Gorgias lived in Sicily, and was likely a contemporary of Socrates; he apparently relocated to Greece, and died there around 375 B.C.
Xenophanes is the most well-known of the three, a pre-Socratic from Ionia who also travelled around Greece. He is thought to have died around 478 B.C.
Questions about the pseudo-Aristotelian text include: Who wrote it? When was it written? Where? What did the author know about Xenophanes? How accurately did the author explain the views of Xenophanes?
Famously, Xenophanes asserted, and possibly introduced, a strikingly modern concept of God. Pseudo-Aristotle asserts that Xenophanes argued for the eternal origin of God (977a14).
Xenophanes declares that if anything is, it cannot possibly have come into being, and he argues this with reference to God, for that which has come into being must necessarily have done so either from that which is similar or from that which is dissimilar; and neither alternative is possible.
On the principle of “like begets like,” God must have existed for eternity, because anything which could give rise to God would have to be like God. A chicken can produce another chicken, and tree can produce another tree, but this might not be the case with God, to whom Xenophanes might attribute omnipresence, invisibility, omniscience, omnipotence, etc.
Exactly which properties Xenophanes attributes to God is an interpretive question with a plurality of plausible answers, and some details may be lost to history, but the general tenor of his views will have been something similar to what is mentioned above.
Xenophanes might be characterized as arguing that to have a beginning, i.e. to have been begotten or created or generated or produced, is a limitation which is incompatible with his concept of God as unlimited. To be sure, Xenophanes doesn’t use the word ‘unlimited’ in any surviving texts, and so this is already to some extent an interpretation, but a reasonable one.
Pseudo-Aristotle continues:
For it is no more possible for like to have been begotten by like than for like to have begotten like (for since they are equal, all the same qualities inhere in each and in a similar way in their relations to one another), nor could unlike have come into being from unlike.
It is noteworthy that pseudo-Aristotle does not comment on the explicit or implicit monotheism of Xenophanes. Many among both the pre-Socratic and Classical Greek philosophers were, if not detailed monotheists, probably functional monotheists.
Readers sometimes perceive Aristotle, and the Greek philosophers, through the lens of the oft-repeated maxim that Greeks were polytheists. While there is some reason to doubt that the Greeks, taken as a whole, were as polytheistic as is sometimes assumed, there is much more reason to doubt this about the philosophers, both pre-Socratic and later.
For if the stronger could come into being from the weaker, or the greater from the less, or the better from the worse, or conversely worse things from better, then what is not could come to be from what is, or what is from what is not; which is impossible. Accordingly for these reasons God is eternal.
If we accept pseudo-Aristotle as a reliable historian, then Xenophanes is explicit both in his monotheism and in his declaration that God is eternal - more specifically, that God has no finite starting point in time, and no progenitor.
The pseudepigraphic text also seems to claim that Xenophanes asserts that God is omnipotent. Additionally, and mysteriously, pseudo-Aristotle attributes to Xenophanes the assertion that God is spherical.
Perhaps this sphericality is to be understood as an attempt to conceptualize omnipresence in an infinite cosmos. If not infinite in space, perhaps Xenophanes conceived of the universe as infinite in other ways. It is not clear that Xenophanes is arguing for, or against, a cosmos that is spatially or otherwise infinite. Some other pre-Socratics asserted a type of pantheism, identifying God with the universe and the universe with God, and arguing that the cosmos could see and hear. Perhaps Xenophanes was in some way influenced by these colleagues.