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It is said in Greek Mythology that a swear over the river Styx cannot be broken. So what would happen, theoretically of course, if two swears from the same person contradicted one another?
For example, suppose I said:
"I swear by the river Styx that I will murder my father."
and then I said
"I swear by the river Styx that I will prevent the death of my father at all costs."
What would happen?
In your example, the second oath is a reneger of the first. Going by the Olympian rules regarding a Styx oath, the swearer would have to suffer the punishment for failing to fulfill the first one. The second oath is quite a bit more open to interpretation. E.g., if the swearer's father dies, the manner of his death exponentially complicates the question of the swearer's punishability, which would be based on just how well it is deemed that s\he attempted to prevent that death.
While a Styx oath was by no means casual, it was actually not unbreakable. Similar to ancient covenants, the whole point of the oath is the assumption that individuals (even Greek gods, so it would appear) do break promises, and lie, hence the need to qualify the covenant or oath with penalties for such reneging.
In the region on the eastern shores of the Mediterranean Sea, commonly referred to, in "Western" parlance, as the Middle/Near East, a covenant was made between two parties by cutting an animal in two and walking in between and around its pieces (in a sort of Figure 8 formation) so that the participants' feet were drenched in its blood while each said something along the lines of "May it be done to me as it has been done to this animal should I fail to fulfill my obligations in this contract or if I should break this deal." The point of the covenant is not that it is literally impossible for the participant to break it, rather it is meant as a deterrent from breaking one's promise(s) and also it is the kind of thing one does in order to convince others that s\he is as deathly serious as can be about what s\he says.
The principle is the same with the Styx oath. It was the most solemn vow that a [Greek] god could swear because of the consequences involved in breaking such a promise. According to Hesiod's Theogony the reason for taking the oath was because disputes sometimes erupted among the gods on Mt Olympos [Olympus] in which some would suspect or accuse others among them of dishonesty. On such an occasion Zeus would send the super-swift messenger-goddess Iris to fly to the Underworld to fetch water from the Styx River.
Carrying what she'd collected in a golden pitcher, Iris then handed it to the deity who was making the oath so that the swearer could pour the water out as a libation to the primordial deities Sky [Ouranos] and Earth [Gaia] and to those ancient ones in the chasm of Tartaros [Tartarus] (which meant, usually, the Titans and, sometimes, the Tritopatores, who, in rites like these, were honoured as the gods whose reign came after that of Sky and Earth but prior to the time of the Olympians). According to Lycophron's poem Alexandra, Zeus himself had established this practice by pouring out the same libation when he was about to go to war against the Titans, and which he repeated before going into battle against the Gigantes.
The name Styx means "Abomination" or "Abhorrent," a characteristic apparently describing this river's toxic water, which was as black as ink, and supposedly fatal to man and beast if touched or drunk. The beginning of the penalty for breaking a Styx oath was that the god who did so had to drink this same water. For a deity the effect of this was instant madness. Hereafter, in insanity, the offending deity would be stretched out in Tartaros in a sort of coma, deprived of any of the privileges given to deities, including their food and drink, thus rendering the offender unable to speak (doubtless as retribution for misusing his/her speech). That would be for a complete "Great Year," which is equal to nine years among humans in ancient Greek calendars. After this the deity would remain in his/her demoted condition incarcerated for another eight Great Years so that his/her total sentence would be 81 human years.
Circling back to your example, making the two oaths therein could end in some quite dire results. After being punished for breaking the first one, the offender would not have been available to prevent his/her father's death, in which instance s\he could end up in a fresh round of punishment: in the renewed cycle of an additional nine Great Years.
No sources really say anything about this. Very well. From pure logic, I will create three theories.
A quote that carries some base information.
So Jupiter [Zeus] spoke, and then by [Styx] the stream of his Stygian brother, the banks where boiling pitch flows in black maelstrom, he nodded, confirming his promise: the nod caused all Olympus to tremble.
If both vows were placed, then each would nudge you to do whatever it said you to do. They would then get so strong, they would explode your mind. Or, if you fulfilled one of them, then you would go insane because you broke your Styx vow. Very unpleasant.
I have a feeling that the Greeks saw through this, and did NOT want to make people's mind explode. So if you were to make two contradictory vows, then the second one was the only one you had to fulfill.
In the quote, Zeus spoke. The River Styx could only make Olympus tremble if a god/ goddess did it. If you are a god/goddess then resort to 1 or 2.
