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Notice

AISB event Bulletin Item

CALL FOR PAPERS: Functions, proofs, constructions, 20-23 Feb 2014, Tuebingen, GERMANY


Aim of the workshop:
---------------------------
The notion of function lays at the core of constructivism. According
to the intuitionistic explanation of the meaning of logical constants,
a proof of an implication is understood as a function which gives
proofs of the consequent when applied to proofs of the antecedent.

How this should be exactly understood is a non-trivial matter and any
attempt at clarifying it requires, implicitly or explicitly, to
embrace some particular view on the nature of functions. More
generally, different ways of accounting for the notion of proof
reflect different conceptions of functions.

Gentzen?s methods of proof-analysis depict deductive reasoning as
being ultimately constituted by ?atomic? operations. Via the
Curry-Howard isomorphism these can be viewed as corresponding to basic
ingredients of computations. Proofs are thus assumed to be linguistic
entities or, at least, that it is through language that proofs are
primarily accessed.

An explanation of a different kind (such as Goodman and Kreisel?s
theory of constructions or the more recent research programme called
?logic of proofs?) is one willing to grasp the notion of proof
?directly?. Viewing proofs as abstract entities, the focus is not much
on the internal structure of their linguistic presentations, but
rather on what may be called their ?behaviour? (for instance how they
can be combined with each other to produce new proofs).

The apparent dichotomy between proofs as constituted by inferential
steps, and proofs as abstract ?unstructured? entities reflects the
duality of the notion of function itself. Should functions be viewed
as procedures?piecewise constituted by instructions - or are functions
sorts of black boxes to be identified by what they do - giving a value
for each input - rather than by how they do it? Are functions
primarily given as the denotation of linguistic predicates (in a
Fregean manner), or are they rather an already given domain which we
disclose through language?

We invite philosophers, historians as well as mathematician and
computer scientists willing to take part to the workshop to submit the
extended abstract
(max 2 pages) of a talk suitable for a 45 minutes to 1 hour presentation.

[Abstracts should be sent per email to fun.pro.con@gmail.com]


Confirmed speakers:
---------------------------
? Mark van Atten
? Stefania Centrone
? Thierry Coquand
? Walter Dean
? Fritz Hamm
? Alberto Naibo
? Dag Prawitz
? Peter Schroeder-Heister
? Stewart Shapiro
? Gran Sundholm


Organizers:
---------------
Luca Tranchini (Tbingen) and Marco Panza (IHPST Paris)


Important dates:
---------------------
? Submission Deadline: September 1, 2013
? Notification of Acceptance: October 30, 2013
? Workshop: February 20-23, 2014