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Most arguments for the existence of God provide evidence based in probability (a la Pascal) rather than proofs to a mathematical certainty. You can always wiggle-out of them by denying this-or-that.
By way of illustration, a painting may exist, but how does a painting "prove" the existence of a painter in general, or a specific painter in particular -- couldn't the painting have been formed by some as-yet undiscovered natural cause(s)? In the absence of actually presenting the painter who painted it, isn't it best to be skeptical when someone points to a painting, and goes around proclaiming, "painter"?! And, in the case of a 200-year-old painting, the painter, if there ever was one, is now dead, so no proof that there was a painter is now possible.
A lot will depend on how motivated you are to deny the existence of the object in question. In the case of God, many atheists show a high emotional commitment to denying God's existence. For example, in my previous post, one commenter said, "why couldn't something come into existence uncaused?". When the subject in question is the entire universe, the uncaused existence of a mere painting should be a walk in the park. A second commentator threatened me with physical violence. So, when it comes to God, a lot of people on both sides of the issue have a lot invested in it emotionally.
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Thomas Aquinas (born ca. 1225; died 7 March 1274) was a priest of the Roman Catholic Church in the Dominican Order from Italy. He is frequently referred to as Thomas because "Aquinas" refers to his residence rather than his surname.
He was the foremost classical proponent of natural theology, and the father of the Thomistic school of philosophy and theology. His influence on Western thought is considerable, and much of modern philosophy was conceived as a reaction against, or as an agreement with, his ideas, particularly in the areas of ethics, natural law and political theory.
(Wik).
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Here are Aquinas' five classic arguments, offered in concise form. Some are more convincing than others. All reflect a thoughtful philosopher-theologian's attempts to argue from "natural theology" as opposed to revelation.
Aquinas' First Argument, Motion
(1) Objects are in motion.
(2) If something is in motion, then it must be caused to be in motion by something outside of itself.
(3) There can be no infinite chain of movers/movees.
(4) So there is a first, unmoved mover.
(5) This first, unmoved mover is God.
(6) Therefore, God exists.
Aquinas' Second Argument, Causality
(1) Some events cause other events.
(2) If an event happens, then it must be caused by something outside of itself.
(3) There cannot be an infinite chain of cause and effects.
(4) So, there is a first, uncaused cause.
(5) This first, uncaused cause is God.
(6) Therefore God exists.
Aquinas' Third Argument, Contingency
(1) Contingent things exist.
(2) Each contingent thing has a time at which it fails to exist (contingent things are not omnipresent).
(3) So, if everything were contingent, there would be a time at which nothing exists (call this an empty time).
(4) That empty time would have been in the past.
(5) If the world were empty at one time, it would be empty forever after (a conservation principle).
(6) So, if everything were contingent, nothing would exist now.
(7) But clearly, the world is not empty (premise 1).
(8) So there exists a being who is not contingent.
(9) This non-contingent, i.e., "necessary" being is God.
(10) Therefore, God exists.
Aquinas' Fourth Argument, Properties That Come in Degrees
(1) Objects have properties to greater or lesser extents.
(2) If an object has a property to a lesser extent (such as, e.g., "goodness"), then there exists some other object that has the property to the maximum possible degree.
(3) So there is an entity that has all properties to the maximum possible degree.
(4) This entity is God.
(5) Therefore, God exists.
Aquinas' Fifth Argument, From Design
(1) Among objects that act for an end, some have minds, whereas others do not.
(2) An object that acts for an end, but does not itself have a mind, must have been created by a being that has a mind.
(3) So there exists a being with a mind who designed all mindless objects that act for an end.
(4) This being is God.
(4) Therefore, God exists.