In an effort to ‘harmonize’ these seemingly incongruous statements, Viktor Rydberg proposed that Tyr was the biological son of Odin (as Snorri says), and a foster-son of Hymir (in Hymiskviða), having been raised in the giant’s home as part of a peace pact between the Æsir and the giants. Rydberg is relying on a common Germanic custom here. Such arrangements were common in Old Norse society. In the endnotes to his translation of the Völsungasaga (1990), Jesse L. Byock explains:
 
“Fosterage was a Norse custom of having a child raised in another household in order to extend kinship bonds or to form political alliances”
 
 
In his synopsis of the mythic epic, found in the second volume of his Undersökningar i Germanisk Mytologi (1889), Viktor Rydberg, speaking of the earliest mythic ages, writes:
 
“9. The Peace Covenant. All creatures formed a covenant, and to seal it gave one another hostages. …The giant children Gullveig and Loki were admitted into Asgard. The goddesses favored Gullveig; Odin and Loki entered into sworn brotherhood. Odin sent his son Tyr to be fostered by the giant Hymir, and his son Thor, he sent to the giant Vingnir and his wife Hlora."
 
Although he never fully explains his reasons for doing so, Rydberg clearly bases this theory regarding Tyr’s parentage, in part, on this passage in the Prologue to Gylfaginning:
 
“A king in Troy was named Munon or Mennon, his wife was a daughter of the head-king Priam and was named Troan; they had a son who was named Tror, him we call Thor. He was fostered in Thrace by the duke, who is called Loricus. But when he was ten winters old he took his father's weapons. So fair of face was he, when he stood by other men, as when ivory is set in oak; his hair was fairer than gold. When he was twelve winters old he had full strength; then he lifted from the ground ten bear skins all at once, and then he slew Loricus, the duke, his foster-father and his wife, Lora or Glora, and took possession of Thrace; this we call Thrudheim. Then he visited many lands and knew the countries of the world, and conquered singlehanded all the berserks and all the giants, and one very big dragon and many beasts. In the north region he found that prophetess who was named Sibyl, whom we call Sif, and married her.”
 
As Rydberg, elsewhere in his work, explains:
 
      “The Germanic myth about Thor’s childhood has only been preserved in a distorted historicized form; but one finds that, in its essential features, it largely resembles the Vedic form.

      “The prologue to the Prose Edda relates, in its well-known manner, that Thor was fostered in Thrace by a Duke named Loricus. At ten, he inherited his father’s weapons. When he was twelve winters old, he had reached his full strength; then he lifted ten bear pelts off the ground at one time, killed Loricus and Loricus’ wife, Lóra or Gloria, and thus he acquired Thrace. Thereafter, he traveled far and explored all parts of the world and alone conquered all berserkers and all giants, as well as one of the greatest dragons and many wild animals—

“The Duke’s name, Loricus, is freely formed from his wife’s name, Lóra. His actual name is reported in Skáldskaparmál 4, which says that Thor was raised by Vingnir and Hlóra. He is known as fóstri Vingnis ok Hlóru (Skáldskaparmál 11).[1] One learns what type of being this Vingnir is from Thjóðólf’s song about Thor’s battle with Hrungnir, in which Vingnir is used as a giant’s name.[2] In the list of giants (added to Skáldskaparmál), he is likewise included.[3] In Vafþrúðnismál 53, where the old giant predicts that Vidar, after his father’s death, shall split the jaws of Fenrir, the name Vingnir stands in the place of the word “wolf” (vitnir) in Codex Regius.[4] And in the same poem, verse 51, it is said that Thor’s sons shall possess Vingnir’s hammer after the battle of Ragnarök—doubtlessly referred to as such, because Thor received his first hammer either from Vingnir or in a battle with him.[5] Consequently, there can be no doubt that Thor’s so-called foster father Vingnir was a giant.”[6]
 
 
So based on the limited available evidence and a common Old Norse custom, Rydberg has come up with a reasonable explanation which incorporates both pieces of evidence.

Scholars have long speculated on the identity of Týr’s father. The choices are Odin and Hymir. While Rydberg concluded that Odin, was Týr’s biological father, and Hymir was Tyr’s foster-father, there is another viable scholarly theory, which supports Odin as Tyr’s father, by denying the god Týr any role in the poem Hymiskviða.

This theory interprets the word týr found in the poem Hymiskivða, not as a name, but simply as a common noun meaning “god”. Thus, instead of the one-handed god Tyr, this interpretation allows us to substitute any god (‘týr’) into the role. Typically, that “god” is Loki, Thor’s most frequent companion when he journeys to Jötunheim.

This is viable, because the name Týr is also the common word for “god” (týr) found in the plural formation tivar, and occurs as part of names for Odin such as Hanga-týr, the ‘Hanged god”, and Farma-týr, “the god of Cargos”.

The Icelandic-English Dictionary by Cleasby/Vigfusson (1874) defines the words týr and the plural form tívi in this manner:
 
TÝR, m., gen. Týs, acc. dat. Tý; the form tívar, see tívi, may even be regarded as an irreg. plur. to tý-r; cp. Twisco, qs. Tivisco, in Tacit. Germ.; [for the identity of this word with Sansk. dyaus, dîvas = heaven, Gr. GREEK, Lat. divus, O.H.G. Ziw, see Max Müller's Lectures on Science of Language, 2nd Series, p. 425] :-- prop. the generic name of the highest divinity, which remains in compds, as Farma-týr, hanga-týr: as also in Týs-áttungr, the offspring of gods (Gr. GREEK), Ýt.: tý-framr, adj., Haustl. 1: tý-hraustr, valiant as a god: tý-spakr, godly-wise, Edda 16. II. the name of the god Týr, the one-armed god of war; see Edda passim. Týs-dagr, m. Tuesday, (Germ. Dienstag), Fms. ix. 42, N.G.L. i. 10, 343, 348, Hkr. iii. 416; spelt Týrs-dagr (Dan. Tirsdag), Fms. vii. 295, ix. 42, Rb. 572.

[Cleasby/Vigfusson clearly show their support for the Jakob Grimm’s theory that Týr is the Germanic cognate of the Indo-European Sky-father, *Dyuas Pater, with their statement “properly the generic name of the highest divinity.”]
 
TÍVI, a, m., also spelt with f; mostly only used in pl. tívar; a dat. sing. tíva occurs in Haustl. 8; fróðgum tíva (thus Ób., the Kb. has tífi, a less correct form): a gen. sing. tíva, Vsp., in valtíva; [this old word is identical in root with Lat. divus; Sansk. devas; Gr. GREEK (GREEK); cp. also Týr] :-- a god, divinity; þriggja tíva, Haustl. 1; tormiðladr tívum, 3; tíva rök, Vþm. 42; Álfheim Frey gáfu tívar at tannfé, Gm. 5; ríkir tívar, Þkv. 14; mærir tífar, Hým. 4; sig-tívar (q.v.), gods of victory, Ls. 1, 2, Vsp., Gm., Fm., Akv. 29 (Bugge); val-tívar, the gods of the slain, Vsp. 50 (Bugge); sæki-tívar, the martial gods, Landn. (in a verse); kykvir tívar, living beings, applied to men, Ó.H. (in a verse of the Christian time), all the other references being heathen.
 
In his translation of the Elder Edda (2011), Andy Orchard argues that the word “týr" which occurs in Hymiskviða doesn’t refer to the one-handed god at all, but actually refers to Loki. He writes:
 
“Other  translations and interpretations have assumed that in Hymiskviða, Thor is accompanied by Týr, and that Hymir is Tyr’s father, although there is no evidence for either identification. The word  týr does indeed occur in stanza 4, but while it may signify the god’s name (as it clearly does in e.g. Lokasenna 38, 40), it can also mean simply ‘god; and given the allusive nature of the language of Hymiskvida as a whole, one might find the later more likely. This god in offering ‘welcome advice’  tells us that he has the ‘hugely wise’ and ‘fierce’ giant Hymir for a father (5), and when Thor asks if Hymir’s cauldron can be obtained, answers laconically: ‘If friend, we two do it with cunning’ (6). He accompanies Thor on the journey, where they leave the goats that pull Thor’s chariot with Egil (7), presumably the ‘lava-dweller’ (giant) who has to give up two of his children as recompense for damaging one of Thor’s goats (37, 38). Butt he god who is described elsewhere as cunning, offering advice, having a giant for a father, accompanying Thor on expeditions to the Giants’ Domain, and being present when Egil was forced to offer Thor his children is Loki. And the laming of Thor’s goat is explicitly attributed to him in 37 (‘vice-wise Loki caused it.’); Loki is ‘vice-wise’ (læviss) in  Lokasenna 54. The argument in Lokasenna that he deliberately provokes the gods at the feast in order  to bring Ragnarök closer gains a particular poignancy if he is also responsible for bringing in the cauldron.”
 
 
However, despite this theory, other scholars disagree, among them Eysteinn Björnsson who argues:
 
“Týr is described here as Þórr's trusted friend and advisor. His role (and paternity) in this poem is unique, and would fit Loki better, as has been frequently suggested. However, there is no escaping the fact that the poet clearly meant Týr to be Þórr's companion on this quest - he is mentioned again by name in stanza 33. [An ill-informed idea, almost too ludicrous to mention, crops up in the literature every now and then: i.e. that týr in this poem simply means "god", and thus "Loki"! Apart from the fact that Loki would hardly be named thus, there is no evidence for such a usage of the word "týr" in the singular, neither in prose nor poetry. The mere idea is absurd, anyway: a whole Eddaic poem about a quest of Þórr's and Loki's which fails to mention Loki by name until the antepenultimate stanza, and consistently calls him "týr"!]”

Scholars have and will continue to speculate on the matter of Týr’s parentage. The matter cannot be conclusively settled based on the limited and seemingly contradictory information available to us. So, all in all, we are left with two equally valid choices, only one of which can be correct. Rydberg’s theory, however, does have the advantage of incorporating both pieces of evidence (the one from Hymiskviða and the one from Snorri’s Edda) regarding Týr’s parentage, without dismissing one or the other as an invention of the Hymiskviða poet or Snorri.