He is a self-styled protagonist of dialectical logic as a rigidly
mathematical theory, with virtually no regard for current academic
philosophy. He is completely self-centered, and not (like any decent
contemporary academic philosopher) in hot pursuit of the truth. Rather
he is in it only for himself and his own peace of mind. In fact he
thinks he doesn't need the nepotistic system of the epigones for his
research and even less so for his credibility. This in itself will be
sufficient evidence for the average clear headed person to establish
beyond doubt that he is a dangerous fanatic who will not hesitate to
disturb the moronic harmony of the philosophical clerus. As a matter of
fact, he has never really managed to get over his anti-authoritarian
phase, only that his disdain has now shifted from an old generation of
philosophers to his own generation, which has grown pretty old by now
anyway. He is in desperate need of a fresh brain-alignment to get in
touch with the doctrinal philosophy of the day, but, of course, like all
people who live in their own world of thought, he stubbornly refuses to
acknowledge the authority of the mediocracy.
Like Frege before him, he cherishes Leibniz' idea of a mathesis
universalis. He does so despite the fact that already Hegel had
dismissed it as an immature idea (and Heidegger even more so) and had
made it very clear that philosophy can never borrow its method from an
inferior discipline such as mathematics. He is unwilling to listen to
the good advice of experienced Hegelians, to finish his mathematical
studies and turn to Hegel interpretation. Even less does he acknowledge
Heidegger's dictum that philosophical thinking manages only to
attain an epigonal renaissance. In fact he thinks that the Ancient
Greeks only provided an interesting beginning and that the actual
development of a first philosophy (metaphysics) still lies
ahead; like physics and logic had interesting starting points in
Aristoteles' philosophy, but were far from fully developed theories. To
make things even worse, he is interested in notions of purely
mechanical reasoning (if this can be called "reasoning" at all) and
where and when exactly undecidability appears on the scene. He thinks
that even in so rudimentary a form of reasoning as that of mechanical
calculating there is something that is at odds with itself and that this
is sufficient to provide for a foundation of thought forms in the
spirit of Hegel's idea of a speculative philosophy. He actually goes so
far as to hope that his work will take metaphysics (in the form of
speculative logic) out of the hands of philosophers and vest it in
mathematics.
He has acquired some basic skills in mathematical logic in the late
sixties and early seventies at the Mathematical Institute in Munich
under Kurt Schütte. This enabled him to pursue the question of how
to restrict classical logic in order to allow unrestricted abstraction
with the result of realizing some time in 1977 that in the absence of
contraction, cut elimination does not require an induction on the
complexity of the cut formula and would therefore make allowance for
consistently adding unrestricted abstraction. Despite otherwise lagging
roughly 25
years behind the development in mathematical logic, he feels
satisfied
that the idea of building a type free system on the basis of
a
contraction free logic has now been endorsed in theoretical computer
science, more specifically in the context of Jean-Yves Girard's
approach
to the problem of formulating a polytime logic.
The point of a type-free logic is the availability of self-reference
(the fixed point property).
This brings us to his main obsession: self-reference. He is infatuated
with self-reference to the point of playing with the reader's patience
by responding to the question regarding his philosophical interest with
the answer:
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