J. Goguen's Concept of Proof Events: Current State of Research and
Perspectives
In 2001, Joseph Goguen posted a short note on proof, suggesting a
general concept of proof designed to cover apodictic, dialectical,
constructive, and non-constructive proofs, as well as proof steps and
computer proofs, relying on concepts and methods from cognitive
science, semiotics, ethnomethodology and modern philosophy of
science. Proofs are viewed as social events evolving in space and
time.
Goguen did not advance this idea further, and his paper fell into
oblivion until we attempted with Petros Stefaneas (2014) to suggest an
interpretation of Goguen's idea as a general meta-methodological
concept possessing seven aspects: the social and the communicative
aspects, the fundamental distinction between provers and interpreters,
the processes of interpretation, understanding and validating proofs,
the historical(-cultural) and stylistic aspects.
The talk will expose the advances attained in the theory of proof
events, the question of its possible formalisations, the applications
of proof events in the history of mathematics and the problem-solving
activity in research and mathematics education (Vandoulakis 2020)
based on a cognitive interpretation of discovery proof events
(Stefaneas et al. 2014). Finally, the open questions will be posed,
and their possible solution will be outlined.
Ioannis Vandoulakis
Last modified: Wed Nov 29 21:51:34 EET 2023