Breakdown of Heimspekin leitar að hinu eilífa.
að
for (searching for)
leita
to search
hinn
the (formal definite article)
heimspekin
the philosophy
Questions & Answers about Heimspekin leitar að hinu eilífa.
How does the phrase hinu eilífa function as a noun, and why is it in the dative case?
This is an abstract nominalisation. By combining the formal neuter article hið with an adjective, you create an abstract concept—in this case, 'the eternal' or 'that which is eternal'. It is in the dative case (hinu eilífa) because it is the object of the preposition að.
Why does the adjective eilífa end in -a?
The formal article hið (and its declined forms like the dative hinu) is always followed by an adjective in its weak declension. For a neuter adjective in the dative singular, the weak ending is -a (from the dictionary form eilífur).
I thought the verb leita took the genitive case. Why are we using að plus the dative here?
You're right that leita can take a direct genitive object (like leita hjálpar, 'to seek help'). However, it is very common to use the phrasal verb leita að to mean 'to search for' or 'to look for'. The preposition að always forces the following noun phrase into the dative case.
What is the literal meaning of heimspekin?
It literally translates to 'the world-wisdom'. It is a compound of heimur (world) and speki (wisdom), with the feminine definite article -n attached at the end to mean 'the philosophy'.