Firstly, consider that in Eddard IX, AGoT, Ned mentions that he hadn't thought about Rhaegar in years.
Years . That would be impossible if he'd been raising his son, plain and simple. So, if Jon isn't Rhaegar's, whose is he? Well, here's a really cool literary connection between Jon Snow and a certain Dornish house.
In Eddard X, AGoT, Ned has his famous fever dream about the Tower of Joy, when he tried to protect and save his sister Lyanna. He recalls a battle outside the tower where he and six of his friends (7 people) fight against 3 knights of the kingsguard - Ser Oswell Whent, Ser Gerold Hightower, and Ser Arthur Dayne.
In Jon IV, AGoT, there is another fight where a precious person is being fought over - Alliser Thorne pits 7 recruits against Jon Snow, Grenn and Pyp, and they have to protect Samwell Tarly. There are some crazy ridiculous connections between these two fights - particularly between the kingsguard knights and Jon's team.
Ser Oswell is of House Whent of Harrenhal - Harrenhal and House Whent are frequently associated with bats throughout the series; the sigil of House Whent is nine bats on a yellow field. So we have Ser Oswell, who is associated with bats.
The Lord-Commander of the Kingsguard was Ser Gerold Hightower. The Hightowers are shrouded in mystery, and they practice sorcery and dark arts. What happens in Oldtown stays in Oldtown. What's important is that Ser Gerold's nickname was "the White Bull." So we have Ser Gerold, who is associated with bulls.
Ser Arthur Dayne was the Sword of the Morning, a title always held by a great knight of House Dayne, along with their Valyrian greatsword
Dawn . What's interesting here is that Arthur's sister, Ashara, seemed to have an affection for Brandon Stark (Ned's brother). So we have Ser Arthur, who was Sword of the Morning.
In Jon's fight at Castle Black, on his team are Pyp and Grenn. In the same chapter, shortly after the fight, Pyp is described as having the ears of a bat. So we have Pyp, who is associated with bats.
Grenn's nickname, as given by Alliser Thorne, was Aurochs. An Auroch is a specific type of oxen, or bull. So we have Grenn, who is associated with bulls.
If we have Ser Oswell Whent and Pyp being associated with bats, and Ser Gerold Hightower and Grenn being associated with bulls, that screams that there is a connection between Ser Arthur Dayne and Jon Snow.
Spoiler for :
Is Jon Snow the next Sword of the Morning, the heir to House Dayne? Are there
two fire and ice couples? Rhaegar + Lyanna, Brandon + Ashara.
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