## 1. Medieval Physics



For Avicenna, the proper subject of natural philosophy, in its
broadest or most general sense, is body insofar as it is subject to
motion. Beyond general physics (*al-sama'
al-tabi'i*), the physical sciences are
further divided into various special sciences distinguished according
to either the kind of motion investigated or the kind of body treated.
While Avicenna himself does not explicitly identify his decision
procedure for dividing the special natural sciences, it is evidenced
in the way that he divides up the books of his monumental encyclopedia
of philosophy and the sciences, *The Cure
(al-Shifa`)*. For example, his book *On the Heavens
and Earth (Fi l-Sama` wa-l-'alam)* from
*The Cure* generally treats rectilinear and circular motion;
*On Generation and Corruption (Fi l-Kawn wa-l-fasad)*
deals with change as it occurs in the Aristotelian category of
substance, whereas *On Actions and Passions (Fi
l-Af'al wa-l-infi'alat)* concerns how
bodies are affected and affect one another with respect to, for
example, the primary qualities of hot-cold and wet-dry, which they
possess. Avicenna distinguishes additional special natural sciences
according to the specific sort of body being considered, namely,
whether the body is inanimate--generally the subject matter of
*Meteorology* (*al-Ma'adin wa-l-athar
al-'ulwiyya*)--or the body is animate--the subject
of psychology (literally, the science of the soul or animating
principle). Avicenna further divides the study of living bodies into
general psychology (*'ilm al-nafs*), botany
(*al-nabat*) and zoology (*taba`i'
al-hayawan*). The focus of the present study is limited
primarily to Avicenna's general natural philosophy, although at
times the discussion is supplemented with developments in the special
physical sciences.


### 1.1 Physical Causes and the Principles of Nature



The hallmark of natural philosophy and indeed of any science (sing.
Gk. *episteme*, Ar. *'ilm*) for Avicenna
and the entire Aristotelian tradition is to uncover and to grasp the
basic causes (sing. *'illa*) of the phenomenon under
consideration. Like Aristotle before him, Avicenna identifies four
sorts of causes: the matter, form, agent (or efficient cause) and end
(or final cause) (Avicenna, [Ph], 1.10 and Avicenna, [MPh], bk. 6).
For Avicenna the material cause is a wholly inert substratum for form.
The matter explains any passivity or potentiality to be acted upon
that a body might have. The form (*sura*) is the
cause, primarily, of a body's being the actual kind or species
that it is and performing the various actions associated with that
species; secondarily, a form might be the cause of the accidental
features and determinations that belong to that body (Avicenna
occasionally uses *hay`a* for this second sense of form).
In general then, the form is the cause of any actuality, that is
positive features or actions, that the body has or does. The efficient
cause accounts for a body's undergoing motion and change (or
even for its existence), while the final cause is that for the sake of
which the form occurs in the matter.



Unlike Aristotle, Avicenna also recognizes a broader division of
causes into physical causes and metaphysical causes (Avicenna, [Ph],
1.10 [3]). The distinction is best approached by considering the
Aristotelian division between substances and accidents as found in the
ten categories. (Within the Aristotelian tradition, including
Avicenna, the ten categories purport to provide the broadest
classification of ways things are found (*mawjud*) in the
world; Avicenna, [Cat], 1.1 and [MPh], 3.1.) The primary category is
that of substance, which for Avicenna is the existence that belongs to
a thing through itself, for example, the existence that belong to a
human as human or a dog as dog (Avicenna, [MPh], 2.1 [1-2]).
Accidents are what exist in another, namely, in a substance, and
include a substance's quantity, quality, relation, where, when,
position, possession, activity and passivity. Metaphysical causes
involve what accounts for the existence and continual conservation of
a substance, or, more exactly, of a concrete particular. Physical
causes in contrast involve those factors that bring about changes in
the accidental features of bodies, primarily changes of quality,
quantity, location and position. For example, a father is responsible
for seeing that his semen becomes located within the mother, and the
mother ensures that the right womb temperature for the fetus is
maintained and that the fetus is fed. Location, temperature,
possession of nutriment and the like belong to categories of
accidents, not to that of substance. Consequently, for Avicenna the
father and mother are most properly physical agents, that is, the
cause of accidental changes that prepare the matter for the form. As
such the parents are not the cause of the existence of the
offspring's species form by which it is the specific substance
it is. Instead, the metaphysical agent--the one who imparts the
species form to the matter such that there comes to be a substance of
the same kind as the parents--is a separate (immaterial) agent,
which Avicenna calls the Giver of Forms (Avicenna, [Ph], 1.10 [3];
[AP], 2.1; [MPh], 6.2 [5] & 9.5
 [3-4]).[1]



Regardless of whether one is considering physical or metaphysical
causes, any motion or change (whether of some specific existence
itself or just of some new accident), Avicenna explains, requires
three things: (1) the form that comes to be as a result of the change,
(2) the matter in which that form comes to be and (3) the
matter's initial privation of that form (Avicenna, [Ph], 1.2
[12-13]). These three--the form, matter and
privation--are frequently referred to, following Aristotle, as
"principles of nature" (cf. Aristotle, *Physics*,
1.7). While Avicenna happily agrees that these three factors are
present in every instance of something's coming to be after not
having been, he is not as happy as to whether all three of these
features are equally "principles" (sing.
*mabda`*). His concern is that, strictly speaking, causes
and principles exist simultaneous with their effects, whereas
privation is only ever *prior to* the change and passes away
with the change (Avicenna, [Ph], 1.3 [14]; McGinnis 2012, Lammer 2018,
SS3.3). More properly speaking, Avicenna contends, privation is a
precondition for change rather than a principle. Still, he concedes
that if one is lax in one's use of "principle" so as
to understand a principle as "whatever must exist, however it
might exist, in order that something else exists, but not
conversely" (*ibid*) privation would count as a principle
of change. Avicenna reasons thusly: The elimination of the privation
from something as changeable renders that thing no longer changeable,
whereas the elimination of that changeable thing itself does not
eliminate the privation. In other words, insofar as something is
changeable, it depends on or requires that there be some privation.
Conversely, privation does not depend on and does not require that
there be anything changeable. For example, for Avicenna, the celestial
Intellects--think Angelic host--are not subject to change;
nonetheless, they all possess some privation of existence and
perfection, which is found in God. Thus privation has a certain
ontological priority to the changeable. There can be privation without
the changeable, but there cannot be the changeable without
privation.


### 1.2 Nature



Closely related to causes and principles is the notion of a nature
(Gk. *phusis*, Ar. *tabi'a*), for
Aristotle defined a nature as "a principle of being moved and
being at rest in that to which it belongs primarily, not accidentally
but essentially" (Aristotle, *Physics*, 2.1,
192b21-3). Before commenting Aristotle's definition of
nature, Avicenna begins his chapter "On Defining Nature"
from *The Cure* (Avicenna, [Ph], 1.5) by distinguishing between
the motions and actions that proceed from a substance owing to
external causes and those that proceed from a substance owing to the
substance itself. For instance, water becomes hot as a result of some
external heat sources, whereas it becomes cool of itself. Avicenna
next identifies two sets of parameters for describing those motions
and actions that proceed from a substance owing to that substance
itself. They may either proceed from the substance as a result of
volition or without volition. Additionally they may proceed either
uniformly without deviation or non-uniformly with deviation. Thus
there are four very general ways for dividing and describing all the
motions and actions that are found in the cosmos.




|  |  |  |
| --- | --- | --- |
|  | *volitional* | *non-volitional* |
| *non-uniform* | animal soul | plant soul |
| *uniform* | celestial soul | nature |



(1) Motions and actions may proceed as a result of volition and do so
in a uniform and unvarying way, such as the motion of the heavenly
bodies. The internal cause in these cases, Avicenna tells us, is a
celestial
 soul.[2]
 (2) Other motions and actions may proceed as a result of volition but
do so in a non-uniform and varying way, like the motions and actions
of animals; the internal cause in these cases is an animal soul. (3)
Again, other motions and actions may not proceed as a result of
volition and are non-uniform and varying, like plant growth; the
internal cause in these cases is a plant soul. Finally (4) some
motions and actions may proceed without volition while doing so in a
uniform and unvarying way, like the downward motion of a clod of earth
and the heating of fire; the internal cause in these cases is a
nature.



Next, he turns to Aristotle's own account of nature and begins
by chiding Aristotle for his cavalier assertion that trying to prove
that natures exist is a fool's errand, since it is self-evident
that things have such (internal) causes. While we are immediately
aware of motions and actions that seemingly proceed from substances of
themselves, that there truly exist *internal causes* of these
actions and motions is certainly in need of demonstration. Indeed, one
who first encounters the motion of a magnet, Avicenna gives as an
example, might imagine that its motion is a result solely of itself
rather than of iron in the vicinity. Moreover, during Avicenna's
time the question of whether natures existed at all was a hotly
debated topic between philosophers in the Graeco-Arabic tradition,
like Avicenna, and thinkers in the Kalam tradition, the tradition
of Islamic speculative theology and cosmology.



Proponents of the Kalam tradition, such as
al-Baqillani (950-1013) and
 al-Ghazali
 (1058-1111), had a two-stage critique. First, anticipating Hume
by at least 700 years, these thinkers noted that observation alone
could not distinguish between causal connections and mere constant
conjunctions. (A contemporary example often found in statistic classes
is that the summer sun's heat seems to be causally connected
with ice cream's melting, whereas eating ice cream is only
constantly conjoined, at least in the US, with an increase in violent
crimes.) Observation alone, these thinkers warn us, cannot determine,
for example, whether the cotton's burning, which follows upon
placing fire in the cotton, or intoxication, which follows upon
imbibing alcohol, is causally connected with the natures of fire and
alcohol respectively, or whether these sets of events are merely
constantly conjoined. Indeed the concurrence of two events may be a
result of God's habit or custom (*'ada* or
*sunna*) of causing the one event together with the other.
While one might think that appealing to God to explain the various
mundane events that we constantly observe around us is extravagant,
Kalam thinkers countered that it was in fact the philosophers who
are ontologically profligate, for the theologians assume only one
class of causes, namely, willful agent(s), whereas the philosophers
are committed to two ontologically distinct classes of causes, if not
more. This point leads to the second stage of the Kalam critique
of natures. God's (omnipotent) causal power extends to every
actual or even possible event. God's causal power is either
sufficient to produce these effects or it is not. If God's power
is not sufficient, then either the deity needs the added
"boost" of natural powers, or it needs natures as a tool
or instrument, etc. This later position flirts with impiety. If,
however, God's causal power is sufficient to produce every
effect and there are also natures, functioning as internal causes,
every event is over-determined. Indeed it is not clear at all what
causal role natures have to play. A principle of parsimony, so the
Kalam critique concludes, suggests that natures be jettisoned and
one reserve all causal power to God alone. While Avicenna addresses
the issue of the existence of natures and offers up a demonstration
for their existence in the *Metaphysics* (4.2, 9.2 & 9.5;
also see Dadikhuda 2019), he also notes that the science of physics is
not the proper place to undertake such an enterprise. That is because
the existence of a science's subject matter, Avicenna notes
following Aristotle, is never demonstrated within that very science
itself but only in a higher science.



Having set aside the issue of whether natures exist and for present
purposes posits that they do, Avicenna now unpacks Aristotle's
definition. Before considering his analysis, however, it should be
noted that there is a certain ambiguity in Aristotle's overall
treatment of nature. The ambiguity involves whether nature should be
taken in a passive sense: is nature a cause of a substance's
*being moved*? Or, alternatively, should nature be taken in an
active sense: is a nature a cause of a substance's (self)
motion? In *Physics*, 2.1, the text where Aristotle defines
nature, he suggests, although does not explicitly claim, that nature
can be understood in both senses: a passive nature, which corresponds
with a substance's matter, and an active nature, which
corresponds with the form of that substance, and so is a cause of its
motion. In contrast, later in the *Physics*, he argues that
natures should be understood exclusively as passive (Aristotle,
*Physics*, 8.4, 225b29-256a3). This conclusion follows
upon Aristotle's principle that everything that is moved must be
moved by something, which he established at *Physics*, 7. The
principle is significant for a key element in Aristotle's his
natural philosophy, namely, his proof for an unmoved mover. (The
unmoved mover is intended to explain why there is motion at all.) The
aforementioned principle is significant because if all natural
substances were capable of self motion, it is no longer clear that
there is a need for an unmoved mover to account for the motion of the
cosmos. This ambiguity in Aristotle account of nature, namely, whether
nature is an active source of moving or a passive factor of being
moved, was the source of much discussion among Aristotle's
subsequent Greek commentators, who included
 Alexander of Aphrodisias
 (ca. 200 CE) and the late Christian, Neoplatonic Philosopher
 John Philoponus
 (ca. 490-570). (For more detailed studies of this tradition see
Macierowski & Hassing 1988, Lang 1992, 97-124 and Lammer
2015, 2018, ch. 4).



Aristotle's definition of nature as it came down to Avicenna in
Arabic literally translates into English as "the primary
principle of motion and rest in that to which it belongs essentially
rather than accidentally" (quoted in Avicenna, [Ph], 1.5
 [4]).[3]
 A "principle of motion," Avicenna tells us, means
"an efficient cause from which proceeds the production of motion
in another, namely, the moved body" (ibid). Immediately we
recognize that a nature for Avicenna can be understood as an active
cause that produces motion. Such a position is to be contrasted with
Aristotle's claim at *Physics* 8.4 that a nature is not
an internal cause of a thing's motion, but of its *being
 moved*.[4]
 Next we learn that "primary" in the definition means that
the nature causes the motion in the body without some further
intermediary cause. As for "essentially," (Gk. *kath
hauto*, Ar. *bi-dhatihi*) it is an equivocal notion
with two senses, Avicenna tells us. In one sense,
"essentially" is predicated relative to the mover, while
in another sense it is predicated relative to what is subject to
motion, namely, the body. Thus, on the one hand, when
"essentially" is said relative to the mover, a
substance's nature, as efficient cause, essentially produces
those motions and actions that typify the substance as the kind that
it is. On the other hand, when "essentially" is said
relative to the body, it refers to the body's essentially being
subject to those naturally characteristic motions and actions. In
effect, by distinguishing the two relative senses of
"essentially," Avicenna has made room for
Aristotle's definition to include nature as an active and as
passive principle. To sum up, for Avicenna, a substance's nature
is the immediate efficient cause for all of the naturally
characteristic actions and motions it produces (active nature) as well
as explaining why the body is subject to those characteristic actions
and motions (passive nature).


## 2. Bodies and Magnitudes


### 2.1 General Background



With the distinction between nature as active and nature as passive in
place, it becomes clear why Avicenna identifies the proper subject
matter of natural philosophy with body insofar as it is subject to
motion, for the science of physics studies nature in both of its
active and passive senses. Nature as passive refers to that which is
subject to motion, namely, bodies, while nature as active refers to
the causes and conditions of the motions and actions that bodies
naturally undergo. In this section, I begin with Avicenna's
general introduction to bodies. I then take up his critique of
atomism, specifically as that theory was developed within Kalam.
Thereafter, I turn to Avicenna's theory of the continuity of
magnitudes and his conception of infinity, concluding with a brief
survey of his theory of the elements.



Sensible body (*jism* or occasionally *jirm*), one can
assume, is an aggregation of parts. Starting from this assumption,
Avicenna next says of the body that it either (1) has *actual*
parts or (2) has no *actual* parts. Avicenna effectively
divides the logical space for a discussion of the aggregation of body
into two categorical propositions: either "Some parts in a body
are actual" or "No parts in a body are actual."
These are logically contradictory propositions, and so along one
dimension they exhaust all logically possible options. In the case of
"some parts," the obvious question is, "How
many?" where "finite" and "infinite"
exhaust the possible options. Of course, the question, "How
many?" is irrelevant when applied to no or 0 parts. Thus, there
are three possible positions: body is an aggregate of (1) a finite
number of actual parts, a position identified with that of the
atomists; (2) an infinite number of actual parts, a position
identified with that of Ibrahim al-Nazzam
(c. 775-c. 845); (3) no actual parts, a position associated with
the Aristotelian tradition and the contention that bodies are
continuous and so not an aggregate of *actual* parts, even if
potentially divisible ad inifinitum.



Avicenna makes short work of (2), al-Nazzam's
position (Avicenna, [PR], *namat* 1, ch. 2; and [Ph], 3.4
[1]). The parts are units of the whole, which must have either no
magnitude or some magnitude. If the units have no magnitude, then
while multiplying them may increase the number of units present in a
body, it will not increase the size of the body. Consequently, bodies
would not have any magnitude, an obviously false conclusion. If the
units have some magnitude, be it ever so small, and the body is
composed of an actual infinity of these units, then complains
Avicenna, "the relation of the finite units to the infinite
units would be the relation of a finite to a finite, which is an
absurd contradiction" (Avicenna, [PR], *namat* 1,
ch. 2, p. 162). For instance, assume that
al-Nazzam's unit measures some extremely small
yet positive amount of distance, for example, 1.5 x 10-35
of a meter, then:



> 
> [?] al-Nazzam's-units : 1 m :: 1.5 x
> 10-35 al-Nazzam's-units : 1 m.
> 



Thus [?] : 1.5 x 10-35, that is, an infinite is
proportional to a finite, which, as Avicenna notes, is absurd.



Avicenna's more important target was Kalam atomism, which
is significantly different from the Democritean atomism, which
Aristotle had criticized. Thus, let us consider it quickly before
turning to Avicenna's critique of atomism.


### 2.2 Avicenna on Atomic/Discrete Magnitudes


#### 2.2.1 Kalam Atomism



Aristotle had in his physical writings addressed and critiqued atomism
(e.g., Aristotle, *Physics*, 6.1 and *On Generation and
Corruption*, 1.2). In the time between Aristotle and Avicenna,
however, there were a number of developments in atomic theory both by
Epicurus, one generation after Aristotle, and by Muslim theologians,
that is, proponents of Kalam, most of whom were atomists (Dhanani
1994, 2015). As a result, Avicenna's critique of atomism needed
to address new innovations and challenges. One such innovation, which
can be traced back to the Greek world, is a distinction between
physical divisibility and conceptual divisibility. Thus, for example,
the atoms of
 Democritus
 (d. 370 BCE) have as one of their properties shapes. If atoms have a
shape and to have a shape is to have definite limits, then one might
reason that Democritean atoms have distinct limits into which they can
at least be conceptually divided, even if not physically divided.
Aristotle in fact exploited this point in his critique of Democritus.
In contrast, the minimal parts of
 Epicurus
 (d. 270 BCE) had no shape, and so were not subject to the same
criticism. Indeed, Epicurean minimal parts are purportedly not merely
physically indivisible but also conceptually indivisible. To provide a
rough and ready image of an Epicurean minimal part, one might think of
the surface thickness of a plank, and the plank itself as the
aggregation of such surfaces. For example, then, when the surfaces of
two planks are brought together tightly, intuitively one may think
that the two surfaces remain two distinct physical things; the bottom
of the top plank, for instance, is distinct from the top of the bottom
plank. When some enormous number of these surfaces is aggregated, a
plank with a definite thickness, one might imagine, results. So how
thick are these surfaces? One cannot fathom, but again being so thin
that dividing it further is inconceivable is the very point of
Epicurus' minimal parts. Whatever the chain of transmission, it
was something much like Epicurus' minimal parts that Muslim
atomists identified with their atoms, or more precisely, indivisible
parts (*sing. al-juz` alladhi la
yatajazza`u*)--a spatial magnitude that was not merely
physically indivisible but also conceptually indivisible.



Another difference between the theory of atomism that Aristotle
addressed and the one that Avicenna does is the very nature of the
atoms themselves. Democritus' atoms with their differences in
shapes as well as differences in possible arrangement and positions
are best considered as corpuscles, that is, small bodies. Thus when
speaking of Democritus, we can speak of "corpuscular
atomism." Such is not necessarily the case with Epicurean
minimal parts or Kalam atoms, which, while making up the parts of
bodies, were not themselves considered bodies. While there is some
dispute about this point concerning Epicurus, Kalam atomists are
fairly consistent in saying that the sole property of their atoms is
that they occupy space (*mutahayyiz*) but otherwise lack
any other determinations. In fact, Kalam atoms might best be
thought of as a matrix making up all space, with the individual atom
representing the smallest spatial magnitude necessary for the
occurrence of some co-incidental event, determination or accident,
like being red or hot or wet or even possessing power. In this
respect, Kalam atoms are comparable to the pixels on a modern-day
TV or computer screen. The two are comparable in that both are the
smallest relevant units in which a sensible effect occurs, whether
some color for modern pixels or any accident more generally for
Kalam atomists. Consequently, this variety of atomism might be
called "pixelated atomism" to contrast it with the
corpuscular atomism that had been the target of Aristotle's
criticisms. The significant point is that Avicenna could not simply
appeal to Aristotle and his attack on corpuscular atomism when
critiquing atomism as he found it.



Regardless of what form of atomism one endorsed, a common argument in
atomism's favor appeals to the notion of a sensible body's
being an aggregation of parts. The argument is directed against the
idea that a continuous magnitude, which for the philosophers included
the natural sensible bodies that make up the world, can be potentially
divisible ad infinitum (cf. Aristotle, *Physics* 3.7, 207b16).
The most general form of the argument rests on two principles: (1) the
impossibility of an *actual* infinity, a premise that even most
Aristotelians accepted; and (2) an analysis of potentiality in terms
of an agent's power, namely, to say that some action ph is
potential is to say that there exists an agent who has the power
actually to do ph. As part of a reductio-style argument, one is
asked to assume (3), bodies are potentially divisible infinitely. In
that case, from (2), there must exist some agent (e.g., God) that can
actually bring about the division. So let the agent enact the
potential division. Either the result is an actually infinite number
of parts or a finite number of parts. From (1), recall, an actual
infinity is impossible. Therefore, the totality of potential parts
that actually can be produced from the division is finite, but it was
assumed that they were infinite, a contradiction. Since (1), (2) and
(3) are mutually incompatible, one of these assumptions must be false.
The atomists point to the assumption of infinite divisibility and a
potentially infinite number of parts. Thus, the argument concludes,
the parts from which sensible bodies are aggregated must be finite,
whether actually or potentially.


#### 2.2.2 Avicenna's Criticisms of Atomism



Avicenna's response to this argument against the potentially
infinite divisibility of bodies is considered when discussing his
theory of
 continuity.
 Prior to that, his reasons for rejecting atomism must be examined. To
start, Avicenna accepts that division with respect to body is of two
sorts: physical division and conceptual division. In physical
division, there is the actual fragmentation of a body, with the parts
of the body becoming physically separated and at a distance from one
another. An example would be when one takes a single quantity of water
and places part of it in one vessel and the other part in another
vessel. Avicenna concedes that it well may be the case that bodies
have some physical limit beyond which they no longer can be physically
divided and still remain the same sort of body. To provide an example
of Avicenna's point, our quantity of water can be divided as
water until one reaches a single water molecule; division beyond that
point, while producing hydrogen and oxygen atoms, does not produce
smaller particles of water. A single water molecule, then, is
physically indivisible as water; it no longer remains as water after
any further division. Still, inasmuch as a single water molecule
occupies some space, however small, one can conceive of half of that
water molecule, and so it is conceptually divisible qua magnitude.
Whether there actually are such physically indivisible units, Avicenna
insists, requires proof, which I consider when looking at
 Avicenna's elemental theory.



The form of atomism that Avicenna rejects is that there exist minimal
parts that cannot even be conceptually divided further. These are the
minimal parts of Epicurus and the atoms of Kalam.
Avicenna's arguments against this conception of atomism takes
two forms: one, arguments showing that there is a physical absurdity
with such atoms and, two, arguments showing that this form of atomism
is incompatible with our best mathematics, namely, that of Euclidean
geometry. The following two examples give one a sense of how
Avicenna's physical-style and mathematical-style criticisms work
(Avicenna, [PR], *namat* 1, ch. 1 and [Ph], 3.4; Lettinck
1988). While all the arguments considered are specifically directed
toward a theory of pixilated atomism, they apply equally well to
corpuscular atomism. Additionally, Avicenna has a series of arguments,
not considered here, showing the absurdities that would follow on the
purported motion of corpuscular atoms.



While some of Avicenna's physical-style arguments are quite
complex and sophisticated, showing that the aggregation of bodies
would simply be impossible on the Kalam atomists' view (an
example can be found in Section 2.3 of the entry on
 Arabic and Islamic natural philosophy and natural science),
 the following thought experiment is perhaps more intuitively obvious.
Posit a sheet of conceptually indivisible atoms between yourself and
the sun. Certainly the side facing the sun is distinct from the side
facing you, for if the side that the sun is illuminating is the very
same side upon which you are gazing, there is no sense in which the
sheet of atoms is *between* you and the sun. Thus on the
assumption that it is physically possible for this sheet to exist
between you and the sun, all the atoms composing the sheet have a
sun-side and a you-side, and these two sides are distinct.
Purportedly, conceptually indivisible atoms have been divided, a
contradiction.



Avicenna's mathematical-style critique of Kalam atomism
frequently appeal to issues associated with incommensurability. In
this vein he argues that such geometrical commonplaces as diagonals
and circles would be impossible on the assumption of conceptually
indivisible atoms. For example, in the pixilated atomism of the
Kalam, the atoms might be thought to form a three-dimensional
Cartesian coordinate system with each atom corresponding to some
ordered triplet on this space. A two-dimensional plane, then, would
look something like a chessboard. Avicenna now has us describe a right
isosceles triangle on this chessboard, setting the two equal sides,
for instance, at 3 units. Given the Pythagorean Theorem, A2
+ B2 = C2, we should be able to solve for the
length of the hypotenuse, which is [?]18 [?] 4.25. Avicenna,
next observes that assuming Kalam atomism, the hypotenuse of our
triangle must fall either well below the solution given by the
Pythagorean theorem--namely, it would be 3 units if one just
counts the 3 squares along the diagonal of a 3x3 chessboard--or
significantly exceed it--for instance 6 units, if the atoms can
somehow be stair stepped. Alternatively, one might consider units
smaller than the atoms, but such a move is to give up atomism.
Kalam atomism, then, cannot even approximate the answer of the
Pythagorean Theorem, and yet the Pythagorean Theorem is arguably the
most well-proven theorem in the history of mathematics. Given the
choice between a dubious physical theory and our best mathematics,
Avicenna sides with Euclidean geometry and its assumption of
continuous
 magnitudes.[5]


### 2.3 Continuity



Having rejected atomism, with its central claim that sensible bodies
must be aggregates of a finite number of conceptually indivisible
parts, Avicenna must explain and defend his preferred account of
bodies. Avicenna adopts a modified form of Aristotle's theory of
the continuity of bodies. Aristotle himself had provided no fewer than
three different accounts of continuity (Gk. *sunecheia*, Ar.
*ittisal*):


1. AB is continuous iff AB can be divided into things always capable
of further division (*Physics*, 3.7 & *De Caelo*,
1.1)
2. A is continuous with B iff the extremities of A and B are one and
the same (*Physics*, 6.1)
3. A is continuous with B iff there is a common boundary at which
they join together (*Categories*, 6)



Precisely because these three accounts are different, Avicenna starts
his own discussion of continuity, claiming that "being
continuous is an equivocal expression that is said in three
ways" (Avicenna, [Ph], 3.2 [8]). Two of these senses, he
continues, are relative notions, while only one, i.e., (3) above,
identifies the true essence of what it is to be continuous. In fact,
he even goes as far as to say that account (1) is not truly a
definition of being continuous at all; rather, it is a necessary
accident of the continuous that must be demonstrated, a point to which
I return when I look at what Avicenna considers to be the proper
account of continuity.



As for the relative notions of continuity, the explanations can be
quick. First, discrete objects might be said to constitute a
continuous whole relative to a motion. For example, all the connected
cars on a moving locomotive are clearly distinct and separate things,
and yet they move together as a continuous whole. Second, discrete
objects might be said to be continuous according to Aristotle's
definition (2) relative to some shared extremity. For example, for any
angle [?]ABC greater than or less than 180deg, the lines AB and BC
share one and the same extremity, B, and yet are distinct and jointed.
Neither of these senses is strictly speaking the target of the
atomist's critique nor the thesis concerning the continuity of
bodies and magnitudes that Avicenna (or other Aristotelians) is keen
to defend. Thus for Avicenna only (3), that two things are continuous
if and only if there is a common boundary at which they join together,
captures the proper definition of continuity.



A continuous sensible body (or any magnitude), Avicenna insists, must
ultimately lack any parts and instead must be considered entirely as a
unified whole. Admittedly, one can posit parts in this unified whole,
like the left-part and the right-part, but such accidental parts are
wholly the result of one's positing and they vanish, claims
Avicenna, with the cessation of the positing.



> 
> [Such parts are] like what happens when our estimative faculty
> imagines or we posit two parts for a line that is actually one, where
> we distinguish one [part] from the other by positing. In that way, a
> limit is distinguished for [the line] that is the same as the limit of
> the other division. In that case, both are said to be continuous with
> each other. Each one, however, exists individually only as long as
> there is the positing, and so, when the positing ceases, there is no
> longer *this* and *that* [part]; rather, there is the
> unified whole that actually has no division within it. Now, if what
> occurs through positing were to be something existing in the thing
> itself and not [merely] by positing, then it would be possible for an
> actually infinite number of parts to exist within the body (as we
> shall explain), but this is absurd (Avicenna, [Ph], 3.2 [8]).
> 



To press Avicenna's point a bit further, a continuous body has
no parts in it, not even potential parts, if by "potential
parts" one means points or the like latent within the body
waiting for some power to actualize them or divide the body at them.
To appreciate Avicenna's point here fully, a few words must be
said about his conception of the form-matter constitution of bodies
and the relation of his view of continuity to psychological
processes.



Like Aristotle and other Aristotelians both before and after him,
Avicenna is convinced that bodies are constituted of matter and form.
If one considers just body as such, that is, disregarding any specific
kind of body it might be, then this absolute body, Avicenna tells us,
is a composite of matter (*hayula*) and the form of
corporeality (*sura jismiyya*). Avicenna conceives
matter as wholly passive, having no active qualities or features. (For
discussion's of Avicenna theory of matter see Hyman 1965;
Buschmann 1979; Stone 2001; McGinnis 2012; but also see Lammer 2018,
SS3.2 for corrections of some of these earlier views.) In fact,
Avicennan matter has no positive characterizations of its own at all
by which it can be defined; rather, for Avicenna, matter is best
understood solely in relation to the forms by which it is actualized
and informed. Avicenna's matter, then, is intimately linked with
relative privation (*'adam*), that is, some lack, which
under the right conditions can be realized. Given matter's
essentially privative character, it, then, cannot be the explanation
for a sensible body's having the positive characteristics of
being unified and one, nor the cause of that body's being
extended so as to be subject to division. Instead, according to
Avicenna, what makes a body a unified whole and subject to division is
its form of corporeality.



For a determinate body to exist at all, Avicenna believes, it must
have a determinate shape, and so be three dimensional, and so be
localized in space. Both of these features are the result of its
corporeal form (For a fuller discussion see Hyman 1965; Shihadeh 2014;
Lammer 2018, SS3.1). When the form of corporeality comes to inform
matter, there comes to be a single unified body, existing on account
of its particular and individual form of corporeality. Should the body
be physically divided, the particular and individual form of
corporeality is not so much divided as destroyed and replaced with two
new particular and individual forms of corporeality corresponding with
two new bodies. It is essentially the form of corporeality that
unifies and makes a body numerically and actually one. Additionally,
while the form of corporeality makes the body *actually* one,
it also makes the body *potentially* many. That is to say, the
form of corporeality is the cause of a body's being
three-dimensional such that one can posit such divisions as right-side
and left-side in it.



We are now led to the role of psychological processes in
Avicenna's account of a continuous body's infinite
divisibility. While it is true for Avicenna that continuous bodies can
conceptually be divided without end, such a feature is not the result
of any positive attribute within the body. This potentiality for
division does not correspond with any positive features latent within
the body. Instead the potentiality for infinite division refers to a
privation in the matter of the body. The matter, extended and
possessing quantity as a result of the form of corporeality, does not
preclude or prevent one from positing imagined divisions within the
body as small as one wants. Indeed, this psychological process of
imaging or positing divisions in principle has no end. Thus, looking
at, for example, a meter stick, one can posit a halfway point, then
the halfway point of one side and then a further halfway point and so
on as long as one likes; however, as soon as one stops the process of
imagining halfway points, the imagined points (regardless of how many
one has imagined) do not magically remain but altogether cease with
the cessation of their being posited. The body remains as it always
was, a unified whole, whose unity is only ever lost by actual physical
division, not conceptual division.



With this conception of continuity in place, the Kalam argument
against potential divisibility ad infinitum dissolves. Again that
argument assumed two principles: (1) the impossibility of an
*actual* infinity; and (2) an analysis of potentiality in terms
of an agent's power, namely, the view that some action ph is
potential if and only if there is an agent who has the power actually
to do ph. In point of fact, Avicenna rejects both principles (his
conception of infinity is discussed at
 2.4);
 for now he simply questions the theologians' inference from
something's being potential to the possibility of its being
realized all at once at some moment or other. The original Kalam
argument assumed that a potential infinity of divisions existed in a
continuous body. In that case, the argument continued, let God
actualize that potential, and one is confronted with an actual
infinity. Avicenna in contrast understands the potential infinite
divisibility of bodies in terms of an ongoing process of positing
successive divisions within the magnitude, a process that by
definition has no end. Of course, there is a contradiction here in
assuming that some agent, even God, can get to the end of some process
that has no end, but such a contradiction does not tell against
Avicenna's theory of continuous bodies. In fact,
Avicenna's conception of potential infinite divisibility is
compatible with (2), since there is no immediate contradiction in
saying that God eternally and without ceasing posits ever-decreasing
halfway points in some magnitude. Still even in this case, there never
is an actual infinity of such halfway points, as the proponents of
Kalam atomism maintain.


### 2.4 Infinity and the Shape of the Cosmos



With the introduction of continuity and its corresponding notion of
infinite divisibility one is also obliquely introduced to the notion
of infinity (*la nihaya*). Avicenna, following
Aristotle's account of the infinite (*apeiron*) at
*Physics*, 3.6, defines it as "that which whatever you
take from it--and any of the things equal to that thing you took
from it--you [always] find something outside of it"
(Avicenna, [Ph], 3.7 [2]). In natural philosophy, the immediate issue
is whether an infinity exists either in quantities that posses some
position or in numbers in an ordered series (Avicenna, [Ph], 3.7 [1]).
The mutakallimun, that is, the proponents of Kalam, were for
the most part opposed to predicating the infinite of anything other
than God. This opposition included both actual infinity and potential
infinity, as we have seen. While it is notoriously difficult to give a
precise account of the difference between the actual as opposed to the
potential infinite, a rough characterization is this: In the case of
an actually infinite magnitude, all the parts of that magnitude are
somehow simultaneously and fully present, whereas in the case of the
potentially infinite there is an going process or succession in which
the units come to be, never wholly existing as actual at some given
point or moment. While Avicenna happily accepts the reality of
potential infinities, he denies that there are material instances of
either actually infinite qualities, like infinitely large bodies, or
numbers, like infinitely large sets of bodies, all of which exist
 simultaneously.[6]



Avicenna has a number of arguments attempting to show that an actual
infinity in nature is impossible (for a presentation and assessment of
some of these arguments see Zarepour 2020). These arguments can be
divided into those that appeal to motion as part of the proof, and
those that do not appeal to motion. Here I merely consider one of
Avicenna's non-motion proofs against an actual (spatial)
infinity. The argument, which I present, is not the preferred proof in
either *The Cure* or *The Salvation*, although he had
toyed with it in *The Cure* (Avicenna, [Ph], 3.8 [5-7]).
Still it is his preferred and indeed only argument against an actual
infinity in his shorter and last philosophical encyclopedia,
*Pointers and Reminders* (Avicenna, [PR], *namat*
1, ch. 11, p.
 183-90).[7]
 Moreover, the proof is a uniquely Avicennan one.



The argument asks one to posit some actually infinite ray, AB and then
another actually infinite ray, AC, so as to form an acute angle
[?]BAC. Next Avicenna asks one to consider the gap, BC, between the
two rays. The farther from A that BC is, the larger BC becomes. Since
the two rays are actually infinitely extended, BC should, in
principle, also be actually infinite; however, BC always lies between
AB and AC and of necessity terminates at them, so BC is finite. Thus,
there is a contradiction: BC is both finite and infinite and, claims
Avicenna, what produced the contradiction is the assumption that there
is actually infinite space. Whether Avicenna's new argument is
successful became a matter of intense debate in post-classical Islamic
natural philosophy, with such notables as Abu l-Barakat
al-Baghdadi (1080-1165) and Najm al-Din
al-Katibi al-Qazwini (ca. 1203-1277) finding
it wanting, whereas Nasir al-Din
al-Tusi (1201-1274) and Mulla
Sadra (1571-1636) considered it defensible (McGinnis
2018).



Avicenna's arguments against an actual infinity in nature are in
general all directed against the possibility of infinite spatial
magnitude. Consequently, since space must be finite (i.e., limited),
all bodies must be limited, and in being limited they have shape. This
conclusion holds for the cosmos as a whole as well. As for the shape
of the cosmos, while such a topic takes us slightly afield from a
discussion of infinity, it does round out Avicenna's abstract
discussion of body. For a number of reasons, Avicenna thinks that the
shape of the cosmos must be spherical. While in some ways Avicenna
takes this claim to be a matter of empirical observation, he also
argues that since the nature of the heavenly bodies is completely
homogeneous and unvarying, there cannot be dissimilarities in a
heavenly body such that a part of it would be angular and another part
rectilinear or such that part of it has one sort of curve and another
part a different sort (Avicenna, [DC], 3; also Avicenna, [Ph], 1.8 [2]
provides the general argument, albeit there it is applied to showing
the sphericity of the Earth). Inasmuch as the cosmos is spherical, it
must have some center, which, at least from the point of physics,
Avicenna identifies with the Earth. (Strictly speaking the Earth is a
bit off center in accordance with the demands of the Ptolemaic
astronomy, which Avicenna adopts.)



We thus now have a general picture of Avicenna's conception of
body in the abstract. Body is not composed of conceptually indivisible
atoms but must be continuous and finite. In the next section I briefly
consider body not in the abstract, but particular kinds of bodies,
namely, the so-called elements.


### 2.5 Simple Bodies and the Elements



When Avicenna speaks of elements (sing. *ustuquss*) and
(elemental) components (sing. *'unsur*), he means
simple bodies, that is, bodies that are not composed of other sorts of
bodies in the way that flesh, blood and bones, for example, are
composed of more basics elements. Despite being simple, the elements
are form-matter composites (Avicenna, [DC], 1). On account of their
form and matter, elements have two powers: an active power following
upon the element's form and a passive power following upon its
matter.


#### 2.5.1 The Motions and Qualitative Powers of the Elements



Additionally, Avicenna specifies different kinds of elements based
upon three kinds of natural motions. The three kinds of natural motion
are (1) motion around the center, (2) motion toward the center and (3)
motion away from the center (Avicenna, [DC], 2). Celestial bodies are
in turn identified with those bodies whose natural motion is around
the center. Terrestrial bodies are identified with those undergoing
rectilinear motion either toward or away from the center. By
convention, what moves away from the center moves upward, while what
moves toward the center moves downward. Avicenna believes that moving
around the center, circular motion, is generically simple inasmuch as
he thinks that there is no contrary to circular motion (Avicenna,
[Ph], 4.6 [7-11] & [DC],
 2).[8]
 Consequently, the very nature of a celestial body is to move
circularly (Avicenna, [PR], *namat* 2, ch. 12). As for
the terrestrial bodies, moving upward and downward are also generic
descriptions; however, Avicenna continues, each of these genera also
has two species, corresponding with the different termini of the
motion. Thus, for example, those bodies that move downward are
generically alike in that they move away from the surrounding
celestial sphere; however, they can differ in that some have the
center as their proper place or terminus for their motion, whereas the
terminus of other downward-moving bodies falls short of the center.
Any body that has the center as its proper place has absolute downward
motion, while a downward-moving body whose terminus falls short of the
center has relative downward motion. The same holds *mutatis
mutandis* for bodies that move upward. Those that have the limit
of the surrounding celestial spheres as their terminus have absolute
upward motion, while those whose terminus falls short of that limit
have relative upward motion.



In order to explain the specific differences of the terrestrial
elements, Avicenna, following a long tradition, which can be traced
back at least as far as Hippocrates (460-370 BCE), appeals to
certain basic qualitative powers. These qualitative powers are
hot/cold, which are seen as active powers following upon the form, and
wet/dry, which are seen as passive powers, following upon the matter
(Avicenna, [DC], 1). Additionally, Avicenna claims, the downward
motion of those elements so naturally inclined, namely, earth and
water, is the result of their being qualitatively cold and being
directed to their natural places, that is, toward the center.
Analogously, the upward motion of those elements so naturally
inclined, namely, fire and air, is the result of their being
qualitatively hot and being directed to their natural places, that is,
away from center. The elements, earth and water's natural
inclination (*mayl*) downward is referred to as their
heaviness, while fire and air's natural inclination upward
references their lightness (Avicenna, [DC], 2). As for the qualities,
wet and dry, these passive powers refer to a body's
susceptibility or lack thereof to the impressions and actions of some
form. For example, what is wet or fluid more easily receives the
impression of a form (just think of wet clay). In contrast, what is
dry, while more readily retaining any impressions made in it, does not
easily yield to being impressed (now think of kiln-dried clay). Given
these differences in motions and qualitative powers, Avicenna, again
following in this tradition, identifies four terrestrial elements: (1)
fire, which is hot and dry with an absolute upward motion, (2) air,
which is hot and wet with a relative upward motion, (3) water, which
is cool and wet with a relative downward motion and (4) earth, which
is cool and dry with an absolute downward motion. Finally, and for
completeness, (5) celestial bodies are neither hot nor cold (and so
neither heavy nor light) nor wet nor dry, but instead are solely
identified in term of their natural circular motion.


#### 2.5.2 Natural Minimums



In section
 2.2.2,
 it was noted that while Avicenna denied the possibility of
conceptually indivisible atoms, he allowed for the possibility of
physically indivisible natural minimums. In other words, there might
be limits beyond which some specific kind of natural body cannot be
divided further and remain that same kind of body. It was further
noted that a proof was required whether there actually were such
natural minimums. We are now in a position to consider
Avicenna's proof for this thesis (Avicenna, [Ph], 3.12). Recall
that for Avicenna there are two forms of division. One involves merely
positing imagined divisions within a magnitude, so as never actually
to destroy the continuity of the body. The second involves actually
fragmenting and separating parts of the body such that the parts are
at a distance from one another. Avicenna's proof for natural
minimums involves this second form of division, namely, bringing about
a separation of the parts. It additionally presupposes the theory of
elements just presented and particularly the qualitative powers that
are the necessary concomitants of the terrestrial elements.



While the details and argumentation of Avicenna's theory are
complex, the heart of the theory can be grasped through the following
example. (For a discussion of the history and details of
Avicenna's account of natural minimums see McGinnis 2015.)
Avicenna first observes that the smaller something is compared with
its surrounding environment, the faster and more easily that
environment acts on what is surrounded. For example, a blast furnace
melts a kilogram of ore more readily than it does a metric ton of ore.
Now, the example continues, isolate some relatively small quantity of
water, e.g., a milliliter, in a beaker. The water qua the element
water has the essential qualities of being cold and wet. Additionally,
inasmuch as the water is isolated, and so not part of a lake or the
like, it is surrounded by ambient air, which, according to the
elemental theory that Avicenna adopts, is hot and wet. Provided that
the quantity of water is sufficiently large, it can counteract the
heating influences of the surrounding air; however, as one physically
separates off smaller and smaller quantities of the water, the natural
heat of the surrounding air more readily and effectively acts on the
diminishing quantity of water. At some point, the heat of the
surrounding air fully overcomes the coolness of the small quantity of
water such that the coolness is replaced with the same degree of heat
as the surrounding air. In that case, there is no longer a cold-wet
element but a hot-wet element, and so there comes to be air. What the
example indicates is that there are natural limits of smallness beyond
which the qualitative concomitants of a given element can no longer be
sustained in isolation, and instead a new set of concomitants, now
associated with dominant ambient element, come to be. These limits
beyond which a particular kind of body cannot be physically divided
and remain the same kind of body are the natural minimums.


## 3. Motion



Again the proper subject matter of physics is body inasmuch as it is
movable. We have just looked at Avicenna's conception of body
and associated issues. I now turn to his theory of motion, followed by
discussions of some of the conditions necessary for motion, like time
and place. Avicenna's theory of motion is best understood
against the background of Aristotle's account of motion and
developments surrounding that account that emerged in the later Greek
world. (For detailed discussions of Avicenna's theory of motion
see Hasnawi 2001; McGinnis 2006a; and Ahmed 2016).


### 3.1 Motion as First Actuality



In *Physics*, 3.1, Aristotle defines motion (Gk.
*kinesis*, Ar. *haraka*) as the
*entelecheia* of potential as potential. Aristotle himself
apparently coined the term *entelecheia*, which might mean
either "actualization," as in a process, or
"actuality," as in the completion of a process. Given the
ambiguity of this term, it was a matter of some concern among later
Greek commentators to understand Aristotle's precise meaning.
The details of the Greek debate need not concern us unduly, since the
issue for philosophers in the medieval Islamic world was all but
settled by the choice of the Arabic translator of Aristotle's
*Physics*, who rendered *entelecheia* as
"perfection" or "completion"
(*kamal*). Consequently, for philosophers such as
Avicenna, motion was understood as a sort of actuality or perfection,
as opposed to an actualization or a process.



Greek commentators provided additional glosses on the term
*entelecheia*, which proved significant in Avicenna's own
account of motion. Drawing upon other Aristotelian texts (e.g., *De
anima*, 2.5), these commentators identified both a first actuality
and second actuality. A first actuality is like the student who
actually knows a particular language but is not speaking it at that
moment, whereas the second actuality is like that student when
actually speaking that language. Avicenna follows suit and formally
defines motion as "a first perfection of what is in potential
insofar as it is in potential" (Avicenna, [Ph], 2.1 [3]). To
clarify, Avicenna notes that in every category there are those things
that are actual and other things that, while actual in one respect,
are potential in another. In the case of motion with respect to
*x* (where *x* is some possible location or quantitative
or qualitative feature of a body), the body before the motion is in
potentiality to *x*--as well as any number of other places
or states, *y*, *z*, etc. After the motion, the body is
in a state of second actuality with respect to *x*, that is,
*x* has been fully and completely reached or actualized. During
the motion, then, the body is in a state of first actuality with
respect to *x*. Avicenna understands this first actuality as a
type of "being directed toward" *x*
(*mutawajjih*) as opposed to being directed toward *y*
or *z*. There is motion as long as the body is directed toward
*x* and there still remains some potentiality with respect to
*x*, that is, the place or state of *x* has not been
fully reached or actualized. For example, as long as I sit in my home,
there are any number of places that I might visit; however, once I get
up and begin going to the pub, as long as I remain directed toward the
pub but have not yet reached it, there is the motion that is my
walking to the pub.


### 3.2 Two Senses of Motion: Traversal and Medial Motion



Thus far, Avicenna's discussion of motion is little more than a
sophisticated commentary on Aristotle's definition of motion.
Avicenna's analysis goes beyond Aristotle's inasmuch as
Avicenna recognizes that "motion" is an equivocal term
with two senses. He identifies these two senses of motion, namely,
traversal-motion and medial-motion. As for motion qua traversal, we
sometimes speak of motion as the whole continuous magnitude stretching
from the initial potential state to the final actual state, such as my
complete walk from my home to the pub. Now at no point does the whole
of my walk exist in the way that the whole of the spatial distance
covered between my house and the pub exists. Indeed, no sooner do I
step outside the door of my home on my way to the pub than the initial
potential state (being in my house) ceases to be and is replaced with
some new medial potential state (being on my porch). The same is true
for each subsequent state of the walk. Instead, observes Avicenna, the
whole and complete walk only ever exists as whole and complete in the
mind, namely, I remember my being at home and then relate that mental
impression with my being in the pub. In other words, motion qua
traversal has no extra-mental existence but only ever has a mental
 existence.[9]



In contrast, medial-motion corresponds with motion inasmuch as it
exists extra-mentally in the moving body itself. In other words,
medial-motion refers to the form that every moving body must have at
any moment it is in motion in order to explain its being in motion.
Avicenna describes this form thus:



> 
> 
> This is the form of motion existing in the moved thing--namely,
> an intermediacy between the posited starting and end points inasmuch
> as at any limiting point at which it is posited, it did not previously
> exist there nor will it exist there afterwards, unlike [its state at]
> the points of the two extreme limits (Avicenna, [Ph], 2.1 [6]).
> 
> 
> 



While Avicenna is careful to avoid using any overtly temporal
language, like "time," "instant" or
"now," what he has described is motion at an instant as
opposed to the extended conception of motion captured in
traversal-motion. In other words, motion as it exists extra-mentally
occurs just in case a body exists at some point or in some state for
only an instant. For if a body is at some point or in some state for
only an instant, then at any subsequent instant it must be at some new
point or in some new state, and consequently must have changed or
undergone motion. Such a position is not to concede that spatial,
kinematic or temporal magnitudes are composed of points. They are not,
for again natural magnitudes are continuous according to Avicenna.
Instead, Avicenna means that as one can considers a smaller and
smaller uniform motion over a smaller and smaller spatial magnitude,
the elapsed time of the motion becomes proportionally smaller too. At
the limit (*taraf*) of this process of considering
smaller and smaller increments of motion, there is motion at an
instant, or, more in keeping with Avicenna's description, at any
point you posit the body in the continuum, it was not there before nor
will it be there after. "This," Avicenna concludes,
"is, in fact, the first perfection," which is motion
(Avicenna, [Ph], 2.1 [6]).


### 3.3 Motion and the Categories


#### 3.3.1 The Genus and Species of Motion



Avicenna dedicates two chapters of the *Physics* of *The
Cure* (2.2 & 2.3) to motion's relation to the
categories: one to motion's genus and the other to the species
of motion. As for the first issue, Avicenna attempts to identify to
which category motion generically belongs inasmuch as the categories
supposedly provided the most generic ways that (material) things might
exist. While in the end he concedes that given the canonical ten
categories, motion seems most aptly to fall under passion (Gk.
*paskhein*; Ar. *infi'al*), he is also
uncertain whether Aristotle's ten categories are truly
exhaustive and at least suggests that motion might be *sui
generis* (Avicenna, [Ph], 2.2 [8]; Hasnawi 2004; and McGinnis
2006a).



As for the species of motion (Avicenna, [Ph], 2.3), Aristotle and the
tradition up to Avicenna had recognized only three specific kinds of
motion. These include motion with respect to the categories of
quantity, quality and place. Motion with respect to quantity involves
augmentation and diminution, while motion with respect to quality
includes such changes as alterations in color, temperature and the
like. Finally, on the traditional categorization, there is change of
place, that is, locomotion, which for a number of reasons was believed
to be the most significant or even primary species of motion. Avicenna
accepts all three kinds of motion identified by the tradition. He
additionally adds to these three, motion with respect to the category
of position, that is, the rotation of an object that remains in the
same place, like a spinning orb. The reason for his addition is
obvious on consideration; for clearly an orb spinning in place is not
changing its quantity or quality and by supposition it is remaining in
the same place, yet clearly it is moving. Thus what kind of change is
it undergoing? Only the relative position of its parts, claims
Avicenna, is changing, and thus he concludes rotating objects must be
changing with respect to the category of position.


#### 3.3.2 An Analysis of Positional Motion



The introduction of positional motion, however, brings with it a new
challenge. According to Avicenna, motion always involves a
*terminus a quo*, that is, a "from which,"
(*ma minhu*) and a *terminus ad quem*, that is, a
"to which" (*ma ilayhi*) (Avicenna, [Ph], 2.1
[12 & 20-22]). His reason for insisting on this point is
that motion, as noted, is the actuality of potential as potential,
where the initial state of potentiality corresponds with the
*terminus a quo* and the final state of actuality corresponds
with the *terminus ad quem*. The difficulty is that there need
be no starting and ending point for rotation, particularly if, as
Avicenna believes, the rotation of the heavens has neither beginning
nor end. Avicenna's response to this challenge involves a
sophisticated analysis of the various ways of understanding actuality
and potentiality (including an appeal to the first and second
actuality already noted but also introducing a notion of remote and
proximate potentiality). Without going into the details, the general
intuition of his response is simple enough (for a detailed account see
McGinnis 2006b). As a matter of supposition, one can posit within the
continuous rotational motion of, say, a celestial sphere some point,
for example, the sun's position when it is directly overhead. In
positing that point, one by supposition indicates an initial
*terminus a quo* of the motion, but that same point also
indicates a *terminus ad quem* for that motion (although the
two termini are in a sense also different since there is a difference
in time between the two instances of being at that point). Thus, for
example in our case, a complete sidereal day is actualized when the
sun moves from a position directly overhead--the *terminus a
quo*--and then returns to that position--the
*terminus ad quem*. Of course, nothing about this analysis
requires that the rotation must cease once this sort of *terminus
ad quem*, which is a proximate potency, has been actualized.
Indeed it can be posited as a new *terminus a quo* for a new
rotation. In short, rotational motion still has a *terminus a
quo* and a *terminus ad quem* corresponding with a
potentiality and actuality, even though such motion need have no
absolute beginning or ending point.



An added benefit of Avicenna's introduction of this new species
of motion is that it provides him an easy answer to what has been
called "la grande question" of ancient celestial physics
(Hasnawi 1984). As a bit of background to the problem, Aristotle
defined a thing's "where," or place, with the
outermost containing limit of the surrounding body (Aristotle,
*Physics*, 4.4, 212a20) and Avicenna followed Aristotle
faithfully on this point (Avicenna, [Ph], 2.9 [1-3]; Lammer
2018, SSSS5.1-2). Thus, only a body that has a body
outside of it and containing it can have a place. Consequently the
outermost celestial sphere "beyond" which there is
absolutely nothing, by definition cannot have a place. The problem,
then, is this: We observe the outermost celestial sphere apparently
making a complete rotation once approximately every twenty-four hours,
but what specific sort of motion is the outermost celestial sphere
undergoing? Aristotle and the earlier tradition had identified only
three species of motion: motion with respect to quantity, quality and
place. Clearly the motion of the heavens is neither a change in
quantity nor a change in quality, but it is also not a change of
place, since, as we have seen, the outermost celestial sphere has no
place. Avicenna's introduction of positional motion provides an
obvious solution: the outermost celestial sphere is moving with
respect to the category of position. Moreover, Avicenna's
solution is not ad hoc, since he has integrated his account of
positional motion into his general analysis of motion and
motion's relation to the categories.


## 4. Conditions for Motion



Again physics is the study of bodies insofar as they are subject to
motion. We have just seen Avicenna's account of motion and
before that considered his views about bodies and magnitude more
generally. A discussion of Avicenna's treatment of certain
necessary conditions associated with motion and moving bodies is now
in order. These necessary conditions are, one, how to identify the
place of a body and, two, the time required for motion.


### 4.1 Place and Void



An account of place is particularly significant given that motion with
respect to place was frequently viewed as the primary species of
motion (although Avicenna would rank positional motion along side
local motion, if not above it). The reason for giving priority to
place or position is that change in quantity involves the increase or
decrease of the *place* that a body occupies; and change in
quality involves a body's coming into proximity with some cause
that brings about the alteration, where "coming into
proximity" refers to a *change of place* either in the
body or in the cause (Avicenna, [Ph], 4.9).



As noted when discussing positional motion, Avicenna follows the
Aristotelian tradition and identifies the technical definition of
place (Gk. *topos*, Ar. *makan*) with "the
surface that is the extremity of the containing body" (Avicenna,
[Ph], 2.9 [1]). The general structure of his argumentation for this
thesis involves showing that all other candidates for what place might
be are wanting in some way. To this end, Avicenna provides us with, as
it were, the logical space for an account of place (Avicenna, [Ph],
2.6 [2]). Place can be either intrinsic or extrinsic to body, that is,
essential or accidental to it. If place is intrinsic to a body, then
it is either (1) the matter or (2) the form of the body, whereas if it
is extrinsic, then the place is either (3) what the body exactly
encompasses, that is, an interval (*bu'd*) or (4) what
exactly encompasses the body, that is, the surface that is the
extremity of the containing
 body.[10]
 Avicenna quickly eliminates (1) and (2). That is because a body can
change with respect to place, that is, depart from one place to
another, whereas a body cannot depart from either its matter or form
without undergoing generation and corruption. Hence only (3) and (4)
are truly live options. Account (4) is just the Aristotelian one,
which Avicenna himself prefers. As for (3), namely that a body's
place is the interval it occupies, Avicenna believes that it
ultimately stands or falls with whether a void
(*khala`*), an empty interval, is possible. Avicenna
dedicates a long chapter (Avicenna, [Ph], 2.8) to showing that a void
is impossible. If his argument there is successful, then (4), namely,
place is the innermost limit of the containing body, remains the only
viable definition of place.



Aristotle before Avicenna had also dedicated a long section of his
*Physics* (4.6-9) to a refutation of the void.
Aristotle's arguments might all best be described as physical
ones inasmuch as they all appeal to physical concerns associated with
the void. More specifically, Aristotle's arguments attempt to
show that motion would be impossible on the assumption of a void.
Avicenna reproduces many of Aristotle's physical arguments,
often giving them his own unique twist. Additionally, however,
Avicenna develops what might be called a conceptual critique of the
notion of void. In this critique, Avicenna attempts to show that the
very idea of a void is conceptually vacuous or a vain intelligible.
The criticism begins with a logical/physical principle: Anything that
actually exists within the natural order can be defined in terms of a
genus and difference. (The general idea is that the things that make
up the physical world must be of some kind or species if they exist at
all, and it is the genus and difference that identify the kind or
species.) He then adds one further qualification: Inasmuch as these
actual existents positively make up the world around us, their genus
and difference must refer to positive (as opposed to negative)
notions; a species properly understood answers the question
"what *is* it?" and a genus or difference given in
negative terms simply would not tell us what something *is*,
but what it *is not*. (For a discussion of Avicenna's
theory of genus and difference and how it relates to his criticism of
the void see McGinnis 2007b.)



With these preliminaries in place, Avicenna's conceptual
critique begins (Avicenna, [Ph], 2.8 [1-4]; also see McGinnis
2007a, 2007b; and Lammer 2018, SS5.3). He first asks whether the
void actually exists or is absolutely nothing. If one says that the
void is absolutely nothing, Avicenna happily agrees; for if it is
absolutely nothing, then it does not actually exist. Those who affirm
that the void actually exists, then, cannot simply say that it is
nothing, but must provide some positive features about it. Avicenna
next notes that void space is frequently described as being of either
a greater or lesser extent, for the void space between two cities on
Earth, for example, is less than the void space between the Earth and
the heavens. This property of being more or less is none other than
that of quantity. Thus if a void should exist, it would possess some
quantity either essentially or accidentally. If quantity belongs to
void accidentally, and every accident must belong to a substance, then
void is joined to a substance possessing quantity. The quantity in
question is necessarily three-dimensional, but as noted when
discussing continuity, three-dimensionality follows upon the form of
corporeality. The form of corporeality, however, causes the existence
of a body. Thus void would belong to a body as an accidental feature
of it, a seeming contradiction.



In contrast, if the quantity is not accidental to the void but is
essential to it, then void would be a species of quantity. Avicenna
now challenges the defenders of void to provide some positive
difference that would make up void's species. It cannot be that
void is a material quantity, since again a material quantity is body.
If one claims that void is immaterial quantity, Avicenna demands some
non-negative difference, for while there are immaterial substances,
like angels, one can provide a positive characterization of them as
*intellectual* substances. Avicenna offers a number of
suggestions, but finds every attempt wanting or ultimately telling us
what void is not rather than what it is. Since no definition of void
can be given in terms of a positive genus and difference, Avicenna
concludes that our idea of void is nothing but empty imaginings.



Again, place had to be either (1) the matter or (2) the form of the
body, or either (3) what the body exactly encompasses or (4) what
exactly encompasses the body (i.e., the surface that is the innermost
extremity of the containing body). As noted (1) and (2) are
non-starters, and as just argued, (3) involves a conceptual confusion.
Consequently, Avicenna concludes place must be the innermost surface
of the surrounding body.


### 4.2 Time and the Age of the Universe



Among the conditions associated with motion, time (Gk.
*chronos*, Ar. *zaman*) is at least as important as
that of place and void, for it is a necessary concomitant of motion.
(A number of studies on various aspects of Avicenna's temporal
theory exist and include Shayegan 1986; McGinnis 1999; Mayer 2007; and
Lammer 2018, ch. 6.) In order to appreciate time's relation to
motion, there is a more basic question that must be answered first:
Does time exist? An affirmative answer will seem obvious to many, but
Aristotle at *Physics*, 4.10 had offered a series of
objections, four in all, that cast doubt on the reality of time.
Moreover, in his own positive account of what time is, Aristotle does
not address all of the objections or even provide a general proof that
time must exist in light of the objections. One may then criticize
Aristotle's account of time in light of his own theory of
science: Aristotle has proceeded to a theory of *what* time is
before providing us with a proof *that* time
 is.[11]



After presenting the objections to and opinions about time, Avicenna
begins his own account of time (Avicenna, [Ph], 2.10-13) by
filling this lacuna in Aristotle's presentation.
Avicenna's general strategy is to take as empirically obvious
certain facts about motion and then show that these facts cannot be
explained unless there is associated with motion a certain magnitude,
which we commonly identify with time. Only having shown that time
exists does Avicenna then provide a scientifically adequate
explanation of what time essentially is.



Avicenna's
 proof that time exists assumes these initial facts about moving
bodies:


1. If two moving bodies, which have the same speed, start and stop on
the same mark (say a blast of a horn), then they traverse the same
distance;
2. If two moving bodies, which again have the same speed, both stop
on the same mark, but start on two different marks, the body that
started on the second mark traverses less distance than the body that
started on the first mark;
3. If two moving bodies, which now have different speeds, start and
stop on the same mark, then the slower moving body traverses less
distance than the faster moving body.



On the basis of these facts, Avicenna observes that associated with
moving bodies there is a certain possibility or capacity
(*imkan*) to traverse some spatial magnitude. Moreover,
this capacity corresponds with the starting and stopping of the motion
(that is, a kinematic magnitude). When the body is moving slower, a
greater amount of this possibility is required to cover the same
spatial magnitude as that of a faster moving body. Given this
possibility's relation and correspondence with both spatial and
kinematic magnitudes, Avicenna concludes that this capacity must be
some magnitude that stands in some relation to the distance and speed.
This magnitude is neither the magnitude of the body, whether the
body's bulk or weight, nor the magnitude of the motion, whether
the speed or motivity, nor the magnitude of the distance traversed.
Instead, this magnitude--again, the possibility belonging to a
moving body to cover more or less distance at a fixed
speed--concludes Avicenna, is what we call time
(*zaman*).



While identifying time with a certain possibility to traverse some
spatial magnitude, provides one with a criterion for recognizing time,
it does not provide a proper scientific definition of what time
essentially is, that is, a definition in terms of genus and
difference. Thus, having shown that time exists, Avicenna next turns
to defining time and showing what time essentially is. In general,
Avicenna follows Aristotle and defines time as a "number of
motion when it is differentiated into prior and posterior parts"
(cf. Aristotle, *Physics* 4.1, 219b1-2). Time's
genus, then, is a certain number, that is, some measurable aspect or
magnitude, belonging to motion. Its difference is having essentially
prior and posterior elements. Here is it important to note that for
Avicenna, priority and posterity (*taqaddum* and
*ta`akhkhur*) are generic notions, with a number of
different species, like priority in eminence or location or time. For
Avicenna, the prior and posterior in Aristotle's definition
refers to what is prior and posterior in the distance traversed as
determined by the directedness of the motion over that distance. Thus,
the charges of some, particularly Galen, that Aristotle's
definition of time is circular, since it appeals to purportedly
temporal notions of before and after, is avoided. (See Lammer 2018,
ch. 6.2).



In all three of Avicenna's philosophical
encyclopedias--*The Cure, The Salvation* and *Pointers
and Reminders*--he notes that, more precisely, time is a
magnitude of *circular* motion with respect to the prior and
posterior. His insistence on circular motion rather than just motion
in general is that only circular motion can potentially have neither
beginning nor end. In other words, only circular motion can be
infinitely extended into the past and future.



While Avicenna has any number of arguments for the eternity of time
and the world, his proof for the existence of time in terms of a
possibility to traverse greater or lesser spatial magnitudes at a
fixed velocity provides the basis for one of his central physical
arguments for that thesis. The argument, which is a *reductio ad
absurdum* has one assume that God created time, and so motion and
moving bodies, at some first moment, *x*, in the finite past,
for example, 10,000 years ago. Prior to *x* nothing but God
existed, not even time. (Here let years be measured in solar rotations
as measured by the apparent motion of our sun. Also allow that the
present moment marks the completion of the 10,000 solar rotations, so
that right now is the second terminal point for this motion.) Avicenna
next observes that it is certainly possible that God could have made a
time, and so motion and moving bodies, 20,000 solar rotations in
duration, where this possible duration again reaches to the present
moment as its second terminal point. In this second scenario, 10,000
years of the full 20,000 year duration would exactly correspond with
the 10,000 years in the first scenario, namely, the period extending
from the present moment back to *x*. The remaining duration of
this possible 20,000-year motion would correspond with the possibility
for 10,000 solar rotations, which now would terminate at *x*
rather than beginning at *x*. (We can intuitively say that this
remaining possibility is prior to or earlier than *x*, although
Avicenna is careful not to beg any questions.) Now to say that there
is a possibility for 10,000 solar rotations (prior to *x*) is
just to say that (prior to *x*) there exist a possibility for a
sun (or other body) to traverse a certain distance (that is, number of
rotations) at a fixed speed. From Avicenna's earlier proof for
the existence of time, however, recall that the possibility for a
moving body to traverse a given distance at a fixed speed refers to
time. Consequently, since this possibility exists, time must exist.
Yet in order for time to exist, as Avicenna argued, motion and moving
bodies must exist. Therefore, concludes Avicenna, when nothing but God
existed, time, motion and a moving body also would have necessarily
existed, a blatant contradiction. It is the assumption that time is
finite, claims Avicenna, that gives rise to the contradiction. Since
this same argument applies to any finite duration of time, during
which one may suppose the world to exist, Avicenna concludes that
time, and so motion and moving bodies, must have existed infinitely
into the past. (For the same reason *mutatis mutandis* time,
and so motion and moving bodies, also must exist infinitely into the
future.)



While I have only scratched the surface of the riches of
Avicenna's natural philosophy, the above discussions provide a
number of the most basic points of his thought.