A complex of interrelated problems plagued the theory of matter during the seventeenth and eighteenth centuries: problems concerning matter's divisibility, composition, and internal architecture. Is any material body divisible ad infinitum? Must we posit atoms or elemental minima from which bodies are ultimately constructed? Are the parts of material bodies themselves material concreta? Or are they merely potentialities or possible existents? Questions such as these—and the press of subtler questions hidden in their ambiguities—deeply unsettled natural philosophers of the early modern period. They seemed to expose serious conflicts in the most basic metaphysical commitments of the new science. Fundamental doctrines that enshrine the new world-view appeared to be at odds with one another.
The simplest way to introduce this cluster of problems and the antinomies they threaten is by way of a dilemma. (This is also the way most early modern philosophers approached the issue.) We can begin with the fact that bodies occupy space and so are divisible into parts. Bodies—at least the medium-sized ones we are acquainted with in everyday life—are spatially extended: they occupy regions of space; they have volume. As such they are divisible, at least logically or metaphysically. Even if a body's spatially distinct subsections are physically indivisible (that is, they are so tightly bonded that they cannot be broken apart by natural forces), their rupture and separation is at least logically possible. For instance, God could destroy the one subsection while preserving the other, or could separate