I think Rav Yosef Ber Soloveitchik’s fascination with Neo-Kantianism was in part due to the similarity between a Kantian antinomy or neo-Kantian dialectic and the Brisker chaqira.
(Another factor was simply that neo-Kantianism was “in” at the time.)
Hegel’s dialectics move development forward by coming to a resolution. Thesis and Antithesis come to a Synthesis, which then becomes the new Thesis and an Antithesis arises, and so on.
Marx’s dialectic view of history was based on Hegel’s, applied to the idea that history is driven by a couple tension between haves trying to control have-nots.
Neo-Kantian dialectics do not always come to a resolution. The focus is more on how in the human condition, it is often the case that two motions that disagree are both true. And often life’s questions are more important than the answers.
So, for example, R SR Hirsch’s Torah im Derekh Eretz is Hegelian. His ideal is the Mensch-Israel a synthesis.
R YB Soloveitchik pushed the idea in YU that Torah uMadda (not his term) were “ramatayim tzofim — twin peaks to look out from” (c.f. Shemuel I 1:1). He didn’t want a “Catholic College”, where the rabbeim would have control over the secular courses. Real life poses conflicting values to pursue, and students need to be exposed to that while still in school and in a daily relationship with a rebbe.
We learn gemara even though the Rif and Rosh each reduce it to a set of conclusions. Because the value of talmud Torah is the dialectic — the gemara‘s discussions. You not only need to know what to do, there is a mitzvah to understand how we got there. (And a rabbi better know, because without understanding the mechanics, he cannot know how to apply the halakhah to special cases! But now I am just talking about the mitzvah of learning in-and-of itself.)
Brisk is very much about what I called (hopefully correctly) a neo-Kantian dialectic. No resolutions. At the end of a day, a Brisker so justified both voices in the dialog he will often follow the stringencies of both. (Despite the biting critique in Tosefta Edios 2:3, quoted in the TY Berakhos 1:4 (vilna 9a), which calls someone who follows the stringencies of both Beis Hillel and Beis Shammai “hakesil haholeikh bachoshekh — the fool who walks in darkness” c.f. Qoheles 2:14.)
Quite different than Hegel or Marx.
This post reminded me of something from my adolescence.
I tried learning Ish haHalakhah at a younger age than I could have possibly understood it. (And before the translation, Halakhic Man, came out.) I got stuck a few pages in on footnote 5.
For some odd reason, Rav Soloveitchik spent much of the footnote talking about the wheel, and how the wheel helped explain things. I was totally confused. Until I got near the end and encountered the word “קירקגור”. That word was clearly too long to be native to Hebrew, so I sounded it out and realized it referred to Søren Kierkegaard. At which point I was able to go back and realize that “הגל” was not some mysterious explanatory Wheel, but Hegel!