The first essay is called "Erinnerung an den Anfang" -- I am translating this either as "Memories of the Beginning", or "Remembering the Beginning". In it, Blumenberg takes up the question (which I think is going to be the theme of the book) of whether consciousness is in physical reality or outside of it.
The accepted "circumstantial evidence" for consciousness not being inside physical reality, is the impossibility of imagining a beginning or an end to consciousness -- beginning with Aristotle's argument that time cannot have a beginning because any imagined "beginning" would have to already be in time, thus there would have to be a time before it, Blumenberg extends this argument to consciousness. Both in terms of the cycle of life (i.e. birth/death) and of a single day (i.e. awakening and going to sleep), we cannot imagine a point of beginning or ending; thus we exist in a state of "known mortality and believed immortality".
My own response to this (speaking now only of consciousness; I am not thinking about beginning/ending of time here) is to say the problem becomes much easier if you abolish the duality of "conscious" and "unconscious" and allow a region of gray where you are both conscious and unconscious a la Julian Jaynes. Every morning when I wake up I repeat the process of infancy, blossoming into awareness, which was itself a repetition of mankind's historical journey into reflexive consciousness -- ontogeny recapitulates phylogeny.
Blumenberg plays with Wittgenstein's statement that "the world is everything that is the case"; he says [in a way that is difficult to translate because of pronoun choice],
[The world] is not everything that is the case; it approaches being that, insofar as exit from and entry into the world is accomplished, opened, made passable.
The world is what can be reclaimed: everyone's in waking, the singleton's in memory, which is nothing other than the assertion of identity against the interruptions of discontinuity, loss, forgetfulness.
Other references in this essay are to Descartes, Kant (this one totally eluded me), Proust (A la Recherce du Temps Perdu translates literally not as "Memories of Things Past" but rather, "In Search of Lost Time", quite germane to this discussion), and Husserl. I didn't really get most of the references but they're nice to have on hand for later on.