Hans Blumenberg positions himself here against the trend of interpreting aspects of modernity as mere vestiges of Christianity, opting to emphasize their unique status instead. He strikes at the heart of a unique conundrum of post-Christian rhetoric where we can, on one hand, see frequent claims of "this is actually just Christianity in secular clothing" type while on the other hand modernity is still decried as something particularly vile. Besides the fact that the massive reliance on historicism perverts any possible real conversion, one can note that the arguments slip thoughtlessly to defending parts that are only accidental to the doctrinal core of Christianity, which after all appears as a technicality in comparison to its secular correlates like tradition or individual rights. The secularization rhetoric is directly related to the recently arisen beastly concept of "cultural christianity" which can be easily criticized but this foregoes the fact that many attempts at converting someone to Christianity via media appeal to non-essential factors, effectively debasing the actual "content" of the religion in favour of modern idols. Christianity finds itself in a paradoxical situation where to preserve its integrity it should become like a Jewish, closed religion instead of an open, proselytising one - otherwise the relation between "incarnation" and "individual rights" or between "church" and "tradition" runs in the wrong direction.
It is not Blumenberg's claim that Christianity did not have a massive and lasting effect on European intellectual history but instead of treating it as a constant undercurrent of modernity he identifies secular modernity as a caesura that reoccupied the functional positions formerly held by Christians ideas which themselves reoccupied functional positions of Hellenic soteriological though. This may be apparent on the level of terminology as well: Christians took over the concept of providence from the Stoics, for example, but invested it with a wholly different background metaphysics. Following this idea, modernity, insofar as it separates itself from Christianity, could be said to have taken up the concept of liberty implied by providence while replacing the traditional Christian background assumptions of providence with pantheistic undercurrents. The presentation of the idea is unwieldy and sometimes confusing but ultimately the message is clear. If one considers this idea in relation to the current rhetoric surrounding Christianity, which is trying to steal French Revolution's liberalism/nationalism-nexus away from liberals, it becomes perhaps tentatively possible to speculate on whether this at least represents an attempt at reoccupation. The mere fact that the past is taken up, as Christians do with liberalism, does not then necessarily reduce the effort to a "liberalizing" equivalent of secularization but we can see in this backwards movement precisely the index of future development which is neither Christian nor liberal. Right away, Blumenberg's concept immediately becomes useful without reducing to tired demands of "standing on the right side of history": we can analyze signs of these types of knot-points in discourse and history, pay attention to how words like "liberty", "tradition","freedom of speech", "rights" perform their deconstructive neither-neither loops via the perceived coincidence of opposites.
In truth, this book is not a systematic presentation of history according to reoccupation idea: it is ultra-erudite and extremely digressive rather than systematic, despite innovating a new concept. Blumenberg focuses heavily on the importance of the transition from scholasticism to Copernican world-view, seeing this as emblematic of the transformation to modern conception of knowledge. He considers this transition as something that enabled man to exert his powers in the world against the passivity implied by the Scholastic world-picture, with its heavy Aristotelian heritage. This was made possible by the concept of method which is a kind of transcendence made immanent, related intimately to developments such as artificial perspective, Cartesian co-ordinates and infinitesimal calculus. Scholasticism was constituted by the tension between the contingency of God's will and human drive to know things, taken up from Aristotle in a manner that separated Scholasticism from the Church Fathers. Christianity, in its relation to Hellenic thought, had identified itself precisely by separating itself from anthropocentric concepts of Nature which considered it as something fundamentally accessible to man as a given and following a necessitarian structure. Christianity's concept of providence could never be cosmic-necessitarian but rather the concept was reoccupied to accommodate a monotheist metaphysics of contingency where nothing is so secure: grace is something that is given by God via his providence. It was natural, then, for Medieval Catholic thought to allow a certain degree of curiosity, something more severely prohibited by Augustine, into the world: as long as it was in the final analysis referred to God at the end of the chain as a stand-in for Aristotle's unmoved mover. This was integrated directly with the astronomical concept of geocentrism, with Earth as the lowest rung of the chain.
While the logic of reoccupation works here to some extent, the ultimate argument of the book is, in fact, misleading in terms of concrete analysis. The focus on Scholasticism in its transition to Copernicanism, infinite universe and method covertly identifies man's ability to exert his powers on Earth with the development of astronomy as a science; even if Blumenberg himself refers multiple times to the story of Thales falling into a well watching the stars, accompanied by the laughter of a Thracian slave-girl. It is also noted that astronomy was considered one of the liberal arts in medieval education but it could as well have been noted that the whole of Trivium and Quadrivium did not contain any science such as engineering or anything related to "down-to-earth" technology. Yet it is widely known the medieval era saw an explosion in technical and agricultural innovation, from windmills to crop rotations: it was as if man truly took control of his destiny "on earth", something Blumenberg surmises must have happened only at the dawn of modernity via the change in relation to the stars. As illustrated by the story of Thales and Thracian woman, though, astronomy is precisely what is farthest from the down-to-earth realities of the slave, whom Christian concept of providence supplied with a notion of personhood. In a historical context, it is either the science of gentlemen or sea pirates. The church in the medieval age was an important counter-force to the excesses of feudal lords and provided the structural preconditions for the development of modern economy, proletariat, cities; all the while stimulating technological development by redirecting society to practical technological accomplishments that helped man to achieve control over his surroundings on Earth.
What is going on here, then? Is this omission merely due to a habitual over-focus on the history of ideas to the exclusion of other factors? The issue might lie at the distinction of the concepts of science and technology: in the medieval times, mathematics and astronomy were "arts" while technology was not even included on the university curriculum and their fusion, physics, is conspicuously absent from the list. Science, indeed, is the child of the modern metaphysics of method that regards the world as a foreign material with no essential or teleological qualities. The union of these two traits is perfectly exemplified by Descartes, whose analytic geometry embeds the geometrical object within a vectorial frame of transcendence that is itself supposed to mark a direction that defines space instead of simply being given in it. Blumenberg does explain how this no longer constitutes a source of problem for modernity but is reinterpreted as a call for activity: we are supposedly here far from the necessitarian repose of the Stoics, strictly within the self-perpetuating dynamo of method before which people could only look in befuddlement at their surroundings. It seems to not matter here that it is precisely with physics that we end up with the problems of laws and occult forces and later on even more outrageous mystifications surpassing the most imaginative treatises on angels and pinheads known to the medieval ages.
While reoccupation is an intriguing and probably useful concept, it would probably have to be modified somewhat so that it doesn't unwittingly lend itself to simplifications of this sort. There is a simple cure: history should be conscious of what happens in the lower depths, in the muds of the Earth and practice, away from the subtle stargazing sight of the gentleman. It is unfortunate that a meaningless lump of rock like Ceres could ruin the subtle Hegelian proof of its impossibility based on the solidly Pythagorean conception of the music of the spheres but such brute facts nonetheless keep intruding the sanctity of "liberal arts" in ever increasing quantities. Blumenberg does address a problematic of modernity that may explain the persistence of teleology if modernism was supposedly all about effectiveness: to partake in infinite approximation of the absolute generates a sense of frustration due to the impossibility of its completion in any single lifetime and thus necessitates an educational aspect to mediate this chaotic state socially.
I would say that the social function and the destabilising function are not simple aspects of the single monolithic abstraction of modernity, which is at any rate projected to the era anachronistically. Both of them are also distinct from technology which is, however, adopted into the new-fangled concept of science and mixed in with liberal arts. If you have a completely historically new concept like science you cannot explain that with a concept like modernity, another historical novelty, that basically includes science in its definition. The destabilization, rather, is something that happens when you clash technology with liberal arts and make them come closer together - these are the "two bottomless whirlpools" that Thomas Carlyle talked about in Sartor Resartus, the slave Earth and aristocratic stars. This parallels modern reality in that the nobilities have been more and more debased by the progress of capitalism and have had to resort to meddling with the guilds; all the while printing press confuses the brains of normal people, producing monstrous fancies and unsustainable delusions which lead to many violent, abhorrent effects. Technology loses its Christian progressive Earthly thrust and becomes confused with liberal arts which amounts to technicians prancing about as the possessors of ultimate truth and status, leading to the fantastic extravagances of modern cosmology and a strange rhetorical style that varies incoherently between technicality of world-manipulation, dishonest Epicureanism in the face of the emptinesses of space and the pomp of the sublime of the tormented genius having psychedelic visions of black holes with equations running over it. The hellenic influences are far from absent from the methodic sciences as we can see from the parallels between natural law, a liberal-aristocratic construct in an attempt to combat the power of princes and banks, and physical laws; in the epicurean effect that the listing out of scientific facts is clearly supposed to have; in the contemplative relation to "our insignificance". It is not a coincidence that the fight against windmills remains the most iconic scene of Don Quixote: the book is an irrational act of fantasy against the technological genius of the middle ages, solidly entrenched in God's providence.
There is far more to say but it is a bit late. In summary, it's a very thought provoking book in some aspects but ultimately it offers a misleading picture of reality.