What does the Rabbi think about the claim that the thirteen principles are not at all from Sinai, but rather from Greek culture, which simply taught the sages to sharpen their ability to draw conclusions and interpret?
Does this claim have any halakhic implications at all? Seemingly not.

In my view, that’s nonsense. Lieberman, in his book Greeks and Greekness in the Land of Israel, found a few faint roots in Eastern cultures, not Greece. But if this were just ordinary inference without authorization from Sinai, then those inferences would be groundless. There is no logic to them.
I’ve dealt with these possibilities quite a bit in several places. Mainly in the second book in the Talmudic Logic series (General and Particular Principles), where we proposed a model that explains the development of exposition from its source at Sinai through influences and human development over the generations, and we showed the significance of this with various proofs for that model.

And regarding the difference between Hillel’s principles and Rabbi Ishmael’s—according to your approach, did Hillel simply not bring all of them?
Sorry, I just don’t have any way to get hold of your books on Talmudic logic.

Thank you very much 🙂

Between Hillel and Rabbi Ishmael, it’s simply a process of further specification. But beyond that, there are also principles that weren’t included.
Examples can be found in the baraita of the thirty-two principles of Rabbi Eliezer son of Rabbi Yose the Galilean. In Sefer Keritut he explains, regarding each one, why it wasn’t included by Rabbi Ishmael—either because it’s a principle of aggadic exposition, or an Akivan principle, or a disputed principle, or a principle whose status is not really exposition at all but simply ordinary interpretation of the text. And even the list of thirty-two is not complete. The overwhelming majority of expositions in rabbinic literature do not use Rabbi Ishmael’s principles, or formal principles at all.

From the phrase “principles by which the Torah is expounded,” it sounds like there is some principle that is earlier and greater than the Torah—as though God had cognitive-literary laws governing Him while He wrote the Torah.

Also, formulating such rules seems to involve “do not add.”

The “rules” by which one may expound the Torah are learned from the Torah itself. For example, in the book of Genesis there are slight variations in wording from verse to verse that hint at different ways the same things can be said, and from them one can discern what is significant and what is not significant. And that too is open to interpretation—each person according to his own understanding.

Not true. The principles can be rules of inference that accompany the Torah. Though I also see no problem even with the assumption that there is something greater that preceded it. The sages write this in several places.
There is no issue of “do not add” here. This is conceptualization and interpretation of the methods of exposition that were given at Sinai.
The overwhelming majority of the methods of exposition cannot be learned from the Torah. Keritut implies that none of them can.