 Current Projects
- Projects of My Own (some language on those will be added soon)
- Philosophy of Mathematics: How Category Theory Can Help
- Turning Manuscripts into Papers and Books
- Turning Lecture Notes into Textbooks
- Current Joint Projects
- Philosophy of Mathematics: Sociological Aspects and Mathematical Practice (PhiMSAMP)
- Current Editorial Projects
- Previous Work
- Doctoral dissertation and related work
I made the critical analysis of arguments
which draw on Gödel's two incompleteness theorems my Ph.D. project. The
first (mathematical) part gives a technically thorough presentation of the
Gödel theorems, all their proof variants available,
and closely related results. The second (philosophical) part argues for
the thesis that Gödelian arguments are of no use except in fields
where the development in the field has already led the relevant community
to consider complete and rigorous formalizations. Further work of mine was
and still is connected to this doctoral work. It comprises technical work
(showing, e.g., why Jeroslov's famous reduction of the derivability
conditions does not deliver what it promises), tackles further issues in
the philosophical significance of the Gödel theorems, and biographical studies. This
work was also my start into the philosophy of mathematics, the history and philosophy of logic, and the
history of analytical philosophy.
- Habilitation thesis
(a second "PhD" as required by the German system of higher education)
Since the distinction between philosophy
proper and the sciences was finally established only during the 19th
century, this work on the philosophy and methodology of science in the
19th century tackles views that cross today's borders. In its current form
the thesis comprises, besides a long introductory essay on historiography
and the philosophy of history, my account of Kant and the development in
19th Century Germany. One result is that the destruction of the classical
conception of probability and the invalidation of Laplace's answer to Hume
is due not to, say, Keynes or von Mises, as the received view has it, but to their sources, i.e.,
philosophers from Lotze and Fries to von Kries. For publication I'll add
my account of the development in England, the USA, and France.
- Further work
Besides these works I have devoted a great deal of
time to purely historical research and, as a service to the community, to
encyclopedia entries. As a result I have written many scholarly articles
for the Historisches Wörterbuch der Philosophie (Historical
Dictionary of Philosophy)---each article tracks down the history of one
concept throughout Western philosophy---and was invited, among others, to contribute to
the new edition of the venerable "Pauly-Wissova,'' the world's leading
encyclopedia of classical antiquity. All these articles were refereed
before publication and "scooped from the sources.''
- A selection of friends, foes, and other folks I'm in touch with ...
|
