Saturday, September 7, 2013
Wednesday, April 24, 2013
The October 2012 issue of Mind (posted today here) has an extended discussion section where mathematical fictionalists of various stripes respond to Colyvan's earlier article "There is No Easy Road to Nominalism". The discussion concludes with a detailed reply by Colyvan. While I am a fan of neither Colyvan's explanatory indispensability argument nor its fictionalist critics, I look forward to reading this discussion and engaging with it soon!
Jody Azzouni Taking the Easy Road Out of Dodge Mind (2012) 121(484): 951-965
Otávio Bueno An Easy Road to Nominalism Mind (2012) 121(484): 967-982
Mary Leng Taking it Easy: A Response to Colyvan Mind (2012) 121(484): 983-995
David Liggins Weaseling and the Content of Science Mind (2012) 121(484): 997-1005
Stephen Yablo Explanation, Extrapolation, and Existence Mind (2012) 121(484): 1007-1029
Mark Colyvan Road Work Ahead: Heavy Machinery on the Easy Road Mind (2012) 121(484): 1031-1046
Thursday, April 11, 2013
Prominent biologist and science writer E. O. Wilson has a provocative Wall Street Journal opinion piece about the link between mathematical ability and scientific achievement. Perhaps the central ambiguity of his argument is illustrated by the two different titles the article seems to have. The browser heading is "Great Scientists Don't Need Math", while the actual title is "Great Scientist Does not Equal Good at Math". While the latter claim is almost trivial, the former claim seems very contentious. Of course, I am biased on this issue, having written a book arguing that mathematics makes several crucial contributions to the formulation and justification of our scientific knowledge. But setting that philosophical discussion aside, it is somewhat disturbing to find such a simplistic view of the way mathematics helps in science being presented by such a distinguished scientist.
Wilson's basic idea is that great scientists don't need to be good at math because they can always call on specialists in the relevant areas of mathematics. On Wilson's picture, the great scientists come up with great ideas, and these ideas are then implemented and tested via mathematical models. But the ideas themselves are completely non-mathematical:
Fortunately, exceptional mathematical fluency is required in only a few disciplines, such as particle physics, astrophysics and information theory. Far more important throughout the rest of science is the ability to form concepts, during which the researcher conjures images and processes by intuition.
Everyone sometimes daydreams like a scientist. Ramped up and disciplined, fantasies are the fountainhead of all creative thinking. Newton dreamed, Darwin dreamed, you dream. The images evoked are at first vague. They may shift in form and fade in and out. They grow a bit firmer when sketched as diagrams on pads of paper, and they take on life as real examples are sought and found.
Pioneers in science only rarely make discoveries by extracting ideas from pure mathematics. Most of the stereotypical photographs of scientists studying rows of equations on a blackboard are instructors explaining discoveries already made. Real progress comes in the field writing notes, at the office amid a litter of doodled paper, in the hallway struggling to explain something to a friend, or eating lunch alone. Eureka moments require hard work. And focus.
Ideas in science emerge most readily when some part of the world is studied for its own sake. They follow from thorough, well-organized knowledge of all that is known or can be imagined of real entities and processes within that fragment of existence. When something new is encountered, the follow-up steps usually require mathematical and statistical methods to move the analysis forward. If that step proves too technically difficult for the person who made the discovery, a mathematician or statistician can be added as a collaborator.Now, it is clear that some ideas that drive scientific discoveries are non-mathematical. But I do not see much evidence that most of these ideas are like that or that scientists should trust non-scientists to implement their ideas in mathematical terms. It is precisely at this stage that some of the most important and innovative work is done, and it is not clear to me how collaborations can work if one side, the scientist, doesn't understand what the other side, the mathematician, is doing.
See here for another critique of Wilson.
Friday, January 25, 2013
First, there is Early Analytic Philosophy 7, hosted by Indiana-Purdue University, Fort Wayne during the weekend of March 15th. The keynote speaker is Michael Mi of Soochow University (Taiwan). The call for papers for this conference closes on Feb. 15th. See here for more details.
Later in the spring, Indiana University will host the Society for the Study of the History of Analytic Philosophy 2 conference. It is scheduled for the weekend of May 9th. The keynote speakers are Warren Goldfarb (Harvard), Joan Weiner (Indiana) and Peter Sullivan (Stirling). The call for papers for this conference closes on March 1st. See here for more details.
Thursday, January 24, 2013
Monday, January 7, 2013
Friday, January 4, 2013
The first is by Stuart Rowlands and was published in the journal Science and Education. The review summarizes the book and makes links to those working in education. I was pleased with how well the author was able to relate the more obscure debates in philosophy that I talk about to questions in science education.
The second is by Juha Saatsi and appeared in the Notre Dame Philosophical Reviews. Juha and I have been working on these topics from somewhat different perspectives for quite a while, so I really appreciated his critical feedback on the book. I think it is fair to say that he is generally quite positive, although he raises a few objections at the end. The most substantial objection concerns my worries about explanatory indispensability arguments for realism about mathematical truth. I claim that plausible restrictions on inference to the best explanation (IBE) undermine these arguments. It is hard to find a good version of IBE that justifies interesting mathematical claims like that there are infinitely many primes.
Saatsi worries that my restrictions on IBE are too restricted:
Although I won't argue for this here, it seems to rule out typical IBEs that some scientific realists take to support our best high-level theories, because such theories can often be replaced with a weaker explanans the content of which falls much short of the theory as a whole. Even if such a replacement is quite arbitrary and unmotivated from the theory's perspective, for a sceptic who has not yet accepted the theory it is an epistemic possibility that only the weaker explanans is true. So, by Pincock's lights, the theory on the whole cannot enjoy any justification deriving from its explanatory success. This 'anti-holistic' viewpoint goes against the view that a theory -- the whole theory -- with appropriate theoretical virtues can enjoy a degree of confirmation by virtue of furnishing us with a good explanation.This is a fair point that I would like to continue to work on. First, what is a plausible form of IBE and, second, what sort of scientific realism does it really warrant if it is does not warrant new beliefs in mathematical truths?
Wednesday, January 2, 2013
A new project that I would also like to discuss is more under the heading of Mathematics and Scientific Change. It appears to me that scientists have gotten better over time at using mathematics in science in ways that avoid a few problems. The main problem I raise in the book is that we don't typically know the right interpretation for a bit of successful mathematics, and it is often not clear that the mathematics should be assigned any physical interpretation. So I now hope to trace out some of ways mathematics was used and misused over the last two or three hundred years. A first step: working through Harper's exciting new book Isaac Newton's Scientific Method.