Essay:Of Islands

I present here an entirely a priori argument for/ against the existence of a God in a finite universe of existence. That is except the a posteriori meaning of the English word "god", and the ascribed properties attributed to the Christian God.

These definitions are however treated as arbitrary, and the proof's validity is not dependent upon the definition for either, but rather treats them quite similar to variables. In fact, this argument works for absolutely anything, for which one might seek a "perfect" instance thereof.

The title refers to Gaunilo's Island, as this proof began with seeking to determine if such an island could possibly exist in a finite universe. The change to have it address the Christian God was motivated by a realization late in the proof, that Gaunilo's Island could not exist, and neither could God. Since the non-existence of the Christian God is a more povocative statement than the non-existence of Gaunilo's Island in our world, I altered the centrum of the proof, but kept a title that related and made an acknowledgement of Gaunilo's Island.

I intended to show with this proof that God cannot exist within a finite Universe, such as the one that we are presumed to be in.

Given that...

 * 1) There exists a set, A, that contains everything
 * 2) The set of A containing everything, must contain all that exists, and does not exist, all that can be conceived, and cannot be conceived, all that is true, and non-true, all that is false, and non-false, and anything for which a truth statement cannot be made.
 * 3) There exists a set, E, that is any arbitrary subset of A
 * 4) There exists a function p whose domain spans A and whose range is a subset of A; such that the returned set contains all elements in A that are statements, if and only if the argument is refered to in that statement.
 * 5) There exists a function q whose domain spans A and whose range is a subset of A; such that the returned set contains all elements of the set produced by applying p to the argument, if and only if the element is truthful.
 * 6) There exists a function g whose domain spans A and whose range is a boolean value; such that the returned value is truthful if and only if the set produced by applying q to the argument contains at least one statement equivalent to the statement that the argument satisfies the meaning of the English word "god".
 * 7) There exists a set B, which is a subset of A; such that the set contains all elements, for which the function g yields a truthful result when applied to that element.
 * 8) There exists a set C, which is a subset of B; such that the set contains all elements that are an element of both the sets B and E
 * 9) There exists a function f, whose domain spans B and whose range is a unique orderable number for all elements of B; such that the returned value is an element of the set produced by applying p to the argument.

It follows that...

 * 1) The cardinality of the set A must be infinite.
 * 2) For all elements of A, the cardinality of the set produced by applying p to the element is infinite
 * 3) The cardinality of the set B must be infinite.
 * 4) The cardinality of the set C can be infinite, or finite.
 * 5) For all elements of B the resulting number from applying f specifically to that element cannot be infinity.
 * 6) Any finite cardinality of the set C must be a discrete value of zero, one, or more than one.
 * If the cardinality of the set C is zero, then there exists no element of A that satisfies the meaning of the English word "god", when restricted to a finite subset of A.
 * If the cardinality of the set C is one, then there exists an element of A that satisfies the meaning of the English word "god", when restricted to a finite subset of A.
 * If the cardinality of the set C is more than one, then there must exist an element of C for which the result of applying g to that element is larger than all other elements of C.
 * If the cardinality of the set C is infinite, then all orderable numbers would necessarily be satisfied when applying f for all elements.
 * If the cardinality of the set C is infinite, then there is an unbounded maximum value in the set resulting from applying f for all elements of C.

As such...

 * Given the definition of "perfect" in this context as case where an element has infinitely satisfied the selection criteria,


 * For any arbitrary weighing of criteria:


 * When restricted to a context that contains no gods, there cannot exist a best god, or a perfect God.
 * When restricted to a context that contains only one god, there is a best god, but this god need not be a perfect God.
 * When restricted to a context that contains any finite number of gods, there is a best god, but that god need not be a perfect God.
 * When restricted to a context that has an infinite number of gods, there is a best god, which is also the perfect God.

Consequently...
Presuming the weighing of criteria to be the conformity to the Christian God:


 * 1) Since the definition of the Christian God is that he is unique in existence, within a context of existence there must necessarily be one and only one god.
 * 2) Since the number of gods is finite, then the context of existence that is chosen must produce a finite number of gods.
 * 3) Since there is only one singular god chosen through selection, that god must by necessity infinitely satisfy the definition of the Christian God
 * 4) The only set of selection of criteria, and context of existence that can result in the existance of a unique and perfect Christian God is to restrict the context of existence and selection criteria deus ex machina to conform to the preselected criteria.

In conclusion...

 * 1) The Christian God must exclusively be a result of an intelligent designer intentionally crafting the context of existence, and selection criteria to perfectly match the Christian God.
 * 2) Since the Christian God cannot legitimately have a creator and still infinitely satisfy the criteria of being identical to the Christian God, the only intelligent designer capable of crafting such a result is a sentient, rational being, of which humans are a subset.