God Exists? Interesting essay I found.

[MalReynolds]

http://forums.livingwithstyle.com/sh...98&postcount=1

"INTRODUCTION

Let me say at the outset that this in no way proves the existence of the Christian God versus the Jewish God versus the Islamic God versus the God of Armchair Intellectuals or what-have-you. But it does indeed prove the existence of some God — some Supreme Being — so long as you accept its two premises.

To be valid, a logical argument must proceed in perfect accordance with the rules of its system. Its inferences (including its conclusion) must follow from one another, and its statements must be wiffs (well formed formulas). Any argument, even a circular argument, is valid in this respect even if its premises are false.

But to be sound, a logical argument must be valid AND all its premises must be true. If an argument is sound, then its conclusion is incontrovertible. Whatever contradicts the conclusion of a sound argument is definitively false. There is no question, no controversy even from atheist philosophers that this argument is valid. The question is whether it is sound. In order to show that it is not sound, you must show that one or more of its premises is false.

Arguing about definitions is pointless. The definition of God will be coherent. Arguing about the rules of logic is pointless. The rules are the standard rules of S5 modal logic, and assume a Euclidean relation among worlds. And arguing about the fallacies of Anselm's ontological argument is pointless. Although this argument is initially based on his, it is not his, and arguing against his is a straw man.

S5 MODAL LOGIC

For those not familiar with modal logic, a modal is a kind of truth. Specifically for S5, there are three modals: (1) necessity, (2) possibility, and (3) actuality.

If a statement is true in all possible worlds, then it is necessarily true. Necessity is indicated by this symbol: [] — two square brackets. (That's the ASCII rendering of a block.) If a statement is true in at least one world, then it is possibly true. Possibility is indicated by this symbol: <> — two angle brackets. (The ASCII rendering of a diamond.) Finally, if a statement is true in the actual world, then it is actually true. Actual truth is indicated predicatively — i.e., without any sign. Thus:

[]A — A is necessarily true. A cannot possibly be false. A is always true in all worlds.

<>A — A is possibly true. A can be true in one world but false in another.

A — A is true in the actual world. It may or may not be true in some other world.

POSSIBLE WORLD SEMANTICS

Strictly speaking, a world is a set of statements. The set of true statements that describes the world we live in is called the "actual world". A set of true statements describing either the actual world or some world other than the world we live in is a possible world. A set of true statements describing every possible world is a necessary world. Note that the actual world is a possible world, but a possible world is not necessarily the actual world.

For example, the statement that a circle's circumference is a ratio of pi to its diameter describes a possible world, but not the actual world and not a necessary world. The statement is true only in a world of flat planes. The actual world is a world of curved space, and while pi can approximate the ratio sufficiently for nearly every conceivable purpose, circles in the actual world conform to non-Euclidean geometries. Therefore, since the actual world is a possible world, and the statement is not true in the actual world, the statement does not describe a necessary world.

A world in which no statements are true is not a possible world. It cannot exist.

Because the modals of S5 are Euclidean, the accessibility condition between necessity and possibility is as follows: (wRv AND wRu) -> vRu, where "w" is a world, "R" is a relation, and "v" and "u" are truth bearers (statements that are either true or false). Therefore, necessity and possibility can be derived from one another. In fact their derivation is intuitive:

[]A <-> ~<>~ A If it is necessary that A is true, then it is not possible that A is not true.

<>A <-> ~[]~A If it is possible that A is true, then it is not necessary that A is not true.

See Stanford University's page on modal logic for a more in-depth introduction.

DEFINITION OF GOD

The term "God" is commonly accepted to mean Supreme Being. (Warning: Dictionary.com sometimes has a popup.) It so happens that S5 modal logic provides a convenient way, via the modal of necessity, to render the term "Supreme Being" into logical symbology. If we accept that supreme is a superlative, then it follows that there can be only one being that is supreme.

To convince ourselves that this is true, we can construct an argument ad reductio. Suppose for the sake of argument that it were possible for a being to be supreme but not necessary. And suppose that it were possible for a being to be necessary but not supreme. Since a necessary being must (by definition) exist in all possible worlds, then that would mean that there is at least one world in which there exists a being that is supreme but NOT necessary. Thus, he is not supreme at all, because there is a necessary being in his world. Since we've reached a contradiction, the reductio premise must be false. There is one and only one Supreme Being.

So we may use "necessary" as the logical equivalent of "supreme". And we may use "existence" as the ontological equivalent of "being". (See the definition of existence.) A being that is necessary exists in all possible worlds, and thus is supreme. For our logical tableau, we will refer to God as that which exists necessarily, or Necessary Existence (NE).

It can be shown that Necessary Existence is true in S5, and that the S5 Axiom is itself true. We are now sufficiently armed to write up our proof.

PROOF THAT GOD EXISTS IN ACTUALITY

Given []G = NE, prove G

1. <>G Premise

2. [](G -> []G) Premise

3. <>[]G The Kripke Principle ([](<>A AND ([](A -> B)) -> <>B) applied to 1, 2

4. <>[]G -> []G The S5 Axiom

5. []G Modus Ponens on 3, 4

6. []G -> G Necessary existence is true in S5

7. G Modus Ponens on 5, 6

QED

(Plain English Translation)

1. It is possible that God exists.

2. Necessarily, if God actually exists, then He exists necessarily

3. Therefore, it is possibly necessary that God exists (because it's necessary that if it's possible that A is true, and it is necessary that A implies B, then it is possible that B is true)

4. If it is possibly necessary that God exists, then it is necessary that God exists (otherwise the frame would not be Euclidean)

5. Therefore, it is necessary that God exists (because it is possible that He does)

6. If it is necessary that God exists, then God exists in actuality (otherwise the system would not be S5)

7. Therefore, God actually exists (because it is necessary that He does)

POINTS FOR DISCUSSION/DEBATE

As stated in the introduction, there can be no reasonable controversy over any part of the proof other than (1) and (2) — the premises. Let's examine those.

Premise 1 — <>G It is possible that God exists

To negate either the modal (<>) or the term (G) would be a semantic disaster because of the coherent definition of God. ~<>G would mean "it is not possible that a being that exists in all possible worlds exists", and <>~G would mean "it is possible that a being that exists in all possible worlds does not exist". But how can this be? It would be like saying that it is not possible that a bachelor is unmarried. Or that it is possible that a red car is not red.

Premise 2 — [](G -> []G) Necessarily, if God actually exists, then He exists necessarily

Surely this is not controversial. If the actuality of a thing implies the necessity of it, then the implication must itself be necessary. Otherwise, the actual world would be the only possible world, and there could be no true statements in any abstract symbological system. In other words, logic itself (and math itself) would be untrustworthy, since there would be the possibility of false statements."

I really don't have much else to add to that. I'm sure a few higher-level thinkers on here should have no problem tearing it apart, and look forward to it