Abstraction: Philosophy and Mathematics

Abstraction: Philosophy and Mathematics 
Summer school and workshop
University of Oslo, 22 - 24 May 2014

Organized by Salvatore Florio and Øystein Linnebo


THEME

According to Frege, the notion of abstraction has a central role to play in a philosophical account of classical mathematics. For instance, Frege regarded the direction of a line as somehow "abstracted from" the line in question, governed by the principle that the direction of one line is identical with the direction of another just in case the former line is 
parallel with the latter. Principles of this form are known as abstraction principles and play a central role in the neo-Fregean abstractionist programme initiated by Bob Hale and Crispin Wright. 
   This combined summer school and workshop aims to take stock of the abstractionist programme after three decades of intensive philosophical and technical study, as well as to make progress on some questions that have recently received much attention, such as the metaontology of abstraction and the variety of responses to the bad company problem, including the possibility of a more "dynamic" approach to abstraction (recently advocated by Øystein Linnebo, James Studd, and others), which sees abstraction as a process whereby ever greater domains of abstracta are "generated".

SPEAKERS

Francesca Boccuni, Sean Ebels-Duggan, Matti Eklund, Bob Hale, Graham Leach-Krouse, Øystein Linnebo, Jonathan Payne, Agustín Rayo, Stewart Shapiro, James Studd, Sean Walsh, Crispin Wright


FUNDING

This event is made possible by the generous support of Kansas State University and the University of Oslo. 

SCHEDULE

THURSDAY, MAY 22 

9:15 – 9:30: Welcome

9:30 – 11:00: Tutorial on the state of the art and metaontology of abstraction by Matti Eklund and Bob Hale

11:15 – 12:30: Jonathan Payne, "Neo-Fregeanism and Quantifier Variance"

Lunch

1:30 – 2:45: Øystein Linnebo, "Recarving of Content"

3:00 – 4:15: Matti Eklund, "Neo-Fregeanism and Obstacles to Existence"

4:30 – 5:45: Graham Leach-Krouse, "Structural Abstraction Principles"

7:00: Dinner



FRIDAY, MAY 23  

10 - 11: Tutorial on abstraction beyond arithmetic by Stewart Shapiro

11:15 – 12:30: Francesca Boccuni, "A Theory for Fregean Concepts and Objects"

Lunch

1:30 – 2:45: Bob Hale, "Definition by Abstraction"

3:00 – 4:15:  Sean Ebels-Duggan and Sean Walsh, "Relative Categoricity of Abstraction Principles"

4:30 – 5:45: Crispin Wright, "What Was Frege's Mistake?"

7:00: Dinner



SATURDAY, MAY 24 

9.30 – 11.00: Tutorial on bad company and dynamic abstraction by Øystein Linnebo and James Studd

11.15 – 12.30: Stewart Shapiro, "Intuitionistic Frege's Theorem"

Lunch

1.30 – 2.45: James Studd, "Abstraction Reconceived"

3.00 – 4.15: Agustín Rayo, "Compositionalism"


For any questions, please contact Salvatore Florio at [email protected]