One of the major distinctions Heidegger makes throughout his work is between “fundamental questions” and derivative ones. Fundamental questions touch the deepest, incalculable parts of existence. Derivative questions concern the realm of calculation, ratiocination, comparison, evaluation.
Here is Heidegger in Introduction to Metaphysics:
To philosophize is to ask “Why are there beings rather than nothing?” Really to ask this question signifies: a daring attempt to fathom this unfathomable question by disclosing what it summons us to ask, to push our questioning to the very end. Where such an attempt occurs there is philosophy.
For Heidegger, the most fundamental question is not only unanswerable, but even un-askable. When we ask it, or attempt, failure after failure, to ask it, to consider it, to formulate it, we are engaged in philosophy.
If Heidegger’s definition of philosophy holds, it’s a far cry from what philosophy departments think it is, namely, knowledge production, advancing the field, offering “original research.” One can’t advance in philosophy, because it’s always the same—to ask the unanswerable, fundamental questions.
Can one be better or worse at doing this? Yes. One can be worse at it by not asking, or by asking in a way that is still too “derivative.” The Heideggerian insult is that a thinker asks after things which are not fundamental. The great critique of Heidegger, in response, is that the concern for the fundamental is both pretentious and escapist. We should care less about so-called fundamental questions like “Why is there something rather than nothing” and more about “real” questions like “What’s the matter with Kansas”?
Hannah Arendt shares much in common with her teacher, Heidegger. One commonality is her insistence that freedom is to be found in original thinking, but not in applied thinking. In this, she echoes Heidegger’s distinction between the fundamental and the derivative. Great thinking is not about completing a project of systematic thought, but of opening a path for new questions, for an encounter with wonder.
In Arendt’s terms, the phenomenon that makes thinking original is called “natality.” New, unprecedented events give the thinker food for thought. Yet the task of the philosopher is not to explain phenomena, but to illuminate them. For Arendt, the thinker is a bridge between the old and the new.
In Kabbalistic terms, we might say the thinker cares about keter; while the academic and scientist care about daat. For Heidegger, the thinker may care strictly or mostly about keter; while for Arendt, the thinker is the broker between the pure and the applied.
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Sums my philosophy up