Jeremiah Genest
Date: 8/17/98 6:19 PM

A great deal of recent discussion has been about the elements and the need
for requisites. In particular whether ice needs a Terram requisite or is
even Terram. I would like to view this process by looking at the subject
the way a medieval scholar would, and thus what I would consider an opinion
your average mage would hold.

First I will consider Plato. Until the thirteenth century Plato dominated
the Medieval world (and the world of late antiquity before that). Bonisagus
would certainly have been aware of Plato (or the Latin redactions of his
thought). Furthermore, Hermetic theory shows a heavy bias toward Platonism,
especially in its use of the Realm of Forms, not only for Creo but
throughout the published material. Rather than give a long essay on Plato's
realm of Forms and his cosmology, I will instead focus on his idea of
elements. More detailed information can be acquired elsewhere.

For Plato the cosmos was constructed on geometrical principles. He took
over the four roots or elements of Empedocles: earth, water, air and fire.
Under Pythagorean influence, he reduced them to something more fundamental
-- triangles. He thus formulated a "geometrical atomism." As
two-dimensional figures, triangles are of course incorporeal; however, if
suitably combined, they can be made into three-dimensional corpuscles, each
different shape corresponding to one of the elements. There are five, and
only five, regular geometrical solids (symmetrical solid figures formed of
plane surfaces, all identical); these are the tetrahedron, the cube, the
octahedron, the dodecahedron, and the icosahedron. Plato associated each
element with a figure -- fire with the tetrahedron (the smallest, sharpest
and most mobile of the regular solids), air with the octahedron, water with
the icosahedron, and earth with the most stable of the regular solids, the
cube. Finally, Plato found a function for the dodecahedron (the regular
solid closest to the sphere) by identifying it with the cosmos as a whole.

This scheme allows the elements to mix in various proportions to produce
variety in the material world. More importantly for Ars Magica, it allows
for transmutation of the elements from one to another, thus accounting for
Muto spells (and other magics). For example, we can dissolve a single
corpuscle of water (the icosahedron) into its twenty constituent
equilateral triangles, which can then recombine, into, say, two corpuscles
of air (the octahedron) and one of fire (the tetrahedron). Only earth,
which is composed of squares (and the square divided diagonally does not
yield equilateral triangles), is excluded from this process of
transmutation. Furthermore, note that ice was always considered a water.
Plato pointed out that an icosahedron (or an octahedron) for that matter
cannot be broken down into a square. Thus ice is just water that is at
rest. At no point does he ever confuse it with earth. Nor will you find a
single platonic thinker who would hold this (neither middle, neoplatonism
nor any other Platonism).

After the reception and assimilation of Aristotle's philosophy in the
twelfth and thirteenth centuries, the principles in question were broadly
Aristotelian - though obscurity, incompleteness and inconsistency in the
various Aristotelian texts where these principles were set out left plenty
of room for further articulation of the theory and for discussion and
debate about the fine points. Let us begin with a brief review of some of
the basics of Aristotelian natural philosophy.

According to Aristotle, all objects in the terrestrial realm ("substances"
he called them) are composites of form and matter. Form, the active
principle or agent, bearer of the properties of the individual thing,
combines inseparably with matter, the passive recipient of the form, to
produce a concrete corporeal object. If the object in question is a
"natural" object (as opposed to one produced artificially, by an artisan),
it also has a nature (determined primarily by its form but secondarily by
its matter), which disposes it to certain kinds of behavior. Thus fire
naturally communicates warmth, rocks naturally fall (if lifted out of their
natural place), babies naturally grow and mature, and acorns naturally
develop into oak trees. These natures we discern through long and
persistent observation: whatever cannot be the product of chance (because
of the regularity of its occurrence) or of artifice (because no artificer
had anything to do with it) must be the result of nature. Because natures
are the determining factors in all cases of natural change, they are
necessarily of great interest to the physicist or natural philosopher.

Aristotle's medieval followers, contemplating this scheme, identified two
kinds of forms - one of them associated with essential properties, the
other with incidental properties. The defining characteristics of a thing,
which make it what it is, are conveyed by what came to be called its
"substantial form." Substantial form combines with absolutely propertyless
first matter to give being or existence to a substance and to endow it with
those properties that make it the kind of thing it is. However, besides
essential properties, every substance also has properties of an incidental
or accidental sort, associated with "accidental form." Thus the family dog
may be short-haired or long-haired, lean or fat, friendly or ferocious,
housebroken or not, and yet it retains the characteristics (supplied by its
substantial form) that enable us to identify it unmistakably as a dog.

Aristotle's theory of form, matter and substance is nicely exemplified in
his theory of the elements. Aristotle accepted the position of his
predecessors, Plato and the pre-Socratics, to the effect that the familiar
materials or substances of everyday experience are complex rather than
simple. That is, sensible things in the sublunar world are compounds or
mixtures, reducible to a small et of fundamental roots or principles,
called "elements." Aristotle adopted Empedocles' and Plato's list of four
elements - earth, water, air and fire - and argued that these combine in
various proportions to produce all of the common substances. Aristotle
agreed with Plato that the four elements are not fixed and immutable, but
undergo transmutations; and the scheme that explained how this was possible
was his theory of form and matter.

Each of the elements, he argued, is a composite of form and matter; since
the matter in question is capable of assuming a succession of forms, the
elements can be transformed onto one another. The forms instrumental in
producing the elements are those associated with the four primary or
"elemental" qualities: hot, cold, wet and dry. Primary matter informed by
coldness and wetness yields water; and so forth. This primary matter has
the capacity to receive any of the four elemental qualities. Therefore if
the quality of dryness in a piece of the element earth yields to wetness
through the action of a suitable agent, that piece of earth will cease to
exist, and an appropriate amount of the element water will take its place.
Aristotle argued that such transformations are occurring constantly, and
the elements are therefore constantly being transmuted one into another.
Changes of this kind proved capable of accounting for many of the familiar
phenomena that we associate today with the disciplines of chemistry and
meteorology.

The basic form-matter theory was easily understood, but its application to
the real world posed a variety of problems. The world seemed to contain a
hierarchy of forms and matters, and the Aristotelian definitions outlined
above worked better at some levels than at others. Aristotle's definition
of matter as the totally unqualified recipient of forms applies nicely to
the constitution of the elements: the matter that receives the elemental
forms of the primary qualities (hot, cold, wet, dry) is totally without
properties of its own, apart from the ability to receive the elemental
forms. Of itself, it is imperceptible, unknowable, and without actual
existence. Aristotle, referred to this as "primary matter." Accidental
forms are imposed on matter that already has independent, substantial
existence: the marble out of which a statue is to be made exists as a
concrete thing, with a variety of properties (size, shape, color, density
and hardness), before the sculptor endows it with the accidental forms that
make it into a specific statue. In the same way, the hair that turns gray
(thus serving as the matter for the accidental form of grayness) was
already a substantial thing, with specific, identifiable characteristic,
before it changed color. Reflection on problems such as this caused
Aristotle's ancient and medieval followers to sharpen his definitions and
to clarify the distinction between the insubstantial primary matter of the
elements and the substantial secondary matter encountered in cases of
accidental change.

The matter-form theory was elaborated in Islam by Avicenna (Ibn Sn,
980-1037) and Averroes (Ibn Rushd, 1126-98) in ways that would prove
influential in the West. The two Muslim commentators thought it impossible
to derive the elements from the imposition of the elemental forms directly
on primary matter. An intermediate step was required, which would first
invest the primary matter with three-dimensionality. To this end, they
developed the notion of "corporeal form," which must first be imposed on
primary matter to yield a three-dimensional body. The elements emerge,
then, when this three-dimensional body (a kind of secondary matter)
receives the elemental forms. The idea of corporeal form was transmitted to
Christendom, where it proved both influential and controversial. Robert of
Grosseteste adopted this position when he identified corporeal form with
light.

Aristotle had placed form and matter on essentially equal footing - neither
was subordinate to the other, and each had its function - but this balance
proved difficult to maintain. Within the Neoplatonic tradition (Avicenna is
a good example) there was a tendency to demote matter, to see it as virtual
nothingness, while elevating form to a position of quasi-autonomy.
Avicenna's younger contemporary Avicebron (d. 1058) veered in the other
direction, elevating matter at the expense of form. Avicebron's influence
may help to explain the willingness of Western scholars (especially
Franciscans, such as Richard of Middleton and Duns Scotus) to argue that
God can create matter without form.