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Title[Alnoor Dhanani] the Physical Theory of Kalam Ato(Bookos.org)
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Page 1

ISLAMIC PHILOSOPHY
THEOLOGY AND SCIENCE

Texts and Studies

EDITED BY

H. DAIBER and D. PINGREE

VOLUME XIV

THE PHYSICAL THEORY
OF KALAM

Atoms, Space, and Void in Basnan M u ctazih Cosmology

BY

ALNOOR DHANANI

E.J. BRILL
LEIDEN · NEW YORK · KÖLN

1994

Page 2

THE PHYSICAL THEORY OF KALÄM

Page 57

1 0 4 CHAPTER FOUR

Thus, in his discussion of Euclid's First Proposition— On a given line
to construct an equilateral triangle—Proclus states that Zeno had held
that this consequence could not be established unless one were to fur­
ther concede that two intersecting lines cannot have a common seg­
ment. While the interpretation of this statement is controversial, schol­
ars who ascribe mathematical atomism to Epicurus and his followers
consider it to mean that this consequence is
only valid if the lines that are constructed do
n o t have a thickness, for in the Epicurean
schem e, lines must have a thickness of one
minimal part, and therefore two intersecting
lines must have a common segment as we
can see in the diagram.39 Here the common
segm ent of the two intersecting lines has
b een shaded.^0

Hence, in accordance with such a view of
a line in two-dimensional space, points in three-dimensional space
must also have minimal length, depth, and breadth and
resembles the cubes of Euclidean geometry as can be seen
here in the accompanying figure.

This concept can be extended to other geometrical
magnitudes, namely surfaces which have length and
breadth but minimal depth, and bodies which have length,
breadth, and depth. Moreover, it is clear that in two-dimensional space,
th e requirement of minimal depth is no longer relevant. Since these
geometrical objects are usually depicted on a two-dimensional surface,
terms that denote two-dimensional concepts, for example surface area,
are sometimes confused for their three-dimensional counterparts,
w h ich in our exam ple is volum e. Such a tendency to use two-
dimensional terms is also encountered among the mutakallimün for

39 Sedley, “Epicurus and the Mathematicians,” 24. Vlastos, on the other hand, regards
Zeno to be a friendly critic whose aim was to fill the logical gaps of Euclid's argument
(“Zeno of Sidon,” 154; cf. Jürgen Mau, “Was there a Special Epicurean Mathematics?” in
Exegesis and Argument: Studies presented to G. Vlastos, Phronesis, Suppl. 1(1973),
421-430).

40 Scholars are divided over whether the Epicurean minimal part has shape, since
Epicurus does not address this question. On the grounds that the minimal part must be
three-dimensional, Vlastos has postulated that it must be a cube with the dimensions of
one minimal part, while Furley allows any shape that can interlock without leaving in­
terstitial spaces (Furley, Two Studies, 116-117; Vlastos, “Minimal Parts,” 128). On the
other hand, Konstan, Sorabji, and Sedley have denied that it has shape, although it is
difficult to see how it can have magnitude but no shape (Konstan, “Problems,” 405;
Sedley, “Epicurus,” 23; Sorabji, Time, Creation, and the Continuum, 372). See also White,
T he Continuous and the Discrete, 233-234.

A /
/—

7

ATOMS AS MINIMAL PARTS 105

they state that the atom has surface area and that it has the shape of a
square instead of their three-dimensional counterparts, namely that the
atom has magnitude or volume and the shape of a cube, which would
have been more accurate.

What would be the definition of a line in such a discrete geometry?
Can one two-dimensional minimal part form a line? This does not ap­
pear to be the case because a line in discrete geometry must, like its
Euclidean counterpart, have two extremities, and consequently must
consist of at least two minimal parts, one at each extremity. Therefore,
the concept of length, in such a discrete geometry, requires at least two
minimal parts. Such a concept of length is clearly foreign to a geometry
of continuous magnitudes, for in the latter system, any part having
magnitude must possess length, breadth, and depth, and as such, be a
body, no matter how small. Consequently, the minimal part or point of
discrete geometry· must, from the perspective of a geometry of contin­
uous magnitude, have length, breadth, and depth. This statement,
however, is false in discrete geometry where the dimension of length is
formed only when at least two minimal parts are contiguous because a
line must have two extremities. It follows that statements which are
true in the geometry of continuous magnitudes may be false in a dis­
crete geometry and vice versa.

In Epicurean atomism, then, the evidence is suggestive of the
stronger version of discrete physical theory, namely, that not only
matter, but also space, time, and motion, are also constituted out of in­
divisible minimal parts. Therefore its accompanying geometry must
also be a discrete geometry with appropriate definitions of geometrical
objects, magnitude, and linear dimension. Moreover, the analysis of
physical phenomena must be a discrete analysis. On the other hand, in
the weaker version of discrete physical theory, matter only is discrete
while space, time, and motion are continuous. This would then allow
for a continuous geometry and continuous analysis of physical phe­
nomena. Aristotle’s arguments against atomism, however, did not leave
much room for the adoption of the weaker version of discrete physical
theory.41

Minimal parts and kaläm atomism
Let us now, after this long digression, return to the atomism of the
Basrian Mu‘tazilis. Are there sufficient grounds for the hypothesis that
kaläm atoms are akin to Epicurean minimal parts and that kaläm
atomism is to be regarded from the perspective of a discrete geometry

41 See also White, The Continuous and the Discrete, 194-258.

Page 58

106 CHAPTER FOUR

o f the kind that has been sketched above? W e do not. as is the case for
Epicurus, have an explicit statem ent by the mutakallimün which
affirms their belief in minimals parts which are analogous to Epicurean
minimal parts. In my view, however, there is sufficient evidence on
which one can argue that such minimal parts were upheld by many of
the mutakallimün. The Epicurean premise of minimal parts can be
stated as:

[1] The Atom consists of minimal parts
This premise can, in the Basrian Mu'tazili case, be replaced by the al­
ternative premise that the atom itself is the minimal part and hence that
the atom consists of a single minimal part.

[11 The Atom consists of a single minimal part
This alternate premise, which I propose was held by the mutakallimün
of the fourth and fifth/tenth and eleventh centuries, can be established
on the basis of the following sub-premises:

[A] The Atom has magnitude, that is, it is extended.
[B] The Atom is cubical in shape having dimensions of one minimal

part.
[C] Atoms are homogeneous, therefore all atoms have the same

shape and magnitude.
[D] The Atom is physically and conceptually indivisible, and is

therefore a minimal part.
In the following sections, I hope to establish that these sub-premises
were held by the Basrian Mu'tazilis of the fourth and fifth/tenth and
eleventh centuries. We will also see, in somewhat lesser detail, that
these sub-premises were likewise held by their contemporaries among
the Baghdadi Mu‘tazills and the Ash‘aris.

Premise [A]:The atom has magnitude
W e have, in the previous chapter, already seen that the term
mutahayyiz means ‘the space-occupying object’ and that such an object
occupies space in a manner similar to the occupation of space by a
body, that is to say, mutahayyiz signifies a spatially extended object.
The use of the term mutahayyiz to denote the atom seems to have
been originated by Abu Häshim al-Jubbä’i and was subsequently used
by the Basrian Mu'tazilis, the Baghdadi Mu'tazilis, as well as the
Ash'aris. Moreover, both Mu'tazili and Ash'arî mutakallimün of the
fifth/eleventh century (and perhaps even earlier) also agreed that
atoms have magnitude. Shaykh al-Mufïd reports:

I believe that the atom has intrinsic magnitude (lahu qadrun fi nafsihi) as
well as volume (.hajm) by virtue of which it occupies space (lahu
hayyizun) when it exists. This [is the property] by which an object which

ATOMS AS MINIMAL PARTS 107

is other than the atom is differentiated. Most of the Mu‘tazila ( ahl
al-tawhid) uphold this view .12

The Ash'ari position on the magnitude of the atom is also stated clearly
by al-Bâqillânï: “The atom is that which has magnitude” (mä lahu
hazzun min al-misähati).43 These two reports make it clear that magni­
tude was considered to be an intrinsic property of the atom and further
that the atom must, as a result, have volume. However, the
mutakallimün of the third/ninth century did not, it would seem, con­
ceive the atom in this manner. While we have, in the previous chapter,
considered the space-occupying property of the atom from the per­
spective of the meaning of mutahayyiz, we will here examine another
aspect, namely, what do the mutakallimün mean when they say that
the atom occupies space? We will thus examine the arguments which
the mutakallimün formulated to support the proposition that the atom
has intrinsic magnitude.

Shaykh ai-Mufld, as we have seen, usually inclines to the Baghdadi
Mu'tazili viewpoint.44 It would seem from his statement regarding the
intrinsic magnitude of the atom that both the Basrian as well as
Baghdadi Mu'tazilis were in agreement over the premise that atoms
have magnitude. However the texts of the Basrian Mu'tazilis, namely of
al-Nisäbüri, Ibn Mattawayh, and his commentator, are at odds with
al-Mufid’s account. They depict instead a sharp disagreement between
the Basrian and Baghdadi Mu'tazilis over this premise. Al-Nisäbüri, for
one, states, “Abü Häshim [al-Jubbä’i] inclined to the view that every
atom has magnitude (anna li-kulli juz’in qistan min al-misähati), but
Abü al-Qäsim [al-Balkhi] believed that the atom cannot be said to have
magnitude.”45 Ibn Mattawayh further adds that “Abü 'Ali [al-Jubbä’i] had
denied this and had held that the magnitude of the atom is due to
something else (bi-ghayrihi), just as its length is due to something else.
This is also the view of Abü al-Qäsim. ”46 It is extremely unlikely, if the
accounts of Ibn Mattawayh and al-Nisäbüri are correct, and we have

42 Shaykh al-Mufïd, Awä'il, 74.
43 al-Juwaynl, Shämil, 142.
44 See above, Chapter Three, note 38.
45 al-Nisäbüri, Masä’il, 58. As I have mentioned in note 22 above that the expression

qistun min al-misähati literally means ‘a portion of surface area’ since misäha is the term
for 'surface area'. But it is clear from (1) Shaykh al-Mufid’s account that the atom intrinsi­
cally has a volume (hajm); (2) al-Bâqillânî’s interpretation that mutahayyiz stands for an
extended object having bulk or volume (/irm); and (3) Abü Bakr al-FOrakl’s statement
that the atom is the smallest of what is small with respect to volume; that the atom must
have volume (see above, Chapter Three, 64). Misäha must therefore signify size, magni­
tude, or extent here and the expression qistun min al-misähati must signify a portion of
magnitude.

6 Ibn Mattawayh, Tadhkira, 181.

Page 113

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I
i

ISLAMIC PHILOSOPHY, THEOLOGY AND SCIENCE
TEXTS AND STUDIES

ISSN 0169-8729

l.IBN RUSHD. Metaphysics. A Translation with Introduction of Ibn
Rushd’s Commentary on Aristotle’s Metaphysics, Book Läm, by Ch.
Genequand. Reprint 1986. ISBN 90 04 08093 7

2. DAIBER, H. Wäsil ibn cAtä’ als Prediger und Theologe. Ein neuer
Text aus dem 8. Jahrhundert n. Chr. Herausgegeben mit Übersetzung
und Kommentar. 1988. ISBN 90 04 08369 3

3. BELLO, I.A. The Medieval Islamic Controversy Between Philosophy
and Orthodoxy. Ijmäc and Ta’wil in the Conflict Between al-Ghazäli
and Ibn Rushd. 1989. ISBN 90 04 08092 9

4. GUTAS, D. Avicenna and the Aristotelian Tradition. Introduction to
reading Avicenna’s Philosophical Works. 1988. ISBN 90 04 08500 9

5. AL-KÀSIM B. IBRÂHÎM. Kitäb al-Dalïl al-Kabïr. Edited with
Translation, Introduction and Notes by B. Abrahamov. 1990.
ISBN 90 04 08985 3

6. MARÔTH, M. Ibn Slnä und die peripatetische “Aussagenlogik”.
Übersetzung aus dem Ungarischen von Johanna Till. 1989.
ISBN 90 04 08487 8

7. BLACK, D.L. Logic and Aristotle 's Rhetoric and Poetics in Medieval
Arabic Philosophy. 1990. ISBN 90 04 09286 2

8. FAKHRY, M. Ethical Theories in Islam. 1991. ISBN 90 04 09300 1
9. KEMAL, S. The Poetics ofAlfarabi and Avicenna. 1991.

ISBN 90 04 09371 0
10. ALON, I. Socrates in Medieval Arabic Literature. 1991.

ISBN 90 04 09349 4
11. BOS, G. Qustâ ibn Lüqä’s Medical Regime fo r the Pilgrims to

Mecca. The Risäla fî tadbïr safar al-hajj. 1992. ISBN 90 04 09541 1
12. KOHLBERG, E. A Medieval Muslim Scholar at Work. Ibn Täwüs and

his Library. 1992. ISBN 90 04 09549 7
13. DAIBER, H. Naturwissenschaft bei den Arabern im 10. Jahrhundert

n. Chr. Briefe des Abü 1-Fadl Ibn al-cAmid (gest. 360/970) an
‘Adudaddaula. Herausgegeben mit Einleitung, kommentierter
Übersetzung und Glossar. 1993. ISBN 90 04 09755 4

14. DHANANI, A. The Physical Theory of Kaläm. Atoms, Space, and
Void in Basrian Mu'tazili Cosmology. 1994. ISBN 90 04 09831 3

Page 114

_uö INDEX

.tl-Mutawakkil, Caliph (r. 232-247/847-
861), 8

Mu'tazili mutakallimün
Baghdadi, 6, 8, 10, 11, 12, 13 27n34,

44, 44n80, 46, 49n95, 62, 67, 73, 75,
76, 79, 80, 81, 82, 85, 86, 88, 96, 98,
106, 107, 111, 117, 118, 118n67,
122-123, 123n82, 124, 134, 190

Basrian, 6, 9, 10, 11, 12, 13, 17, 18, 20,
21, 21nl6, 22, 23n21, 24n25, 25,
27n34, 29n37, 30, 31, 32, 33, 34n57,
45n83, 46. 47, 49-50, 49n97, 51,
53-54, 56, 61, 65n28, 67, 68, 69, 70,
73, 74-75, 76, 77, 78, 79, 80, 81, 82,
83, 85, 86, 87, 88, 89, 91, 92, 93, 95,
96, 98, 100, 105, 107, 110, 116, 117,
118-119, 118n67, 121,122, 124, 134,
135nl20, 141, 142, 144, 145, 148,
156n42, 165-166, 167, 190

mutual replacement, Peripateric doctrine
of (antiperistasis, antimetastasis), 82-83

al-Najjär, al-Husayn Cd. ca. 220-230/835-
845), 4, 40n73, 90, 92, 118, 186

• Naqd al-naqd of al-Bäqilläni, 116,
Il6n64

.d-NasIbl, AbO Ishäq (contemporary of
‘Abd al-Jabbâr), 25n27

• Natural Philosophers, see ashab al-tabS'i'
al-NayrizI (d. 310/922), 149
nazar (reflection), 22, 26n32
al-Nazzâm, Ibrâhïm ibn Sayyär (d. ca.

220-230/835-845), 5, 9, 39, 40, 40n73,
43, 43n79, 45, 8 7 n ll l , 91, 92, 92n5, 99,
99n24, 118, 118n67, 118n68, 124, 138,

- 148, 152n34, 152n35, 156n44, 157, 160,
' 161, 162, 165, 169, 172, 176, 176n97,

177, 177nl03, 178, 179, 180, 181,
181nll0, 184, 187, 188

r Neoplatonist(s), 5, 65, 68, 186, 191
ai-Nîsâbürï, Abu Räshid (fl. first half of

5th/llth century), 13, 21nl6, 23n24,
30, 32 33n55, 35n60, 36n63, 4ln75,

< 42n76, 50, 51nl05, 73, 85, 97, 98, 107,
108, 109, 116, 118n71, 119, 124, 125,
126, 127, 190

Non-existent objects, 27n34
Nu‘màn the Dualist (d. ca. 163/780), 183,

185
nuqta (point), 96-97, 102, 104, 105, 111,

150, 167, 174-175, 185, 191, 193

Occasionalism,
absolute, 40n73, 43, 43n79, 45
modified, 43-45

On Indivisible Lines by pseudo-Aristode,
65, 162, 164, 176

Origen, 56n7

Perception,
and attributes, 23-25, 27n33, 35n60

36n63, 50-51, 119, 143, 145
and illusions, 22nl8
and its object, 22, 23, 24, 24n25, 25, 30,

35, 37
source of knowledge, 22, 24, 26n32,

50-51, 144
theory of, I42n4
veracity of, 21, 35, 119

Peripatetics), 5, 60, 68, 69, 70, 71, 72, 74,
77, 81, 83, 89, 185, 186, 188, 191

Philo of Byantium (fl. ca. 250 B.C.), 76
Philoponus, John, 69, 72, 74, 81
Physics of Aristotle, 74, 101, 123, 131,

167
Pines, Shlomo, 97, 98, 99, 100, 101,

135nll7, 137, 164, 191
Place, 70-71, 71n52, 89
Plato, 2, 10
Platonism, 191
Plutarch, 164
Point, see nuqta
Possible objects, see ma‘düm
Pneuma, see rüh
Presocratic cosmology, 2
Presocratics, 2, 10, 15
Proclus, 103, 104, 153n37
Property of an object, see hukm
Pyrrhonists, 103

qalb ai-ajnäs (transformation of class),
35n60

al-Qazwinl, Ahmad ibn Abö Häshim, see
Mânkadîm Shishdev

Qui^ân, 8, 39, 41n75, 42, 157n46, 190,
173

qudra (autonomous power of action),
16, 18nl0, 47, 47n88, 48, 53, 146,
I46nl8

al-Râzl, Muhammad ibn Zakariyä’ (d.
313/925),' 9, 72, 72n55, 72n57, 188, 190

al-Râzî, Fakhr al-dîn (d. 601/1209),
27n34, 43n79, 152n34, 152n35

Rest, see sukün
RisäJa ft al-makän of Ibn al-Haytham, 68
rüh (pneuma), 184

Sabians, 183
Sabra, A.I., I42n4, 187nl5
safha (plane), see sath
Sedley, David, 104n40
al-Sälihl, Abu al-Husayn (fl. last quarter

of third/ninth and first quarter of

INDEX 209

fourth/tenth century), 56, 57, 57nl0,
143-144

sath (surface), 95, 96, 99n24, 100, 104,
112, 115, 148, 149,150

Sextus Empiricus, 131
al-Shahhäm, Abu Ya’qub (fl. later half of

3rd/9th century), 9, 27n34
al-Shahrastâni (d. 548/1153), 151n34
ShâmiJ fï usüi al-dîn of al-Juwaym, 14,

65
al-Shatawi, Ahmad ibn ‘All (contemporary

of Abu al-Qäsim al-Balkhl), 44n80
Sharh al-tadhkira by anonymous author,

13Sharh usOl ai-khamsa, 13
shart (condition), 19nl 1, 36
shay3 (object,existent), 23, 25, 25n30,

27n34, 29, 30, 32n49, 39, 74
shu ‘S‘ (visual ray), 142, I42n4
sifa (attribute), 15, 25, 29, 39
sifatu 1-jins (class attribute), 34 36, 36n66,

92, 93, 118-119
Simplicius, 72, 74, 76, 131, 154, 155
Skepticism, 21, 21nl4
Sorabji, Richard, 90, 104n40, 176n97,

184, 186
Space, see also hayyiz, jiha, khalä\

m akän, muhädhäh
absolute, 68, 72, 75
continuous, 103, 127, 128, 130, 133
discrete, 51, 102, 103, 105, 123, 124,

125, 126, 127, 128, 130, 131, 132,
133,134,135,136-137, 137nl0, 138,
139-140, 171,179, 180, 190

geometrical, 103
is a two-dimnesional enveloping

container, 67, 68, 68n40, 135
is a three-dimensional expanse, 67, 68
occupied, 65, 66
physical, 103
plenum, 55, 67, 80, 82, 83, 89
theory of, 67, 67n37, 68, 68n41, 69
unoccupied, 65n31, 66, 67, 68, 75, 127

Speed, 123, 132, 133, 134nll4, 138-139,
166

Stoic(s), 5, 7, 71, 90, 184, 185, 186, 191
sukQn (rest), 27n34, 40n73, 43n79, 44,

45n82, 47n88, 51, 51nl05, 52, 53,
99n24, 139, 139nl34, 147, 147n22, 180,
181, 184n5

Surface, see basit, $ath

Tadhkira fi ahkâm ai-jawâhir wa aî-a‘râd
of Ibn Mattawayh, 13, 15

tafakkuk (disintegration of a body during
rotational motion), 178-180

tafra (leap), 87, 8 7 n ll l, 88, 138, 152n35,
160,161, 174, 176-181, 176n97

tahayyuz (spatial occupation), 23, 6ln21,
63, 64n27, 90, 92, 108, 120, 121, 143,
144, 145, 156-159

ta’Iif (accident of adhesion, combination),
16, 47, 47n88, 48, 49, 98, 109, 110, 111,
112, 122, 152-160, 153n36, 153n37,
155n4l, 156n44, 157n46, 163, 169, 174

tariq (source of knowledge), 26
tarkîb (composition), 95
tawlid (causation), 20, 20nl2
Tertullian, 56n7
thabata (to affirm to be a possibke

being), 26, 26n31
Themistius, 74
thiqi (heaviness, weight), 7, 87
Thumäma ibn Ashras (d. ca. 213/828), 8
Time, 39, 40, 4ln75, 43, 45, 46, 72, 75,

83, 100, 102, 105, 123, 125, 130, 131,
132, 133, 134, 136-137, 137nl27, 138,
139-140, 161, 162, 171, 176, 188, 189

al-TusI, Naslr al-dln (d. 672/1274), 43n79,
152n34

van Ess, Josef, 10, 43n79, 91, l6ln56
Visual ray, see shu ‘ä‘
Vlastos, Gregory, 103n27, 104n39,

104n40
Void, see also khalä’, farâgh

abhorrence of, 74, 76-81
affirmation of, 66-67, 67n36, 68, 72,

73, 73n62, 81-88, 81n91, 89
definition, 72, 72n58
denial of, 67, 68, 71, 72, 73, 74-81
extracosmic, 71, 73
intercosmic, 71, 73, 74
non-being of, 73, 75, 76
theory of, 67, 190

al-Warrâq, Abu ‘Isa (d. 247/861), 182,
183-184, 184n5, 184n6, 185

Wâ$il ibn ‘Atâ’ (d. 131/748), 7
White, Michael J ., 103n37
Wolfson, H., 191
wujüd (existence), 15, 26n31, 27, 145-146

Zeno of Elea, 160, l6 l
Zeno of Sidon, 103, 104, 104n39
al-Zabldl, Muhammad Murtadâ, 60
Ziyädät al-sharh of al-Nïsâbüri, 13

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