Introduction

Hartry Field's Science Without Numbers (Princeton University Press) was published in 1980. Since then it has become one of the most influential works in the philosophy of mathematics. It contains an original defense of mathematical nominalism, the thesis that mathematical objects such as numbers, functions, and sets do not exist, and a response to the indispensability argument that aims to show that we should believe in mathematical objects because they are indispensable to our successful scientific theories. Field's defense rests on an ingenious and ambitious project of reformulating physical theories in such a way that they no longer refer to mathematical objects at all. Over the last 40 years, the book has produced a large body of literature and its influence can be felt in several subfields of philosophy.

This workshop aims to provide an opportunity to discuss Field's program in light of recent developments in philosophy of mathematics, philosophy of physics, philosophy of logic, and metaphysics.

(An earlier version of the workshop was scheduled as a symposium session at the 2020 Pacific Division meeting of the American Philosophical Association. It was cancelled due to COVID-19.)

Logistics

Organizers: Thomas Barrett (UC Santa Barbara) and Eddy Keming Chen (UC San Diego).

For questions and more information, please email eddykemingchen@ucsd.edu

Conference Program

Note: all times are in Eastern Standard Time (New York time)

November 5, 2020

2:45-3:00 pm Welcome (organizers)

3:00-4:00 pm Mark Colyvan (University of Sydney). "The Explanatory Turn in the Philosophy of Mathematics."

Response from Hartry Field (NYU)

4:00-5:00 pm Mary Leng (University of York). "Science - or Mathematics - Without Numbers?"

Response from Hartry Field

5:00-5:40 pm Open discussion

November 6, 2020

3:00-4:00 pm Eddy Keming Chen (University of California, San Diego). "Varieties of Intrinsicality and the Hardest Road to Nominalism"

Response from Hartry Field

4:00-5:00 pm Vera Flocke (Indiana University Bloomington). "Carnap’s Defense of Quantified Modal Logic"

Response from Hartry Field

5:00-6:00 pm Stephen Yablo (MIT). "Two Roads Diverged: Why Was One Harder?"

Response from Hartry Field

6:00-6:40 pm Open discussion

Lecture slides and video recordings

Day 1.

Mark Colyvan (University of Sydney). "The Explanatory Turn in the Philosophy of Mathematics"

Mary Leng (University of York). "Science - or Mathematics - Without Numbers?"

Open Discussion on Day 1

Day 2.

Eddy Keming Chen (University of California, San Diego). "Varieties of Intrinsicality and the Hardest Road to Nominalism"

Vera Flocke (Indiana University Bloomington). "Carnap’s Defense of Quantified Modal Logic"

Stephen Yablo (MIT). "Two Roads Diverged: Why Was One Harder?"

Open Discussion on Day 2

Participants

Zita Toth, Yuxi Shen, Younes, Yoshihiro Maruyama, Ying Yao, Yifeng Ding, Yao Fan, Xuan Zhu, William Melanson, Weixin Cai, Wei Zeng, Wade Fu, Tomasz Bigaj, Thorben Petersen, Thomas Barrett, Theodore Scaltsas, Susan Hahn, Soowhee Kang, Shimpei Endo, Sherif Salem, Shelly Shi, Seungil Lee, Sebastián Gil, Samuel Schindler, Samuel Elgin, Safia Bano, Ryan Light, Rosalind Chaplin, romil rawat, Rodolfo Hernandez, Robin Berjon, Robert Knowles, Robert Calabro, Rick Lamb, Richard E. Hennessey, Renee Ye, Qiong Wu, Pixie Shen, Pixie Shen, Peter Tan, Paul Hasselkuß, Patrick Walsh, palma, Pablo Dopico, Oliver Kutz, Nurit Matuk, Nuno Maia, Nikolay Shilov, Niki Pfeifer, Nathaniel Gan, Naomi Thompson, Michael Miller, Michael Liston, Mehmet Onur Canpolat, Matthew Turyn, Mashhood Safar, Markus Pantsar, Mark Silcox, Mario Santos-Sousa, Mario Hubert, Manuel Barrantes, Mahmoud Jalloh, Maaneli Derakhshani, Luis Rosa, luca, Louis Doulas, Louis deRosset, Lorenzo Cocco, Laura Franklin-Hall, Korbinian J. Kettnaker, Klarise Marais, Keith Dyck, Justin Clarke-Doane, Juliette Kennedy, Juliette Benitez, Juliette Benitez, Juha Saatsi, Joshua Babic, Josh Hunt, Jon Charry, John Wigglesworth, John Rediske, John P. Burgess, John Barnden, Joan Joel Caceres Ramirez, Jens Jäger, Jenn McDonald, Jeffrey N. Bagwell, James Robert Brown, James Franklin, Jaime Castillo-Gamboa, Jackson LeViness, Jack Himelright, Jace Snodgrass, Jabran, Isaac Wilhelm, Inger Bakken Pedersen, Ian Dunbar, Huub Vromen, Hazhir Roshangar, Hans Halvorson, Hannah Kim, Haggeo Cadenas, Guy Hetzroni, Giang Le, Geoffrey D Hall, Geoffrey D Hall, Gareth R Pearce, Gabriel Târziu, Francisco Pipa, Franci Mangraviti, Fatemeh Shakibafard, Ezra Rubenstein, Evelyn Brylow, Erica, Emmanuel Bilodeau, Sushobhona Pal, Diego Arana, David Schroeren, David J Baker, Daniel Pinkel, Daniel Maher, Daniel Kostic, Daniel Hoek, Daniel Berntson, Cristian Soto, Craig Callender, CONCHA MARTÍNEZ-VIDAL, Clare Moriarty, Christopher Menzel, Christina Kalogeropoulou, Caspar, Byeong-uk Yi, Brian Porter, Brad Weslake, Ben Middleton, Bahram Assadian, Auste Luksaite, Auste, Augie Faller, Ashley Crelin, Anya Yermakova, Anusha Bhattacharya, Annette Zimmermann, Anggha Nugraha, Andy Sin, Andrew Aberdein, Andreas Lüchinger, Andre Mirabelli, Amir Maleknia, Alexander Skiles, Alexander M Aizenman, Alex LeBrun, Alex Fisher, Albinas Plesnys, Ainsley Pullen, Aditya Jha, Achim Vesper