A new argument on the existence of God

Definition 1

Possible is what entails no contradiction.

Definition 2

Impossible is what entails a contradiction.

Definition 3

Necessary is that whose denial entails a contradiction, and exists by itself.

Definition 4

Contingent is that whose denial entails no contradiction, and it may exist by another being or not exist.

Definition 5

Opposite (or incompossible) is what cannot occur simultaneously with a possible being.

Definition 6

Concomitant (or compossible) is what can occur simultaneously with a possible being.

Definition 7

Nothingness, if possible, is the total absence of matter or energy.

Definition 8

The universe, if any, is the totality of matter or energy.

Definition 9

God, if any, is the immaterial being with the power to create the universe.

Axiom 1

An opposite of what is impossible is either possible and not necessary, impossible or necessary (what is impossible is opposed to everything).

Axiom 2

An opposite of what is possible and not necessary is either possible and not necessary or impossible (what is possible is opposed to everything, except to what is necessary).

Axiom 3

An opposite of what is necessary is impossible (what is necessary is concomitant with what is possible and what is necessary, and only is opposed to what is impossible).

Axiom 4

What is not necessary is contingent.

Axiom 5

What is contingent is either possible or impossible.

Axiom 6

What is not impossible is possible. 

Axiom 7

Everything that exists does so by itself or by another being.

Axiom 8

God, the universe and nothingness, if possible, are the only possible beings.

Theorem 1

Any universe is an opposite of nothingness.

Demonstration:

Nothingness, if possible, is the total absence of matter or energy (by Definition 7). The universe, if any, is the totality of matter or energy (by Definition 8). Opposite is what cannot occur simultaneously with a possible being (by Definition 5). Therefore, any universe is an opposite of nothingness.

Theorem 2

Nothingness is either possible or impossible, but not necessary.

Demonstration:

Any non-contradictory universe is possible (by Definition 1). Any universe is an opposite of nothingness (by Theorem 1). An opposite of what is possible and not necessary is either possible or impossible, but not necessary (by Axiom 2). In turn, an opposite of what is necessary is impossible, but neither necessary nor possible (by Axiom 3). Therefore, whether the universe is possible and not necessary, or possible and necessary, nothingness is either possible or impossible, but not necessary.

Theorem 3

Nothingness is possible.

Demonstration:

Nothingness is either possible or impossible, but not necessary (by Theorem 2). God and nothingness are concomitant, since God can either create or not create anything (by Definitions 3, 6, 7 and 9). What is impossible is opposed to everything, i.e., to what is possible, to what is impossible and to what is necessary (by Axiom 1). However, nothingness is not opposed to everything, since it is not opposed to God. Thus, nothingness is not impossible. What is not impossible is possible (by Axiom 6). Therefore, nothingness is possible.

Theorem 4

Any universe is not necessary. 

Demonstration: 

Nothingness is possible and not necessary (by Theorems 2 and 3). Any universe is an opposite of nothingness (by Theorem 1). An opposite of what is possible and not necessary is either possible or impossible, but not necessary (by Axiom 2). Therefore, any universe is not necessary.

Theorem 5

An opposite of a necessary universe is either God or impossible (if the universe is necessary, then God is impossible).

Demonstration:

Necessary is that whose denial entails a contradiction, and exists by itself (by Definition 3). God, if any, is the immaterial being with the power to create the universe (by Definition 9). You can only create what is non-existent. However, if the universe is necessary, it cannot be created, since this would entail that it did not exist at some point, and that it wasn't necessary. Then, an opposite of a necessary universe is either God or impossible.

Theorem 6

It is necessary that the universe, if any, is contingent.

Demonstration:

Any universe is not necessary (by Theorem 4). What is not necessary is contingent (by Axiom 4). Therefore, it is necessary that the universe, if any, is contingent.

Theorem 7

It is necessary that a contingent universe, if any, exists by another being.

Demonstration:

Everything that exists does so by itself or by another being (by Axiom 7). It is necessary that the universe, if any, is contingent (by Theorem 6). Contingent is that whose denial entails no contradiction, and it may exist by another being or not exist (by Definition 4). Therefore, it is necessary that a contingent universe, if any, exists by another being.

Theorem 8

It is impossible that any universe exists by another universe.

Demonstration:

The universe, if any, is the totality of matter or energy (by Definition 8). Thus, there cannot be more than a universe. Therefore, it is impossible that any universe exists by another universe.

Theorem 9

It is impossible that any universe exists by nothingness.

Demonstration:

Any universe is an opposite of nothingness (by Theorem 1). Opposite is what can not occur simultaneously with a possible being (by Definition 5). Therefore, it is impossible that any universe exists by nothingness ("ex nihilo nihil fit").

Theorem 10

God exists.

Demonstration:

I. It is necessary that a contingent universe, if any, exists by another being (by Theorem 7). Any universe is not necessary (by Theorem 4). The universe exists. Therefore, the universe exists by another being.

II. God, the universe and nothingness, if possible, are the only possible beings (by Axiom 8). It is impossible that any universe exists by another universe (by Theorem 8), and it is impossible that it exists by nothingness (by Theorem 9). Then, it is necessary that any universe, if any, exists by God. Therefore, since the universe exists, God exists.

* * *

As for God being possible:

The universe is necessary if and only if it is always necessary.

If the universe is always necessary, then the universe in T1, T2, T3... Tn is necessary.

The universe in T1 and in any other moment (T2, T3... Tn) are incompossible, that is, mutually opposite.

An opposite of what is necessary is impossible (by Axiom 3).

Thus, if the universe in T1 is necessary, then the universe in T2, T3... Tn is impossible.

However, the universe in T2, T3... Tn is possible, since the universe has a temporal nature.

Therefore, the universe is not necessary.

Therefore, nothingness -understood as the lack of any universe- is possible.

So:

God is possible or impossible (by Axiom 6).

God is impossible if and only if he is self-contradictory or incompossible with a necessary entity.

God -as the immaterial being with the power to create the universe- is not self-contradictory.

Neither nothingness nor the universe are necessary (as I have already proved).

God, the universe and nothingness, if possible, are the only possible beings (by Axiom 8).

Therefore, God is possible.

* * *

"Reductio ad absurdum" of the definition depicting the universe as a single 4D object:

Definition 1

The universe (@) is the totality of matter or energy able to exist at every possible time (@Tn).

Axiom 1

Two indiscernible entities have to be regarded as identical.

Axiom 2

The whole is greater than any of its parts.

Theorem 1

The universe in its first state (@T1) is a part of the universe (@).

Demonstration:

It follows from Definition 1.

Theorem 2

The universe (@) is identical to the universe in its first state (@T1) or in any other state (@Tn).

Demonstration:

Suppose the universe in its first state (@T1) and compare it with the universe able to exist at all possible times (@). Both are indiscernible, given Definition 1, since @T1 contains all matter or energy that can exist at every possible time. Thus, they are identical (by Axiom 1). Therefore, the universe (@) is identical to the universe in its first state (@T1) or in any other state (@Tn).

Theorem 3

The universe (@) is identical to any of its parts (@Tn).

Demonstration:

The universe in its first state (@T1) is a part of the universe (@) (by Theorem 1). The universe (@) and the universe in its first state (@T1) or in any other state (@Tn) are identical (by Theorem 2). Therefore, the universe (@) is identical to any of its parts (@Tn).

However, this is absurd (by Axiom 2). Therefore, Definition 1 is incorrect.

Thus, we must assert that the universe is the totality of matter or energy in a particular moment (with a definite structure), but it must be denied that we are allowed to speak of the universe as the aggregate of all its possible times (@). This implies that the universe at any of its possible times (@Tn) is not a single entity but a multiplicity of entities distinct from each other.