God’s Attributes Through the Lens of Set Theory

The nature of God in Abrahamic religions — Judaism, Christianity, and Islam — can be partially understood using the conceptual framework of set theory, which allows us to explore the relationship between what is infinitely unknowable and what is revealed and comprehensible to humans.

Defining the Sets

Set A: The Totality of God’s Attributes

• A represents all possible attributes of God, both those that are knowable and those that are unknowable.
• This set is infinite, transcendent, and beyond human comprehension. Attributes like God’s essence, omniscience, and omnipotence exist fully within A, but their true nature cannot be fully grasped by finite minds.

Set B: Attributes Comprehensible to Humans

• B represents the subset of God’s attributes that humans can understand, either through revelation (e.g., sacred texts), reason, or observation of creation.
• B is finite and shaped by human cognitive and linguistic limitations.

Intersection A ∩ B: Shared Attributes

• A ∩ B contains attributes of God that are part of A (truly God’s) and yet accessible to human understanding.
• Examples include God’s mercy, justice, and love, as conveyed through scripture, tradition, and nature.

Key Observations

The Finite Intersection: A ∩ B ≠ ∅

• There is a non-empty intersection between A and B, meaning some aspects of God are made knowable to humanity. This aligns with the idea of divine revelation in Abrahamic religions.
• However, the attributes in A ∩ B are approximations or filtered versions of God’s true nature. For instance, humans may understand God as “merciful,” but this understanding is limited compared to the infinite depth of God’s mercy.

The Vastness of A: A ∩ B ≪ A

• The attributes humans can grasp (A ∩ B) are vastly smaller compared to the totality of God’s attributes (A).
• This reflects the theological emphasis on God’s transcendence. While God reveals Himself, the majority of His nature remains unknowable. As the Bible states, “For My thoughts are not your thoughts, neither are your ways My ways” (Isaiah 55:8).

The Inaccessibility of the Infinite: A \ B ≠ ∅

• A \ B, the attributes of God that are entirely unknowable, forms an infinite subset of A. These attributes include the full essence of God and the mechanisms of divine omniscience, omnipotence, and transcendence.
• In Abrahamic thought, this underscores the idea that no created being can fully grasp God’s nature. This is emphasized in Judaism’s tanzih (God’s incomparability), Christianity’s mysterium tremendum (divine mystery), and Islam’s tawhid (God’s absolute oneness).

Revelation as a Bridge:

• Divine revelation acts as the mechanism by which attributes from A are made comprehensible in B, enabling humans to encounter God’s wisdom and guidance.

For example:

• The Torah, the Qur’an, and the incarnation of Christ represent points where A ∩ B becomes accessible to humanity.
• The 99 Names of Allah in Islam or the Sephiroth in Kabbalah provide structured ways to approach A ∩ B while acknowledging A \ B.

Theological Significance of A ∩ B ≪ A

The relationship A ∩ B ≪ A is central to understanding the theological position of Abrahamic religions:

Human Limitation:

• The fraction of God’s attributes humans can understand is infinitesimal compared to the infinite scope of A. This aligns with the emphasis on God’s transcendence and mystery.

Divine Generosity:

• Even though A ∩ B is small relative to A, it represents an act of divine generosity. Through revelation, God makes aspects of Himself accessible to finite beings, enabling faith and relationship.

Humility and Reverence:

• The vastness of A \ B, coupled with the smallness of A ∩ B, calls for humility. Humans are invited to worship and contemplate God while acknowledging that much of His essence will remain a mystery.

Illustrative Analogy

Think of A as the entirety of an ocean, infinite and incomprehensible, and B as the portion humans can contain in a small vessel. The water in the vessel (A ∩ B) is truly part of the ocean, but it is not the ocean in its totality. The remaining ocean (A \ B) represents God’s boundless, unknowable attributes.

Conclusion

Using set theory, we can better grasp the relationship between God’s infinite nature and human understanding:

1. Intersection Exists: Attributes in A ∩ B are real but limited revelations of God’s nature.
2. Vast Inequality: A ∩ B ≪ A, emphasizing the smallness of human comprehension in the face of divine infinity.
3. Faithful Encounter: God’s choice to reveal Himself through A ∩ B allows humans to know and worship Him while remaining in awe of His transcendence.

This mathematical perspective deepens our appreciation of the balance between God’s immanence (knowable attributes) and transcendence (unknowable infinity). It affirms that while humans can encounter God meaningfully, His full essence remains gloriously beyond reach.