Brute-Force Logic

I find it odd when theistic philosophers try to prove the existence of God using logic and mathematics. It seems to me that these philosophers treat God as some sort of mere abstract concept that can be manipulated by human thought and can be reduced into logical semantics, syntax, symbols and equations. In my opinion, the purported grandeur and inscrutable mystery of the Supreme Being as seen in the eyes of faith are somewhat diminished in this manner.

Just examine this symbolic ontological argument formulated by the German mathematician Kurt Friedrich Gödel to appreciate what I mean:

Tadah! God’s existence was proven as a logical theorem!

This is actually just one of the many versions of the ontological argument for the existence of God. One of the earliest and most famous formulations of this argument was posited by St. Anselm of Canterbury. The argument attempts in establishing a priori proof by using reason and intuition. It is more akin to argument by definition. St. Anselm’s formulation of the argument can be paraphrased in this manner:

“A being that than which nothing greater can be conceived cannot possibly exist only in the mind. If it exists only in the mind, then it is not really a being that than which nothing greater can be conceived because perfection implies existence. A being that exists both in the mind and in reality is a far more perfect being than a merely imagined one. Hence, God exists in reality because he is the being that than which nothing greater can be conceived.”

At first glance, Anselm’s ontological argument seems irrefutable and self-evident. It is like a tautology or stating the obvious. It would be like saying that a triangle has three sides that intersect on a plane, forming three angles and vertices. In terms of Euclidian geometry, a triangle is basically described as such. All seems to be airtight and reasonable that even simple-minded people could intuitively understand what St. Anselm meant.

However, if the ontological argument is closely examined, the fallacy could be revealed. One does not need to be an atheist or an analytic philosopher to realize the errors of Anselm’s argument. In fact, the very first critic of this argument was not an atheist but a Benedictine monk by the name of Gaunilo. To demonstrate his point, Gaunilo used the analogy of a lost island applying the same line of Anselm’s reasoning. His counter-argument can be summarized thus:

1. The Lost Island is that than which no greater can be conceived.
2. It is greater to exist in reality than merely as an idea.
3. If the Lost Island does not exist, one can conceive of an even greater island, i.e., one that does exist.
4. Therefore, the Lost Island exists in reality.

The objection of Gaunilo was not really a direct refutation of Anselm’s argument but a mere demonstration of absurdity if the same line of reasoning would be applied to other concepts or things. This is called the “overload objection.” It is called as such because if the argument is correct, then the world would be overloaded with all perfect things or beings that we could conceive, such as perfect islands, perfect circles, perfect humans, etc.

Other scholastic and theistic philosophers criticized Anselm’s argument by pointing out the fundamental flaws. For example, St. Thomas Aquinas argued that God’s existence is his essence and the ontological argument can only be meaningful to God himself because he is the only one who completely knows his ‘ontology’ or essence of being.

On the other hand, Immanuel Kant refuted the argument by stating that existence is not a predicate. He distinguished between the analytic and synthetic forms of judgments. In the first type of judgment, the ‘predicate’ merely states something that is already implied or associated with a particular concept. Hence, it would only be a repetition like saying “God exists, therefore he exists.” There is nothing new that can be concluded from the statement. On the other hand, synthetic judgment involves deriving new knowledge or conclusion from the premises or assumptions. Anselm’s argument merely relies on tautology. It could also be considered as a ‘bare assertion fallacy’ because the conclusion is already contained in the premise.

St. Anselm’s Ontological Argument was a failed attempt in providing a ‘proof’ simply because it was unable to conclusively establish the actual existence of God as necessary being beyond conceptual definition. Simply put, one cannot prove something to exist by defining that it exists.



REFERENCE LINKS:

http://plato.stanford.edu/entries/ontological-arguments/
http://en.wikipedia.org/wiki/Ontological_argument
http://sas.uwaterloo.ca/~cgsmall/ontology.html

Godel's Notations Translated:
Definition 1:  x is God-like if and only if x has as essential properties those and only those properties which are positive
Definition 2:  A is an essence of x if and only if for every property B, x has B necessarily if and only if A entails B
Definition 3:  x necessarily exists if and only if every essence of x is necessarily exemplified
Axiom 1:  If a property is positive, then its negation is not positive.
Axiom 2:  Any property entailed by—i.e., strictly implied by—a positive property is positive
Axiom 3:  The property of being God-like is positive
Axiom 4:  If a property is positive, then it is necessarily positive
Axiom 5:  Necessary existence is positive
Axiom 6:  For any property P, if P is positive, then being necessarily P is positive.
Theorem 1:  If a property is positive, then it is consistent, i.e., possibly exemplified.
Corollary 1:  The property of being God-like is consistent.
Theorem 2:  If something is God-like, then the property of being God-like is an essence of that thing.
Theorem 3:  Necessarily, the property of being God-like is exemplified.