On The Existence of God

Priyendra Deshwal
deshwal [at] stanford [dot] edu

(To appear in the XXXth Annual Cerebral Mines Journal)


ABSTRACT

We demonstrate the existence of God using the well-known principle of Mathematical Induction. While many approaches to answering this most profound question have appeared in literature, our argument, based on a universally accepted mathematical truism, offers a kind of deductive certainity that none of these other methods can provide. Our main contribution lies in irrefutably resolving this centuries old debate in favor of the existential stance.

SECTION I - INTRODUCTION

The existence of God ranks among the most vexing questions the human race has attempted to answer. A number of approaches have been put forward which purport to settle the question. Section II begins with a brief review of previous work in the area and pinpoints the shortcomings of some significant attempts to answer the question. Section III details the inductive proof we propose. Section IV concludes by presenting a few noteworthy points.

SECTION II - RELATED WORK

The most oft-cited arguments for the existence of God are the Cosmological and Ontological arguments. As we shall see, both of these are based on imperfect logical reasoning which leaves their conclusions open to serious challenge.

SECTION II(a) - THE COSMOLOGICAL ARGUMENT

A commonly stated version of the argument is as follows:

(1) Everything that exists has a cause of its existence.
(2) The universe exists.
Therefore:
(3) The universe has a cause of its existence.
(4) Nothing can cause itself to exist
Therefore,
(5) A being exterior to the universe caused it to exist
(6) Such a being can aptly be called the Creator or God
Therefore:
(7) God exists.

The argument is easily breached by the obvious follow-up question of what caused the existence of God. If we were to assume that God is a "caused" being, then clearly the argument serves no purpose as it settles one problem, the cause of the existence of the universe, but raises another problem, the cause of the existence of God. On the other hand, if God were to be an "uncaused" being, it would stand in direct violation of Premise (1) used in the proof. Therefore, the argument is unsound.

SECTION II(b) - THE ONTOLOGICAL ARGUMENT

The Ontological argument however, proves to be a much worthier opponent. One of the several forms of the argument is presented below:

(1) God is greater than anything that can be imagined.
(2) God exists as an idea in the mind.
(3) All other things being equal, a being that exists as an idea in the mind and also in reality is greater than a being that exists only as an idea in the mind.
(4) Assume that God exists only as an idea in the mind
(5) Then we can imagine a being greater than God (namely, a being which is equal in all respects to God, but which has the additional quality of existence in reality)
(6) The conclusions of STEP (5) and STEP (1) contradict
Therefore,
(7) Our assumption is wrong and God must exist in reality as well

This argument too has a fallacy, though subtly hidden. Kant was the first to point out its flaws when he noted that while using the existence of beings as a criteria for ordering them according to their greatness, the argument implicitly assumes that existence is a property of the beings. According to Kant, existence is not a property that a being can either possess or lack. When one asserts that God exists, he is not saying that there is a God and he possesses the property of existence. If that were the case, then when one wishes to assert that God does not exist one would say that there is a God and he lacks the property of existence, or in other words, the existence of God would be both affirmed and denied by the same assertion! This again leads us to a contradiction, proving that the Ontological Argument is also invalid.

SECTION III - THE INDUCTIVE ARGUMENT

Most arguments concerning the existence of God fall apart as they are primarily based on premises (explicit or implicit) that are either debatable or downright invalid. Our approach was to base our proofs on a premise whose truth was inviolable. The principle of Mathematical Induction is a universally accepted truism and as we shall shortly see, our argument derives the existence of God directly from the validity of the mathematical principle.

Theorem: God exists

Assumption: God is the master of the universe

Proof: We shall derive the result by induction on B_U, the number of beings in our universe.

Basis: B_U = 1
If the universe has exactly one being, then the universe could truly be said to belong to that being. In other words, the being would then be the master of the universe. Therefore, by our assumption, the being would be God. Hence, God exists

Inductive Step: Assume for B_U = n, God exists i.e. in a universe with exactly n beings, God exists. Now consider a universe with B_U = (n + 1). Clearly, for there to be (n + 1) beings, there must have been an earlier point in time, when there were just n beings and the (n + 1)th being was being born. Since in such a universe, B_U = n, God must exist. Now the birth of a new being cannot by itself be a cause for the death of another being - except of course, in unfortunate cases when a pregnant mother dies due to complications arising out of childbirth. So we have the following three cases:

(CASE A) The birth had no complications
Clearly, since no one died as a result of the birth, if God existed earlier, God must exist now too. Hence, God exists.
(CASE B) The mother dies and she was not God
Clearly, since the mother was not God and no other being died as a result of the birth, if a God existed earlier, it must exist now too. Hence, God exists.
(CASE C) The mother dies and she was God
In such a case, the new being is the child of God and hence, he can rightfully be called God himself. Hence, God exists.

(Q. E. D)

SECTION IV - CONCLUSION
In conclusion, we note the following:

(1) That God's existence has been established as a fact serves as a reminder to all atheists (Aldous Huxley included) that their posteriors shall soon be subjected to intense thermal treatment over the fires of Hell.
(2) The truth about God's existence also brings to attention claims by a certain friend of mine who says he is God himself. (Yep, that's you Asim!)
(3) The questions about God's sex and about the plurality vs. singularity of God are in no way resolved by the above argument or its straight-forward extensions. It is our intention to expand our mathematical framework to deal with these questions next.

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