On what grounds can one reject the existence of, say, the Greek god Zeus, the Norse gods Odin and Thor? Or the thousands of other gods believed to be invented by human beings?
I would approach this question from what might be termed as “perfect being theology.” When one says “God” in this respect, God is thought to be the greatest conceivable being. There is no being that can be conceived of that is greater than God. In fact, if something greater than what we believed to be God existed, then that greater being would be God.
Now, the greatest conceivable being must possess what we might call great-making properties, namely moral perfection, omniscience, and omnipotence. For example, a God that is not omnipotent (all-powerful), such as in its inability and power to control, say, nature or the natural world, cannot be referred to as the greatest conceivable. In other words, in some sense this God would be subject to the physical universe. But surely God, if he exists, is supreme over creation. Moreover, a God that is not omniscient (all-knowing) in that, for example, there are facts in the world that he does not know also cannot be the greatest conceivable being. A being that is infinite in knowledge is greater than a being that is limited in knowledge. Further, a God that exists contingently is limited in that it must owe its existence to something else, and is even at threat of going out of existence at some point in the future.
Thus, quite rightly, if some individual came up to me and said that he is God, I’d reject his or her claim on the basis that human beings are limited, finite, contingent things. Human beings are limited in knowledge, power, and moral goodness, and cannot claim to possess great-making properties, and therefore be God. Thus, a being that is not contingent is greater than a being that is. This presupposition seems to be intuitively and necessarily true, since nothing can be greater than God, and therefore provides a sound framework through which we can understand these other gods of other religions.
Human beings believed/thought to be deities or descended from deities – In a very same way as I mentioned above, human beings are limited, finite, contingent things. In other words, a human being cannot be rightly called God. Human beings were born, the greatest conceivable being must exist eternally. Human beings die, the greatest conceivable cannot die. Human beings possess limited and sometimes inaccurate knowledge, the greatest conceivable possesses both infinite and accurate knowledge. So, humans historically considered to be God or divine, such as pharaohs, some Japanese, Chinese and Roman emperors, Romulus, Homer, Alexander the Great, the Buddha, and so on were nothing of the sort since none of them possess great-making properties.
Finite gods – This is also known as “finite godism,” which is the term used to refer to gods that are limited in some way as in, for instance, goodness, strength, or wisdom.
i. Morally bankrupt gods – Many mythological gods, specially those invented by the Greeks, were morally evil. On one hand many of them were capable of compassion and justice while on the other cruelty and spite. Take Ares, for example, he was the god of war which no doubt entailed slaughter, bloodshed, and carnage. Such a god or being is morally evil and repulsive, and given that the greatest conceivable being must be morally perfect, such a god cannot rightly be called God. The same can be said of Poseidon of whom committed moral evils such as rape, and Aphrodite who was petty and vain (for instance, it is believed she had an arrogant view of herself due to her sexual attractiveness). Countless other Slavic, Viking, Egyptian, and Roman deities similarly qualify.
ii. Contingent gods – One way to determine if these gods are finite is on whether or not they are contingent. It is clear that these gods owe their existence to other things. The Aztec God, Huitzilopochtli, was born, Mithras was born from a rock, Sekhmet, an Egyptian deity, owes his existence to a divine eye from which he came, Hephaestus was born (a cripple nonetheless), and Sedna, in Inuit mythology, had a birth and was later killed. These, and countless other deities, are not eternally existing, nor are they all-powerful. An eternally existent entity does not owe its existence to anything else, like a birth or some other creative agency. Moreover, an all-powerful being cannot be killed, nor is it subject to elements within creation.
iii. Omnipotently limited – Gods thought to exist or account for certain facts and workings of nature and natural laws are limited, especially the nature deities believed in African, Egyptian, Norse, Aztec, and Japanese circles. They are often associated with ruling limited domains such harvests (Demeter, Osiris), fertile lands (Poseidon, Ash), forests (Berstuk, Oko, Dryads, Negen), mountains (Latobius, Dali), animals (Diana, Aranyani, Yum Caax), weather (Brigid, Jupiter), the sky (Horus, Anshar, Hathor), and cosmological objects (Amaterasu, Ekhi). Even the greatest gods in Greek and Roman mythology, Zeus and Jupiter, are limited. Jupiter’s domain is limited to the sky while Zeus’ control is over lightning. The Egyptian gods Horus and Amun, like many other gods, were limited in power and even susceptible to bodily harm. Thousands and thousands of deities from dozens, if not hundreds, of cultures are limited in this scope, and therefore cannot satisfy the criteria for being the greatest conceivable being. The greatest conceivable being will necessarily be one that has power over all domains, including the natural and spiritual worlds, and exist as a being that could never be at risk of physical harm or death.
Theism & Mythological gods, the Difference – A last point I want to make is one that for many will be intuitively obvious, or will be assumed to be obvious by many modern people. This is that, from the privileged vantage point of modern science, we don’t need these deities as explanations for natural phenomena and natural laws within the universe. For example, we know that things like pregnancy, childbirth, and the growth of vegetation occur naturally, hence we don’t need the Aztec god Xochiquetzal to explain them. Likewise, there is no reason so associate things like agriculture and wine with the Celtic god Sucellus, and we know that growth in nature occurs through natural means, hence we don’t need Persephone to explain that either. The more science progresses the more these thousands of gods are seen to be irrelevant. However, these mythological gods differ enormously to a theistic concept of God traditionally believed by Christians and Jews. The theistic God is one that is transcendent over and above creation, existing eternally beyond space and time, and who is the creative agent responsible for creating the entire universe with all its natural laws. Thus, rather than progress in the hard sciences making such a deity irrelevant it would seem to be quite the opposite. The further the sciences progress the more human beings learn about the creative acts of God, one who is responsible for the beautiful complexities in nature and biology, from the immense fine tuning of the cosmological constants to make the universe compatible for biological life to the biological organisms themselves and the wonders of DNA, and so on.
So, on these grounds alone, I believe that we are sound in rejecting the multitudes of mythological gods invented by human beings.