[FOM] Two preprints on Gödel
Mark van Atten
vanattenmark at gmail.com
Fri Jun 21 04:50:41 EDT 2013
Here are the abstracts of two preprints on Gödel that are
available from me on request.
1. `Gödel and intuitionism'
Forthcoming in J. Dubucs and M. Bourdeau (eds),
Constructivity and Computability in Historical and
Philosophical Perspective. Dordrecht: Springer.
After a brief survey of Gödel's personal contacts with
Brouwer and Heyting, examples are discussed where
intuitionistic ideas had a direct influence on Gödel's
technical work. Then it is argued that the closest
rapprochement of Gödel to intuitionism is seen in the
development of the Dialectica Interpretation, during which
he came to accept the notion of computable functional of
finite type as primitive. It is shown that Gödel already
thought of that possibility in the Princeton lectures on
intuitionism of Spring 1941, and evidence is presented that
he adopted it in the same year or the next, long before the
publication of 1958. Draft material for the revision of the
Dialectica paper is discussed in which Gödel describes the
Dialectica Interpretation as being based on a new
intuitionistic insight obtained by applying phenomenology,
and also notes that relate the new notion of reductive proof
to phenomenology. In an appendix, attention is drawn to
notes from the archive according to which Gödel anticipated
autonomous transfinite progressions when writing his
2. `Gödel's Dialectica Interpretation and Leibniz'
Forthcoming in Gabriella Crocco (ed.), Gödelian Studies on
the Max-Phil Notebooks (vol. 1). Aix-en-Provence: Presses
In an envelope of material relating to his work on the
translation and revision of the Dialectica paper in 1968,
Gödel kept a note that is in shorthand but in which one
immediately notices the longhand name `Leibniz'. When
transcribed and put into context, the note allows one to
show that Leibniz was a source of inspiration for Gödel's
revision of the Dialectica interpretation.
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