Nach - Neviyim and Kesuvim was written way after the revelation at Sinai. Why is it considered as part of Torah Shebiksav (written Torah) and not as Torah Shebaal Pe (Oral Torah)?
One difference between torah she-bi-khtav and torah she-b-al peh is form:
- a fixed, finite text, with every letter counted and the number of letters never changing, for torah sh-bi-khtav
- a fluid communication of meaning, with continual expansion over time, and continual change to meet and absorb the particularities of everyday life in new times and places, for torah she-b-al-peh
Nevi'im and Ktuvim have that fixed, set form (even if they have a different status than Humash)--the number of letters and words in each book set and limited and never added-to or changed.
Torah sheBichtav refers to books written while there was still Nevua and\or the Jews lived in Israel with a Beit Mikdash. Torah sheBaal Peh refers to anything written after the end of this holy era, and also includes any discussion and interpretation of sheBichtav.
Let's flip the question around:
Why is Yehoshua (and the rest of Neviim Rishonim) not part of "Torah," as they appear to be a simple continuation of the story? If Devarim, which is Moshe's speech (and thus wasn't revealed at Sinai), is part of Torah, then why isn't Yehoshua or Shmuel, which are Yehoshua's and Shmuel's narrative and speeches, respectively?
The answer to this, and to your question, is that at some point in Jewish history some books were accepted as "super-holy" (or similar, can't really express it), and were raised to a new level. They were then categorized as such, and no new books were allowed to be added to them.
This happened in several stages. The first stage was for Torah, which was "closed" when the Jews entered Israel. The second stage was for Neviim, which was closed with Churban Bayit Rishon (appx) and the end of Nevua. And the third stage was Ketuvim, which was closed with Churban Bayit Sheini. (This also explains why Daniel, for example, is part of Ketuvim and not Neviim.) After the destruction of both Batei Mikdash, that era of holiness and prophecy was over, and no new books could be added to Torah sheBichtav at all.
Source: Yeshiva University's Intro to Bible class
Rashi on Malacha 1:1 "The burden of the word of the Lord to Israel in the hand of Malachi"
"in the hand of Malachi" - [Rashi] It was already delivered into his hand for many days. From here, our Sages expounded in a baraitha of Mechilta that all the prophets stood on Mount Sinai and there the prophecies were delivered to them, and so [Isaiah (48:16)] says: “From the time it was, there was I, and now, the Lord God has sent me, [and His spirit].”
hence, just because it was written later does not mean it did not already exist in some form.
"Torah sheb'al peh" refers to the explanations that accompanied the 1st Five Books (Breishit - Devarim). This was eventually written into what we have as the mishna, with gemarrah being an explanation on this. I am uncertain if any of the books of either Nevi'im (Prophets) or Ketuvim (Writings) would even be considered "Torah Shebichtav" or they are a separate category.