Mathematics and Scientific Representation now available for Google preview

Despite not actually being in print, my forthcoming book can now be previewed on Google books here.

Mathematics and Scientific Representation book cover

My book Mathematics and Scientific Representation will soon be released. Here is the recently unveiled book cover:

More substantial discussions of the book's contents will be added here soon!

Classic Mr. Show: 24 is the highest number

Some inspiration to start the semester:

The unplanned impact of mathematics (Nature)

Peter Rowlett has assembled, with some other historians of mathematics, seven accessible examples of how theoretical work in mathematics led to unexpected practical applications. His discussion seems to be primarily motivated by the recent emphasis on the "impact" of research, both in Britain and in the US:

There is no way to guarantee in advance what pure mathematics will later find application. We can only let the process of curiosity and abstraction take place, let mathematicians obsessively take results to their logical extremes, leaving relevance far behind, and wait to see which topics turn out to be extremely useful. If not, when the challenges of the future arrive, we won't have the right piece of seemingly pointless mathematics to hand.

For philosophers, the most important example to keep in mind, I think, is the last one, offered by Chris Linton: the role of Fourier series in promoting the later "rigorization" of math:

In the 1870s, Georg Cantor's first steps towards an abstract theory of sets came about through analysing how two functions with the same Fourier series could differ.

Rowlett has a call for more examples on the BSHM website. Hopefully this will convince some funding agencies that immediate impact is not a fair standard!

Revised SEP Entry: Mathematical Explanation

The Stanford Encyclopedia Entry on "Mathematical Explanation" has just been updated and revised. Thanks to Paolo Mancosu for this important resource!

Babies are Bayesians?

From the abstract of a recent paper in Science:

When 12-month-old infants view complex displays of multiple moving objects, they form time-varying expectations about future events that are a systematic and rational function of several stimulus variables. Infants’ looking times are consistent with a Bayesian ideal observer embodying abstract principles of object motion. The model explains infants’ statistical expectations and classic qualitative findings about object cognition in younger babies, not originally viewed as probabilistic inferences.

Group Selection Explains "Why We Celebrate a Killing"?

In an otherwise thoughtful piece in the New York Times on the reactions to Bin Laden's killing, Jonathan Haidt throws in a weird flourish

There’s the lower level at which individuals compete relentlessly with other individuals within their own groups. This competition rewards selfishness.

But there’s also a higher level at which groups compete with other groups. This competition favors groups that can best come together and act as one. Only a few species have found a way to do this. ...

Early humans found ways to come together as well, but for us unity is a fragile and temporary state. We have all the old selfish programming of other primates, but we also have a more recent overlay that makes us able to become, briefly, hive creatures like bees. Just think of the long lines to give blood after 9/11. Most of us wanted to do something — anything — to help.

So,

last week’s celebrations were good and healthy. America achieved its goal — bravely and decisively — after 10 painful years. People who love their country sought out one another to share collective effervescence. They stepped out of their petty and partisan selves and became, briefly, just Americans rejoicing together.

The claim seems to be that the origins of these reactions in group selection means that displaying these reactions now is "good and healthy" because group selection benefits groups? Not the best argument, I would say.

Periodical Cicadas Invade Missouri!

Those interested in mathematical explanations of physical phenomena should take note: May 15th is the predicted date for the emergence of swarms of the "Great Southern Brood" of cicadas, whose life cycle is 13 years. More details are provided by the Columbia Missourian:

Periodical cicadas survive on a strategy of satiating their predators. They emerge in such large numbers that there will always be some left over to reproduce. After a while, predators get tired of eating the cicadas and leave them alone.

“If you walked outside and found the world swarming with Hershey Kisses, eventually you would get so sick of Hershey Kisses that you would never ever want to eat them again,” Kritsky said.

The mathematical explanation answers the question: why is their life cycle a prime number?

Why I Will Not Boycott Synthese

Yesterday Brian Leiter posted a long entry on his blog discussing the dispute surrounding a special issue of Synthese on "Evolution and Its Rivals". Leiter mentions several concerns, and I encourage anyone interested in the issue to read over what he has posted.

The main problem he identifies is that journal editors inserted the following preface to the special issue:

Statement from the Editors-in-Chief of SYNTHESE

This special issue addresses a topic of lively current debate with often strongly expressed views. We have observed that some of the papers in this issue employ a tone that may make it hard to distinguish between dispassionate intellectual discussion of other views and disqualification of a targeted author or group.

We believe that vigorous debate is clearly of the essence in intellectual communities, and that even strong disagreements can be an engine of progress. However, tone and prose should follow the usual academic standards of politeness and respect in phrasing. We recognize that these are not consistently met in this particular issue. These standards, especially toward people we deeply disagree with, are a common benefit to us all. We regret any deviation from our usual standards.

Johan van Benthem

Vincent F. Hendricks

John Symons

Editors-in-Chief / SYNTHESE

This insertion was made over the objections of the guest editors of the special issue.

Leiter calls for a boycott of the journal:

I would urge all philosophers to stop submitting to Synthese; to withdraw any papers they have submitted at Synthese; and to decline to referee for Synthese until such time as the editors acknowledge their error, and make appropriate amends.

Based on what I can find out about this, a boycott seems unwarranted. The editors of Synthese have elected to dramatically expand the number of issues they publish, and this has involved a proliferation of special issues where much of the editorial work is delegated to guest editors. Full disclosure: I am currently co-editing one such issue now. So, for me, the issue concerns the propriety of the journal editors inserting a preface over the objections of the guest editors. I believe that the journal editors should be allowed to exercise their judgment on such an issue. Of course, others might have acted differently. But the editors of the journal are ultimately responsible for the articles printed in the journal, and for this reason they should not be expected to delegate all questions about a special issue to the guest editors.

For Leiter, the issue seems to be related to debates about intelligent design. I would concede that a pattern of behavior which suggested that the editors were advocating for intelligent design at the expense of competing views would be disturbing and might warrant a boycott of the journal. However, there does not seem to be any such pattern, and a boycott would damage not only the editors, but also the many contributors whose articles meet the high standards of scholarship of a leading philosophy journal.

New Book: Scientific Structuralism

Alisa Bokulich and Peter Bokulich have edited a helpful new volume with the title Scientific Structuralism, as part of the Boston Studies in the Philosophy of Science. There are nine contributions, which approach structuralism in the philosophy of science from a variety of perspectives: ontological, epistemic, representational and even in connection with structural explanation.

Here is the table of contents:

STRUCTURAL REALISM: A NEO-KANTIAN PERSPECTIVE, Michela Massimi
IN DEFENCE OF ONTIC STRUCTURAL REALISM, Steven French and James Ladyman
STRUCTURALIST APPROACHES TO PHYSICS: OBJECTS, MODELS, AND MODALITY, Katherine Brading
MATHEMATICAL STRUCTURAL REALISM, Christopher Pincock
STRUCTURAL EMPIRICISM, AGAIN, Otávio Bueno
STRUCTURAL REALISM: CONTINUITY AND ITS LIMITS, Ioannis Votsis
STRUCTURALISM ABOUT SCIENTIFIC REPRESENTATION, Martin Thomson-Jones
ONTIC STRUCTURAL REALISM AS A METAPHYSICS OF OBJECTS, Michael Esfeld and Vincent Lam SCIENTIFIC EXPLANATION AND SCIENTIFIC STRUCTURALISM, Mauro Dorato and Laura Felline

Some readers should be able to access the book online here.

Postdoc at University of Calgary in Logic/Philosophy of Science

Here is another exciting opportunity for those working in logic or the philosophy of science!

Is experimental philosophy a part of science?

If we can trust the journal Science, then the answer is "yes".

PhD Fellowships in Mathematical Philosophy at Munich

Here is an exciting, and rare, opportunity for students pursuing the philosophy of mathematics.

Mathematics and Scientific Representation, Claim 3: Some Contributions

Continuing the key claims of my book, once we have decided to individuate contributions by content, it is natural to consider several different contributions:

3. A list of these contributions should include at least the following fi ve: concrete causal, abstract acausal, abstract varying, scaling and constitutive.

The contrast between concrete causal and abstract acausal is perhaps the most intuitive. Many successful scientific representations purport to accurately represent the causal relationships which obtain in a target system. Different accounts of causation present different views on what this special causal content comes to. For example, one may require the representation of a certain sort of process or mechanism. Alternatively, approaches like Woodward's insist only on the representation of what would happen under a certain kind of intervention or manipulation of the system. If this is how we understand causal representations, then it is clear that many representations are acausal. They may abstract away from the constituents and their causal interactions. This can happen in several ways. In this chapter of the book I consider how mathematics helps both with causal representations and with acausal representations.

There is a second sort of abstraction: abstraction by varying. In this case, we have a family of representations with a different physical interpretation, but with a core overlap in their mathematics. In such cases, the mathematical links between the representations take center stage. It may be the case that all members of the family are causal representations, or some may abstract away from causes.

Aspects of many successful representations turn on considerations of scale. The scale of a feature can be thought of as a comparison between that feature and some given parameters. So, for example, we may consider the relative time scales of two processes and use this comparison to adjust our representation of some target system. More generally, procedures for understanding the relative scale of this or that magnitude are central to simplification and idealization. Unsurprisingly, there is a central place for mathematics in determining which manipulations are acceptable and what the best interpretation of the resulting representations should be.

Finally, I distinguish between constitutive and derivative representations. As neutrally as possible, we can think of a derivative representation as one which is successful only if some related 'constitutive' representations are successful. Carnap, Kuhn and Michael Friedman have all tried to motivate this distinction, and for each philosopher mathematical claims play a central role in the story. I side largely with Friedman on the need for constitutive representations, but try to pin down exactly what sort of success is at issue and how these two sorts of representations are related.

Mathematics and Scientific Representation, Claim 2: Individuate Contributions via Content

With the move to Missouri complete and my book safely in press, there is now an opportunity to continue blogging through the key claims of the book. The first key claim is that mathematics contributes many things to the success of science. Next comes

2. These contributions can be individuated in terms of the contents of mathematical scienti c representations.

In principle, we might divide up the contributions which mathematics makes in any number of ways. These include historically, by scientific discipline, by the most successful and by mathematical technique. But it seemed most productive to consider different sorts of scientific representations, where the 'sorts' were isolated by the content of that representation. The hope is then that representations are available which are more or less pure instances of this or that kind of representation. And, for the successful representations, we can then look at the mathematics and see how it is contributing to the success of that sort of representation.

Approached in this way, there is a crucial difference between two ways in which some parts of mathematics might relate to a given representation. Some mathematics will be intimately part of the mathematics, in the following sense: the content of the representation is that some mathematical structure bears some structural relation to a target system, under some interpretation. So, the mathematics related directly to that structure is what I call intrinsic to the representation. This has immediate consequences for grasping the content of the representation, which I think of as given by the accuracy conditions for that representation. To understand the representation, one must believe that the claims of the intrinsic mathematics are true.

On the other hand, there may be additional mathematical claims which are extrinsic to the representation, but which are still relevant to the success of that representation. As a central example, consider the case where some stronger mathematical theory is deployed to solve the equations given in some weaker mathematical theory. It is wrong to say that an understanding of the representation requires a belief in the stronger mathematical claims, but these claims are still relevant to a consideration of the ultimate success of the representation. More generally, the mathematical relationships between representations may go beyond the intrinsic mathematics of the representations, but these relationships can still be central to an account of the success of the representations.