My main research interests lie at the intersection between philosophy of mathematics and philosophy of science. By focusing on how mathematics is applied in science, I aim to gain insights both into traditional metaphysical and epistemological questions concerning the nature of mathematics, and into methodological questions about science.
Philosophy of Mathematics
My PhD dissertation was on the Quine-Putnam 'Indispensability Argument' for mathematical Platonism, which argues that we ought to believe in the existence of mathematical entities such as numbers and sets because our best scientific theories unavoidably quantify over such entities. Below are links to two journal articles based on chapters of my dissertation.
- The Indispensability Argument and Multiple Foundations for Mathematics [pdf]
- Mathematics, Indispensability and Scientific Progress [pdf]
More recently I have been developing an 'enhanced' version of the Indispensability Argument that focuses specifically on the explanatory role that mathematics (I claim) sometimes plays in science. This project is pursued in the following three articles:
- Are There Genuine Mathematical Explanations of Physical Phenomena?[pdf]
- Mathematical Explanation in Science [pdf]
Science-Driven Mathematical Explanation
This work has also led to a broader engagement with the topic of mathematical explanation, including whether (and, if so, how) a distinction might be drawn between explanatory and non-explanatory proofs of mathematical theorems.
- Mathematical Accidents and the End of Explanation [pdf]
- Mathematical Induction and Explanation [pdf]
Another interest of mine conerns methodological issues within mathematics, and in particular the use of 'experimental' methods in mathematics.
Philosophy of Science
I am pursuing research on various more general issues in the philosophy of science, including
- theory choice, especially appeals to simplicity and to simplicity-related principles such as Occam's Razor
- Simplicity [web link]
- Quantitative Parsimony and Explanatory Power [pdf]
- scientific models, especially the role of idealization and issues involving fictionalism and explanation
Following the award of a 'New Directions' Fellowship from the Andrew W. Mellon Foundation, I spent the 2008 - 09 academic year in England investigating the newly emerging field of complexity science. I am interested in several conceptual and methodological issues connected to complex systems, including
- definitions of complexity
- the concept of emergence and its relation to complexity
- the rise of the 'network approach' to the study and analysis of complex systems
- explanation in complex systems
In 2012 I received follow-up funding from the Mellon Foundation for further work in the area of complex systems. This has led to a collaboration with Stuart Kauffman (MacArthur fellow, and one of the founders of the Santa Fe Institute) using formal games to investigate emergence in complex systems.
In addition to the papers mentioned above, links to other of my publications can be found at http://www.swarthmore.edu/library/facbib/detail.php?author=Baker,%20Alan%20R.
Article: "Philosopher in Residence" on my 2006 stay at Whitehall, George Berkeley's former home in Middletown, RI
Faculty Lecture: "Experimental Mathematics, Armchair Physics", Swarthmore College, November 2007
New York Times feature on "Multiple-Choice Philosophy", featuring questions (and answers) from my midterm exam for Phil 1 (Paradox and Rationality)
On a trip to Japan in 1996 I discovered the Japanese version of chess, known as shogi. I returned with a portable, magnetic shogi set and since then have become fascinated with the game. In 2004 I founded the Swarthmore College Shogi Club, which remains - as far as I know - the only college shogi club outside Japan. In 2008 I won the 13th U.S. Shogi Championship, held in Chicago. Later that same year I represented the U.S. at the 3rdWorld Shogi Forum in Japan, winning the bronze medal. In April 2011, Swarthmore College hosted the U.S. Shogi Championship.
- "Shogi and Me" [feature story from Swarthmore College homepage]
- Report on the 3rd World Shogi Forum
- Report on the 150th Anniversary of the first recorded shogi game in America
Prior to my discovery of the Japanese version of the game, I was a keen chess player, and I continue to enjoy playing chess. While a student at the University of Cambridge, I played twice in the Oxford-Cambridge Varsity Chess Match (in 1990 and 1991), the oldest annual chess fixture in the world. In 1998 I won the New York State Amateur Chess Championship.
I am an active squash player and a member of the Healthplex Sports Club. During my three years living in the Midwest, I represented Cincinnati in the annual Hahn Cup tournament against Louisville and Indianapolis. I was Assistant Coach of the Swarthmore College Men's Squash team from 2009 to 2011.
I am a keen cyclist and have undertaken cycle trips of various lengths in over 20 countries. These include three major trips during my undergraduate college days. The first was from England to the northern edge of the Sahara desert (via France, Andorra, Spain, and Morocco). The second was around Lake Victoria in East Africa (through Kenya, Tanzania, Burundi, Zaire, and Uganda). The third was from France to Istanbul (via Switzerland, Germany, Czechoslovakia, Hungary, Romania, and Bulgaria).