God Just Doesn’t Add Up

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Einstein said “Pure mathematics is, in its way, the poetry of logical ideas” Math is rightfully viewed as the key to understanding the physical world. The sciences themselves rely on different types of math (i.e statistics). So it makes sense that some have tried to use math to prove the existence of God.  Mathematics, when done correctly, is absolute and if someone could use it to prove the existence of God then that would easily be one of, if not thee, greatest discoveries in human history.

There has been a few very solid attempts at proving God mathematically and warrant exploration.

Godel

Kurt Godel was an influential mathematician who was best known for his incompleteness theorems. He also made a strong case for the ontological argument for the existence of God. First, the Ontological Argument:

  1. It is a conceptual truth (or, so to speak, true by definition) that God is a being than which none greater can be imagined (that is, the greatest possible being that can be imagined).
  2. God exists as an idea in the mind.
  3. A being that exists as an idea in the mind and in reality is, other things being equal, greater than a being that exists only as an idea in the mind.
  4. Thus, if God exists only as an idea in the mind, then we can imagine something that is greater than God (that is, a greatest possible being that does exist).
  5. But we cannot imagine something that is greater than God (for it is a contradiction to suppose that we can imagine a being greater than the greatest possible being that can be imagined.)
  6. Therefore, God exists. (1)

Premise three is the primary failing of this argument. Premise three makes the assumption that a being necessarily exists both in the mind and in reality. While the idea of God certainly exists in the mind there is no evidence that such a being exists in reality as well.

 ‘there are many theologically threatening sets of properties which also conform to that specification? In other words: Godel’s own argument can used to prove God’s Non-existence too'(Stanford Encyclopedia of Philosophy)

The Ontological Argument can be used to prove anything simply by changing the words to suit whatever it is you are trying to prove, for example:

  1. It is a conceptual truth (or, so to speak, true by definition) that Santa Claus is a gift-giving being than which none greater can be imagined (that is, the greatest possible gift-giving being that can be imagined).
  2. Santa Claus exists as an idea in the mind.
  3. A being that exists as an idea in the mind and in reality is, other things being equal, greater than a being that exists only as an idea in the mind.
  4. Thus, if Santa Claus exists only as an idea in the mind, then we can imagine something that is a greater gift-giving being than Santa Claus (that is, a greatest possible gift-giving being that does exist).
  5. But we cannot imagine something that is a greater gift-giving being than Santa Claus (for it is a contradiction to suppose that we can imagine a being greater than the greatest possible gift-giving being that can be imagined.)
  6. Therefore, Santa Claus exists.

The Ontological Argument also fails for the following reasons:

  1. Existence is not a predicate. Immanuel Kant correctly pointed out that to say something exists  is not to attribute existence to that thing.
  2. The concept of God is meaningless (theological non-cognitivism).
  3. Ontological arguments are ruled out by “the missing explanation argument
  4. Ontological arguments presuppose a Meinongian approach to ontology. There are different modes of being for a variety of objects of thought.

Godel’s Theorem

Godel goes one step further and uses pure, mathematical modal logic to support the existence of God.

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.

This version again is begging the question. There are  at least two things within that argument that are undefined such as as ‘positive property’ and ‘God-Like’.

Baye’s Theorem

Bayes’ theorem is a formula that describes how to update the probabilities of hypotheses when given evidence. ‘It follows simply from the axioms of conditional probability, but can be used to powerfully reason about a wide range of problems involving belief updates.(brilliant.org)’. Baye’s Theorem fails as it uses statistical probability to try and prove the existence things that are spiritual or religious in nature and for which there is no other evidence to support their existence. Accepting evidence based on assumptions is dangerous and gullible and so this method can also be dismissed

“The theorem is good for dealing with concrete things like tests for cancer, developing spam filters, and military applications but not for determining the answer to questions about reality that are philosophical by nature and that would require an understanding of realms beyond, realms of which we know nothing.” -Patheos

Mathematical attempts to prove God fail because they make assumptions about existence and the nature of theological/mythical concepts, thus they are eliminated by the rules of logic and Occam’s Razor.

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