Numbers in Mind: The Philosophy of Numerical Cognition
18 February 2017, 9.30am - 7.00pm
Institute of Philosophy
Conference / Symposium
The Court Room, First Floor, Senate House, Malet Street, London WC1E 7HU
Numbers in Mind: The Philosophy of Numerical Cognition
Saturday 18th February 2017.
Court Room, Senate House. London.
Organised by Prof Brian Butterworth (UCL) and Dr Ophelia Deroy (IP)
In connection with the Royal Society Meeting
What are the minimal conditions for possessing number concepts? How are number concepts acquired? Can this acquisition be gradual (knowing some, but not all numbers)? Is this acquisition special, by comparison with other concepts? What's the importance of being taught external symbols for number concepts - and is part of numerical cognition intrinsically social? Is there a link between the development of numerical cognition/numerical symbols and the development of other cognitive capacities?
Recent work in numerical cognition, in humans as well as animals, has re-shaped our understanding of numerical abilities. This workshop will examine the relevance of this work for philosophical problems about mathematics, and numbers more specifically.
Space in the conference is limited, therefore we would ask those interested in attending to provide a short (circa 100 – 150 word) justification outlining how attendance at the workshop will be of benefit to their research. Some prior knowledge of the topic is presupposed. Please send applications to IP@sas.ac.uk
Speakers
Helen de Cruz (Oxford, UK)
Numerical cognition and its metaphysical implications
Valeria Giardino (CNRS, Nancy, France)
Counting and numbers
Max Jones (Bristol, UK)
Seeing Numbers as Affordances
Paula Quinon (Lund, Sweden)
Conceptual Content of Arithmetical Terminology: From Number Cognition to Mature Mathematics
Richard Samuels (Ohio State University, USA)
Basically Natural: On the Relative Fundamentality of Ordinal and Cardinal Conceptions of Number (Samuels, Shapiro and Snyder)
Mario Santos Sousa (UCL)
Numbers Incorporated: Numerical representations and their distinctive structural features
Eric Synder (Ohio State University, USA)
Neologicism, Frege's Constraint, and the Frege-Heck Condition (Snyder, Samuels and Shapiro)
John Wigglesworth (LMU, Munich, Germany)
Numerical abilities and mathematical structure.
Discussants
Marcus Giaquinto (UCL)
Stewart Shapiro (Ohio State University)
Cedric Villani (UMPC/ CNRS)
Programme
Each session: 40 min position paper; 20 min questions. 2 x 30 communications with 15 min questions each.
9.30am Coffee and registration
Session 1 – 10:00 – 12:30
10:00 Richard Samuels (Ohio State University, USA)
Basically Natural: On the Relative Fundamentality of Ordinal and Cardinal Conceptions of Number (Samuels, Shapiro and Snyder)
11:00 Mario Santos Sousa (Madrid, Spain)
Numbers Incorporated: Numerical representations and their distinctive structural features
11:45 Valeria Giardino (CNRS, Nancy, France)
Counting and numbers
12:30 – 13:30 Lunch break
Session 2 – 13.30 - 16.00
13:00 Max Jones (Bristol, UK)
Seeing Numbers as Affordances
14:30 Eric Synder (Ohio State University, USA)
Neologicism, Frege's Constraint, and the Frege-Heck Condition (Snyder, Samuels and Shapiro)
15:15 Paula Quinon (Lund, Sweden)
Conceptual Content of Arithmetical Terminology: From Number Cognition to Mature Mathematics
16:00 – 16:30 Coffee break
Session 3 – 16:30 – 18:30
16:30 Helen de Cruz (Oxford, UK)
Numerical cognition and its metaphysical implications
17:30 John Wigglesworth (LMU, Munich, Germany)
Numerical abilities and mathematical structure.
18.15 Drinks and general discussion.