Comments on Nick Allen’s thinking about myth and epic, Part II: On the dyadism of Achilles and Odysseus in the Homeric Iliad and Odyssey

2022.02.21| By Gregory Nagy

Part II (Nagy 2022.02.21) is a continuation from Part I (Nagy 2022.02.07)

II§0. In Part I of this bipartite essay, I have highlighted an article by Nicholas J. Allen (2014; also his book, published in 2020) where he adds two more “functions” to the three mythological “functions” posited in Volume I Part I of a book by Georges Dumézil (1968) about Indo-European traditions of mythmaking in epic. As we saw, the terms used by Allen for these two additional functions are “transcendence” and “devaluation.” Now we will see that Allen applies both these terms to the epic roles of the ancient Greek heroes Achilles and Odysseus in the Homeric Iliad and Odyssey. And I will argue here, in Part II of my bipartite essay about Nick Allen’s rethinking of Dumézil’s theories, that Allen’s categories of “transcendence” and “devaluation” can be rethought further in terms of a mythological principle that I describe as “dyadism ”with reference to the epic roles of Achilles and Odysseus.

The Embassy to Achilles, with Odysseus (left) and Achilles (right),
The Embassy to Achilles, with Odysseus (left) and Achilles (right), both seated. Attic red-figure hydra by the Kleophrades Painter, ca. 480 BCE. Berlin, Staatliche Antikensammlungen, inv. No. 8770. Image via Wikimedia Commons.

II§1. In terms of Dumézil’s model of trifunctionalism, as we have seen in Part I of my bipartite essay, at I§1, the three “functions” of heroes and gods in mythological traditions mediated by Indo-European languages are clearly visible in the epic roles of the Pāṇḍava-s, central heroes in the greatest epic of India, the Mahābhārata. The roles of these heroes in that epic correspond to the three mythological “functions” of the gods who fathered them in the narrative. Using Allen’s abbreviations F1 F2 F3, I review here the relevant roles of the divine fathers in terms of the three “functions”:

{F1} The first-born hero, Yudhiṣṭhira, is fathered by Dharma, who can be viewed in the Mahābhārata as the god of whatever is sacral.

{F2} The next two heroes, Bhīma and Arjuna, are fathered by Vāyu and Indra, in that order of birth, who can both be viewed together as gods of war.

{F3} The last two heroes, Nakula and Sahadeva, are twins fathered by gods named the Aśvin-s, who are twins in their own right and who can be viewed together as gods of productivity.

II§2. As we have also seen, however, in Part I of my bipartite essay, at I§2, Nick Allen (2014:3) adds to these three functions two more, F4+ and F4-, and these additions give us the essence of his “pentadic” theory. He explains F4+ in terms of “transcendence” and F4- in terms of “devaluation.” As I pointed out already in Part I, at I§4, the category that Allen calls F4+ applies in situations where a hero can be assigned to epic roles that are typical of more than one function; as for the category that Allen calls F4-, it applies in situations where a negative rather than a positive aspect of a function is emphasized. As we will see in what follows, both these two additional “functions,” F4+ and F4-, are relevant to what I describe as the “dyadism” of Achilles and Odysseus in the Homeric Iliad and Odyssey.

II§3. In the case of transcendence, which is Allen’s category F4+, I have already noted in Part I at I§4 the most obvious example in the Mahābhārata, where all five of the Pāṇḍava-s are viewed as warriors, F2, not only Bhīma and Arjuna.

II§4. But I have yet to deal with devaluation, that is, Allen’s category F4-. I start by focusing again on the warrior heroes Bhīma and Arjuna, both of whom—when they are paired together—can be classified as F2. But now I note that one of these same two heroes has a different function as well, in terms of Allen’s pentadic model-building. That warrior hero is Bhīma, whose different function is an example of devaluation, F4-. By contrast with the warrior hero Arjuna, who represents what is seen as the positive aspects of war—where violence is regulated by the protocols of warfare—this other warrior hero Bhīma represents the negativity of violence in general.

II§5. There is a comparable contrast to be seen in the pairing of the gods Vāyu and Indra, who respectively fathered Bhīma and Arjuna according the epic narrative of the Mahābhārata. In earlier Indic poetry, both Vāyu and Indra are pictured as stormgods, but the violence of windstorms caused by Vāyu, whose name is ‘wind’ personified, is conventionally elemental, whereas the violence of thunderstorms caused by Indra as king of the gods is more personalized, pictured as helpful for the society that Indra protects—and harmful only for whatever enemy the god wishes to destroy.

II§6. To illustrate the positive picturing of Indra as stormgod, I turn to an old Indic hymn praising him, Rig-Veda 1.32, as translated and interpreted by Jaan Puhvel (1987:51–52). In this hymn, even the thunderbolt wielded by this stormgod Indra is pictured as a life-giving force (1.32.1–2, 8, 11). The word for this thunderbolt is vájra– (1.32.5). The thunderstroke of Indra’s vájra– releases the waters of the world, which are penned up like cattle (1.32.1–2, 8, 11). As Puhvel (p. 51) describes it, the violent thunderstorm of Indra is “a heroic deed that somehow meshes with the release of the pent-up rainclouds (the breaking of the monsoon), so that […] it is sometimes hard to tell where thunderheads leave off and bellowing herds take over.” Thus the rain released by the storm god waters the land, and the watering allows for the grazing of herds—primarily herds of cattle. In another project (Nagy 2010 at “W 253”), I have argued that even the verb-root of the noun vájra-, this specialized word for the thunderbolt of the thundergod, conveys the idea of life-giving power. My argument depends on whether I am right in explaining etymologically the root vaj- of the Indic noun as a cognate of the root ueg- of the Latin verb uegeō, which means ‘enliven’, that is, ‘vivify’—as for example in references to the enlivening of vegetation; even the Latin origins of this word “vegetation” go back to the meaning of uegeō as ‘vivify’.

II§7. In the Vedic hymn that I have just cited (Rig-Veda 1.32), on the other hand, the creative force of Indra’s thunderbolt is matched by its destructiveness, since the thundergod strikes the enemy with his thunderstroke in a singularized act of cosmic violence. This enemy is the demonic dragon Vṛtra, whose name is a personification of the noun vṛtra-, which means ‘holding-up’, derived from the verb-root vṛ-, meaning ‘to hold up’—with reference to the holding-up of cosmic flow. But this same verb-root v-, meaning ‘to hold-up’, can also mean ‘to up-hold’, reflected in the etymology of the noun used for the name of the Vedic god Varuṇa- (Puhvel 1987:48–49): the function of this god Varuṇa is to ‘up-hold’ cosmic stability by way of maintaining ritual correctness and morality (as in Rig-Veda 5.85, a hymn composed in the god’s honor).

II§8. Thus we could say, in Dumézil’s terms, that the god Varuṇa in his positive function of ‘up-holding’ cosmic stability and morality can be categorized as a representative of the first function, F1, which is a priestly domain. But we could also say, again in Dumézil’s terms, that the demon Vṛtra, in his negative function of ‘holding-up’ the cosmic flow of life-giving forces that promote good vegetation—and thus good grazing—can be classified as a representative of the third function, F3, which is the domain of producers such as cultivators and herdsmen. In this case, however, the classification F3 can operate only negatively, in terms of the function F4-.

II§9. Here, then, is where Dumézil’s functions F1 and F3 can be reconciled with each other in terms of Allen’s two additional functions, F4+ and F4-. For Allen, the aspects of the god Varuṇa as a representative of F1 in a positive sense and the aspects of the demon Vṛtra as a representative of F3 in a negative sense can be reconciled by way of qualifying both F1 and F3 in terms of F4+. If F1 is interchangeable with F3 and if F3 is interchangeable with F1, then the meaning, as signaled by the category F4+, is that these two functions are interchangeable in a positive (+) sense, which transcends differences between F1 and F3. In a negative (-) sense, on the other hand, transcendence is not possible, since the demon Vṛtra is exclusively a negative force, as signaled by the category F4-. To be contrasted with the negativity of the demon Vṛtra is the positivity of the god Varuṇa, who is transcendent: even if this god may be linked with traits that are negative in other contexts, such traits will be seen as positive in his own domain. Such is the case with māyā́, which is a negative force, to be translated as ‘illusion’—that is, “bad magic”—in the domain of demons who are defeated by Indra (as in Rig-Veda 8.14.14). But māyā́ remains a positive force—that is, “good magic”—in the domain of Varuṇa (as in Rig-Veda 5.85.5). So the negative aspects of māyā́ as linked with demons are secondary and are therefore subsumed by the positive aspects as linked with gods like Varuṇa—aspects that are primary. Even if Varuṇa were capable, as a god, of occasionally inducing māyā́ in a negative sense of ‘illusion’, such negativity would not and could not be exclusive as it is in the case of demons who are representatives of māyā́ as ‘illusion’ in an exclusively negative sense (again, Puhvel 1987:48–49).

II§10. A comparable pattern of transcendence is evident in the basic opposition between the god Indra and the demon Vṛtra. The god, in striking the demon with his thunderstroke, is a representative of the second function, F2, since he wields his thunderbolt as a weapon, just as warriors wield their own weapons of war against their enemies. But the demon who has been struck by the god’s thunderstroke is a negative representative of the first and the third functions, that is, his function is F4- with reference to both F1 and F3, since he obstructs not only the stability of the cosmos, maintained by the gods of F1, but also the cosmic flow promoted by the gods of F3, who preside over the thriving of vegetation and the grazing of herds. Thus the striking of Vṛtra by the thunderbolt of Indra transcends the function of the stormgod as a warrior, F2, and this function becomes interchangeable with F1 and F3. That is, this function of F2 is the F4+ of transcendence. Similarly, the function of Indra’s vájra– as a weapon of destruction in the domain of a warrior, F2, becomes in its own right transcendent, F4+. And that is because the divine weapon can now be seen also as a divine instrument of two other functions. Now there is cosmic stabilization, a function that fits F1, and there is also cosmic revitalization, a function that fits F3—since the vájra- brings the cosmos back to light and life by way of restoring vitality for cultivators and herders.

II§11. Having applied Allen’s “pentadic” theories in the general case of Indic gods and demons in early Vedic poetry, I will now apply, briefly, these same theories in the specific case of the Indic heroes Bhīma and Arjuna in the later epic poetry of the Mahābhārata. To start with the obvious, I note that both heroes, as warriors, represent the function abbreviated by Allen as F2, but only one of them, Arjuna, transcends F2. Like his Vedic father Indra, who is king of the gods, Arjuna is more kingly than Bhīma, as I noted already in Part I, at I§4. As such, his function is transcendent, fitting Allen’s category F4+. Conversely, the function of Bhīma is devalued, fitting Allen’s category F4-. And here is where the term “dyadism,” as I introduced it at II§0 above, becomes applicable.

II§12. So also in the ancient Greek epic traditions of Homeric poetry, the term “dyadism” can be applied. This time, the application extends to the two main heroes of the Iliad and the Odyssey respectively, who are Achilles and Odysseus. But here the dyadism of these two heroes is inversely symmetrical in the two epics. Odysseus in the Odyssey is more kingly than Achilles, but Achilles in the Iliad is more kingly than Odysseus.

II§12a. The first point that I have made here, that Odysseus in the Odyssey is figured to be more kingly than Achilles, is likewise made by Allen (2014), who goes on to describe the kingliness of Odysseus in terms of transcendence, category F4+, to be contrasted with what happens to the status of Achilles in the same epic, the Odyssey. Allen views this contrasting status in terms of devaluation, category F4-. The devaluation is made explicit in Odyssey 11.489-491, where the shade of Achilles in Hades declares that he would rather be alive than dead even if the living Achilles were a lowly serf working the land, that is, even if he belonged only to the third function, F3; even such a lowly status, says the dead Achilles, would now seem more valuable to him, now that he is dead—more valuable even than being king of the dead. So, Achilles here in the Odyssey opts for devaluation into the third function, F3, over transcendence into the category signaled as F4+ by Allen.

II§12b. As for the second point I have made, that Achilles in the Iliad is figured to be more kingly than Odysseus, here I differ with Allen (2014), who thinks that the function of Achilles in the Iliad is to be viewed in terms of devaluation, classified as F4-. I disagree here. I think that there is transcendence, F4+, to be seen in the fact that, in the “Embassy Scene” of Iliad 9, Odysseus avoids reporting to Achilles a claim made by Agamemnon at lines 160–161, before the Embassy gets underway. In those lines, Agamemnon declares that he is more kingly than Achilles. The fact that Odysseus, speaking first in the “Embassy Scene,” avoids reporting this claim means, I think, that he recognizes that the claim of Agamemnon is not valid—and that Achilles would firmly reject such a claim if he, Odysseus, were to report it. As I have argued in some detail in my commentaries on Iliad 9 (Nagy 2016–2017), the fact that Odysseus does not repeat to Achilles the claim made by Agamemnon actually devalues the status of Odysseus himself in the Iliad. It seems to me that Odysseus knowingly suppresses what Agamemnon claims about kingly superiority because he knows that the premise of the claim is wrong. Agamemnon had made explicit his motive for offering gifts of compensation to Achilles: acceptance of those gifts, Agamemnon assumed, would prove that he is more kingly than Achilles. If Achilles had accepted on such terms the offer of Agamemon as incompletely reported to him by Odysseus, then the principal hero of the Homeric Iliad would have been aborting his own epic—and his own trascendence.

II§13. I should add that the dyadism of Achilles and Odysseus on the level of meaning is reflected, on the level of form, in the evolution of the formulaic system that produced, ultimately, the Homeric Iliad and Odyssey. The statistical evidence for the formulaic dyadism of the names ‘Achilles’ and ‘Odysseus’ in Homeric diction is most persuasively presented in Classical Continuum by Gregory Crane 2022.02.17. (On the formulaic system of “Homeric diction,” as Milman Parry described it, I refer to §6 in this essay: Nagy 2017.11.12. For an updating of my “evolutionary model” for reconstructing Homeric poetry “forward in time,” I refer to §§5–6 in this essay: Nagy 2021.08.30.)


Allen, N. J. 2011. “The Indo-European background to Greek mythology.” In A companion to Greek mythology (ed. K. Dowden and N. Livingstone) 341–356. Oxford.

Allen, N. J.  2014. “Heroes and pentads: Or, how Indo-European is Greek epic?” Bulletin of the Institute of Classical Studies 57:1–19.

Allen, N. J. 2020. Arjuna-Odysseus: Shared Heritage in Indian and Greek Epic. London.

Crane, G. R. 2022.02.17. “Achilles and Odysseus, formulaic counterparts of Tweedle-Dee and Tweedle-Dum.” Classical Continuum.

Dumézil, G. 1968, reprinted 1986. Mythe et épopée I. L’idéologie des trois fonctions dans les épopées des peuples indo-européennes. Paris.

Dumézil, G. 1971, 2nd edition 1986. Mythe et épopée II. Types épiques indo-européens: un héros, un sorcier, un roi. Paris.

Dumézil, G. 1973, 2nd edition 1978, 3rd edition 1981. Mythe et épopée III. Histoires romaines. Paris.

Dumézil, G. 1975. Fêtes romaines d’été et d’automne, suivi de dix questions romaines. Paris.

Dumézil, G. 1980. Camillus: A Study of Indo-European Religion as Roman History. Translated by A. Aranowicz and J. Bryson. Edited and with introduction by U. Strutynski. Berkeley and Los Angeles. = Part 2 of Mythe et épopée III = Dumézil 1973, plus Appendices 1 and 2 of Dumézil 1973, plus Appendices 3 and 4 of Dumézil 1975.

Dumézil, G. 1982. Apollon sonore et autres essais. Vingt-cinq esquisses de mythologie. Paris.

Dumézil, G. 1983. La Courtisane et les seigneurs colorés et autres essais.Vingt-cinq esquisses de mythologie (26–50). Paris.

Dumézil, G. 1983b. The Stakes of the Warrior. Translated by D. Weeks. Edited, with an Introduction, by J. Puhvel. Berkeley and Los Angeles. = Part 1 of Mythe et épopée II = Dumézil 1971.

Dumézil, G. 1985. L’oubli de l’homme et l’honneur des dieux, et autres essais. Vingt-cinq esquisses de mythologie (51–75). Paris.

Dumézil, G. 1986. The Plight of the Sorcerer. Translated by D. Weeks and others. Edited by J. Puhvel and D. Weeks. Introduction by D. Weeks. Berkeley and Los Angeles. = Part 2 of Mythe et épopée II = Dumézil 1971.

Dumézil, G. 1994. Le roman des jumeaux et autres essaisVingt-cinq esquisses de mythologie (76–100). Edited by J. H. Grisward, with preface at pp. 9–15. Paris.

Dumézil, G. [1995.] Mythe et épopée I, II, III. New combined and corrected edition of the original three volumes, with original paginations retained in the inner margins. Preface by J. H. Grisward, pp. 7–30. Paris.

Dumézil, G. [2003]. Esquisses de mythologie. New combined edition of Dumézil 1982/1983/1985/1994, with original paginations retained in the inner margins. Preface by J. H. Grisward, pp. 7–27.

Muellner, L. 2021.01.23. “Research in France on Homeric εὔχομαι since the publication of Leonard Muellner, The Meaning of Homeric EYXOMAI Through its Formulas, 1976. Classical Inquiries.

Nagy, G. 1981. “Essai sur Georges Dumézil et l’étude de l’épopée grecque.” In Cahiers “Pour un temps”: Georges Dumézil, ed. J. Bonnet et al., 137–145. Aix-en-Provence. Rewritten as part of Chapter 1 in Nagy 1990.

Nagy, G. 1990. Greek Mythology and Poetics. Ithaca, NY. Revised paperback edition 1992.

Nagy, G. 2008. Review (part 1) of West 2007. Indo-European Studies Bulletin 13:60–65.

Nagy, G. 2010. Review (part 2).of West 2007. Classical Review 60:333–338. Expanded version

Nagy, G. 2015.04.10. “Who is the best of heroes, Achilles or Odysseus? And which is the best of epics, the Iliad or the Odyssey?” Classical Inquiries.

Nagy, G. 2016.05.12. “Variations on a theological view of Zeus as god of the sky.” Classical Inquiries

Nagy, G. 2016–2017. “A Sampling of comments on the Iliad and Odyssey.”

Nagy, G. 2017.11.12. “Draft of a declaration by the founding authors of A Homer commentary in progress.” Classical Inquiries

Nagy, G. 2020.02.14. “Comments on comparative mythology 1, about Apollo.” Classical Inquiries

Nagy, G. 2021.08.30. “A question of ‘reception’: how could Homer ever outlive his own moments of performance?”Classical Inquiries.

Puhvel, J. 1987. Comparative Mythology. Paperback edition 1989. Baltimore, MD.

West, M. L. 2007. Indo-European Poetry and Myth. Oxford.

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