Is there any logical proof that God exists?

It is not possible to provide any logical proof that God exists. That is a matter of faith only.

If logical proof is to be found for the existence of God, it must be found in the Bible. The Bible does report ancient Hebrew people actually seeing God. If those reports could be verified, they would be prima facie evidence of the existence of God. However, the reports were written centuries after the supposed events and could be considered to be coloured by legend and conviction. Objectively, reports at such a distance in time are no more reliable than a twenty-first century belief that only King Arthur of medieval times could pull the sword from a rock. Moreover, biblical accounts of the prophets' personal acquaintances with God are so contradictory as to defy logical explanation. It remains a matter of faith, and faith alone, that the biblical accounts are correct.

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Actually I believe that there is more than faith involved and the logical existence of God can be determined (as described by the bible) you can perceive him by the the things around us. he created you and me, so we ourselves are proof.

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Here is my logical proof

God is Perfect.

Not to exist is Not Perfect

Therefore, God exists.

(Note: Hence, be careful when you say something is Perfect. Being Perfect has many implications!)

Answer

It is a dogma of the Catholic Faith that God can be known through natural reason: "God, our Creator and Lord, can be known with certainty, by the natural light of reason from created things." (de fide) That God can be known through causality is not dogmatically defined but is judged proximate to the Faith (fidei proxima). The philosophical history that eventually led to this declaration is interesting.

Probably quoted the most from the early Church doctors is the ontological proof of St. Anselm. He reasoned thus (familiarity with the philosophical concepts of universals and particulars will aid in understand his argument a bit better):

  1. God exists in our understanding. This means that the concept of God resides as an idea in our minds.
  2. God is a possible being, and might exist in reality. He is possible because the concept of God does not bear internal contradictions.
  3. If something exists exclusively in our understanding and might have existed in reality then it might have been greater. This simply means that something that exists in reality is perfect (or great). Something that is only a concept in our minds could be greater by actually existing.
  4. Suppose (theoretically) that God only exists in our understanding and not in reality.
  5. If this were true, then it would be possible for God to be greater then he is (follows from premise #3).
  6. This would mean that God is a being in which a greater is possible.
  7. This is absurd because God, a being in which none greater is possible, is a being in which a greater is possible. Herein lies the contradiction.
  8. Thus it follows that it is false for God to only exist in our understanding.
  9. Hence God exists in reality as well as our understanding.

This argument ultimately is unsatisfactory as it confuses the idea with the reality, act with potency.

St. Thomas Aquinas next set forth the five proofs of the existence of God. These proofs are fairly well known:

  • Motion
  • Causation
  • Contingency
  • Degrees of Perfection
  • Design

You can read more about them through the link below.

Christian metaphysics, however, esteems vertical causality as the best natural proof of God's existence. Unlike the horizontal series presented in the five ways that stretch back historically until time and space become redundant, vertical causality is proved in the present moment. That is, the fact of existence, of now, is proof of "God". This is declared since no object is the source of its own present existence, nor is any object responsible for its maintenance in time and space. Metaphysically, every moment is different, no object is the same as it was an instant before. This is because existence in time is particular to every specific moment. The way you were .01 seconds ago is not the way you exist now, for to exist now is a different thing then any other point of your existence.
Since existence is not proper to any object, it must be a participation. Existence itself, that thing whose purpose is to exist, allows other things to partake of Existence here and now, in any given moment. The five proofs help define the nature of this Existence (intelligence, etc.) however, the fact that anything exists now is only because of a participation in Existence itself.

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