Does Omniscience Entail an Actual Infinite?

By Mohammad Abu AbdurRahman

In the Name of God, the Most Gracious, the Most Merciful

All praise is due to God. May He elevate the mention of His final Prophet and Messenger, Muhammad ﷺ.

According to Ibn Taymiyyah, the rational arguments for theism conclusively lead to a singular eternal God who exists beyond the material universe spatially and before it temporally, influencing it from above through His independent creative agency. Within this created universe, many forms of perfection that are definitionally praiseworthy in every respect, entailing no aspects of deficiency – such as power, knowledge, and life – are found to be physically possible in created beings, meaning that they are all the more possible in God. Since God is absolutely independent, as demonstrated through the sound rational arguments, He must be said to possess all such forms of absolute perfection necessarily, invalidating any need for an outside Cause that grants Him these perfections.

All of God’s attributes are perfect, necessary, and uncreated. Yet some of His attributes eternally accompany His essence – such as His life – while others are voluntary attributes that occur successively within His essence, such as His creative acts and His spoken words. It is categorically impossible for any one individual action or spoken word to accompany God from all eternity. This is the case even if the genus of divine actions and words is said to be eternal and God is said to have always been creating and speaking by His will.

The fact that God is devoid of individually eternal acts does not mean that He lacks a possible form of perfection and is dependent on another agent for its attribution. Indeed, due to their impossibility, no outside Cause is required to explain why God lacks individually eternal acts rather than possessing them. Thus, God’s maximal perfection is compatible with the fact that He must act in succession. God is accurately recognized to act successively in and of Himself on account of His own independent and perfect nature.

Analogical arguments

Through recognizing that God is maximally perfect by necessity, it becomes possible to infer many of the scripturally attested attributes of God – such as His power, knowledge, and life – through independent analogical arguments of the "a fortiori" kind. For example, it becomes possible to infer that God has more right to possessing the attributes of power, knowledge, and life than we do, because He is the Source of our existence and is worthier of existence than we are.

Additionally, it becomes possible to establish, by way of equal analogy, many truths about the faultless extent of God’s perfection, such as the extent of His omniscience and omnipotence. This type of analogical inference is specifically achieved by measuring one aspect of God against some other perfect aspect of His own Self.

For example, once we recognize that God possesses two eyes, we must further appreciate – through equal analogy – that neither one of His eyes can be less perfect than the other. Given that one of God’s eyes is healthy, His other eye can equally be healthy. Thus, both of God’s eyes are healthy necessarily, disproving the Antichrist’s claim to divinity. The fact that the Antichrist is blind in his right eye entails his dependence on an external Maker to explain why he is deficient in that eye rather than not.

Likewise, once it is recognized that God possesses perfect power over the actualized possibilities in the material world, then by analogy, He must have power over all things, namely: all the physical possibilities, both the ones He actualizes and the ones He does not. Similarly, once it is recognized that God perfectly knows what He creates, He must also perfectly know all things. He knows everything that is knowable, including all the infinitely many past and future states and all hypothetical possibilities. 

The "actual infinity" objection

Crucially, an actual infinity is impossible according to the ancient and contemporary rational minds. It is not possible for an infinite number of substances to exist all at once, nor for an infinite number of attributes to subsist in a substance simultaneously. For example, at any given moment, the universe cannot contain an infinite number of matter particles. Likewise, the ocean cannot carry an infinite number of waves at a given moment, nor can light possess an infinite frequency.

In light of this impossibility, critics of Abrahamic monotheism have sometimes claimed that God’s omniscience is incoherent because it involves an actual infinite. Some atheists have even raised this objection in a recent debate with Muslims, arguing that if God is truly omniscient and His knowledge pertains to infinitely many knowable things such as states and hypotheticals, then an infinite number of ontologically positive "beliefs" must subsist in His essence simultaneously, which is impossible.

This difficulty was also discussed by Kalam theologians in the Muslim tradition, sometimes leading them to adopt theologically unacceptable solutions. For instance, reasoning that an actual infinite in knowledge is impossible, al-Juwayni argued that God’s omniscience pertains to all future substances, but cannot pertain to all individual accidents that arise successively within them, for accidents are infinitely many. Instead, God’s knowledge must be said to "pass over" the individual accidents in a general way, a concept referred to as "istirsal". The Kalam theologians severely criticized al-Juwayni for this inappropriate view (may Allah have mercy on him).

Importantly, Ibn Taymiyyah has also authored an entire book on the nature of God’s omniscience. However, since that book is now lost, readers are often left puzzling as to how Ibn Taymiyyah could have resolved the "actual infinity" objection. Insha'Allah, I will propose in this article a plausible reconstruction of Ibn Taymiyyah’s theory of omniscience, one that is faithful to his well-established philosophical commitments and axioms. I will also quote supporting evidence from his writings at specific points in the article. That said, I have not read much of the Taymiyyan corpus, nor examined all of Ibn Taymiyyah’s statements on the topic of God’s omniscience. Thus, my reconstruction remains open to correction in light of new evidence and should be taken with a pinch of salt.

Ibn Taymiyyah's commitments

On the topic of divine knowledge, Ibn Taymiyyah upheld all the following three philosophical commitments, which might make his position seem paradoxical or even inconsistent:

First, Ibn Taymiyyah was opposed to the doctrine of divine simplicity. He maintained that God is not a simple, attribute-less Cause, but is instead an eternally massive Creator described with multiple real attributes of perfection that are inseparable from His essence. Furthermore, in this view, God’s attribute of knowledge is characterized by a real "attributional" multiplicity, and is not defined as a singular, indivisible attribute that merely connects to the infinitely many knowable things through infinitely many relations. For example, God’s knowledge of Jesus is not identical with His knowledge of Muhammad (may Allah elevate their mention), nor is His knowledge that Adam will exist identical with His knowledge that he has already come into existence.

Secondly, Ibn Taymiyyah rejected al-Juwayni’s position of "istirsal", maintaining instead that God knows all universals and particulars in a perfectly complete manner. Thus, God’s knowledge encompasses every individual thing in detail, without passing over some of the individual things generally. His knowledge must be said to truly pertain to infinitely many knowable things, e.g. all future states and hypothetical possibilities.

Thirdly, Ibn Taymiyyah categorically rejected the actual infinite, even employing its axiomatic impossibility in his explanation of the Qur'anic arguments for God’s existence. For example, he famously argued that the substances in the material world cannot be infinitely divided in the actual sense, for it would imply that they constitute an actually infinite number of particles. Instead, the substances must be said to undergo complete substantial change at some final point of division, ceasing to exist entirely and giving rise to completely different material entities that come into being. Similarly, for Ibn Taymiyyah, the infinitely many material substances do not exist all at once; rather, they originate and annihilate in succession. This proves the fact of substantial origination within the material substrate, which in turn definitively proves the existence of an external Originator, an eternal God who exists outside of the material system.

But how is it possible for Ibn Taymiyyah to maintain all three commitments, namely: that (i) God’s knowledge is characterised by real "attributional" multiplicity and (ii) encompasses infinitely many knowables, while (iii) an actually infinite multiplicity is impossible? Reconciling all three in a way that truly respects Abrahamic monotheism might seem like an impossible task to the serious philosopher. If it is truly impossible, the Taymiyyan will be obligated to forsake at least one of the three commitments, accepting either (i) some version of the doctrine of divine simplicity, (ii) al-Juwayni’s position on "istirsal", or (iii) the possibility of an actual infinite, undermining Ibn Taymiyyah’s theological project in the process.

Alternatively, the Taymiyyan could dangerously bite the bullet and endorse the position that God does not permanently know all things. In this erroneous view, God would be assumed to know only a finite subset of the infinitely many knowable things at every given moment, eventually discovering a different subset of knowable things in the course of His internal divine succession, while entirely losing His knowledge of the previous subset. In other words, God would be moving from ignorance to knowledge and vice versa, a claim that is worse than al-Juwayni’s "istirsal".

Fortunately, based on Ibn Taymiyyah’s principles, a promising reconciliation between all his three commitments can be constructed without falling into such heresies and – as far as I can tell – contradicting any of his explicit statements. We turn to this reconstruction below.

The proposal

Admittedly, the proposed theory of omniscience operates using notions of "divinely stored" and "divinely accessed" information, in a way that is vaguely analogous to how a human "stores" memory and later "retrieves" it as he focuses on different pieces of information. Therefore, it is important to first emphasize that God’s knowledge is maximally perfect and unlike the knowledge of created beings, which is necessarily deficient. God’s knowledge is not affirmed univocally, but rather analogically in an "a fortiori" manner respecting His transcendence. The proposed theory is thus not an attempt to uncover the true modality of God’s omniscience, which is known only to God, but is rather a limited human effort to describe His omniscience in a coherent way that avoids the charge of contradiction while maintaining sufficient theological clarity.

Three main features stand out in my proposed theory. First, the theory suggests that God possesses a truly Eternal attribute of knowledge that pertains to all the infinitely many knowable things. I based this aspect of my theory on a famous statement by Ibn Taymiyyah in his Wasitiyyah creed. 

Importantly, the Eternal knowledge of God is structurally fixed and unchangeable, permanently "storing" all the knowable information. This is unlike human memory which develops with time, changes through experience, and can be damaged by illness.

Moreover, to avoid the actual infinite, the Eternal knowledge must be ontologically finite in its "attributional" multiplicity. However, it must also be incredibly "complex" such as to meaningfully cover all the infinitely many knowable things. Hence, God meaningfully knows all things at all times in this "stored" manner, without implying an actual infinite or the doctrine of divine simplicity.

I partly base this nuance on a statement by Ibn Taymiyyah in the sixteenth volume of Majmu' al-Fatawa. There, Ibn Taymiyyah describes the multiplicity of knowledge using structurally qualitative terms, giving the loose example of continuous water flow, rather than describing it in discretely quantitative terms, such as in the example of accumulated silver coins.

Plausibly, the nuance can be further argued in an "a fortiori" manner from technological concepts like Turing machines. If a designed system can be finitely complex in its foundational structure yet give rise to infinitely many outputs, then why deny that God’s Eternal knowledge is ontologically finite in its multiplicity yet covers infinitely many knowable things such as future states and hypotheticals? If a boundless richness is plausible in designed systems, then it should be all the more plausible in God.

Secondly, my proposed theory suggests that God is truly attributed with a volitional knowledge that arises successively on top of His Eternal knowledge. Through this eternal volitional activity, God continuously accesses particulars from His Eternal knowledge as required by His perfect nature.

For example, God voluntarily accesses future particulars in the context of His decree-writing. As it is narrated in Sahih Muslim, God wrote down the decrees of this world – i.e. everything that will occur from the onset of this world till the Day of Judgement – fifty-thousand years before creating the heavens and the earth. The future of the universe is voluntarily accessed, decreed, and recorded by God long before it is actualized via His creative will.

Furthermore, as God is actualizing the worldly matters that were previously accessed and decreed, He additionally conceives of them as actually coming into being through His creative act, before He conceives of them as having already come into existence. This implies a real "change" within God that allows the divine conceptions to be accessed voluntarily in a tensed way. In other words, God’s knowledge of the fact that something (i) will come into existence at its appointed time, (ii) is actually coming into existence at that appointed time, and (iii) has already come into existence at that time, is not identical.

Crucially, God’s act of accessing the information from His Eternal knowledge is immediate and occurs without delay; thus, it does not imply forgetfulness, unlike humans who exert much effort in recalling the stored information. Furthermore, God’s act of accessing the information is completely volitional, not an unintentional reaction. Unlike human beings, who are often reminded of information unintentionally when confronted with unexpected circumstances, God accesses the information from His Eternal knowledge independently and in and of Himself, without being caused to do so through external influence.

Thirdly, the proposed theory suggests that God – although truly in possession of infinite knowledge in a "stored" manner as previously established – can never be said to "access" infinitely many knowable things from that Eternal knowledge all at once. This nuance is potentially supported by a statement of Ibn Taymiyyah in his treatise Fana al-Nar, where he mentions that it is categorically impossible for human beings to enumerate infinitely many things simultaneously, whether verbally or through conception.

The statement from Fana al-Nar could be read as hinting at the universal impossibility of infinite enumeration, which in turn would imply that not even God simultaneously "accesses" infinitely many knowable things in a single moment, for it would lead to an actual infinite. In light of this, the proposed theory suggests that while God truly knows – via His Eternal knowledge – all the infinitely many future details of the bliss of the inhabitants of Paradise, He never "accesses" all of that detail simultaneously.

This is perhaps just as God never utters an infinite number of words simultaneously even though His words are infinitely many and can never be exhausted. Indeed, if God is said to simultaneously utter infinitely many words or access infinitely many knowable things, then an actual infinity of "utterances" or "beliefs" would be subsisting in His essence, which conflicts with Ibn Taymiyyah’s philosophical commitments that were discussed earlier.

Further confirmation

Remarkably, although Ibn Taymiyyah’s book on omniscience is lost, history has recorded that his opponents accused him of believing that God’s conception does not pertain to the infinite future bliss of the people of Paradise. In one of his books, Shams al-Din ibn Tulun reports that Abu Sa'id al-'Ala'i, a contemporary of Ibn Taymiyyah, accused him of adopting this position, polemically linking it to al-Juwayni’s "istirsal".

This accusation by al-'Ala'i confirms my suggested reading, namely: that Ibn Taymiyyah actually believed that God never simultaneously "accesses" all the infinitely many future details of the bliss of Paradise. However, in his accusation, al-'Ala'i seems to polemically dismiss Ibn Taymiyyah’s other statements – such as in his Wasitiyyah creed – that indicate that God truly knows all future details via His Eternal knowledge, which certainly covers all the future details of the bliss of Paradise.

Also remarkably, in a statement in Mas'alat Huduth al-'Alam, Ibn Taymiyyah blames al-Juwayni’s position of "istirsal" on his failure to recognize that God perpetually acts in succession from the infinite past.

Ibn Taymiyyah’s argument in that statement seems to be the following (though I could be mistaken):

1- Given that al-Juwayni rejects the view that God acts in succession, he is not open to the view that God "accesses" the future particulars in a successive manner from His eternally "stored" knowledge.

2- Thus, al-Juwayni expects God’s knowledge to pertain to all the future particulars in a permanent and simultaneous manner, in a continually "accessed" mode.

3- However, such a permanent "accessing" of the infinitely many particulars, at every single moment, entails an actual infinity, which is impossible according to al-Juwayni.

4- Therefore, according to al-Juwayni, God’s knowledge cannot truly pertain to all the infinitely many particulars, such as all the individual accidents that originate successively within the future substances.

5- Instead, God’s knowledge must be said to "pass over" these individual accidents generally, implying "istirsal" which, for other Kalam theologians, implies imperfection in God’s knowledge.

6- By contrast, since Ibn Taymiyyah holds that God perpetually acts in succession, he is able to envision God as "accessing" the infinitely many future particulars in a successive manner from His eternally "stored" knowledge, not all at once, thereby avoiding the actual infinite without falling into al-Juwayni’s "istirsal" and other unfavourable solutions.

In short, to summarize my proposed theory of omniscience which – as far as I can tell – is consistent with the Taymiyyan principles: There is a real distinction between (i) God’s Eternal knowledge – which is permanent, unchanging, and encompasses all particulars – and (ii) His voluntarily originating knowledge, which He effortlessly accesses in time. Although God simultaneously knows all things in detail – such as all future states and hypotheticals – via His Eternal knowledge, He accesses only a finite subset of these particulars through His will at any given moment, especially in the process of writing His Decree.

Countering objections

Finally, let us respond to three potential objections to the proposed theory of omniscience.

The first objection states that, while the theory might convincingly distinguish between (i) divinely "stored" information that subsists eternally in God and (ii) divinely "accessed" information that arises voluntarily in time and relates to events in a tensed way, the theory completely ignores the third, important category of "eternally accessed" knowledge, such as God’s non-volitional knowing of His own eternal essence and the eternal attributes that accompany it, like His life and His hands. In response to this objection, I suggest that the theory can easily accommodate this element of permanent "accessing" within the Eternal knowledge without resulting in an actual infinite, specifically because these permanently "accessed", non-volitional attributes of God are not ontologically infinite.

A second objection states that, while the theory reasons that God perfectly knows all things at all times in a "stored" manner, it does not guarantee that God "accesses" absolutely all knowable hypotheticals through His will. In response to this objection, I suggest that God’s true perfection consists in knowing absolutely all knowable things – including all hypotheticals – via His Eternal knowledge, and in further being able to effortlessly "access" them whenever He pleases. As for the claim that God must actually "access" every knowable hypothetical in the course of His internal succession in order to be truly perfect, it is not an evident claim. Instead, God’s perfection entails that He divinely "access" the right information from His Eternal knowledge whenever His perfect nature demands it. For example, He must be said to perfectly "access" all of the details of the Divine Decree since writing them down in the Preserved Tablet.

The third and last objection accuses the theory of rendering God’s promise of never-ending bliss in Paradise unreliable. The objection argues that, in order for God to reliably state that the believers will enjoy blessings in Paradise {without end}, as explicitly mentioned in the Qur'anic verse, He must first be said to conceptually "access" all of the infinitely many individual blessings of Paradise. However, such a simultaneous "accessing" of infinitely many details involves an impossible actual infinite.

In response, it should be emphasized that God is able to effortlessly "access" universal propositions from His Eternal knowledge just as He is able to "access" the individual particulars. Thus, the universal proposition “There is no end to Paradise” can be directly accessed by God from His Eternal knowledge without Him having to simultaneously enumerate all of the infinitely many days of Paradise. God does not infer the universal propositions inductively, even though His perfect knowledge of all particulars indeed entails His perfect knowledge of all universals.

In conclusion, while I do find my reconstruction very plausible, coherent, and compatible with Taymiyyan theology, I cannot confidently ascribe my theory to Ibn Taymiyyah without further definitive evidence. It remains to be seen if Ibn Taymiyyah agreed with my reconstruction fully, and to what extent if he did partially.

May Allah elevate the mention of His Prophet Muhammad ﷺ, his household, and his companions. May He send upon them His peace and His blessings.

And the last of our prayers is:

{All praise is due to God, the Lord of the worlds}.

Article on the Internet Archive (Alternative link)

Link to thread (Way Back Machine, on X)

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Also see "Ibn Taymiyyah on Divine Simplicity" by Dar al-Arqam Publishing