God (יהוה)

Table of Contents

This website explores how mathematics can help us understand God.

God transcends language and math [Isa 40:28], yet he desires that we know him [John 17:3]. He gave us both word and reason [1_Pet 3:15]. God himself is the Word [John 1:1]. Therefore language and mathematics become tools for understanding his creation and his plan for us.

Who is God? He is the creator of all things [Gen 1:1], [John 1:3], yet he himself is uncreated [Col 1:17]. The Catechism says it this way:

God, infinitely perfect and blessed in himself, in a plan of sheer goodness freely created man to make him share in his own blessed life. [CCC ¶1]

Names for God

YHWH (יהוה)

The divine name revealed to Moses [Ex 3:14], associated with the Hebrew phrase ehyeh asher ehyeh-"I am who I am." In declaring this name, God identifies himself as being itself:

The revelation of the ineffable name "I AM WHO AM" contains then the truth that God alone IS. The Greek Septuagint translation of the Hebrew Scriptures, and following it the Church's Tradition, understood the divine name in this sense: God is the fullness of Being and of every perfection, without origin and without end. All creatures receive all that they are and have from him; but he alone is his very being, and he is of himself everything that he is. [CCC ¶213]

Hashem (הַשֵּׁם)

"The Name." The ancient Hebrews used this substitution to guard against violating the [Third Commandment's] prohibition on taking the Lord's name in vain.

Yehoshua (יהושוע)

This name joins "Yah" (from יהוה) with the Hebrew word for salvation (יְשׁוּעָה)-literally, "Yah saves."

Qualities of God

God's nature is traditionally understood through three divine attributes, each pointing toward infinity:

Proofs for God's Existence

Throughout history, philosophers and theologians have developed rational arguments for the existence of God. While faith transcends reason, these proofs demonstrate that belief in God is not contrary to rational inquiry [CCC ¶156].

Anselm's Ontological Argument

In his Proslogion (1078), St. Anselm of Canterbury formulated the first ontological argument-a proof proceeding purely from reason, without appeal to empirical observation:

God is that than which nothing greater can be conceived… And certainly that than which a greater cannot be conceived cannot exist only in the understanding. For if it exists only in the understanding, it can be conceived to exist in reality as well, which is greater.

Anselm's insight is that existence itself is a perfection. If we can conceive of a maximally perfect being, that being must exist-for a being that exists only in the mind would be less perfect than one that exists in reality.

Aquinas's Five Ways

In the Summa Theologica (1265–1274), St. Thomas Aquinas presented five arguments for God's existence, approaching the question through natural philosophy:

  1. The Unmoved Mover: Everything in motion is moved by another. There must be a first mover, itself unmoved.
  2. The First Cause: Nothing can cause itself. There must be a first efficient cause.
  3. Necessary Being: Contingent beings depend on something else for existence. There must be a necessary being.
  4. Gradation of Being: We observe degrees of perfection. There must be a maximum, the source of all perfection.
  5. Teleological Argument: Natural bodies act toward ends. An intelligent being must direct them to their purpose.

Gödel's Ontological Proof

Kurt Gödel, the mathematician renowned for his incompleteness theorems, developed a formal ontological proof using modal logic. Building on Anselm's framework, Gödel axiomatized the concept of "positive properties" and proved that a being possessing all positive properties necessarily exists.

In 2013, Christoph Benzmüller and Bruno Woltzenlogel Paleo achieved a remarkable result: they automated Gödel's proof using higher-order theorem provers. The systems LEO-II and Satallax verified the theorem:

Necessarily, there exists God.

The proof was further confirmed in the interactive proof assistants Isabelle/HOL and Coq. This represents a significant intersection of mathematics, computer science, and theology-demonstrating that formal methods can engage with metaphysical questions.

For the technical details, see: Automating Gödel's Ontological Proof of God's Existence with Higher-order Automated Theorem Provers