Classical Kalām and the Laws of Logic

As the nascent field of English-language Islamic philosophy and theology grows, it has become popular to draw parallels between modern thought and classical kalām. Classical kalām is often distinguished from post-classical kalām historically and methodologically: (i) historically, the classical period is that which comes before the interventions of Fakhr al-Dīn al-Rāzī (d. 606/1210) and (ii) methodologically, the post-classical period is characterized by deeper engagement with Peripatetic philosophy and the adoption of logic as its primary tool, whereas the classical period adopted a ‘dialectical’ approach. Some commentators have gone as far to assert that, before this transformation in methodology, classical kalām was ‘a-logical,’ and did not even accept the principle of non-contradiction or the law of excluded middle.[1] Some go further by stating that it was not even ‘propositional,’ as if the very idea of stringing together declarative sentences was an invention of Aristotle.[2] It was Aristotle, somehow, who had imposed this belief on them. In turn, this new methodology restricted the creativity and growth of the post-classical kalām tradition, and caused it to atrophy. It is quite an odd reversal of the old orientalist thesis that the tradition atrophied because it distanced itself from Aristotle.

These views are mistaken. Suffice it to say that with respect to the adoption of logic, both orientalists and revisionist writers conflate the form of the argument, with the form of the inference. The form of an argument is the way one orders their premises when they express the inference, as in a formal syllogism, for example: (i) the world began to exist; (ii) everything which begins to exist has a cause, therefore: the world has a cause. The form of the inference, however, describes what the inquirer is actually doing when they draw the inference, which is to infer from the existence of an effect to the existence of a cause. The evidence for the conclusion drawn in the inference is not the syllogism itself, but rather, it is what the syllogism is trying to express, namely, how the changing world around us indicates the existence of an unchanging, eternal cause.

Thus, if someone were to ask, ‘What is the proof for God’s existence?’ the answer, in short, would be ‘the world,’ insofar as it is contingent or temporally originated. Both classical and post-classical authors are reflecting on the same object, namely the world and its properties, from which they infer that it stands in need of a cause which is distinct from the world in all the ways that would make it stand in need of a cause, i.e., a necessary being. Formulating this in a categorical syllogism has no impact on the soundness of the inference. It is strictly a tool, a very useful tool, by which we can clarify our thoughts in increasingly precise ways. Several commentators on this development in kalām grossly exaggerate the impact of this change on the nature of kalām. Nevertheless, the engagement with peripatetic philosophy was no doubt one of the most fruitful philosophical endeavours in the history of Islamic civilization.

“Now then, the main contention of this short piece is to deal with the laws of logic, such as the principle of non-contradiction and the law of excluded middle, among classical Ash‘arī figures.”

Now then, the main contention of this short piece is to deal with the laws of logic, such as the principle of non-contradiction and the law of excluded middle, among classical Ash‘arī figures. Proponents of the revisionist reading of classical kalām cite two theories to demonstrate that they rejected the law of excluded middle: (i) the Ash‘arī formulation of the relationship between God and His attributes[3]; and (ii) the theory of abstract modes (aḥwāl).

Some have mentioned even more unlikely candidates for demonstrating this, which are hardly worth consideration except to dispel some confusion. For example, some have suggested that the statement, ‘God is neither in physical contact with the World, nor physically separated from the World,’ implies a denial of the law of excluded middle; they claim that there is no problem here, because God ‘transcends the laws of logic,’ just like – apparently – quantum phenomena. But this is an egregious error, because it fails to distinguish between contrary opposition and contradictory opposition. (i) A contrary opposition holds between any two properties which cannot both be predicated of a subject at the same time; (ii) a contradictory opposition is one of affirmation and negation directed at the exact same predicate in the exact same way, and thus, they cannot both be true, nor both be false. For example, knowledge and ignorance are contraries, because Zayd cannot be ignorant of something in the same sense while at the same time having knowledge of that thing in the same sense. On the other hand, a contradictory opposition is one where an affirmation and a negation are directed at the exact same predicate under all the same conditions. For example, ‘Zayd is a knower’ and ‘Zayd is not a knower.’

Likewise, the denial of a contrary-pair is impossible if and only if the subject in question is in principle describable with either one of the contrary pair, therefore, denial of both is possible when the subject is not describable by either one; in contrast, the denial of a contradictory pair of propositions is always impossible. A stone, for example, does not have knowledge, nor does it have ignorance, because being-knowledgeable or being-ignorant both require that the subject in question, i.e., the stone, is something which could be either one of the two. Being ignorant implies a capacity for knowledge, and since stones are inanimate objects with no such capacity, we do not say they are ‘ignorant,’ but rather we say, they have ‘no knowledge.’ The predicate ‘no-knowledge’ is more general than the predicate ‘ignorant,’ because every ignorant agent lacks some knowledge, but not every non-knower is ignorant (e.g., stones, dirt, tables, etc.). In short, there is no absurdity in denying the contrary-pairs of ‘the stone is neither knowledgeable nor ignorant,’ but there is an absurdity in the contradictory-pairs of stating ‘the stone is neither knowledgeable nor not-knowledgeable.’

Now, the example cited, namely, that ‘God is neither in physical contact with the World, nor physically separated from it,’ is an example of contrary opposition. Thus, the reason why there is nothing ‘suprarational’ or logic-bending about asserting that ‘God is neither in physical contact with the World, nor physically separated from the World,’ is because these two predicates can only hold of physical objects. God is not a physical object, that is, His existence is not conditioned by time and space, both of which He has created; therefore, it makes no sense to claim that God is in ‘physical contact’ with the World or that God is ‘physically separated’ from the World, and we can deny both without violating the law of excluded middle. To take an even more obvious example of contrary opposition: sentences are said to be grammatical or ungrammatical, but a tree is neither ‘grammatical’ nor ‘ungrammatical,’ but no one goes around saying that trees are suprarational beings that transcend the laws of logic.

In what remains of this essay, I will present evidence from classical authors that demonstrate that neither the theory of the attributes nor the theory of abstract modes imply the rejection of the laws of non-contradiction or excluded middle; early sources indicate that some Mu‘tazilī versions of aḥwāl theory could potentially be interpreted as such, but I think the more likely opinion is that these were strictly speaking unintended consequences of the view which their opponents used to refute them by. A closer look at the evidence indicates that these theories were ontological in nature, not logical, and that their proponents tried as best they could to make them as logically coherent as possible. We find no indication, whatsoever, that these figures flaunted the laws of logic.

The Theory of the Attributes in Classical Sunnī Kalām

It was common to describe the classical kalām principle on the relation between God and His attributes as follows:

P1: The attributes are not identical (‘ayn) to the Essence (dhāt), nor are they other (ghayr) than the Essence.[4]

If one believes that the term ‘other’ used in this formulation means ‘not identical’ then the formula would mean:

P1’: The attributes are not identical (‘ayn) to the Essence and the attributes are not ‘not identical’ to the Essence.

In other words, it would appear that one has grounds to think that this understanding between God and His attributes entails the rejection of the law of excluded middle, because the attributes are not-p and also not-not-p. But this is deeply mistaken.

“Classical kalām authors used the term ghayr and ghayriyya with a clearly delineated meaning: namely, metaphysical separability. That is: when they say that the attributes are not ghayr with respect to the Essence, they only mean that the attributes are not separable…”

Classical kalām authors used the term ghayr and ghayriyya with a clearly delineated meaning: namely, metaphysical separability. That is: when they say that the attributes are not ghayr with respect to the Essence, they only mean that the attributes are not separable, which is another way of saying: they necessarily coexist with the Essence. This does not mean, however, that there is a plurality of existent subjects in eternity, because the existence of any attribute – even created attributes – is inconceivable without a subject for those attributes, and the only problematic kind of plurality in eternity is a plurality of subjects, not a plurality of attributes.

One might quibble about why they chose to use ambiguous language, but really, it is only ambiguous to those unfamiliar with the technical terminology, which classical authors took time to clarify in several instances. Let us look at some examples. In his Kitāb al-Luma‘, in the chapter on affirming God’s knowledge as a real, existent attribute, Al-Ash‘arī writes:

Furthermore, the meaning of gharyiyya is the possibility of separation of one of two existent things from the other in one way or another. Thus, when it was demonstrated that God and His knowledge are eternal, it is impossible for them to be ghayrayn.[5]

In other words: what it means to be “other” is for it to be separable in one way or another. That separability can be a separability in substrate, or a separability in existence, or a separability in time or location. But since God’s knowledge necessarily exists in Him, and they are both eternal in their existence, it follows that they are inseparable, and therefore, not other.

Ibn Fūrak provides us with more details on this view in his summa of Ash‘arī’s views, the Mujarrad Maqālāt:

[Ash‘arī] said: attributes in general are of two types. Some are separable (mufāraqatuhā) from the subject characterized by [the attributes], and some which are not separable. That which is separable from [the subject] is that which is possibly ghayr (‘other’) with respect to it, and what is impossible to be [separable], then it is impossible for it to be ghayr (‘other’) than the subject characterized by it. And [Ash‘arī] said: in general, the attributes of created things are other in themselves and other to the subjects characterized by them, while the attributes of God are of two types: (a) some of which it is not said that they are other (ghayr) than Him, namely, those which subsist in Him, while (b) some which are necessarily other (ghayr) than Him, because they subsist in another, namely, those descriptions, statements, and reports about Him and His Attributes.[6]

Again, we have another clear statement on what Ash‘arī means by the term ‘ghayr’: separability. Here he explains that in general, all the (additional) attributes of created beings are other to each other, and other to the subjects they characterize, and this is for the basic reason that we are not necessarily characterized by our attributes: just as we can gain knowledge, we can lose that knowledge. Thus, the relationship that created beings like ourselves have to our attributes, and the relationship our attributes have to each other, is one of ghayriyya or separability. God on the other hand, is not subject to such contingencies, and all of His Attributes are necessary for Him. As such, Ash‘arī informs us that it is impossible to hold that God’s essential attributes – which he describes above as those which subsist in Him – can be called ‘other,’ than God.

However, Ash‘arī points out that some of His attributes, such as His ‘being-described’ or ‘being-spoken of,’ are separable from Him and therefore are other than Him. That is because these properties are actually grounded in the rational agents who are describing God or discussing Him. For example, when we say or report or remember or mention that ‘God is one,’ it implies two properties of God: the actual unity of God, which is an attribute of His Essence, and the property of ‘being-discussed,’ which does not exist in God Himself, but in the human or angelic agents carrying out the discussions, rememberings, mentionings, and reportings; and therefore, these attributes are other, i.e., separable, with respect to God.

Let us move on to al-Qāḍī al-Bāqillānī, another favourite target of the revisionist view of classical kalām. In the chapter on attributes (chapter 17) of his Tamhīd, he explains to us the meaning of ghayr:

It is said to them: If you mean by your statement that the knowledge of the Eternal (i.e., God) is different (mukhālif) to Him that [the knowledge] is ‘other’ (ghayr), and that [the knowledge] is of one kind and the Creator is of another kind – just as it is said with regard to the colour of black and the colour of white – then that is impossible by virtue of the proof establishing that the knowledge of the Eternal is not ‘other’ (ghayr) than Him, insofar as it is not possible for it to be separated from Him in time, or place, or existence and nonexistence; and it has been established that the meaning of two ‘others’ (al-ghayrayn) and the reality of their being described as such is that it is possible for them to be separated in one of these three ways.[7]

Notice the resemblance between this statement and Ash‘arī’s above in his Luma, except that Bāqillanī affords us with an added detail of the specific ways separability may occur: by time, by place, or by existence and nonexistence. Without getting into further details, the passage clearly indicates that being-other just means being separable.

“Notice the resemblance between this statement and Ash‘arī’s above in his Luma, except that Bāqillanī affords us with an added detail of the specific ways separability may occur: by time, by place, or by existence and nonexistence. Without getting into further details, the passage clearly indicates that being-other just means being separable.”

Yet another major classical figure – and one who was unimpressed by Aristotle’s logic – is the Ash‘arī theologian, jurist, and mathematician ‘Abd al-Qāhir al-Baghdādī. In his ‘Iyār al-naẓar, he provides us with the (exact same) definition of being-other and the subsequent rationale behind the denial that God is other than His attributes:

They differed on the meaning of ‘two others’ (al-ghayrayn). Some believed that they are ‘two things.’ Our school (aṣḥābuna) said: they are the two entities for which it is possible for one to be separated from the other, by virtue of the existence of one and the nonexistence of the other, and it is for that reason we do not say that the attributes of God are others [to each other], nor that [the attributes] are other than [God], because it is impossible for some of them to exist while others do not exist.[8]

As we saw earlier in the citation in Ibn Fūrak, Baghdādī clarifies that it is not just that the attributes are not ‘other’ with respect to God’s Essence, but they are also not ‘other’ with respect to each other. So, just as the attributes have this not-identical and not-separable relation to the Essence, they also have the same not-identical and not-separable relation to each other. Yet, no denial of the law of excluded middle can be found.

Let us move on to another classical kalām author: Abū l-Ma‘ālī al-Juwaynī. In the chapter of his Irshād on the fact that God is not other (ghayr) to His Attributes, Juwaynī writes the following:

What the later scholars among our Imāms have stated on the reality of two beings that are ‘other’ (al-ghayrayn) is that they are: (a) the two existent beings for which it is possible for one to be separated from the other by time, or location, or existence or nonexistence. This is clearer than the statement of those who said: (b) two beings that are ‘other’ are every two things where it is possible for one to exist while the other is nonexistent.[9]

Here Juwaynī contrasts two possible definitions of what it means for two entities to be other and he opts for the definition drawn from the work of al-Bāqillānī, as is clear if one compares the two. We do not, however, see any sign of a denial of the law of excluded middle. Juwaynī clarifies this further by stating the following: “So, just as the attributes are not described as being other to the Essence, they are not said to be [the Essence] either; but we do not shy from stating that the attributes are existents, and that [God’s] knowledge and His Essences are two existents.”[10] From the two quotes above, the meaning of the formulation should be demystified. By denying otherness, the classical authors are rejecting metaphysical, temporal, or spatial separability. By denying identity (ʿayniyya), they are merely stating the obvious: God is not knowledge, but rather, God possesses knowledge. Therefore, His knowledge is not Him. It is because this is what was obviously meant by the classical school that the post-classical authors such as Fakhr al-Dīn al-Rāzī, to take just one example, sufficed by stating that God’s attributes are additional (zāʾid) to His Essence, although Rāzī himself entertained more than one way that they can be said to be additional.[11] Rāzī’s notion of additionality, however, is rather minimalistic: a close examination of his arguments indicates that it does not commit him to more than the fact that the attributes are conceptually distinct from the Essence, and to follow this path further would take us too far afield.

Other authors, such as ‘Aḍud al-Dīn al-Ijī in the Mawāqif, assert the very same analysis of ghayriyya that we saw earlier, as does his chief commentator al-Sayyid al-Sharīf al-Jurjānī. Nevertheless, due to all the critiques of the formulation by friend and foe, he found the language used by his predecessors to be muddled and unclear. Thus, possibly basing himself on Rāzī, Ijī makes the following comments in his discussion on the notion of being-other:

Know that their statement ‘It is not Him nor other than Him,’ is one deemed farfetched by many, for [they held that] it implies affirming the excluded middle, while others excused this as a merely verbal disagreement, while affirming the permissibility of the statement. And the truth is that what they meant by the statement ‘not Him’ is with respect to the concept (al-mafhūm), and ‘not other than Him,’ is with respect to the individual essence (huwiyya), just as is necessary in the case of predication. But because they did not affirm mental existence, they did not make explicit that the distinction is in the mind, while the unity is in extramental reality.[12]

First let me note that, it is not Ijī who believes that the principle violates the law of excluded middle, but that opponents of the Ash‘arī view have charged them with its violation in the later period. From what we saw above, however – as is confirmed by al-Ijī and Jurjānī in his commentary – the Ashʿarīs had something else in mind entirely. Nevertheless, Ijī seizes the opportunity to provide his own interpretation of their view (which Jurjānī and Siyālkūtī criticize).[13] As a result – as he argues in an early section on the question of how existence relates to essence – Ijī believes that one can interpret the principle of the classical school through the newly developed theoretical tool of mental existence. Since the early school did not affirm mental existence, they were unable to draw the distinction that Ijī thinks they were after. It is plainly obvious, of course, that the attributes are conceptually distinct. But in the external world, according to Ijī, there is only one unified being, which is God. Presumably then, through some process of reflection, one can conclude that this unified being also comprises the said attributes. Following this line of thought would take us too far afield.

The Theory of Aḥwāl

The theory of awāl, or abstract modes, is roughly what we may call the ‘indigenous theory of universals’ in classical kalām. Drawing on the notion of a ḥāl in grammar (an adverbial notion), it was first discussed by the Mu‘tazilī thinker Abū Hāshim al-Jubbāʾī with the express purpose of making sense of God’s attributes without affirming multiple concrete eternal entities. Ashꜥ‘arī authors who affirmed the awāl affirmed the existence of real attributes in addition to the abstract attributes, but they did not have the same concerns as the Muʿtazila. Instead, they were motivated by making sense of knowledge, be it in the form of definition, inference, and, more generally, grounding resemblance relations between distinct extramental entities. So, if we say that my chair is burgundy and my shirt is burgundy, then there must be some abstract property which is true of both which can make sense of the fact that I am using the exact same predicate in both statements. Likewise, if I know that ‘my shirt is burgundy,’ and I know that ‘my shirt is a body,’ and that ‘my shirt is originated,’ then, according to the proponents of the awāl theory, each of these objects of knowledge must be distinct from one another, because if they were the same, then my knowledge would not increase with the knowledge of each proposition. Furthermore, that object of knowledge cannot be identical to the shirt itself, and therefore, it must be something additional to the shirt.

But to affirm the ‘existence’ or ‘reality’ (thubūt) of the abstract modes in the extramental world seems to cause problems as well, for, presumably, the abstract mode of ‘being burgundy’ would share in the abstract mode of ‘being a colour’ with other abstract modes, and therefore, that abstract mode would require another abstract mode. Furthermore, each of them would have the further abstract mode of being-existent, and being-known, which in turn would need further modes to become intelligible themselves, entailing an actual infinity of properties. This is precisely why Ash‘arī rejected the modes and affirmed that things resemble one another and differ from one another by themselves, without the need of positing a further universal property.[14] In other words, Ash‘arī held that one could ground that knowledge in various aspects of the same object, without postulating the existence of further entities.

“The theory of awāl was often caricatured as denying the law of excluded middle and, by the later period, the rejection of awāl was often justified by the fact that its detractors reject any medium between existence and nonexistence. “

The theory of awāl was often caricatured as denying the law of excluded middle and, by the later period, the rejection of awāl was often justified by the fact that its detractors reject any medium between existence and nonexistence. While this may have been a consequence of the version of the awāl theory presented by Abū Hāshim, an examination of the relevant passages in authors like Bāqillānī and Juwaynī indicates they had no such intention. Instead, all they intended by their statement was to affirm a type of property that has no independent existence; rather, its reality was utterly derivative and dependent on the existence of some particular principle (in a very similar way to Aristotle holding that universals were ‘secondary substances’). Because of this, it was quite easy to replace the theory of awāl with some kind of perspectival or conceptual property that is revealed through mental process of abstraction.

Let us first turn to Bāqillānī, the first Ash‘arī scholar who accepted the theory of aḥwāl (at least in his later and most substantial work, the Hidāya). In the chapter against Abū Hāshim’s theory of aḥwāl, he writes the following in the Tamhīd:

Since this abstract mode is known, it is necessary that it is either existent or nonexistent. If it is nonexistent, it would be impossible for it to necessitate a judgment and for it to relate to Zayd instead of ‘Amr, or to the Eternal instead of the originated. And if it is existent, then it is necessary that it is a thing and an attribute related to the knower; and this is our position which we hold to be true. The dispute is only in the expression and in naming this thing knowledge or mode, but this is not a substantive dispute. Therefore, it is necessary to judge the validity of what we have held in the affirmation of the attributes.[15]

Bāqillānī first argued that, on Abū Hāshim’s formulation, the modes are neither existent nor are they even known. The reason why they may have felt the need to deny that aḥwāl are known, of course, is because being-known requires one to postulate a further mode. By denying the knowability of the aḥwāl, Abū Hāshim may have been trying to avoid an infinite regress of properties. Instead, on his view, the modes were quasi-entities by means of which other entities become known. Bāqillānī, rightly points out that this is incoherent. Then, he proceeds to presenting his own view above, namely, that if they hold that the mode is real, then the dispute is verbal, for that is all he means when he affirms the existence of the attributes. Without delving further, the point here is that, in the argument above, we find no sign of a denial of excluded middle. Indeed, at the beginning of the text, Bāqillānī, as was common for classical kalām, divided all knowables (al-malūmāt) into the existent and the nonexistent, without any middle.

Bāqillānī’s young contemporary, ‘Abd al-Qāhir al-Baghdādī is even more aggressive in his rejection of the theory of aḥwāl. In his Iyār, he writes the following:

And among [Abū Hāshim’s] heinous positions is his affirmation of the aḥwāl, namely, his statement that every knower has a mode by which they are distinguished from non-knowers, and yet that mode is neither existent nor nonexistent, nor known or unknown, nor mentioned, but he has mentioned it in his very statement that it is not mentioned, so he has contradicted [himself] by mentioning it as being unmentioned…And on this basis, he cannot deny anything among the impossibilia which rational agents have denied, for everything rejected among those impossibilia is not any worse in its impossibility than his statement that modes are neither existent nor nonexistent, not known nor unknown.[16]

So unlike Bāqillānī, Baghdādī takes a far less conciliatory tone; in any case, it is clear that he does affirm the law of excluded middle, and he finds at least Abū Hāshim’s formulation to be utterly unintelligible. The consequence Baghdādī draws is even more dire: if you accept one absurd view, then, you must accept every absurd view.

Juwaynī was one of the most influential of the classical kalām writers, and his repertoire indicates that he was far more amenable to Bāqillānī’s approach to kalām, as opposed to that of al-Baghdādī. Juwaynī’s Irshād in particular was very influential and elicited several major commentaries. In the chapter on affirming the abstract modes, Juwaynī uses a formulation which may appear to be denying the law of excluded middle, but as we shall demonstrate, he had no such view in mind. He writes:

The abstract mode (al-ḥāl) is ‘an attribute of an existent being that is not described with existence or nonexistence.’ Among these modes are those which hold for entities by virtue of an additional property (mu‘allal), while others hold without an additional property. These extrinsic (mu‘allal) states are every judgment that is true of an entity by virtue of a property that subsists in it…as for the modes which are not caused by an additional property, then they are every affirmative property that holds of an entity without an additional cause over and above the essence itself, such as ‘being-located’ for atoms: for it is additional to its existence, and every property of an existent being which cannot exist independently nor is it caused by an [additional] existent, then it is of this category.[17]

So, the abstract modes are (i) attributes, (ii) they hold only of existent beings, and (iii) they are not themselves attributed with existence or nonexistence. Does this entail a rejection of the law of excluded middle? It may appear to be the case in English, because English lacks a term like the Arabic adam, whose distinct trilateral root prevents one from easily making such an inference. That is, the Arabic term for ‘nonexistence’ is not literally lā-wujūd. Evidence for the rejection of excluded middle would have to be formulated as affirming a third between affirmation (ithbāt) and negation (nafī), which is a wholly other issue – as we shall get to later.

So, what is Juwaynī saying here? What he means to say is that there are properties which do not have any independent existence of their own, but they are real, and they hold for existent entities. For example, if we say that ‘Zayd exists,’ then his property of existence cannot also be existent, because if it was, we would be off on an infinite regress. It also seems unintuitive to say that it is nonexistent, because how can something nonexistent account for the reality of Zayd? It is forms of reasoning like this that led figures like Juwaynī to opt for the aḥwāl theory, and it is precisely its awkwardness and unintuitive formulation that led the majority to reject it.

Nevertheless, as we saw with Bāqillānī above, Juwaynī will actually equate Ash‘arī’s position of affirming knowledge of aspects as an alternative to affirming modes to amount to the same thing. He writes: “And the majority of the [classical] mutakallimūn rejected the aḥwāl, and they believed that ‘the atom’s being-located’ was identical to its existence. Their position is the same for everything which we judged to be an abstract mode that is additional to its existence.”[18] This passage is telling for two reasons: (i) Juwaynī tells us that the majority of the classical authors rejected the theory of aḥwāl, so it would be quite a stretch to claim, over and above the affirmation of the modes, that the majority of classical kalām rejected the law of excluded middle until their minds were ‘corrupted by Aristotle’; (ii) that this is a dispute on the nature of certain types of attributes that do not appear to have any existence of their own. Both parties agree that knowledge of the existence of an atom is distinct from knowledge of its being in a location, but they disagree on whether or not this implies the addition of a distinct attribute in the external world. As we saw before, Ash‘arī’s answer is no: rather, the atom’s being in a given location is an aspect of the same entity which is revealed by a pure act of intellection, while for Juwaynī, there is a further abstract property called a ḥāl that is revealed by an act of intellection, but it also has no existence of its own over and above the existence of the entity it qualifies.

Juwaynī, in fact, does not see any substantial difference between the two positions. He writes:

One who engages in this science cannot proceed without recourse to the modes: either by calling them modes (aḥwāl), or aspects (wujūh), or intrinsic properties (ṣifāt nafs). And further, one of knowledge should not be pained by the exaggerated intimidation of the negaters of the modes by virtue of the fact that the mode is not attributed with existence or with nonexistence, for the extent of what they say is mere implausibility and pure claim, and it is not possible for them to claim epistemic necessity or a cogent proof.[19]

In other words, some dependence on abstract properties is inevitable in kalām, and it ultimately comes down to a difference in wording. We may not agree with this position – nor did many of the mutakallimūn, but the important thing to note here is that there is no rejection of excluded middle. That is, it is no rejection of ‘p or not-p’, but it is a rejection that the opposition between mawjūd and madūm is an instance of ‘p or not-p.’ That is because, for Juwaynī, there is another kind of entity which is real (thābit), but is not described with existence, nor is it described with nonexistence. We can join the chorus of classical mutakallimūn and claim this is unintelligible, surely, but this is not the same as stating that Juwaynī here intends a rejection of the law of excluded middle.

“In his much more detailed ­Shāmil, Juwaynī presents an argument against the aḥwāl theory that relies on the law of excluded middle. As we shall we see, Juwaynī’s response to this argument is not a denial of the law of excluded middle, but rather, a denial that the aḥwāl theory is a denial of it.”

In his much more detailed ­Shāmil, Juwaynī presents an argument against the aḥwāl theory that relies on the law of excluded middle. As we shall we see, Juwaynī’s response to this argument is not a denial of the law of excluded middle, but rather, a denial that the aḥwāl theory is a denial of it. This is because the law of excluded middle is not an ontological thesis at all, but a merely logical and epistemological thesis. It is for this reason that the law of excluded middle equally applies whether you are reasoning about nonexistent items or existent ones. The theory of aḥwāl, however, is an ontological theory that is meant to describe a class of properties that have no independent existence in order to make sense of our knowledge of distinct aspects of an entity. Juwaynī writes:

They said: the mode which you have affirmed is either described by existence, or it is not described by [existence]. If it is described by existence… then it entails an infinite regress of existent entities. And if it not attributed with existence, then it is necessary to describe it with negation and nonexistence, for there is no degree between existence and nonexistence, just as there is no degree between affirmation and negation.[20]

Notice that even the opponents of the aḥwāl theory, figures that are even more ‘classical’ than Juwaynī, needed to make an inferential step from the exhaustive disjunction between affirmation and negation to an alleged exhaustive disjunction between existence and nonexistence. It is this that al-Juwaynī denies, just as he denies the complaints by his opponents that it is unintelligible. He writes:

Perhaps our opponent in this discussion will say: I do not understand a degree between existence and nonexistence, nor do I hear any arguments in favour of what is unintelligible. For sticking to the path of reflection in rejecting a position or accepting it is dependent on its intelligibility. So, we say to the one who ridicules this position: ‘Do you understand existence?’ If he says ‘Yes, and necessarily so.’ Then it is said to him: ‘Then do you understand negation?’ If he says ‘Yes,’ then it is said to him: ‘Then we affirm a property (waṣf) for existence, and we negate existence and nonexistence from it, then this is intelligible without doubt, and rather the discussion and the debate is on whether this is impossible or not, either by necessity or inference.[21]

As we saw earlier, the dispute is an ontological one, and not a logical one. He affirms here that, as such, the theory is logically intelligible and contains no self-contradictions. Beyond that, according to Juwaynī, if it can be shown that the theory of aḥwāl is metaphysically impossible, then that is something that needs to be demonstrated by some form of non-inferential knowledge or by some inference. To make this more palatable for some: take the property of existence in our statement ‘Zayd exists.’ If we affirm that Zayd’s property of existence also exists, then we get an infinite regress of existences. If we say that it does not exist, then the question arises: if existence is a nonexistent property, then negating a nonexistent should make no difference. But negating the existence of Zayd (given that the negation is true) implies his nonexistence; so clearly, the property is making a difference. Therefore, it ought to have some abstract reality which is not qualified with ‘existence,’ but is nevertheless real and extramental.

Suffice it to say, most of the later school denies the theory, but they do not deny what the theory tried to explain. Instead, they analyzed the modes as Ash‘arī held them to be: aspects of a single entity which are revealed to the knower through various modes of investigation and inquiry. In that sense, as reported by Ibn Fūrak, the objects of knowledge are multiplied, but the existent entities in the world are not.

In case you have any doubts, let us look at some other key passages in Juwaynī. In an earlier chapter of the Irshād, on the definition of intellect as a subset of necessary knowledge of first principles, al-Juwaynī writes:

From this survey it emerges that intellect is noninferential knowledge of the possibility of possible beings and the impossibility of impossible things, such as (i) knowledge of the impossibility of the conjunction of contraries, and (ii) knowledge that the existent knowable is necessarily never void of negation or affirmation, and (iii) knowledge that the existent is either originated or eternal.[22]

These three examples are telling. The first is a statement of the principle of non-contradiction. That is, it is self-evident and non-inferentially known that two contrary properties cannot coexist in the same subject. Examples of this would include: it is impossible for Zayd to be living and dead, to be knowing and ignorant, or to be conscious and unconscious, and so on. The second self-evident principle that Juwaynī presents is none other than the law of excluded middle: every knowable existent must either be negated or affirmed, and the same goes for each and every one of its properties. As such, his chapter heading on the theory of aḥwāl is titled “On the affirmation of the modes and the reply to those who reject them.”[23]

Affirmations of the Principle of Non-Contradiction and Law of Excluded Middle

In case there are remaining doubts, I thought it would be helpful for some to see a number of citations from classical kalām authors affirming the principle of non-contradiction and the law of excluded middle. Let us begin with Bāqillānī. In the Tamhīd, Bāqillānī explains the division of knowledge into the non-inferential and the inferential. The categories of non-inferential knowledge are reducible to knowledge by perception through the five senses and to non-inferential modes of knowledge that are created in the self without recourse to the senses. Examples of this include knowledge of one’s own existence, their pains, and their pleasures. More importantly for our purposes, they include “the declarative statement about the existence of something, and that it is of some predicate or another, is necessarily either true or false, and that two reports whose contents contradict one another it is impossible for both of them to be true or false.”[24] He will then apply this principle of non-contradiction and excluded middle in his division of every knowable into the existent and the non-existent (which, as I stated earlier, is not equivalent to the principle of excluded middle). Likewise, his division of existents into the eternal and the originated is an application of this: that every existent either has a beginning to its existence or it does not. If it has a beginning it is originated, and if it is eternal, it does not.[25]

Similarly, al-Bāqillānī, in the section on epistemology in his Taqrīb wa l-Irshād, writes the following:

The sixth type of noninferential knowledge [is that] which is found in the self without the perception of any of the senses, such as knowledge of one’s self…and knowledge of the impossibility of the conjunction of two contraries, and for a body to be in two locations at the same time, and that the knowable is necessarily either nonexistent or existent. By that we mean that it is never void of being an existent and a thing, or it is not a thing. And that the existent is necessarily something which either has an origin or does not have an origin….and that two reports whose contents contradict one another: it is necessary that one is true and the other is false.[26]

Just as the propositions presented by Bāqillānī are self-evident, I will assume that his intentions here are similarly self-evident. Bāqillānī and the classical mutakallimūn are so adamant on this point that they assert that reason itself is constituted by knowledge of such first principles. After arguing that reason (‘aql) must be some subset of non-inferential knowledge, Bāqillānī goes through some possible candidates, then settles on a set which includes the principle of non-contradiction and excluded middle. The following discussion is quite revealing:

And it is impossible for [intellect/reason] to be a knower’s knowledge of their own existence and what they find in pain, pleasure, and health, and so forth, because that would entail that children, animals, and insane folk would be rational, because they have knowledge of their own existence and their inner states, so that is false. Thus, it (intellect/reason) must be some non-inferential forms of knowledge which are specific to rational agents, such as: knowledge that two contraries cannot coexist, and that the knowable is necessarily existent (mawjūd) or not existent (ghayr mawjūd); and that the existent is necessarily either existent with an origin, or is not; and that two is greater than one…[27]

At the risk of beating a dead horse, let us move on to another classical kalām author: Baghdādī. After asserting that, if two people are in dispute, one must be speaking truthfully while the other must be speaking falsely, he entertains the objection that on a given question there may be multiple views, so why is it not possible for both of them to be wrong? He writes:

It is only possible for both their statements to be false if they are disputing in affirmation, and each of them affirms that his statement is the truth, and yet there is a third option on the matter that is distinct to both of them, and in reality, that third is the truth. But if they dispute in negation and affirmation, such that one affirms a statement and the other denies it, then it is necessary that only one of them has the truth, and each of the two disputants affirms his own statement, and denies the statement of the other. That is why we said: it is necessary that one of them is correct either in negation or in affirmation, because it is impossible for the necessary affirmation of something to be false while its negation is also false.[28]

And so, aside from the special case of the liar paradox, which he (and Bāqillānī) treats elsewhere and in an entirely different context,[29] Baghdādī is unequivocally committed to the principle of non-contradiction and the law of excluded middle, and he did not even need Aristotle to teach him. Indeed, the most powerful and important forms of argumentation adduced by the classical kalām tradition was the disjunctive syllogism. They would affirm that a given proposition is either true or false, that is, without any third middle: then they would infer from the falsity of one to the truth of the other, or the truth of one to the falsity of the other.[30] Juwaynī in his Burhān insists that the proof by reductio is one of the most important forms of inference, especially in theology, where we often lack the powers to delve into a matter directly, such as questions of metaphysics and theology. He writes:

Proof divides into two types: direct proof and indirect proof. As for direct proof, it is a type of inference which leads directly to one’s desired conclusion. As for indirect proof (burhān al-khulf), it is that in which the desired thesis does not become immediately evident to one, but rather, the inquirer places that thesis between the two divisions of negation and affirmation. Then establishes proof that negation is impossible, and thus, judges that affirmation is true; or he establishes proof that affirmation is impossible, and judges that negation is true. And all metaphysical-theological judgments rely on indirect proof.[31]

It is unclear to me how such disjunctive proofs could be conclusive if the disjunction between affirmation and negation could be vitiated by a third option. In other words, Juwaynī, just like his predecessors, is stating that something is either p or not-p. When the desired conclusion, for example, is p, and we have no way of examining p directly, then we can prove it true by showing that not-p is false. This is particularly useful, Juwaynī insists, in matters relating to the infinite, the case of God’s eternity and the origination of the world, and the question of atomism and the infinite divisibility of matter.[32]


Anyone trying to show that classical kalām authors rejected the principle of non-contradiction or the law of excluded middle are facing an uphill battle. More careful attention is needed before making such implausible statements about it. Indeed, before one throws the very principles constitutive of rationality out the window for the latest fads, one should at least make an honest attempt of dealing directly with some of the statements found in the primary sources. Of course, everyone is ‘free’ to make any claim they like about the principle of non-contradiction and the law of excluded middle, but it is another thing entirely to project their dreams onto the Islamic tradition.

God’s blessings and peace be upon His Emissary and his kinfolk.

Abdurrahman Mihirig is a PhD candidate in Philosophy at Ludwig-Maximilian University in Munich.

[1] See for example, Abbas Ahsan, “The logical inconsistency in making sense of an ineffable God of Islam,” in Philotehos 20.1 (2020), pp.68-116.

[2] See for example, Ayman Shihadeh, “The Argument from Ignorance and Its Critics,” in Arabic Sciences and Philosophy, p.173.

[3] See for example, Hamza Yusuf, The Creed of Imam al-Ṭaḥāwī, p.20.

[4] For example: al-Taftāzānī, Sharḥ al-‘Aqāʾid al-Nasafiyya, vol.1, pp.107-109; al-Juwaynī, al-Irshād, ed. M. Yūsuf Idrīs, p.177.

[5] Al-Ash‘arī, Kitāb al-Luma, ed. Al-Sayrawān, p.90.

[6] Ibn Fūrak, Mujarrad Maqālāt al-Shaykh Abī-l-Ḥasan al-Ash‘arī, ed. Daniel Gimaret, p.40, lines 1-6.

[7] Al-Bāqillānī, Kitāb al-Tamhīd, ed. McCarthy, p.211, lines 7-12.

[8] Al-Baghdādī, ‘Iyār al-naẓar, ed. Aḥmad ‘Arrūbī, pp.324-325.

[9] Al-Juwaynī, al-Irshād, p.177.

[10] Ibid, pp. 177-178.

[11] For example, Fakhr al-Dīn al-Rāzī, al-Muḥaṣṣal, pp.260-262 (Cairo: Maktabat al-Azhariyya lī-l-turāth, 2015); Kitāb al-Arba‘īn fī uṣūl al-dīn, eds. ꜥ‘Abd-Allah Ismā‘īl and Ibrāhīm Suwaylim, (Cairo: Al-Azhar al-Sharīf Majma‘ al-Buḥūth al-Islamiyya, 2020), vol.1, pp.502-505.

[12] ‘Aḍud al-Dīn al-Ijī, al-Mawāqif fī ‘ilm al-kalām, (Beirut: ‘ālam al-Kitāb, n.d.) pp.80-81.

[13] See: al-Sayyid al-Sharīf al-Jurjānī et al, Sharḥ al-Mawāqif, (Cairo: Maṭba‘at al-Sa‘āda, 1907) vol.4, pp. 57-59.

[14] Ibn Fūrak, Mujarrad Maqālāt, p.229, lines 5-22.

[15] Al-Bāqillānī, al-Tamhīd, p.201, §341, lines 10-15.

[16] Al-Baghdādī, Iyār, p.655.

[17] Al-Juwaynī, al-Irshād, 127.

[18] Ibid, 127.

[19] Ibid, 128.

[20] Al-Juwaynī, al-Shāmil fī uṣūl al-dīn, ed. al-Nashshār, p.639.

[21] Al-Juwaynī, al-Shāmil, p. 641.

[22] Al-Juwaynī, al-Irshād, pp.70-71.

[23] Ibid, 127.

[24] Al-Bāqillānī, Kitāb al-Tamhīd, ed. McCarthy, p.10, lines 9-11.

[25] Al-Tamhīd, pp.15-17.

[26] Al-Bāqillānī, Kitab al-Taqrīb wa l-Irshād, ed. Abu Zayd, vol.1, pp. 190-191.

[27] Al-Bāqillānī, al-Taqrīb, p. 197.

[28] Al-Baghdādī, Iyār al-naẓar, p. 213.

[29] They were interested in showing the self-contradiction inherent in the Dualist/Manichean division of the world into substances of good and evil, and also the Mu‘tazilite position of stating that volitional actions are objectively good and bad, and not to actually claim that contradiction is possible. See the relevant sections of Bāqillānī’s Tamhīd  and Baghdādī’s Uṣūl al-dīn.

[30] Al-Baghdādī, Iyār al-naẓar, pp.418-419.

[31] Al-Juwaynī, al-Burhān, ed. al-Dīb, pp.156-157.

[32] Ibid, p.157.