Does God exist?

1. Proposition: Everything that exists has properties.

   Proof

   Suppose that some entity exists and has no properties. But if it exists, it has a reference to it. But the reference of an entity is a property of the entity, so a contradiction. QED
   
   NB. The reference could be external or internal.
2. Definition: Nothing is the content of an empty set.

   Note

   Nothing is the non-existent content of the empty set, not the empty set itself, which is something. Equivalently, "nothing" is not anything, not a single thing in any domain. "Nothing" does not exist, except as a term denoting non-existence. An example for nothing is a self-contradictory definition, e.g. a square-circle in a plane.
   
   NB. "Nothing" as a pronoun, not a noun. Nothing as a noun is a logical fallacy.
3. Corollary: Nothing has no properties.

   Proof

   Contrapositive of Proposition 1 – no property belongs to the non-existent, so no properties belong to nothing. QED
4. Proposition: Nothing comes out of nothing.

   Proof

   Although self-evident we will affirm this premise. Since "nothing" has no properties we will use proof by contrapositive:

   1. Nothing comes out of anything – is false:
      • In the physical realm, from thermodynamics (and elsewhere) matter always transforms and never disappears.
      • In the abstract realms of information, information does not disappear (it may become unavailable). The only way for information entity to vanish is if it is self-contradictory and dismissed, but if self-contradictory it would not exist on a first place, which is exactly "nothing comes out of nothing" (the proposition).
   2. Anything comes out of nothing – false:
      • In the physical realm this premise contradicts the laws of thermodynamics. Note that the "Big-Bang" theory is an unobserved theoretical proposition which is known to have multiple issues of observational and theoretical nature. Hence we remain faithful to logic and observation.
      • In the abstract realms of information, the premise breaks the laws of logic:
        • one wrong is wrong;
        • more than one wrong together does not make right.
   3. Anything comes out of anything (something comes out of something) – true, but this is the contrapositive of the proposition, so it is also true. QED

   
   NB. Observe that if we assign Nothing = false and Anything = true, then the "comes out of" operator resembles the XOR function.
5. Proposition: Infinity does not exist.

   Proof

   Proof I: Premise: Everything in the world is uniquely identifiable, in other words if two objects have the same identifier in some complete identification scheme, then it is the same object.
   
   Therefore, infinity does not exist, for 5 is not 6, but 5 + ∞ is the same as 6 + ∞ is the same as ∞. Where 5 and 6 are some objects able to relate to infinity via some operation called "+". So either infinity does not exist or no such operation exists. If infinity does not exist, we are done. Suppose infinity does exists and no such operation "+" exists. But if no operation on infinity exists, then we cannot even refer to infinity, as reference is also an operation, but if infinity cannot be referenced then it does not exist. QED
   
   
   Proof II: Every object has at least two properties:

   1. It lives in a space, i.e. it has a location (locality), i.e. every object is localizable.
   2. It has a type, i.e. specification.

   
   But infinity:

   • has no location, for if it had a location we could point it out, and we cannot; and
   • has no type, for infinity has no specification.

   (If objected, one needs to demonstrate a definition for infinity that is consistent and can be instantiated at will, subject to appropriate (well-defined) but existent conditions and circumstances.)

   
   So infinity is not an object. But, if infinity is not an object, then it must be a type, but types live in metaspace, so types are objects in the metaspace. However, infinity is not an object, so infinity does not exist since its instantiation (and identification) is never reached, always regressing into an upper and upper metaspace. So the definition of infinity is, at best, by infinity, but this is a circular definition and so it is invalid. So infinity does not exist. QED
   

   The entire article on Infinity is available at: Infinity - Does it exist? Can we Prove it?
6. Proposition: Personal Creator of the Universe does exist.
   Proof:

   1. You know that you exist (at least metaphysically), so something does exist (at least you).
      (Something exists.)

      Proof

      If something does not exist then it does not think. (Indeed, it does nothing at all.) True by Corollary 3 above as the ability to think is a property. Take the contrapositive: If something thinks then it exists. In particular, "I think, therefore I exist". QED
   2. You know that you exist (at least metaphysically), but you don't know how you function (at least metaphysically), so there is more than you in this world.
      (More than one thing exists.)

      Proof

      If the knowledge of how you function is outside of "you" then it is in addition to "you". QED
   3. You know what you are (at least metaphysically), but you don't know how you came into existence (at least metaphysically), so something outside of this world exists, which created this world, including you.
      (Something outside of this world exists, which created the universe.)

      Proof

      By proposition 4, nothing comes out of nothing, so you have come out of something. Indeed, you came out of your parents physically, (we know nothing about the metaphysical person, what it is and how it comes to be). Your parents came out of their parents and so the process continues recursively, to either the first couple, or the "primordial soup".

      1. Suppose "Macro Evolution does not exist. Then it is necessary that the first couple was created by something or someone, by proposition 4. Then this something or someone has to have been created by something or someone else, and the process continues recursively.
      2. Suppose "Macro Evolution does exist. Then the process continues recursively back to the "primordial soup" and the formation of the planet. The latter has to have been created by something or someone else, and the process continues recursively.

      
      In both cases, the recursion progresses into an infinite regression, but infinity does not exist, by proposition 5, so then it follows that it started from somewhere. But nothing comes out of nothing, by proposition 4, so there must be a Creator that is external to this Universe which is outside of time and space, since the latter belongs to this Universe. QED
      
      NB.

      1. By proposition 5, time is not infinite, so time has ends on all sides.
      2. By proposition 5, space is not infinite, so there is an end of space on all sides.
      3. The above propositions do not affirm that everything existing is created, but that "nothing comes out of nothing." This by no means concerns anything that exists by definition, e.g. by the necessity of its own nature (, e.g. numbers).
   4. You know who you are (metaphysically), but you cannot define (what is) "yourself", then it follows that the thing that created you is at least as much person as you are.
      (The Creator of "You" (metaphysically) is a Person.)

      Proof

      As above; by proposition 4. nothing comes out of nothing, so the metaphysical "I" was created, by something or someone. But a metaphysical substance requires a metaphysical source, but a metaphysical object is always a person, so a Creator. QED