[All translations from the original Greek are my own]
Xenophanes is one of the 'pre-Socratic' philosophers of the sixth and fifth centuries BC. The biographical testimony of him ascribes his birthplace to the town of Colophon in Ionia, western Asia Minor, but it is also agreed that he eventually settled in Greek-speaking Sicily. According to Censorinus (A7), Xenophanes lived for more than a hundred years, and by Xenophanes' own account, we have a lifespan extending to at least 92 years:
ἠδη δ' ἑπτα τ' ἐασι και ἑξηκοντα ἐνιαυτοι
βληστριζοντες ἐμην φροντιδ' ἀν' 'Ελλαδα γην·
ἐκ γενετης δε τοτ' ἠσαν ἐεικοσι πεντε τε προς τοις
εἰπερ ἐγω περι τωνδ' οἰδα λεγειν ἐτυμως
("Already 67 years have been tossing my thought through the land of Greece, in addition to the 25 years already at my birth, if I indeed know how to speak about these things truthfully"- B8).
Like other pre-Socratics such as Parmenides and Empedocles, Xenophanes aimed to give an air of authority to his work by composing in poetic meter, including hexameter, taking after Homer and Hesiod who were already of great renown by the mid-sixth century BC, regarded as sources of 'universal knowledge' on account of the range of topics touched upon in their works. Xenophanes himself acknowledges the status of Homer among Greeks of his own time:
ἐξ ἀρχης καθ' 'Ομηρον ἐπει μεμαθηκασι παντες...
("Since from the beginning all have learnt according to Homer…"- B10).
At the same time, Xenophanes fits in a broader pre-Socratic trend of responding critically to Homer and Hesiod; thus:
διδασακαλος δε πλειστων 'Ησιοδος· τουτον ἐπιστανται πλειστα εἰδεναι, ὁστις ἡμερην και εὐφρονην οὐκ ἐγινωσκεν· ἐστι γαρ ἑν
("And Hesiod is the teacher of most people. They believe that he knew most things, he who did not understand day and night. For they are one"- Heraclitus B57).
In the above fragment, Heraclitus is presumably criticizing Hesiod's conception of day and night as separate divinities in the Theogony, as part of his development of a broader λογος theory that entails an underlying unity in opposites. Conversely, Xenophanes, who was himself criticized by Heraclitus (Heraclitus B40), focused his criticism of Homer and Hesiod on moralistic and aesthetic grounds as regards the depiction of the gods:
παντα θεοισ' ἀνεθηκαν 'Ομηρος θ' 'Ησιοδος τε,
ὁσσα παρ' ἀνθρωποισιν ὀνειδεα και ψογος ἐστιν,
κλεπτειν μοιχευειν τε και ἀλληλους ἀπατευειν
("Homer and Hesiod have attributed to the gods all things that are sources of rebuke and disgrace among men: stealing, committing adultery and deceiving each other"- B11).
From this moralistic distaste with the Homer and Hesiod's anthropomorphic conception of the gods, Xenophanes proceeds to make a more general argument against anthropomorphism via a reductio ad absurdum, beginning with the observation that different peoples depict the gods in their own likeness:
'Αιθιοπες τε < θεους σφετερους > σιμους μελανας τε
θρηικες τε γλαυκους και πυρρους < φασι πελεσθαι >
("The Ethiopians say that their gods are snout-nosed and black, the Thracians that they are blue-eyed and red-haired"- B16).
From which the more general conclusion arises:
ἀλλ οἱ βροτοι δοκεουσι γεννασθαι θεους,
την σφετερην δ' ἐσθητα ἐχειν φωνην τε δεμας τε
("But mortals consider gods to be born, and to have their clothing, voice and form"- B14).
And then the reductio ad absurdum:
ἀλλ' εἰ χειρας ἐχον βοες < ἱπποι τ' > ἠε λεοντες
ἠ γραψαι χειρεσσι και ἐργα τελειν ἁπερ ἀνδρες,
ἱπποι μεν θ' ἱπποισι βοες δε τε βουσιν ὁμοιας,
και < κε > θεων ιδεας ἐγραφον και σωματ' ἐποιουν
τοιαυθ' οἱον περ καὐτοι δεμας εἰχον < ἑκαστοι >
("But if cows, horses or lions had hands and could draw with their hands and do what men do, horses would depict the forms of the gods like horses, and cows like cows, and they would each make the bodies just as the own shape they possess"- B15).
Though these texts are fragmentary and there is no definite proof that they were part of the same poem, it seems likely with the connective particles- specifically ἀλλ' ("but")- that they form part of an extended argument against anthropomorphism.
Contrasting with the Homeric and Hesiodic depictions, Xenophanes offered his own picture of the divine, in what is arguably the most well-known fragment attributed to him:
ἑις θεος, ἐν τε θεοισι και ἀνθρωποισι μεγιστος,
οὐτι δεμας θνητοισιν ὁμοιιος οὐδε νοημα
("One god, greatest among gods among men, not like mortals in form or thought"- B23).
This fragment, composed in hexameters, has often been interpreted as advocating monotheism in some way. Thus, Daniel Graham writes in his commentary: "Xenophanes at least adumbrates the concept of monotheism for the first time in the Greek tradition" (Texts of Early Greek Philosophy, p. 131). In further support of this interpretation of Xenophanes, one might wish to tie this fragment with his demythologization of Iris, the goddess associated with rainbows, as part of a model of physics whereby all living beings are composed of earth and water, and the great sea as the origin of clouds, winds and rivers (B29 and B30):
ἡν τ' 'Ιριν καλεουσι, νεφος και τουτο πεφυκε,
πορφυρεον και φοινικεον και χλωρον ἰδεσθαι
("The one they call Iris, this too is actually cloud, purple and scarlet and green to behold"- B32).
However, on the surface of it, fragment B23 affirms the existence of more than one god in speaking of "gods and men" and, in positing a supreme god, actually resembles the Homeric and Hesiodic conceptions of a hierarchy, in which Zeus is ultimately supreme among gods and men- a status particularly emphasized in Homer's Iliad and Hesiod's Theogony, in the latter of which the functions of the various divinities were assigned by Zeus following the defeat of the Titans (a myth rejected by Xenophanes: B1). The only difference is Xenophanes' rejection of anthropomorphism. Those who argue that Xenophanes is a monotheist explain away "gods and men" as simply a formulaic phrase that means "all," which we should not take literally.
However, I find this explanation unconvincing: why would Xenophanes, who clearly wishes to distinguish himself from Homer and Hesiod, use a formulaic phrase associated with these poets articulating the existence of more than one god if he aimed to advocate monotheism? It is notable anyway that nowhere does Xenophanes criticize Homer and Hesiod for postulating the existence of more than one god, but rather for anthropomorphism.
Further, the uncompromising nature of monotheism is incompatible with Xenophanes' skepticism on obtaining knowledge, on which subject Xenophanes draws a link, bound up in Indo-European etymology, between seeing and knowing (IE *weyd-, wherein the o-grade is reflected in perfect formation οἰδα- 'I know'- and the zero-grade in aorist formation ἰδον- 'I have seen/saw'):
και το μεν σαφες οὐτις ἀνηρ ἰδεν οὐδε τις ἐσται
εἰδως ἀμφι θεων τε και ἁσσα λεγω περι παντων
εἰ γαρ και τα μαλιστα τυχοι τετελεσμενον εἰπων,
αὐτος ὁμως οὐκ οἰδε· δοκος δ' ἐπι πασι τετυκται
("And no man has clearly seen or will ever know for sure about the gods and all things I speak of, for even if he were to be wholly successful in speaking about what has come to pass, still he does not know, and opinion is wrought over all"- B34).
Notice too that this fragment, like Xenophanes' other ponderings on the divine, is written in hexameter meter, and in the second line he could have equally used genitive singular θεου rather than plural θεων, which would have made sense if Xenophanes wanted to articulate a doctrine of monotheism. Similarly:
οὐτοι ἀπ' ἀρχης παντα θεοι θνητοισ' ὑπεδειξαν
("Not from the beginning have the gods shown all things to mortals"- B18).
It would have equally made sense and fitted the hexameter meter to use singular forms θεος and ὑπεδειξεν, if Xenophanes were aiming for a monotheistic doctrine.
A problem also lies in the ambiguity of language particularly when we consider that the definite article is still not used consistently at this point, and there is not a proper indefinite article: thus, to take an example:
εἰ μη χλωρον ἐφυσε θεος μελι, πολλον ἐφασκον,
γλυσσονα συκα πελεσθαι
("If a god/the god/divinity had not created yellow honey, men would say that the fig is by far sweeter"- B38).
In this case Xenophanes is focusing on the limits of human aesthetic perception, but we are also faced with the question of what exactly he means by θεος here, as I have indicated by the multiple ways of translating the word.
As far as attributes go for Xenophanes' supreme deity, there is nothing particularly revolutionary, minus the anthropomorphism, beyond the conception of Zeus, especially if we compare Xenophanes' deity with Zeus as portrayed in Hesiod's Works and Days. For instance, Xenophanes' description of his supreme deity as seeing, thinking and hearing as a "whole" (i.e. articulating some sort of omniscience- B24) has an anthropomorphic equivalent in Works and Days, speaking of Zeus' thirty thousand immortal, invisible guardians on the earth that keep watch over what happens, and inform him of when men commit evil (252 ff.).
Hesiod also emphasizes Zeus' omniscience here; the emphasis on 'seeing' and 'thinking' in these lines is my own, as I wish to highlight the parallel with Xenophanes' fragment envisioning the supreme deity.
παντα ἰδων Διος ὀφθαλμος και παντα νοησας,
και νυ ταδ', αἰ κ' ἐθελῃσ', ἐπιδερκεται, οὐδε ἐληθει
("The eye of Zeus sees and considers all things, and now looks on these things [deeds of injustice], if he so wishes, and they do not escape his notice"- Works and Days 267-8).
οὐλος ὁραι, οὐλος δε νοει, οὐλος δε τ' ἀκουει
("He sees as a whole, he thinks as a whole, he hears as a whole"- Xenophanes B24).
That said, I would emphasize that Xenophanes' own formulation is most likely aimed at passages in the Homeric corpus where Zeus' attention can be diverted hither and thither, preventing him from knowing all that is going on at once, whence also Xenophanes' depiction of his supreme deity as not moving about (B26). As for being able to shake things with its mind (B25), this is parallel to the conception of Zeus' use of the thunderbolts.
In short, I do not consider the evidence sufficient to point to Xenophanes as an advocate of monotheism. Admittedly, as with many of the pre-Socratic philosophers, we face a problem of limited data points. Xenophanes lived a long life, and yet we have very little of the corpus of his poetry, let alone the order, names or extended structures of his poems. We have little idea, if there was any, of the evolution of Xenophanes' thought over time.
Yet I think we can say with a good degree of confidence that Xenophanes' outlook does not focus on attacking the belief in more than one god, but rather just the anthropomorphism. However, it could be said that Xenophanes himself ironically falls into an anthropocentric conception of the divine in positing the existence of a hierarchy, besides his insistence on a supreme deity far removed from πονος ("toil"- B25).
Note on citation: the system of A and B followed by a number x derives from the original compilation of fragments of the pre-Socratic philosophers by Diels-Kranz, in which A is later testimony discussing a given philosopher and B features citation of actual fragments of the philosopher's work.