## 1. The Atomism of *Kal&amacr;m*


### 1.1 Atoms and Accidents



Although some early Muslim theologians maintained that there are
basically only accidents and that bodies are composites of bundles of
accidents, while others held that there are only corporeal bodies and
that everything else is constituted out of the interpenetration of
these bodies, most Muslim theologians included both
 atoms[1]
 and accidents in their ontology and additionally God. One way that
this ontology was justified was to begin with a proof for the world's
temporal creation. It was argued that if the world were not created,
then an infinite number of past days would have been traversed;
however, it was held as self-evident that an infinite, let alone
traversing it, is impossible. Thus the world must have been created at
some first moment. In that case, however, the world must have a
Creator. Thus there is what creates, namely, God, and what is created.
What is created was divided further into what occupies space, namely,
substances or atoms, and what does not, namely, accidents.



Occupying space (*tahayyuz*) was for the Muslim theologians the
necessary result of any thing's being a substance, and it was this
attribute of occupying space that confirmed the existence of
substances; for occupying space was held to be an attribute that was
directly perceived by the senses and as such could not be gainsaid.
Thus that substances exist was a matter of direct knowledge. Most
Muslim theologians additionally maintained that these substances also
have an atomic structure. This is not to say that they thought humans
could directly perceive an individual atom taken in
isolation--they did not; however, they believed that one could
demonstrate that the ultimate material constituents of the world must
be discrete rather than continuous. In general, their arguments for
atomic rather than continuous substances used paradoxes involving the
infinite. For example, it was argued that if a body were continuous,
then it would be divisible infinitely, in which case the body would
have an actually infinite number of parts that all adhere together to
form the body and that correspond with the infinite number of
divisions. The existence of an actual infinite is absurd, however, and
so the division of the body must terminate at a finite number of
indivisible parts or atoms. It does no good to say that the body has
only a potentially infinite number of parts corresponding to the
divisions rather than an actually infinite number; for it was argued
that if something is truly potential, then some agent, such as God,
must have the power to bring about or actualize that potentiality.
Thus, let God bring about the purportedly potentially infinite number
of divisions, in which case there would be an actually infinite number
of parts, which again is absurd. Similarly, it is of no avail to say
that the divisions are neither actual nor potential, but only
imagined, since what is truly impossible cannot be imagined, and the
existence of an actual infinite, it was believed, is truly impossible.
Another argument for the atomic structure of matter was a variation on
Zeno's dichotomy paradox, couched in terms of an ant's creeping over a
sandal. If a body were continuous, the argument runs, then should an
ant attempt to cross a sandal, it would first need to reach the
halfway point on the sandal, but before it could reach the halfway
point, it would need to reach its halfway point and so on infinitely.
Since an infinite cannot be traversed, the ant could never cross the
sandal, but of course a body such as a sandal can be crossed, and thus
bodies cannot be continuous, but must be composed of a finite number
of atomic parts. Yet another argument observed that differences in
size are accounted for by difference in the number of constituent
parts that make up the body. Now if bodies were continuous and so
composed of an infinite number of parts, then the number of parts
constituting a mustard seed and the number of parts constituting a
mountain would be the same, namely, infinite. Consequently the two
bodies should not differ in size; for one infinite cannot exceed
another, and yet such a conclusion is patently false. In the end, most
Islamic speculative theologians concluded that the matter constituting
the cosmos must be discrete rather than continuous.



Scholars have varied, however, concerning whether the indivisible
parts posited in the physics of these theologians should be viewed as
extended or point-like. Shlomo Pines argued that although later Muslim
theologians took atoms to have a certain measure and so were
considered extended, earlier theologians conceived of them as points.
Pines wrote his groundbreaking study of Islamic atomism,
*Beitrage zur islamischen Atomenlehre*, in 1936; however,
since then more *kal&amacr;m* texts have become available. In light
of these new sources, Alnoor Dhanani (Dhanani 1994, 90-140) has
successfully challenged Pines' suggestion and argued in its place that
the atoms of both early and later Muslim theologians are akin to
Epicurean minimal
 parts.[2]
 In this respect, the atom is the minimal space-occupying unit having
a wholly simple internal structure. As such the atom has neither
physical nor conceptual features into which it could be divided. As a
result of this understanding of atoms, although they function as the
components of the various magnitudes composed of them, such as lines,
planes and solids, they technically cannot be said to have length,
width and depth; for length, width and depth are always bounded by
extremities, whereas atoms simply cannot have any extremities, but
instead play the role of the extremities themselves of those things
that possess length, breadth and depth.



Atoms in themselves again are space occupying; however, among created
things the Muslim theologians also posited things that were in
themselves not space occupying, but rather inhered in atoms. Things of
this latter sort are the so-called 'accidents.' Muslim
theologians had argued for the existence of accidents from the fact
that atoms as such are similar or homogeneous, and so if there are
perceptible differences among bodies (and there clearly are such
differences), those differences must be due to differences among the
accidents that inhere in the atoms. The Muslim theologians then went
on to identify no less than twenty-two different kinds of accidents,
which include the obvious ones such as taste, color and smell as well
as adhesion, force, power and willing, but also less obvious ones such
as life and ceasing to exist.


### 1.2 Space and Time



In addition to God, atoms and accidents, certain Muslim theologians
also posited (empty) space. Averroes claimed that they did so in order
for there to be a place in which God temporally creates the atoms and
accidents, although such a claim is not clearly stated by the
theologians themselves. Concerning space two questions were debated
among the atomists: one, "Is space discrete (like the atoms that
occupy it) or continuous?" and, two, "Is there any
unoccupied space, or more exactly, could there be interstitial void
spaces between atoms or is the cosmos a plenum?"



While the Islamic theologians were virtually unanimous that matter is
discrete, they varied concerning the make up of the space that atoms
occupied, namely, whether space is constituted out of exactly fitting
atom-sized cells, or whether it is an open continuous expanse. The
debate centered on the issue of whether an atom could be placed on top
of two atoms such that the top atom straddles both of the bottom atoms
equally, for instance like the top block on a small pyramid made up of
three equally sized blocks. Those who argued that space must be
discrete did so on the basis that if it were not, then atoms would
turn out to be at least conceptually divisible, yet all Muslim
atomists agreed that atoms are not only physically indivisible, but
also conceptually indivisible. One of their most common arguments
began with the premise that the atom represents the smallest possible
magnitude. If space is continuous such that an atom could straddle two
atoms at their boundary and so form something like the aforementioned
three-block pyramid, then imagine two such pyramids joined at their
bases so that a gap is formed between the two top atoms. In that case,
the two top atoms would be separated from one another by a magnitude
less than an atom. Since the atom is the least possible magnitude, and
yet the magnitude between the two top atoms is purportedly less than
an atom, there is a contradiction; for there is a magnitude less than
the smallest possible magnitude. Those who argued for a continuous
space in contrast began with the premise that an atom can occupy and
measure any vacant space that is of a sufficient size to hold it. Thus
they had one imagine a line three atoms long and then two more atoms
on top of these, where one atom is exactly over the far-right, bottom
atom, for example, and another atom is exactly over the far-left
bottom atom. Next they had one imagine that at the exact same moment
two equal forces push the two top atoms towards each other. Either the
two atoms straddle the two boundaries of the three bottom atoms or
not. If they straddle them, then space must be continuous and not
discrete. If the opponent denies that they straddle the boundaries,
then he owes us an answer as to why they do not. Certainly the two
atoms can be moved in the manner described; for the only thing that
could prevent the motion would be the presence of an obstacle, and yet
the adjacent space into which the atoms are moved is supposedly empty.
Although this last argument offered a serious challenge to the notion
of discrete space, most of the later theologians were in fact inclined
to make all magnitudes discrete, whether that magnitude was corporeal,
spatial or even, as we shall see, temporal.



The second question concerning space involved the possible existence
of interstitial voids and focused on whether two atoms could be
separated from one another without a third atom's existing between
them. Dhanani (Dhanani 1994, 74-81) has classified the arguments
against such a possibility into two types: those involving non-being
and those involving the principle 'nature abhors a void.'
An example of the first kind of argument is the following. Assume that
two atoms are separated and that purportedly nothing exists between
them. Since one cannot perceive what does not exist, then in the
present case one should not be able to perceive a truly empty space
between the separated atoms; however, it seems evident that one would
be able to perceive the space between them and so that space could not
be truly empty, but must be occupied by an atom. An example of the
second sort of argument against interstitial voids is taken from the
medical arts and the use of cupping glasses for blood letting. It is
observed that when a cupping glass is placed over a vein and the air
is withdrawn, the flesh is drawn up into the cup. The detractors of
interstitial voids used this phenomenon as a verification of the
principle that nature abhors a vacuum. Consequently, since nature does
abhor a vacuum, void spaces will not exist in nature. Interestingly,
the proponents of interstitial voids were able to turn the cupping
glass phenomenon against their opponents to show that a void must
exist. They had one imagine that a sheet of atoms one atom thick is
placed between two cupping glasses and then the air is simultaneously
removed from both glasses. Either the sheet is drawn into one or the
other glass or it is not. If the sheet is drawn into one cupping
glass, there is a void in the other; if the sheet is not drawn into
one or the other cupping glass, then there is a void in both. In
either case a void has been produced.



As for time, although Moses Maimonides would claim in the *Guide of
the Perplexed* that Muslim theologians had a single atomic theory
of time, such a claim seems to be gainsaid by earlier sources
available to us (Maimonides 1963, ch. 73, premise 3). The theologian
al-Ash'ar&imacr; lists no less than three different accounts of the
moment and time (al-Ash'ar&imacr; 1980, 443). One theory makes time an
aggregate of moments, where the moment is a 'certain duration
between one action and the next action' (Ibid). It is not clear
whether the duration in question is some minimal temporal unit or some
potentially divisible temporal unit or even whether it could be either
depending upon the action in question. If it is some minimal temporal
unit, or time atom, then such a view would clearly advocate time's
having an atomic structure. A second theory considers the moment an
accident. The philosopher Avicenna (980-1037), who was writing a
little more than a generation later, commented on this view and noted
that the moment-accident posited by certain theologians is what
temporally locates an atom and that time is simply a collection of
such accidents. The final theory of time, which was by far the most
popular among the theologians, made the moment simply some
conventionally specified event, such as someone's entering a house,
and as such it has no special ontological status, whereas
'time' is just another name for the motion of the heavens.
It should be noted, however, that if the motion in question had an
atomic structure, then *ipso facto* time would be atomic, and
indeed many of those who held this conception of time endorsed atomic
motion. Although it not clear whether Muslim theologians explicitly
espoused a theory of atomic time, as we shall see in the next section,
some of them adopted a theory of occasionalism, which at least
implicitly endorses such a view.


### 1.3 Change and Causality



At least among those theologians who posited both atoms and accidents
in their ontology, most changes were explained in terms of one
accident's being replaced by its contrary or at least by something
acting like a contrary. In this case the atom changes, not the
accident, which in fact is annihilated by its contrary. Although
accident-replacement was the most general account of change, changes
that involve one type of body coming from another type of body (as for
example when fire is produced from burning wood or a spark is produced
from striking stones together) presented a special case that needed a
different analysis of change. Many theologians explained this sort of
change in terms of a theory of latency (*kum&umacr;n*), which
maintained that the fire atoms were already present in the wood or
stone, albeit latent in them, and then were made manifest through the
action of burning or striking.



Concerning the more prominent sort of change, namely,
accident-replacement, two further questions were debated: one,
"Does change form a single kind or not?" and two,
"Where does locomotion occur, that is to say, do the initial
atoms prior to the motion or the subsequent atoms after the motion
receive the accident of motion?" One argument used to show that
there are several kinds of motion observed that a single kind cannot
bring about contradictory things, as for example, a fire does not
produce cooling and heating; however, motions do bring about
contraries such as being to the right or being to the left or being
black and being white. Thus motion cannot form a single kind. An
interesting response to this line of thought, which itself constituted
an argument that motion forms a single kind, was the following. When a
person determines to move, say to the right, then at the next moment
there is both a motion and together with the motion a state of being
to the right, and so there is a rightward motion. Similarly, should
one choose to move to the left, there would be both a motion together
with a state of being to the left, and so a leftward motion. Motion
then can be analyzed into both a motion and a particular state or
manner of being that accompanies the motion (where perhaps the
accompanying state is understood as the result of the motion, although
it is not explicitly described as such). The motion considered in
itself is different from both the accompanying state (or result) as
well as the composite of the state and motion. Motions considered in
themselves, then, are similar with respect to being motion, but differ
with respect to the state or manner of being that accompanies the
motions, and so motion considered apart from the accompanying state is
a single kind.



The second issue debated by Muslim theologians concerning motion was
whether motion should be thought to occur in the first or second
moment, as for example whether there is motion at the very moment that
one determines to move rightward or at the moment when one is to the
right. There were no less than three answers given to this question:
one was that the accident of motion occurs at the initial location of
the moving body; another located the motion in some second location;
and finally one maintained that motion requires the body's being at
two locations at two different moments. Those who maintained that the
accident of motion occurs at the initial locations claimed that motion
is the force of a body that necessitates its being in the second
location. Since the force must be initially present in the body if it
is to move to the second place, and motion is identified with this
force, the accident of motion must be present while the body is still
in the initial place. Those who maintained that the accident of motion
occurs in the second location did so on the basis of a linguistic
analysis of the term 'motion'; for 'motion'
means there is a passage or transference of a body; however, there has
been no passage or transference of a body while it is still in its
initial location. Thus the accident of motion must occur in the second
location. Ab&umacr; Hudhayl (d. 841), who held that motion is different from
either the state or composite of state and motion, maintained that
motion requires two places and two moments; 'The body's motion
from the first place to the second place occurs in [the body] and [the
body] is in the second place at the exact moment it is in [motion],
which is the transference and emergence of [the body] from the first
place ... and so local motion inevitably involves two places and
two moments' (al-Ash'ar&imacr; 1980, 355).



Associated with issues concerning motion and change was that of
causality, namely, "What or who is the agent that brings about
change?" Many of the earlier theologians subscribed to a theory
of engenderment (*tawallud*), which preserved a degree of
causal efficacy for humans, whereas most later theologians adopted an
occasionalist worldview, which reserved all agency for God and God
alone. For the earlier theologians causal agency required a full
knowledge (*'ilm*) that one is acting as well as the
knowledge of what results from that action. Thus causal agency is
limited to God and humans. That humans had the power to engender
certain actions was assumed by most of the earlier theologians. The
question, then, was whether humans had the power to engender action
solely in themselves or in other things as well. One of the arguments
used by those who thought humans could engender effects in things
other than themselves came from the knowledge criterion for agency. It
took as an example that when a person beats another, he knows the
beating of the other, in which case the knowledge is of the action of
the one beating the other (al-Ash'ar&imacr; 1980, 401-402).
Generalized, the argument seems to be that if one knows that one is an
agent (and again it was taken for granted by the early theologians
that humans are agents), then one must know the effects of his action,
and yet one knows that the effects of certain actions are in others,
as in the case of beating and so causing pain. In contrast, others
argued that humans only engender actions within themselves, and it is
God who brings about the effect in others, as for example, a human may
produce the action of willing to throw a stone, but it is God who
actually causes the stone to move. One way of defending this thesis
was to observe that God creates bodies all at once and that at each
moment He recreates them (Ibid, 404). The assumption seems to be that
since God recreates bodies, human or otherwise, at every moment, no
body survives between two moments such that an action willed in the
human body at one moment could be causally efficacious on some other
body at a second moment; for in one sense any purported efficacy of
what was willed at one moment is wholly disconnected with the events
of some second moment.



This latter argument taken to its logical conclusions, however,
virtually entails occasionalism, that is, the view that at each moment
God recreates the world, its atoms and accidents as well as all
actions, whether that of a human or not, and so it is God alone who is
occasioning the events that occur in our world. Indeed later
theologians would embrace such an occasionalist worldview. Their
preferred argument for occasionalism, however, was not the one
sketched above, but one based on the notion of possibility
 (*istit&amacr;'a*).[3]
 The argument roughly was that a creature only performs some action if
it possesses the possibility to perform that action. Whenever the
creature possesses this possibility, the possibility is either
actualized or not. On the one hand, to affirm a non-actualized
existing thing, such as an un-actualized possibility, is tantamount to
affirming a non-existing existing thing, which is a patent
contradiction. On the other hand, if the possibility is actualized,
then the creature must be performing the correlative action, and will
always be doing so when it possesses the actualized possibility, but
of course created things sometimes act and sometimes do not. Therefore
the possibility for a creature to perform any given action must be
created for it at any time it acts, and it is God who is constantly
creating the possibility to act, and so in effect the correlative
action, at every moment something acts. In short, all agency must
belong to God and God alone.


### 1.4 Al-Nazz&amacr;m and Leaps



Again as a general rule most of the speculative theologians adopted an
atomistic framework for explaining natural phenomena; however, such a
position was not without its critics even within the *kalam*
tradition itself, and the most notorious of these critics was Ibrahim
al-Nazz&amacr;m (d. ca. 840). Al-Nazz&amacr;m denied the atom-accident ontology of
most theologians and instead maintained that with the one exception of
the accident of motion everything else in our world was a body.
Moreover, bodies, as well as space, did not have an atomic structure,
but a continuous one according to al-Nazz&amacr;m. Affirming continuous
space and motion left al-Nazz&amacr;m vulnerable to Zeno-style paradoxes,
and indeed the atomist Abu Hudhayl openly confronted him with the
ant-sandal paradox sketched above. Al-Nazz&amacr;m's solution was to
maintain that a moving object, such as an ant, could cross a
continuous space with its infinite number of halfway points by means
of a leap (*tafra*). The general idea was that a moving body
could cover a continuous space by making a finite number of leaps and
that during each leap the moving body is not in the intervening
spaces. In other words, a moving body leaps from some first place to a
third place on a continuous magnitude without having passed through
any second place between the two.



Despite the counterintuitive nature of al-Nazz&amacr;m's suggestion, he
argued that even the atomists had to posit leaps as well. He had one
imagine the rotation of a millstone. Now in a single rotation an atom
at the outer edge of the wheel would traverse a distance equal to the
circumference of the wheel, whereas an atom at the hub would traverse
a shorter distance equal to the circumference of the hub. Since the
atom at the outer edge is traversing a greater distance in an equal
time as the atom at the hub, the atom at the outer edge must be moving
faster than the atom at the hub. Al-Nazz&amacr;m next observed that there is
only one of two ways to explain this phenomenon: either the atom at
the outer edge leaps over some of the intervening atomic cells, or the
atom at the hub rests at some of the atomic cells for a few moments
while the atom at the outer edge catches up. The preferred atomist
solution to differences in velocity was to posit that slower moving
objects have a greater number of intervallic rests than faster moving
objects; however, al-Nazz&amacr;]m disallowed this solution with respect to
the rotating millstone on the grounds that in that case the millstone
would fragment as certain atoms rest while others keep moving. In
other words, some atoms that at the beginning of the motion had been
next to other atoms would have moved away from each other as the ones
nearer the rim kept moving in order to cover the greater distance and
the ones nearer the hub rested in order to cover only their respective
distance, and so by the atom's moving away from each other, the
millstone as a whole would fragment and break up. Yet, argued
al-Nazz&amacr;m, it is directly observable that the stone does not fragment,
and thus even the atomists must be committed to leaps. (For a discussion of al-Nazz&amacr;m's theory of leaps and possible historical sources available to him see Chase (2019).)


## 2. *Falsafa*: Neoplatonized Aristotelianism in the Islamic World


### 2.1 The Definition and Form of Motion



The above provides a very general outline of one of the prominent
intellectual approaches to natural philosophy in the Arabic-speaking
world of the medieval period. The second major tradition of natural
philosophy, *falsafa*, had its origin in Aristotle's physical
writings and the Graeco-Arabic commentary tradition that arose up
 around them.[4]
 Since natural philosophy, at least as it occurred in the
Greek scientific tradition, is the study of natures, and natures are
causes of motion or change, understanding what motion is and the
conditions necessary for motions within a broadly Aristotelian
framework was the primary focus of natural philosophers working in the
*falsafa* tradition. Aristotle himself had defined motion as
"the *entelekheia* of potential insofar as it is
such" (*Physics*, III 1). One of the exegetical issues
with which earlier Greek commentaries struggled was how to understand
the enigmatic term *entelekheia* in Aristotle's definition, a
term it would seem that Aristotle himself coined. Some argued that
*entelekheia* must refer to a progression or process towards
some end or perfection. Others argued that *entelekheia* must
refer in some sense to the completed actuality of some partial end or
perfection. The dispute in the ancient world, then, settled upon
whether *entelekheia* is itself a process term or not. If
*entelekheia* is a process term then it is clear how
Aristotle's definition of motion describes a process, but it does so
by assuming a process term in the definition, whereas Aristotle's
definition of motion was intended to provide the most basic account of
what a process is and so should not presuppose a process. If
*entelekheia* is not a process term, then Aristotle's
definition avoids circularity, but it is no longer clear how it
describes a process, since a completion or perfection is the end of a
process, not a process itself. The above roughly presents a key
philosophical debate surrounding Aristotle's definition of motion as
it reached Arabic-speaking
 philosophers.[5]



Part of this terminological issue was resolved by the Arabic
translation of Aristotle's *Physics* itself; for there
Aristotle's definition is rendered "motion is the perfection
(*kam&amacr;l*) of what is in potency inasmuch as it is such,"
where the translation of *entelekheia* as
'perfection' would decidedly bias Arabic-speaking
Aristotelians against the process interpretation of that term. Thus
the primary issue for these philosophers involved explaining how
Aristotle's definition of motion actually describes a process. Perhaps
the most sophisticated solution to this issue was that of Avicenna,
who in effect argued for motion at an instant (Avicenna 2009, II.1,
4-6; Hasnawi 2001; McGinnis
 2006a).[6]
 Avicenna begins his analysis by distinguishing two senses of motion,
one of which might be termed 'traversal-motion' and the
other 'intermedial-motion'. Traversal-motion occurs when
one observes an object in two different, opposing states, for example,
being *here* and then being *there*. Now in the world, a
moving object is not simultaneously partially here and partially there
during its motion. Consequently, in the world, motion is not some
continuous thing that at any moment actually extends between here and
there in the way that the distance continuously extends between two
points; rather, the relation between these two states is impressed
upon the mind, and it is this mental impression that gives rise to the
idea of traversal-motion, that is, the idea of motion as a continuous
extended magnitude.



As for intermedial-motion, that is, the motion that exists
extra-mentally, here is where Avicenna's novel analysis of motion at
an instant comes to play. He first notes that the perfection in
question in Aristotle's definition could not refer either to the
starting point or to the ending point of the motion, since in the
first case the motion has not yet begun and in the second case the
motion is already completed. Thus the perfection must refer to some
perfection of the moving object while it is in an intermediate state
between these two extremes. So, for example, an object moving between
*x* and *z* is not in motion at either *x* or
*z*, but only while it is in the space between *x* and
*z*. That intermediate state, in turn, could refer either to
the whole continuous medium between the two extremes or to a point.
So, again, the intermediary state might refer to the whole of the
motion along the entire continuous distance between *x* and
*z* or to the moving object's being at one or another single
point along the distance, as for example, *y*. Avicenna next
observed that at every instant during a moving object's continuous
motion it is moving, and yet there is no instant at which the whole of
the motion exists as some extended magnitude. Thus the perfection in
the definition of motion must refer to the perfection of the moving
thing at one or another point between the starting and ending points,
albeit, as the moving thing is at that point for only an instant. It
is the very fact that the moving object is only at the intermediate
point for precisely an instant that guarantees that the object is
undergoing motion; for should it remain at some point for more than an
instant, and so for a period of time, the object would in fact be at
rest at that point.



Not all were pleased with Avicenna's interpretation of Aristotle's
definition of motion and some authors challenged not merely Avicenna
but even the need for Aristotle's own recondite definition of motion
in term of an *entelekheia*. Such an attitude was certainly the
case in the Islamic East during the period immediately following
Avicenna as witnessed in the works of Ab&umacr; l-Barak&amacr;t al-Baghd&amacr;d&imacr; (d.
1165) and Fakhr al-D&imacr;n al-R&amacr;z&imacr; (d. 1209). Ab&umacr; l-Barak&amacr;t, although part
of the *falsafa* tradition, was also a critical reader of both
Aristotle and Avicenna, whereas Fakhr al-D&imacr;n al-R&amacr;z&imacr;, while working
within the *kal&amacr;m* tradition seriously engaged the philosophers
and even wrote a commentary on one of Avicenna's shorter philosophical
encyclopedias. They preferred to define motion as a gradual or
not-all-at-once emergence from potency to act. Avicenna himself had
considered this definition but found it wanting. Specifically,
Avicenna complained that this definition is ultimately circular
(Avicenna, 2009, II.1, 3). Thus he noted that gradual/not-all-at-once
are understood in terms of time, and time, following Aristotle, is
defined in terms of motion, namely, as the measure of *motion*
with respect to before an after. Consequently, complains Avicenna, an
understanding of time requires that one already understand motion, but
the suggested understanding of motion appeals to an understanding of
time. In response to this objection, Ab&umacr; l-Barak&amacr;t noted that both
Aristotle (*Posterior Analytics*, 1.13, 78a22-b32) and
Avicenna (*Kit&amacr;b al-burh&amacr;n*, III.2, 202-3) recognize a
difference between something's being *better known to us* and
being *better known by nature*. Something is better known to
us, if it is a matter of direct sensible observation, whereas it is
better known by nature if one grasps the underlying causal
explanation. The standard example is drawn from the observation that
what is near does not twinkle, and the planets do not twinkling. Thus
Aristotle and Avicenna observe that from the fact that the planets do
not twinkle (a fact better known to us) one can infer that the planets
are near. One can then convert this conclusion and use it a
demonstration that causally explains why the planets do not twinkle,
namely, because they are near (now a fact better known by nature). The
appearance of circularity is purportedly illusory, since in the two
inferences, the premises are not being used in the same way: in one
case the premise explains something better known to us and in the
other something better known by nature. Whether one accepts Aristotle
and Avicenna's analysis is less important than that both of them
seemed committed to it, and Ab&umacr; l-Barak&amacr;t exploits this fact. He
argues that the supposed circularity underlying defining motion in
terms of the gradual emergence from potency to actuality is nothing
more than a case of a conversion from something better-known-to-us to
something better-known-by-nature.


1. time-better-known-to-us &Rarr; motion
2. motion &Rarr; time-better-known-by-nature



Fakhr al-D&imacr;n al-R&amacr;z&imacr; in his *al-Mabahith al-mashriqiyya*,
moreover, approvingly repeats Ab&umacr; l-Barak&amacr;t's suggestion:



> 
> 
> Conceptualizing the true nature of "all-at-once,"
> "not-all-at-once" and "gradual" are all
> primitive conceptualizations owing to the aid of sensation. Sure, we
> understand that these things are known only by reason of the now and
> time, but that requires a demonstration. It is possible that the true
> nature of motion is known by these things, and thereafter motion fixes
> a knowledge of time and the now, which are reasons for those first
> things' being conceptualized, but in that case no circle is entailed.
> This is a fine answer. (ar-R&amacr;z&imacr;, Fakhr al-D&imacr;n, 1990, vol. 1, 670)
> 
> 
> 



Al-R&amacr;z&imacr;'s idea, like Ab&umacr; l-Barak&amacr;t's, is that notions like all-at-once
and gradual are known immediately through sensation. While it is true
that time and the now, respectively, provide the basis in reality for
our perceptions of things emerging gradually or all-at-once, such a
relation must be demonstrated and is not immediate. Since the notions
of gradual and all-at-once are immediate, they can provide us with the
true nature of what motion is. Having identified what motion is, one
can use it then to define time and so explain the gradual and the
like.



Ab&umacr; l-Barak&amacr;t and al-R&amacr;z&imacr;'s definition of motion was in turn picked up
by the polymath, Ath&imacr;r al-D&imacr;n al-Abhar&imacr; (d. 1262 or 1265), who used it
in his highly successful textbook of natural philosophy, *Hidayat
al-hikma*. The definition would be common at least until it was
challenged by the great Shia philosopher and theologian, Mull&amacr; Sadr&amacr;
(d. 1636). Drawing on Avicenna's earlier account of motion, which
Mull&amacr; Sadr&amacr; defends at least in his *Sharh al-Hidaya* (Mull&amacr; Sadr&amacr;, 2001, 103-105), he reminds his reader that motion is
itself an equivocal term and is said in no less than two ways:
traversal-motion and intermedial-motion. Ab&umacr; l-Barak&amacr;t and Fakhr
al-D&imacr;n al-R&amacr;z&imacr;'s rejoinder to Avicenna's original charge of
circularity works, observes Mull&amacr; Sadr&amacr;, only if the sense of motion
is the same in the two converted premises. They are not maintains
Mull&amacr; Sadr&amacr;. While it is true that time-better-know-to-us can be used
to understand motion, the motion in question is traversal-motion, that
is, the idea of motion that, according to Avicenna, exists only
mentally. In contrast, the sense of motion used to explain the nature
of time is not traversal-motion but intermedial-motion, that is, the
extra-mental motion that exists in the world. Thus the actual premises
are not those noted by Ab&umacr; l-Barak&amacr;t and Fakhr al-D&imacr;n al-R&amacr;z&imacr;, but the
following two:


1. time-better-know-to-us &Rarr; traversal-motion
2. intermedial-motion &Rarr; time-better-known-by-nature



The conversion thus does not go through, since none of the terms in
the two premises are common. Mull&amacr; Sadr&amacr; then concludes his account of
motion by repeating and defending Avicenna's idea that the form of
motion as it exists in the world involves motion at an instant, and it
is this account that comes to predominate in the Muslim East
(certainly Muslim India) until at least as late as the 1850s. (For a discussion of Avicenna's conception of motion and the post-Avicennan reception of that definition see McGinnis (2018).)


### 2.2 The Infinite and the Continuous



Although the above argument provides some of the medieval Arabic
accounts of the form of motion as discussed within the
*falsafa* tradition, there are other causal factors and
necessary conditions involved in the analysis of motion. Some of the
most significant conditions are (1) the infinite (particularly as it
appears in descriptions of the continuous, e.g., the continuous as
what is potentially divisible infinitely), (2) place and, closely
related to place, (3) void, and also (4) time.



The standard argument against the *actual* existence of the
infinite can be traced back at least as early as al-Kind&imacr; and
stretches throughout the entire classical period of Arabic or Islamic
philosophy up to at least as-Suhraward&imacr; (al-Kind&imacr; 1950, 115-116 &
202-203; Avicenna 1983, III.8, 212-214; id., 1985, IV.11,
244-246; Ibn B&amacr;jja 1978, 36-37; Ibn Tufayl 1936,
75-77; and as-Suhraward&imacr; 1999,
 44).[7]
 A simplified version of the argument runs as follows. Imagine two
rigid beams, which cannot give way so as to stretch. Moreover, suppose
that these beams extend from the earth infinitely into space. Next,
imagine that some finite length, *x*, is removed from one of
the beams, for instance, the distance between the earth and the end of
our galaxy; call that beam from which *x* has been removed
*R*. Now imagine that *R* is pulled toward the earth,
and then is compared with the beam from which nothing had been
removed. Call that Original beam *O*. In this case, since the
beams are rigid, *R* could not have stretched so as to extend
the extra length *x*. Consequently, *R* must be less
than *O* by a length equal to *x*. Now imagine the two
beams lying side-by-side and compare them. Since they are
side-by-side, either *R* corresponds exactly with *O*
and so is equal to *O* in spatial extent, or *R* falls
short of *O*. On the one hand, if *R* does not fall
short of *O* but exactly corresponds with, and so is equal to,
*O*, then *R* is not less than *O*. But it was
posited that *R* is less than *O* by the length
*x*, and so there is a contradiction. If, on the other hand,
*R* falls short of *O* on the side extending into space,
then where it falls short of *O* is a limit of *R*, in
which case *R* is limited on both the side extending into space
and on the earth side. In that case, *R* is finite, but it was
assumed to be infinite, another contradiction. In short, if an
actually infinite extension could exist and can be shortened by some
finite amount (which is assumed as given), then the shortened amount
must be either equal to or less than the original infinite extension;
however, either case leads to contradiction. Therefore, the premise
that gave rise to the contradictions, namely, an actually infinite
extension could exist, must be rejected.



Al-Kind&imacr; went on to use the conclusion of this argument to maintain
that time itself must be finite and consequently that the period of
time during which the world has existed must be finite. Therefore, he
concluded on the basis of this argument that the world must have been
created at some first moment of time and so is not eternal (al-Kind&imacr;
1950, 121-122 & 205-206). Al-Kind&imacr;'s argument for the
temporal finitude of the cosmos is also the same one preferred by
advocates of *kal&amacr;m*, and is none other than the
"*Kal&amacr;m* Cosmological Argument," recently
re-popularized by William Lane Craig (Craig, 2000). In opposition to
al-Kind&imacr;'s application of the foregoing argument to time, most
subsequent philosophers in the *falsafa* tradition took the
conclusion of the above argument to entail only that an actual
infinite magnitude or number of things could not exist, that is to
say, there cannot exist some wholly completed infinite all of whose
parts exist at one and the same moment in time. In those cases where
not all of the magnitude or its parts exist together at a single
moment--as in the case of time and its parts, the past, present
and future--then an infinite, they argued, could exist, albeit
only potentially.



In addition to offering a means of understanding the eternity of the
universe, the notion of a potential infinite was also useful for many
natural philosophers in that it provided a way to explain the
continuous. Although strictly speaking Arabic-speaking philosophers
followed the definition of the continuous given by Aristotle in
*Physics* V 3, which is in terms of two touching limits
becoming one and the same, they nonetheless further glossed this
definition in terms of being divisible into ever smaller portions
without limit, that is, as being potentially divisible infinitely.
Clearly the notion of the continuous ran afoul of the atomists'
arguments against continua, which we have seen above. In response to
such arguments, the philosophers insisted that a continuous magnitude
is properly speaking one and unified and as such it is not composed of
an infinite number of parts and so does not have an actually infinite
number of divisions (e.g., Avicenna 1983, III.2, 8-10). They
further maintained that properly speaking one cannot even say that a
continuous magnitude has an infinite number of potential divisions, at
least not in the sense that an infinite number of non-actualized
divisions exist latently in the continuous magnitude such that they
could ever all come to exist so as to be all actualized at once. For
the philosophers, there is no real sense that the divisions are in the
magnitude, whether actually or potentially; rather, the sense in which
a continuous magnitude is potentially divisible *ad infinitum*
is that one can mentally posit accidental divisions within the
magnitude without end. These accidental divisions would be like the
*left side* when pointing to the left, and the *right
side* when pointing to the right. There are not real left- and
right-divisions within the magnitude apart from the positing. In other
words, nothing in the magnitude precludes or hinders one from mentally
positing ever-smaller divisions. For example, think of 1/2, and 1/2
again, and so forth; however, those halves are not really or actually
in the magnitude until unless one goes through the process of mentally
(or even physically) marking them off. Consequently, when the
philosophers say that the continuous is potentially divisible
infinitely, they mean that it is impossible to complete the process of
division such that the resultant is an actually infinite number of
parts. Thus, there is an inherent contradiction in the theologians'
objection that if the continuous is potentially divisible infinitely,
there must be a power, such as God, that can actualize all the
potential divisions; for such an argument absurdly entails that what
by definition cannot be completed is completed.


### 2.3 The Criticism of Atomism and *Minima Naturalia*



Having shown how the notion of the continuous does not lead to the
absurdities presented by the atomists, the philosophers next argued
that atomism is itself conceptually incoherent. Perhaps the most
important thing to bear in mind when considering Arabic-speaking
philosophers' arguments against atomism is the nature of the atoms
that they want to reject. "Atom" comes from the Greek
*atomos* and literally means that which cannot be cut or
divided. Within the medieval Muslim world, philosophers and
theologians alike recognized two sorts of division: "physical
divisibility" and "conceptual divisibility." The
first and true sense of divisibility for Avicenna, physical
divisibility, is the form of division that actually brings about a
separation and discontinuity within the magnitude. It involves
physically dividing a magnitude into two actually distinct parts. The
second type of division, namely, conceptual divisibility, involves
only the accidental partition of the magnitude. The parts involved in
this type of divisibility are the accidental parts noted above that
result from a certain psychological process, namely, division through
mere positing. As for their critique of atomic theories of magnitude,
they came in two general forms: arguments attempting to show that
atomism cannot even approximate our best mathematics and arguments
attempting to show that the notion of minimal parts that are not even
conceptually divisible is inadequate to describe certain basic natural
phenomena.



The most common mathematical criticism against atomism was that if
atomism were correct, then one could not even approximate the
Pythagorean theorem, and yet the Pythagorean theorem is the best
attested theorem in mathematics (e.g., Avicenna 1983, III.4, 190). The
argument begins by envisioning atomic space something like a
chessboard, which is a fair approximation of how the theologians did
think of atomic space. Next imagine inscribed on this atomic space a
right isosceles triangle, whose legs are four atoms longs. The length
of the hypotenuse of the triangle must equal the number of atoms that
run down the diagonal of the purported atomic square; however, given
that the space is atomic, that length would be only four atoms long.
Now since according to the Pythagorean theorem the square of the sum
of the legs should equal the square of hypotenuse, one would have
42 + 42 = 42, if the space were
atomic, but this is clearly false. Since the absurdity arose from
taking jointly the two assumptions that the space is atomic and the
Pythagorean theorem, one of them must be rejected, and the obvious
candidate is to deny that there are minimal atomic units of magnitude.
It does no good to say that the diagonal of an atom is longer than its
sides; for such an assumption entails that there are lengths shorter
than the smallest part, namely, that amount by which the atom's
diagonal is supposedly longer than its side, but a length shorter than
the shortest length is a contradiction. In short, it would seem that
if the Pythagorean theorem is correct, then the atomism of the
theologians is false.



A second type of argument used against atomism involved showing that
that the notion of conceptually minimal parts was philosophically and
scientifically wanting (e.g., Avicenna 1983, III.4, 189-190).
The issue at stake concerned how atoms could be aggregated so as to
give rise to the physical bodies that we observe around us. There seem
to be four possible ways: (1) the atoms could be in succession with
one another, but in no way touching one another; or the atoms could be
touching one another, in which case they might do so by being (2)
contiguous with one another, (3) continuous with one another, or (4)
interpenetrating one another. Clearly the bodies we observe around us
are unified wholes, that is, their parts are together and so form
solids rather than being 'cloud like.' Thus the atoms
cannot merely be in succession. If the atoms were in contact with one
another by interpenetrating each other, then bodies would never be
larger than a single atom, but again this outcome is empirically
false. Thus, atoms must be in contact by either being contiguous or
continuous with one another. In that case, however, imagine three
atoms, *A**B**C*, that are either contiguous with
or continuous with one another. In this case, *B* must be
separating *A* from *C*; for if *B* were not
separating *A* from *C*, then, for instance, *A*
could be in contact with *C* despite *B*'s
presence such that *A* would in fact be interpenetrating
*B*; but this alternative has already been excluded.
Consequently, there must be something, *x*, in virtue of which
*B* is in contact with *A* and something, *y*, in
virtue of which *B* is in contact with *C*, and
*x* and *y* must be separate from each other, otherwise
*A* and *C* would not be separate from each other. In
that case, however, *B* can be conceptually divided into
*x* and *y*, and yet *B* was assumed to be a
conceptually indivisible, and so there is a contradiction. In short,
the conceptually indivisible parts of the atomists are inadequate to
explain the existence of the physical bodies that we observe around
us.



Despite their rejection of conceptually minimal parts, certain Muslim
philosophers, following Aristotle (*Physics*, 1.4,
187b13-21) and some of this Greek commentators such as John
Philoponus (d. 570), conceded that bodies do have physically minimal
parts. To be exact they recognized *minima naturalia*, that is
limits to how far a specific kind of body, like water or flesh, could
physically be divided and still remain that specific kind of body and
not instead be converted into some other kind of body (Avicenna, 2009,
III.12, 2-9; Averroes, 1962, *ad* 1.4 & 3.7; for
studies see Glasner, 2001 & 2009, ch. 8; Cerami, 2012; McGinnis,
2015). In order to appreciate one version of their argument for
*minima naturalia* (Avicenna 2009, III.12, 8), one must first
consider the theory of the elements and elemental change, which it
presupposes. According to ancient and medieval elemental theory there
are associated with each of the traditional four elements two primary
qualities, one each from two pairs. These pairs include the primary
qualities hot/cold and wet/dry. The element earth is associated with
the qualities cold-dry, water with cold-wet, air with hot-wet and fire
with hot-dry. These primary qualities are related to the elements'
material cause. When these primary qualities are altered through a
process of physical causation--that is, there is some motion or
change in the element such as an increase or decrease in the degree of
hotness, coldness, dryness or wetness--the alteration prepares or
pre-disposes the underlying matter so that it is suited to receive a
new substantial form. So, for example, when water, which again is
associated with a cold-wet combination, is sufficiently heated, the
underlying qualitative disposition is no longer suited to the
substantial form of water. Consequently, at some point in the heating
process the matter receives a new substantial form that is compatible
with the matter's new underlying qualitative disposition, namely, the
matter receives the form of air. And, indeed, the steam produced from
vigorously heating water does have a definite air-like quality. An
account similar to the one just limned also applies to more complex
cases of mixtures, like blood, flesh, and seeds, which are involved in
animal and plant generation.



As for the proof for the existence of *minima naturalia*
itself, it begins by repeating that division is spoken of in two ways:
physical division--which brings about an actual division,
severance or fragmentation of the magnitude--and conceptual
division--which involves a mere mental division or positing that
leaves the magnitude intact. Again the argument is specifically about
physical divisibility. The argument runs thus: The smaller the
quantity of a given substance the more apt it is to be acted upon by
surrounding bodies. So, for example, all things being equal, it takes
longer for a body of water to cool down a ton of molten iron than for
that same body of water to cool down an ounce of molten iron, and
similarly, a blast furnace is able to heat the same ounce more quickly
than the ton. So again the smaller the physical divisions of a given
substance are, the more disposed that reduced quantity of the
substance becomes to the primary qualities of the surrounding bodies.
Below a certain limit, the ratio between the strength of the primary
qualities of the surrounding bodies and those of the body being
divided is such that the qualities of the surrounding bodies overcome
those of the divided body. At that moment, the divided substance's
underlying qualitative disposition becomes altered so as no longer to
be suitable to its elemental form, and the matter receives a new
substantial form. So, for example, imagine a cup of water that is
surrounded by hot, dry summer air. Now imagine half that amount of
water, and then keep taking halves. At some point the amount of water
is so small that the water simply evaporates as it were
instantaneously, or, as medieval natural philosophers would have it,
the form of water in that minuscule physical quantity is immediately
replaced with the form of air. In short, for these thinkers the
elements, as well as more complex mixtures, have natural minima beyond
which they cannot be divided and still be capable of retaining their
species form, for the primary qualities of the surrounding bodies so
alter that body that it is no longer suitable for sustaining its
initial form. There must be, then, the argument concludes, *minima
naturalia*.


### 2.4 Place and Void



Aristotle in his *Physics* (IV 4, 212a2-6) had argued
that place is the first motionless limit of a containing body. His
account, however, came under heavy criticism from the late Greek
Neoplatonic thinker John Philoponus. Philoponus asserted that place is
a (finite) three-dimensional extension that though never devoid of
body on its own, nonetheless, considered in itself is self-subsistent,
and so in theory could exist independently of a body. One of the ways
that Philoponus defended this thesis was to argue that Aristotle's
account of place was inconsistent with other features of his
philosophical system. Aristotle seemed committed to the following
three claims: one, if something has a place, then given his definition
of 'place' there must be something else beyond that thing
that contains it; two, once approximately every twenty-four hours the
outermost celestial sphere makes a complete westward rotation; and
three, there are only three generic types of motion: motion with
respect to (1) place, (2) quantity and (3) quality. Given these
beliefs, Philoponus posed the following dilemma. Either the universe
as a whole has a place or it does not. If it has a place, then
Aristotle's definition of place is wrong since there is nothing beyond
the universe itself that contains it. If the universe as a whole does
not have a place, then Philoponus asks, "In what respect does
the outermost celestial sphere move during the course of its diurnal
motion?" Again the motion either could be (1) with respect to
the category of place (as when something undergoes locomotion), (2)
with respect to the category of quantity (as when something grows or
shrinks) or (3) with respect to the category of quality (as when
something changes color or temperature and the like). Clearly the
universe's diurnal motion is not with respect to either of the
categories of quantity or quality, and thus it must be with respect to
place; however, in this horn of the dilemma it was assumed that the
universe has no place, and so there is a contradiction. Although
Philoponus had other arguments for his belief that place is the space
occupied by a body, this dilemma is the one that most exercised
subsequent Arabic-speaking natural philosophers.



Virtually all Arabic-speaking philosophers adopted Aristotle's account
of place as the limit of a containing body, and so the challenge was
to explain whether the universe as a whole has a place and in what
sense it can be said to move. There were two approaches to this issue:
one was to deny that the universe had a place and then explain in what
sense it could be said to move, while the other was to assert that the
universe has a place and then show how its having a place is
consistent with Aristotle's definition of place. Avicenna) represents
the first approach, whereas Ibn B&amacr;jja and Averroes (and it would also
seem al-F&amacr;r&amacr;b&imacr;) took the second approach.



So for instance, Avicenna denied that the universe has a place, but he
likewise further denied that the list of the types of motion exploited
by Philoponus in his dilemma is exhaustive: one must further add to
that list, maintained Avicenna, motion with respect to the category of
position (Avicenna 1983, II.3, 103-105.13; McGinnis 2006b).
According to Avicenna, then, all cases of rectilinear motion, that is,
motion from some spatial point *x* to a distinct spatial point
*y*, are cases of motion with respect to the category of place,
whereas all cases of spinning or rotating, where the moving object
does not depart from a given spatial location, are cases of motion
with respect to the category of position. Since the universe during
its daily rotation does not depart from one spatial location to
another it does not need a place and yet it can still move albeit with
respect to the category of position, concluded Avicenna.



A contrasting approach is that of Ibn B&amacr;jja, who, we are told, followed
al-F&amacr;r&amacr;b&imacr;; this position would also be the one that Averroes in
general would adopt, albeit with certain reservations and
modifications (Lettinck 1984, 297-302; Averroes 1962,
141E-144I). Ibn B&amacr;jja begins by slightly modifying Aristotle's
definition of place; instead of being the first *containing*
limit, place is now identified with 'the proximate
*surrounding* surface.' The shift in language is slight,
but it allows Ibn B&amacr;jja the opportunity to distinguish between two
senses of 'surrounding surface.' Things can either be
surrounded by a concave or convex surface, maintained Ibn B&amacr;jja. A
Rectilinear body, that is, a body that undergoes rectilinear motion,
has as its place a concave surface that is outside of it, whereas a
truly spherical body, that is, a body that undergoes circular motion
or rotation, has as its place a convex surface, which is inside of the
rotating body and is in fact the surface of the center around which
the body rotates. Since the universe rotates around the earth, at
least according to ancient and medieval cosmology, the universe is
'surrounded' by the earth at the earth's convex surface,
and thus the universe as a whole has a place, namely, the surface of
the earth. Averroes' modifications make the surface of the earth only
the accidental place of the universe rather than the essential place,
but since Aristotle had spoken of the universe's having a place only
accidentally, the Commentator was satisfied.



Natural philosophers writing in Islamic lands did not necessarily
defend Aristotle's account of place against Philoponus' critique out
of a slavish adherence to Aristotle, but because Philoponus'
alternative account of place entailed that there could be a void
space, and most Arabic-speaking philosophers thought that the
existence of the void was both physically impossible as well as
conceptually incoherent. Aristotle himself had presented numerous
physical impossibilities associated with a void, whereas
Arabic-speaking philosophers explored the conceptually incoherent
aspect of the notion of a void in order to show that its existence is
impossible. For example, in *On First Philosophy* al-Kind&imacr;
observed that the meaning of 'void' is a place in which
nothing is placed; however, he continued, place and being something
placed are correlative terms neither of which proceeds the other, and
so if there is a place, there must be something placed, and if there
is something placed, there must be a place. Consequently there cannot
be a place without something placed in it. Again, however, a place
without something placed in it is precisely what is meant by
'void.' Therefore, concluded al-Kind&imacr;, it is impossible
that an absolute void exists (al-Kind&imacr; 1950, 109).



Al-F&amacr;r&amacr;b&imacr; in a small treatise on the void took a similar approach, but
now from the direction of what is meant by 'body'
(al-F&amacr;r&amacr;b&imacr; 1951). He begins by considering an experiment that might
lead one to conclude that a void exists. The experiment involves
sucking air out of a vial and then placing one's finger on the mouth
of the vial. One next inverts the vial into a bowl of water and then
removes the finger from the mouth of the vial. A certain amount of
water will be attracted into the vial, and so one might conclude that
a void space proportional to the amount of water drawn into the vial
was present while one's finger was over the mouth of the vial. The
conclusion does not follow, argued al-F&amacr;r&amacr;b&imacr;; for he believed that one
must concede that the purported void space in the vial has a certain
volume, but since volume just is a body possessing length, breadth and
depth, there must be a body in the purported void
 space.[8]
 In this respect al-F&amacr;r&amacr;b&imacr; was simply following the standard
definition of 'body' as whatever possesses three
dimensions; however, he also suggested that there is something
incoherent about considering void as some sort of absolute nothingness
possessing three dimensions, since there is no coherent sense in which
nothingness could be the subject for the accidental qualities of
length, breadth and
 depth.[9]
 Given these considerations against the void, continued al-F&amacr;r&amacr;b&imacr;, one
should conclude from the above experiment that the volume of air
expanded, and consequently a smaller amount of air now occupies the
same amount of space. In other words, the particular volume that a
body possesses, and particularly in the case or air, is not essential
to that body, and so given the right causal factors or conditions a
body's volume can expand or decrease. Al-F&amacr;r&amacr;b&imacr;'s suggestion here was
to become the standard among Arabic-speaking natural philosophers when
dealing with purportedly artificially manufactured voids.


### 2.5 Time and Eternity



Like so many issues in natural philosophy, philosophers working in the
*falsafa* tradition took their lead concerning temporal topics
from Aristotle. Thus most Arabic-speaking philosophers defined time as
the measure of motion with respect to priority and
 posteriority.[10]
 Although a number of the most discussed issues and problems
associated with time concerned the eternity of the world, and so in a
sense belonged to metaphysics, there were some pressing questions
concerning the nature of time that remained wholly in the domain of
natural philosophy. Arguably the most important of these physical
question concerned clarifying which motion or motions time measures.
Averroes presented the problem at stake nicely in an extended
digression his *Long Commentary on the Physics* (Averroes 1962,
178F-179I).



Averroes began by asking whether time is associated with every motion
or just one special motion. If time were associated with, and indeed
generated by, every motion, then there would be as many times as there
were motions, and yet it seems immediately obvious that there is but a
single time. Thus it would seem that time must be associated with just
one special motion; and indeed virtually everyone in the Aristotelian
tradition, going back to at least Alexander of Aphrodisias, if not
Aristotle himself, did associate time with one special motion, namely,
the motion of the heavens. Now, continued Averroes, if time were
uniquely associated with this and only this motion, then one's sensing
and being aware of time would be associated with one's sensing and
being aware of the heavens' motion. Consequently, should someone have
never sensed that motion, such as Plato's prisoners in the cave from
the *Republic*, that person would be wholly unaware of time,
and such a conclusion simply seems false. In fact, Averroes
generalized his argument to include all special motions that exist
outside of our souls. Hence it would seem that the motion in question
in the definition of time must refer to a psychological motion, that
is, some motion that our souls undergo. The difficulty with this
suggestion, Averroes concluded, is twofold: first, it implies that
there is no time outside the soul, and second, since there will be as
many psychological motions as there are souls, we have returned to our
initial difficulty of the existence of multiple times.



Averroes' solution is to say that our awareness of time is first and
essentially our awareness of ourselves inasmuch as we have undergone
some sort of change. We are in turn aware that we have undergone some
sort of change by being aware of two different moments, as for
example, I am aware that the moment at which I first began to write
this account is different from the present moment, in which case I am
aware that I have undergone some sort of change. Our undergoing
change, however, Averroes quickly added, only results from the
heavens' undergoing motion, and should *per impossibile* the
heavens cease moving, then we would no longer undergo change.
Consequently, although our awareness of time is associated immediately
with our undergoing change, and so we can be aware of time even though
we are not aware of any particular extra-mental motion, time itself is
associated with the motion of the heavens that is the ultimate cause
of our undergoing motion, and so time is one and not multiplied.



Another temporal issue that was clearly of interest to natural
philosophers in Islamic lands concerned time's topography: "Is
it finite or infinite?" and "Is it
'rectilinear' or 'cyclical'?" Among the
Arabic-speaking philosophers, al-Kind&imacr; was virtually alone in
affirming the finitude of time; most others philosophers argued that
time must necessarily be infinite in that it could have no beginning.
How various philosophers argued for this thesis reveals that both
rectilinear and cyclical conceptions of time were present within the
*falsafa* tradition, where Avicenna advocates a rectilinear
conception of time and Averroes a cyclical conception of time.



Again the area where this issue arose concerned proofs for the
eternity of time. So, for example, in a novel proof for the existence
of time based upon differences in the amount of distance that can be
covered by slower and faster moving objects, Avicenna linked time with
a possibility or capacity (*imk7amacr;n*) for motion (Avicenna 1985,
228-229). He then argued by means of a *reducto ad
absurdum*. He has us assume that time is finite, and so the motion
of the universe must have some first moment when it began. Even if the
motion of the universe began at some first moment, the argument
continues, clearly there would still have been the possibility for the
Creator of the world to make a motion that extended further back. In
that case, there is a capacity or possibility for motion that precedes
the purported first moment, but time according to Avicenna is again
just a certain capacity or possibility for motion. Thus a time would
have preceded the purported first moment, which is absurd. Since the
same argument applies to any purported first moment of time, concluded
Avicenna, time can have no beginning and so must be infinite. Clearly,
the conception of time implicit in Avicenna's argument is that of a
temporal line stretching back infinitely.



Averroes too provided an argument for time's having no beginning, but
now in terms of conceiving time as a circle (Averroes 1991, question
III). As was explained above, for Averroes time is a consequence and
measure of the circular motion of the heavens and so is itself
circular. Now just as any point on a circle is both a beginning and
ending of some arc on the circle, so any moment assumed in time must
be a beginning and ending of some period of time. Consequently time
has no beginning. That it should have no beginning, however, is not in
the sense that a straight line has no beginning, but in the sense that
no point on a circle can be said to be the beginning of the circle.
Although Averroes did not explicitly claim that all events and thing
will come around again, his argument does seem to imply such a
conclusion.


### 2.6 Al-R&amacr;z&imacr; and Absolute Time and Space



As noted most of those working in the *falsafa* tradition drew
their inspiration from Aristotle and his later commentators, the most
notable exception was the independent philosopher-physician Ab&umacr; Bakr
al-R&amacr;z&imacr; (ca. 864-925 or 930), whose natural philosophy and cosmology
happily drew upon Arabic versions of Plato's *Timeaus* as well
as certain non-Greek sources. Al-R&amacr;z&imacr; maintained that there were five
eternals: (1) the Creator, (2) the Universal Soul, (3) prime matter,
(4) absolute time and (5) absolute space (understood as something like
void space) (al-Razi 1939, 195-215). The first three eternal
principles find their counterparts in the natural philosophy of the
Neoplatonizing Aristotelians in the Islamic world, whereas it is the
last two notions that truly set al-Razi apart from other medieval
natural philosophers.



For all of the philosophers we have treated time and place are
relative terms, which respectively depend on a motion and a situated
thing for their very existence. In contrast, al-Razi argued that one
had to distinguish between the relative conception of these notions
and the absolute conception. Thus he distinguished between time (a
relative temporal notion) and duration (an absolute temporal notion)
as well as between place (a relative spatial notion) and void (an
absolute spatial notion). As absolute both duration and void are
substances in the sense that they have an existence independent of
anything else and thus in principle could exist if everything else
failed to exist.



As for the eternity of duration, al-Razi noted that time (the relative
temporal notion) is constantly perishing and coming to be inasmuch as
all past time has ceased to be, while future time is constantly coming
to be. In this case, time itself is changing, but every change
requires a duration during which it changes. If this duration itself
underwent change, there would need to be a further duration and so on
infinitely. To stop the regress al-Razi posited an unchanging
duration, which is itself the precondition for the measured time of
those philosophers following Aristotle.



As for absolute space or void, we have seen how the Arabic-speaking
philosophers had closely linked place with something placed in it. Now
if the space and what is placed in it were essentially correlatives as
the philosophers maintained, then, argued al-Razi, by imagining the
destruction of one correlate, one must likewise imaging the
destruction of the other. Let one imagine the destruction of the
universe. The notion of void or empty space, claimed al-Razi, is not
destroyed along with imagined destruction of everything occupying it.
Thus void and what is placed in it are not correlatives like the
philosophers claimed. Hence one must distinguish between the notion of
void space, which is not destroyed when one imagines the destruction
of the universe, and the notion of place, which is destroyed when one
imagines the destruction of the universe. The former is absolute,
whereas only the latter is relative.