As per requested, here are the logical and scientific arguments that disprove the monotheist God's existence. Let me note that these arguments aren't necessary because the Theist has the burden of proof for their claim, whereas Atheists aren't required to disprove anything.
I am going by this definition from the Stanford Encyclopedia of Philosophy: "Theists believe that reality's ultimate principle is Godan omnipotent, omniscient, goodness that is the creative ground of everything other than itself." -
Monotheism (Stanford Encyclopedia of Philosophy)
And to those who believe in some sort of impersonal God or spiritual force, then these arguments don't apply. Though, I really don't think an impersonal force can be considered "God" because "God" is a personification. Also, if you feel that this God or force plays a role in your life, you pray to it, or it intervenes, then your God is actually a personal God.
If you believe in a God that is unknowable or beyond human comprehension, then your position is ultimately meaningless because you are asserting a concept that we can know nothing about and thus cannot derive meaning from this unknowable concept.
Now, on to the arguments:
The Transcendence V. Omnipresence Argument
P1: If God exists, then he is transcendent (i.e., outside space and time).
P2: If God exists, then he is omnipresent.
P3: To be transcendent, a being cannot exist anywhere in space.
P4: To be omnipresent, a being must exist everywhere in space.
P5: Hence, it is impossible for a transcendent being to be omnipresent (from 3 and 4).
C: Therefore, it is impossible for God to exist (from 1, 2, and 5)
Argument from Quantum Physics
P1: The God-concept designates an omniscient and omnipresent all-observing being (i.e. its knowledge effectively observes all phenomena).
P2: Observation collapses quantum superpositions.
P3: An all-observing being would automatically collapse all quantum superpositions. (from 2)
P4: We observe that not all quantum superpositions are collapsed.
C: Therefore, God cannot exist. (from 1, 3 and 4)
The Omnipresence vs. Personhood Argument
1. If God exists, then he is omnipresent.
2. If God exists, then he is a person (or a personal being).
3. Whatever is omnipresent cannot be a person (or a personal being).
4. Hence, it is impossible for God to exist (from 1-3).
Argument from Evil
P1: If an omnipotent, omniscient, and all-good God exists, then gratuitous evil should not exist.
P2: Gratuitous evil exists.
C: Therefore, an omnipotent, omniscient, and all-good God does not exist.
(Gratuitous evil is random evil that happens for no reason i.e. a baby dies at birth, a young child dies in a natural disaster, etc.)
Omnipotence and Omniscience Paradox
P1: God is omniscient and omnipotent.
P2: If God knows what he will do tomorrow, and does something else, he's not omniscient.
P3: If God knows and can't change it, he's not omnipotent.
C: God cannot exist.
Sources:
StrongAtheism.net - Atheology
Arguments against the existence of god - Iron Chariots Wiki
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