4 September 2011
Milan, Italy
ECAP7 Workshop
Numerical Cognition and Mathematical Ontology
San Raffaele University / University of Milan-Bicocca
September 4th, 2011
CALL FOR PAPERS
(extended) Deadline: March 10th, 2011
The workshop Numerical Cognition and Mathematical Ontology is one of the
Workshop associated to the Seventh Conference in Analytic Philosophy
(ECAP7) organized by the European Society of Analytic Philosophy. The
ECAP7 is locally organized by the San Raffaele University (Milan) and the
University of Milan, and will take place from the 1st to the 6th of
September 2011. All information about the ECAP7 can be found at:
http://www.esap.info/ecap7/ All ECAP7 workshops will take place on Sunday
September 4th, 2011.
The workshop is organized by the San Raffaele University and the University of Milan Bicocca, in collaboration with the Association for the Philosophy of Mathematical Practice.
All information about the workshop can be found at: http://www.esap.info/ecap7/?page_id=29
WORKSHOP DESCRIPTION
Philosophy of mathematics has proved to be one of the most lively areas of philosophy in recent times, and numerical cognition has proved the same with respect to cognitive science. Many traditional issues in the philosophy of mathematics, concerning both our understanding of the concept of number and our conception of mathematical objects, has been seen in a new light under the pressure of the development of cognitive studies. Often, however, we are faced with the stark opposition between those who believe that cognitive results tell us all there is to say about mathematics, pace most traditional philosophical concerns, and those who deny that cognitive aspects of mathematical thinking, interesting how they are on their own, can foster any progress in the solution of as yet theoretically unavoidable philosophical issues.
Many, however, feel the urge of filling the gap, one way or the other. Major and interrelated issues are indeed at stake.
How do children acquire an understanding of number concepts and mathematics, and how much is innate? According to one hypothesis, we have inherited systems for representing at least small numbers, and a related hypothesis is that language plays a key role in the process of upgrading the core systems into a fully competent mathematical mind. But if it is so, are number concepts language-dependent in a non-trivial sense? And can evidence be found also from the neurosciences for specialized neural networks for numerical processing and calculation (both in children and adults), and for their interaction with language-processing networks?
Even once these issues are solved, however, the question remains of how basic number concepts develop into more sophisticated mathematical cognition, dealing with higher mathematical concepts. Can our ability to understand complex and formalized mathematical theories be traced back to some basic numerical ability? And again, what role would be played in this process by language, or by metaphorical or other representational capacities allowing us to extend our mathematical competence into very complex domains?
Cognitive capacities might have a role in a mature philosophy of mathematics only if they can help solve more traditional concerns such as the nature of mathematical objects and the epistemic access that we might have to them. Does the nature of numerical cognition, for example, support a structuralist interpretation of mathematics as opposed to a platonist one? Does it favour a realist conception of mathematical objects as self-standing and mind-independent, or does it rather favour a conception of them as created, mind-dependent, and possibly socially constructed objects?
Basic cognitive capacities, if they are relevant to mathematical understanding, should also play a role in mathematical practice, as well as in visual and diagrammatic forms of reasoning involved in mathematical understanding and explanation. Can these capacities suggest any way out of the epistemic problems over which contemporary philosophers have dwelled at least since Benacerraf?s dilemma?
This workshop aims at bringing together scholars on both sides of the divide, and to offer the opportunity to young researchers of discussing works at the interplay between cognitive science and the philosophy of mathematics.
A provisional list of suggested topics for contributed papers is as follows:
* what is the nature of concepts of natural numbers?
* are concepts of natural numbers innate?
* what is the relation between mathematical abilities and linguistic abilities?
* how can cognitive studies improve our understanding of higher mathematics?
* can numerical cognitive capacities affect our conception of mathematical objects?
* how can cognitive results help solve the traditional epistemological concerns with mathematics?
* to what extent are numerical cognition, mathematical practice and the social aspects of mathematics relevant to mathematical ontology?
INVITED SPEAKERS
Jessica Carter (University of Southern Denmark, Odense; APMP)
Luisa Girelli (University of Milan-Bicocca)
Eric Margolis (University of British Columbia, Vancouver)
Marco Panza (IHPST, CNRS Paris; APMP)
CALL FOR PAPERS
We invite submission for the ECAP7 Workshop on Numerical Cognition and Mathematical Ontology.
FOUR contributed papers will be selected for presentation.
Selected talks will have 20 minutes time for presentation and 10 minutes time for discussion.
Deadline for submission: March 10th, 2011
Communication of acceptance: April 30th, 2011
GUIDELINES FOR SUBMISSION
Submission to the workshop follows the same procedures as the general ECAP7 call for papers (http://www.esap.info/ecap7/?page_id=12).
Abstracts must be written in English and be prepared for blind referee, with all self-reference and personal data suppressed.
Please submit both a short abstract of no more than 200 words, and a long abstract of no more than 1000 words (references included).
Submission is made through the Easychair website. Short abstracts will be inserted in the EasyChair submission page in text format. Long abstracts will be uploaded as files in either .doc or .pdf format.
The EasyChair login page for ECAP7 is at: http://www.easychair.org/conferences/?conf=ecap7
In order to access the submission page, the creation of an EasyChair account will be required. IMPORTANT: Please notice that what is called ?abstract? in the EasyChair ?Title, Abstract and Other Information? section corresponds to the short abstract of this call, and what is called ?paper? in the EasyChair ?Upload Paper? section corresponds to the long abstract of this call.
A visual guide to submission can be downloaded at: http://www.esap.info/ECAP-easyguide.pdf
ORGANIZING COMMITTEE
Elisabetta Lalumera (University of Milan Bicocca)
Andrea Sereni (San Raffaele University, Milan)
In collaboration with the Association for the Philosophy of Mathematical Practice (APMP)
SCIENTIFIC COMMITTEE
Confirmed members of the scientific committee are:
Jessica Carter (University of Southern Denmark, Odense; APMP)
Luisa Girelli (University of Milan-Bicocca)
Gianluigi Oliveri (University of Palermo, APMP)
Mario Piazza (G. D'Annunzio University, Chieti-Pescara)
REGISTRATION
Attendance to the Workshop requires registration to the ECAP7 Conference. Contributed speakers participating only to the workshop day will not be required registration to the ECAP7 conference. General guidelines for the ECAP7 registration can be found here: http://www.esap.info/ecap7/?page_id=42. Please note that the deadline for early registration to the ECAP7 is June 15th, 2011.
IMPORTANT DATES AND CONTACTS
Deadline for submission: March 10th, 2011
Communication of Acceptance: April 30th, 2011
Workshop date: September 4th, 2011
Workshop website: http://www.esap.info/ecap7/?page_id=29
APMP website: http://institucional.us.es/apmp/
For any information: sereni.andrea@hsr.it; elisabetta.lalumera@unimib.it