Mathematical Proof of God
- From Columbia University's daily newspaper, online version
Does God Exist? Yes, Mathematician Says
By Kathy Gilsinan
Spectator Staff Writer
February 17, 2004
Aristotle and Descartes would be pleased to hear Dr. William Hatcher
proclaim that even God Himself cannot defy logic.
Hatcher, who is a self-proclaimed Platonist philosopher with a Ph.D.
in mathematics, delivered a logical proof for the existence of God
before an over-filled auditorium in Warren Hall last night.
The event marked the first in what the Baha'i student organization
hopes will be a series of discussions about religion, science, and
philosophy, and how the three topics interrelate.
"We just felt like there wasn't enough discussion on campus" about
these matters, said Natasha Bruss, BC '05, President of the Baha'i
club at Columbia. Baha'i is based on the teachings of the prophet
Baha'u'llah, who preached that all religions are one, religion is
progressive, and that faith is not meant to be dogmatic.
Hatcher, a Baha'i adherent himself, is similarly uninterested in
dogma. His discussion explored the existence of God and carefully
shied away from any of its implications. Rather, he stated, "we have
to transform the religious discourse from a discourse about belief to
a discourse about truth."
To that end, Hatcher began his discussion with an introduction to
Aristotlean, or attributional, logic and its shortcomings.
Aristotle purported to have proven the existence of God, but he did so
based on a kind of logic that deals with properties of objects, an
approach, he argued, that's less than satisfying considering that
God's attributes cannot be perceived. Aristotle insisted that there
must be a first cause, namely God, in order to avoid the logical
inconsistencies of an infinite regress of causes for the universe.
Avicenna, an ancient Muslim philosopher, employed a different form of
logic in his proof. He examined the relations between objects rather
than their attributes, and in doing so accomplished what Hatcher
called "really amazing stuff." He claimed to have proved the existence
of God without recourse to Aristotle's infinite regression principle.
Hatcher said that though many subsequent philosophers like Thomas
Aquinas and Moses Maimonedes built on Avicenna's proof, they continued
to fall back on the infinite regression principle. Hatcher argued that
this principle is not sufficient to prove the necessity of God's
existence. Modern mathematics demonstrates the logical possibility of
infinite regression; negative integers, for instance, do not have a
minimal element or something that can be labeled a "first cause."
Thus, Hatcher has attempted to wed modern mathematics and ancient
philosophy in a proof of God's existence, drawing on Avicenna's
concept of relational logic. "In relational logic, we want to know how
the object relates to other objects. It turns out that the relational
approach often yields more useful information [than Aristotlean
The proof itself rests on four principles, the first of which is the
assertion that something exists. Even if the world is an illusion, he
pointed out, an illusory self, contemplating an illusory universe, is
still something that exists.
Further, he said, everything that exists does so because of some
cause, and the "principle of sufficient reason" states that every
phenomenon is either caused by something external or caused by itself,
but never both. "Everything that exists has to have a reason for
existing," he said.
Working from these principles, Hatcher first defined what he called
"the minimum criteria for Godhood," and then set about trying to prove
the existence of a phenomenon to fit those criteria. God, he said,
must exist and be unique, and must be self-caused as well as being the
cause of everything else. "Every existing phenomenon is the end effect
of a causal chain of possibly infinite length, starting with God," he
He then delved into Avicenna's discussion of the part-whole
relationship. "All known physical phenomena are composites, except
possibly the elementary particles of quantum mechanics," he stated.
Thus, if A is a component of B, then B is composite, and furthermore a
composite cannot be a cause of one of its components, because it could
not exist without all its components in place.
From these definitions, he said, one can infer that the universe is a
composite of all phenomena. He inferred that the universe itself,
then, cannot bring any of its own components into being, as it could
not have existed before the existence of the components.
Then, the universe could similarly not be self-caused, since it is
caused by the aggregation of its components, and so there must be some
object, G, that causes the universe but is not the universe itself. G
must then be universal because it is a cause, directly or indirectly,
of every component in the universe.
He concluded that G is the unique uncaused phenomenon, because, as the
cause of everything, it can't be caused by something else.
Hatcher said that the strength of the proof is that each assumption it
rests on is empirically grounded and is "far more reasonable than its
David Kline, CC '07, said he was impressed, even though he felt that
the logical proof of God, far from justifying faith, only requires a
different kind of faith. But, with that faith in reason so
characteristic of Columbia students, he said he appreciated that the
talk was "a purely logical representation of the existence of God and
not the meaning of God."