parts, and the task was to disarm the apparent paradoxes of the actual infinite.

Holden's history is what you might call "block history." Dates are minor details; influences are mentioned but not pursued; questions of development are set aside in favor of a systematic exposition of the arguments en bloc. One would like to know, for example, what role the introduction of the notion of force played in making possible the theories of Kant and Boscovich; and whether (as I think) the seventeenth-century demise of Aristotelian form, and consequent troubles attending the notion of substance, help explain why questions on the unity of material substance in particular proved so intractable. On the other hand, I am inclined to think that for this topic the...