Secretum secretorum - De Mirabilibus Mundi - Terrestrial
Background for Ars Magica sagas

The Physics of the Sublunar Region:
Combination and Mixture

One very important class of phenomena to which the theory of matter, form and substance was applicable was that associated with what we would today call "chemical combination." The centrality of this class of phenomena is apparent when we recall that, according to Aristotle, all substances encountered in the real world, including organic tissues, are compounds of the four elements. It comes as no surprise, therefore, that Aristotle should have inquired into the nature of chemical combination and the status of the original ingredients in a compound. He distinguished between a mechanical aggregate, in which the small particles of two substances are situated side by side without loss of individual identity, and a true blending of the ingredients into a homogenous compound in which the original natures disappear; he called the latter a "mixt" or "mixture" (we will employ the Latin terms mixtio for the process and mixtum [plural, mixta] for the product, in order to preserve the technical meaning that Aristotle had in mind), and it is this kind of combination that he considered applicable to the mixing of the elements.

In a mixtum, according to Aristotle, the individual natures of the ingredients are replaced by a new nature that permeates the compound down to its smallest parts. The properties of the mixtum represent an averaging of the properties of the ingredients. If, for example, we combine a wet and a dry element (say, water and earth), the wetness or dryness of the resulting compound will fall on the scale that runs between the extremes of wetness and dryness, at a point determined by the relative abundance of those two qualities. Although the original elements no longer have actual existence in the mixtum, Aristotle made remarks that suggested that they remain a virtual or potential presence that permits them to exercise some kind of continuing influence.

Aristotle's discussion left a number of problems for his commentators. One was to recast the theory of combination or mixtio in the language and conceptual framework of matter and form, for those terms do not appear in Aristotle's account. In the course of that effort it was necessary to inquire how the new substantial form of the mixtum emerges from the forms of the constituent elements. Another problem of critical importance was to determine in what sense the forms of the original elements continue to exist in the mixtum; since it was acknowledged that when the mixtum is destroyed the elements of which it was formed reappear, it seemed evident that they survive in some way within the mixtum. Debates on these matters became extremely intricate, and we must limit ourselves to a few remarks.

Everybody agreed that the substantial forms of the constituent elements are replaced by a new substantial form of the mixtum. Yet how does this come about? It was generally agreed that the way was paved for the emergence of the new substantial form by the mingling of the elements, the interaction of their respective qualities, and possibly the corruption of their substantial forms. However, there was good reasons (drawn from Aristotle) for believing that the new substantial form could not be generated out of these antecedent substantial forms or out of the qualities of the original elements; outside intervention seemed to be required. The usual solution was to invoke higher powers -- celestial forces or celestial intelligences, possibly even God himself -- assigning to them the responsibility for infusing the new substantial form into the primary matter when the preconditions had been met.

As for survival of the elements in the mixtum, everybody saw that it was necessary to find some way of allowing the elements to lurk in the mixtum potentially or virtually, awaiting a suitable opportunity to reveal themselves. Avicenna argued that the forms of the elements survive intact, while their qualities are weakened to the point of insensibility. Averroes maintained that both the forms of the elements and their qualities are reduced in strength or intensity and maintain a potential existence within the mixtum. Since, according to Aristotle, substantial forms do not admit of degrees -- that is, cannot be strengthened or weakened (after all, a given four-legged mammal is either a dog or not a dog; in this context talk of more and less makes no sense) -- Averroes concluded that the forms of the original elements must not be substantial forms but have a status between that of substantial and accidental form. Thomas Aquinas (ca. 1124-74) argued that the forms of the elements are extinguished in the process of mixtio, but that their qualities retains some kind of virtual influence in the mixtum. These and other positions became the basis of lively debate among late medieval natural philosophers.

A final question with which me must deal has to do with the physical divisibility of corporeal substances -- say, wood or stone or organic tissue. Is there a limit to the process of division, and what are the properties of the smallest pieces? Are they anything like atoms (here I refer to the ancient Greek concept, not the modern)? Aristotle had alluded to the smallest pieces of the ingredients of a mixtum, which mingle and interact, and on these remarks subsequent commentators based a theory of what came to be called minima or minima naturalia (smallest natural parts). The theory acknowledged that in principle divisibility should be endless; however small the piece before you, there is no physical reason why you cannot divide it again. However, it was argued that there is nonetheless a smallest quantity of each substance, below which it will no longer be that substance because the form of the substance cannot be preserved in a smaller quantity.

There were attempts in the Middle Ages to construe the theory of minima as a variant of atomism. It is true that both theories acknowledged the particulate structure of matter, but otherwise they were far apart. The particles of the atomists were unbreakable least parts; the minima of the Middle Ages were divisible, though if divided they would lose their identity. All atoms were of identical stuff, differing only in size and shape; minima were as different as the substances to which they belonged. In the atomist vision, properties in the macroscopic world did not, in general, have exact counterparts in the microscopic world: atomists did not explain the redness of a flower, for example, by the redness of its constituent particles. Rather, the atomist program was the reduce the qualitative richness of the world of sense experience to austere, qualitatively bare atoms (characterized only by size, shape, motion and possibly weight). Minimists, by contrast, continued the Aristotelian program, assigning to the last parts precisely the properties of the hole to which they integrally belonged: minima of wood are still wood.

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Last modified: Sun Dec 27, 1998 / Jeremiah Genest