Firstly you will often find Theists attempting to redirect the burden of proof onto the skeptic… It is a futile and intellectually dishonest tactic. However, one can and will be able to prove, through logical laws, that the defined versions of our current god and gods are in fact non-existent to the extent that they are incompatible with our reality. The often retort to this is that one must be omniscient to be able to disprove something like their defined version of god, however, you do not need to have an understanding about everything in the entire universe to know that for example square circles, and cubed balls do not exist.
One examle: The “all powerful” god known by Monotheistic religions (Chrsitianity, Judeism, Islam) cannot exist simply because their god’s deiition is logically contradictory. This has been addressed by a simple problem “If god cannot create a rock so large that he cannot move it” he defies the law of non-contradiction, and therefore it is an illogical and false ideology to base a belief on. This means that Omnipotence is a self refuting concept, and while yes we accept the definition to mean the power to do anything or having unlimited power…. Well, this concept in and of itself is not logical, defined as it is or not, it just doesn’t work.
As far as the Deistic god is concerned, his/her/it’s significance is completely irrelevant because this concept does not dictate the existence of a heaven, a hell, or any type of reward system based on the acknowledgement of his/her/it’s existence, therefore the ideology is useless and does not matter. Also this assumption, does not establish a valid point of referrence. How does the Deist posit god? The assumption is based on a correlation of unexplained with unexplainable and the end conclusion is “God did it”. It is not a proof of a god it is a argument from ignorance. And you might often come in contact with someone who uses the contingency argument for this, but as usual there is no need for intelligence or personality at all for there to be a first cause, it is the deist who will insert some circumstantial justification in order for this to make sense. At this point you might as well call god nature, and nature god. It doesn’t however validate any sense of the monotheistic deity and if a Theist takes this path, you can point that out to shut them up. This simply says, “God is nature and nature is god” But it’s purely cowardice between theism and Atheism.
In regards to Polytheistic religions (Paganism, Hinduism) we have, can, and do, understand how the elements of nature and the emotions of humans work through science. This dictates that the elemental gods of Polytheism are in fact explainable by natural sciences and that the elements do not perform according to faith and prayer. Also the all powerful gods of human emotions in love, war, fertility, etc. They have been explained how they cannot exist with “all power” since they can’t be all powerful over emotions and human biology that we know interact with other emotions. This ulitmately means that these gods also cannot exist.
Now you might ask me to prove that there is no god at all, however, I must ask you to prove something first. Can you prove a universal negative? No, you cannot, which is why I am a Pragmatic Agnostic Atheist in regards to “A god” and yet I am a Practical Gnostic Atheist in regards to the definitions of these mentioned gods. We can and I have shown the logical implication of the existence and it is unreasonable for one to ask anyone to have faith when not only the physicality of god is improvable, but the definitions of the gods are as easily falsifiable to logic.
If something is logically impossible to exist, or the so called powers can be explained by the scientific method without divinity or prayer, I do not care to give them significance through defining them as deities or even pretending to recognize a divinity. So if someone askes you to prove all gods (defined and undefined) cannot exist, we cannot, and I do intellectually concede to that point. But if they want us to prove that the gods that we define here on earth are falsifiable, I have given you the tools to do so. Thank you for your time, hopefully this has at least inspired you to question theological ideologies, if for nothing more than to seek a more solidified position on religion, because I find that the deeper your search into your religion, the less you end up believing it.