The Dark Matter of Heidegger's “Black Notebooks”

Publication of Martin Heidegger's Schwarze Hefte (Black Notebooks) caused a tempest which now appears to be one of the biggest dramas in academic world these days. The chain reaction of comments is gaining power with each conference, book, essay, and blog post dedicated to this issue. Now The New Yorker contributes — again (see older articles here and here) — to the “Heidegger-the-nazi” saga with Joshua Rothman's “Is Heidegger Contaminated By Nazism?”, and I must admit after reading at least a dozen of other recent articles on this very issue, that it is one of the most readable insights.  
The so-called “Heidegger controversy” is a highly complicated, sensitive, and — for the majority of Heideggerians and the continental kind in general — painful matter. In fact, the matter is so dark and delicate, that big words and bold statements seem to be impossible to avoid. Alas, the commanding boldness of the title of Rothman's article. Even the question mark at the end of the title leaves no chances for redemption because of this biologically suggestive term “contamination” — a graphic trope which obviously works very well for the press. The trope has been borrowed from Peter Trawny, director of the Martin Heidegger Institute at the University of Wuppertal in Germany, also the editor of Schwarze Hefte and the author of a book called Heidegger and the Myth of Jewish World Conspiracy. In the latter, Trawny occasionally addresses Heidegger's philosophy in terms of it being possibly “contaminated” by Nazism. However, at the end of his article, Rothman is cautious enough to remark, that “As to the question of ‘contamination,’ Trawny said he regretted, somewhat, the choice of that metaphor. It may have been ‘too strong.’” I would add that in this uneasy and tense silence which often befalls us when we are publically challenged by the terms such as “Holocaust,” “Nazi,” “jew,” or “gas chamber,” every subsequent utterance, no matter how thoroughly premeditated, will always tend to sound a bit “too strong.” Within this field of tension, within this apparent unthinkability of the matter, utterances often become inevitably amplified to the level of dictum, or verdict.  
Speaking of verdicts, some authors (e.g., Emmanuel Faye et al.) would be happy to turn the whole Heideggerian philosophy into an ideological Chernobyl — a zone contaminated by radioactive waste of Nazism. Such attempts are often based on the assumption that Heidegger's early writings, including Being and Time as well as some of the most important seminars of the twenties, allegedly had a bias toward subliminal ideological reasoning, as if Nazi ideology — retroactively — was a condition of possibility in Heidegger's philosophy even before he became a member of NSDP in 1932. By the same token, it would be equally unfair to assume that such bias was evident in Heidegger's work even after this infamous biographical turn — all in all, until the publishing of Schwarze Hefte in 2014, we had no direct hermeneutical evidence of this sort.
Meanwhile, despite the fact that Rothman's article is devoid of conveniently polarized verdicts, I must disagree with his dictum regarding the “math-like quality” of philosophy as such. Rothman puts forth the proposition that philosophy is “not just a vocabulary, but a system. A failure in one part of the system can suggest a failure everywhere.” Such an apparently commonsensical reasoning might seem irrefutable until this “everywhere” is brought into question. In other words, what is “everywhere”? Does it pertain to both philosophy and biographical life?   
The fact that Heidegger wanted Schwarze Hefte to be published at all instead of simply getting rid of them, tells us that he was surely aware of these questions. In Rothman's article we find a passage about the position of Peter Trawny himself, who “saw a way out for Heidegger in one of the philosopher’s own concepts, ‘errancy’—the idea that human beings are not calculators, but conjecturers, and that being wrong is, therefore, an irreducible part of being a person. (In ‘The Essence of Truth,’ Heidegger wrote that ‘the errancy through which human beings stray is not something that, as it were, extends alongside them like a ditch into which they occasionally stumble; rather, errancy belongs to the inner constitution of the [existence] into which historical human beings are admitted.’)”  
In philosophy, dictum veritas is never axiomatic in the mathematical sense. It is not that the principles of logic do not apply or do not matter, but the mere possibility of having the whole philosophical “system” grounded on a certain set of self-evident axioms turns philosophy into a positivist scientific project. The fact that today we consider Plato and Aristotle, Decartes and Locke, and even Spinoza and Leibnitz still worthy of a serious philosophical enquiry is one of the quick ways to argue against such a synonymity between philosophy and mathematics. Despite all the incongruencies, contradictions, and plain errancy of certain arguments and propositions, philosophical “systems” survive because somehow they happen to be more than the sums of their parts.  
If the question of Schwarze Hefte is to be answered, then the answer should not entail the amputation of a whole chapter in philosophy, because amputation of a limb — even if it is a saluting hand of a Nazi — brings us only to a phantom limb syndrome.