New Book: Colyvan, Introduction to the Philosophy of Mathematics

Readers of this blog will be happy to see in print Mark Colyvan's An Introduction to the Philosophy of Mathematics (Cambridge) (Amazon, Google). I have not had a chance to read it yet, but the table of contents looks very encouraging. While traditional questions seem to be addressed in the early chapters, the later chapters take up such topics as fictionalism, mathematical explanation and applicability. There is also an intriguing "epilogue" at the end where mathematical results of general philosophical interest are discussed. Hopefully this introduction will mark a helpful complement to Stewart Shapiro's excellent introductory volume from Oxford.

Note: as part of my move to Ohio State, I have moved all my files to a new webpage: http://pincock-yilmazer.com/chris/. So, some old links on this blog will no longer work. If you can't find something on the new webpage, just let me know.

Preview of Special Issue from Models and Simulations 4

Most of the papers from the special issue of Synthese that I co-edited with Marion Vorms are now online. These papers represent a selection from the Models and Simulations 4 conference. Thanks to my co-editor, the authors and especially all the referees for their contributions to making this issue possible!
Marion Vorms and Christopher Pincock, Preface
Paul Teller, The concept of measurement-precision
Agnes Bolinska, Epistemic representation, informativeness and the aim of faithful representation
Brian Epstein and Patrick Forber, The perils of tweaking
Gordon Purves, Finding truth in fictions: Identifying non-fictions in imaginary cracks
Axel Gelfert, Strategies of model-building and the role of trade-offs in condensed matter physics
Peter Gildenhuys, Classical population genetics and the semantic approach to scientific theories
Marion Vorms, Models of data and theoretical hypotheses: A case-study in classical genetics
Ekaterina Svetlova, De-idealization by commentary: The case of financial valuation models
I will add the links to the remaining papers when they are available.
Update (1/2013): The issue has now been published here.

Conference: Society for the Study of the History of Analytical Philosophy

From May 24-26 at McMaster University, the first annual conference of the Society for the Study of the History of Analytical Philosophy will be held. The keynote speakers are Michael Friedman, Paolo Mancosu and Thomas Uebel. Additional information is available here. Thanks go to Sandra Lapointe for all her hard work of organizing and hosting!

New Book: Mancosu, The Adventure of Reason

While it came out in 2010, some of the readers of this blog may still not be aware of this important collection of Mancosu's articles on the interactions between logic and philosophy in the 1900-1940 period. I recently completed a summary of the book's contents for Zentralblatt Math that might be useful.

Vincent on Mander on British Idealism

Andrew Vincent provides a positive and helpful overview of Mander's recent book, British Idealism: A History. Based on Vincent's summary, it appears that Mander supports the claim that early analytic philosophers never actually "refuted" British idealism, at least in the sense of finding an argument from premises that the idealists themselves would have accepted. Another important theme of the book is the way in which British idealism arose as a reaction to empiricism and naturalism. This a point that Wollheim explored in his now classic study of Bradley. If British idealism is a reaction to British empiricism, especially Mill, then it is hard to accept something else that Vincent says:

In addition to the above philosophical influences, there was a range of issues and debates which also contributed to the rise and popularity of Idealism. For example, Idealism did respond very effectively to the social issues of the time. It was a philosophy that radiated optimism at a time of extreme social dislocation and pessimism concerning the appalling social and industrial conditions of the age. It offered a philosophy and a form of sophisticated understanding of political practice that gave a much needed emphasis to social cohesiveness and to the closeness of the relation between individual and collective responsibility. Its highlighting particularly of the importance of active social citizenship subsequently became an important theme in the early twentieth-century politics of welfare. In this sense many aspects of its output became associated, in some interpretations, with the development of a new social liberalism in the period from 1906 to 1914.

In the case of Bradley, at least, this seems implausible. I get the sense reading Bradley that it was the link between Mill's empiricism and Mill's liberalism that motivated Bradley to attack Mill's empiricism so thoroughly.
A point which Vincent emphasizes and which is more plausible is the internal divisions within British idealism:

By the later 1890s and early 1900s, younger members of the Idealist school began to divide up into factions. The key binary (although it is still a marked simplification) was between Absolute Idealists (Caird, Bradley and Bosanquet) and Personal Idealists (Andrew Seth Pringle Pattison, C.C.J. Webb, Hastings Rashdall, Boyce-Gibson, Henry Sturt and McTaggart). Absolute idealism, because it tried largely to characterise the totality of experience, was indicted for a multitude of crimes. It was accused of losing God in man, or man in God; dissolving things into thought; matter into spirit; abolishing all right and wrong; and truth and error. Its comprehensiveness and inclusivity was a virtue for some, but it was also the source of major problems for others. Idealist and non-Idealist critics alike were concerned largely about the idea of a unity above and beyond the individuals who comprised it, and which had a will of its own. This doctrine of the Absolute can also be found, to a degree, in Green's problematic idea of the eternal consciousness, as well as in Hegel's notion of Geist. What role God has in relation to these terms remained a divisive and unresolved issue, even among the more Absolutist-inclined thinkers. The metaphysical, moral and political danger of a diminution of the individual and subordination to a 'higher' entity was connected by some critics, such as L.T. Hobhouse, to both German militarism and the conflict of the First World War. These critics of Idealism became known as the Personal Idealists. Amongst them, though, there was -- as amongst the Absolute Idealists -- a good deal of internal diversity of opinions. The Absolute / Personalist debate is most vividly illustrated in a meeting of the Aristotelian Society in July 1918 entitled 'Do individuals possess a substantive or adjectival mode of being?'

I hope that Mander's book and other scholarship on the internal history of idealism can lead to new contacts with historians of analytic philosophy who are not always ready to recognize the important internal divisions within their own movement.

"In Stock"

After a bit of a delay, I am happy to announce that my book is now in stock on the Oxford University USA page. Hopefully sales will soon be possible on Amazon and other online retailers as well!

Bursten Against "Mathturbation"

Over at Reaction Crate, Julia Bursten has a strong (and somewhat humorous) take on the role of what she calls "mathturbation" in the philosophy of physics. This seems to be the practice of deploying more math than is needed when making a philosophical argument:

When I am learning math for the sake of learning math, then understanding an equation is its own reward. When I am learning math to try to understand someone’s philosophical point, there had damn well better be a philosophical point at the end of it, and the math had better be necessary to make the point. Otherwise, to return to the road-trip analogy, I’m going to feel like I just blew a tank of gas for nothing. Essays that purport to be philosophical but are really just math lessons, and essays that contain math lessons that have little to do with the paper’s philosophical point, are the ones I find objectionable and mathturbatory.

This is a fair point, but it raises the more general question for me about how far one should go to make an argument accessible and also how narrowly we should think of the range of genuine philosophical problems.
On the first issue, it is sadly sometimes the case that a philosophical argument does require a certain amount of technical background material. In my own work, I try to recognize a certain kind of diminishing returns: eventually too much technical background for too little philosophical return tends to lead to a paper that goes nowhere. This is especially the case when the philosophical issues involve general philosophy of science, epistemology or metaphysics. If your target audience is not likely to appreciate the background you are drawing on, then there is little value in going down that road.
Still, I do not think that philosophers inclined to pursue the philosophical questions that arise in more technical areas should always give in to the low odds that an average reader will see what they are up to. In certain cases, it is very valuable to come across a case study or historical episode that one does not understand. This can shake one's confident pronouncements on how a given philosophical question should be resolved and give a philosopher a real motivation to go out and learn something new. This is one function of more technical material: it can draw attention to complications that more ordinary cases overlook or suppress.
Let me be clear that I doubt Julia would object to either of these points!

Ian Stewart on Black-Scholes

The influential mathematician and writer Ian Stewart has a short article in a recent Guardian that considers the idea that the Black-Scholes model of option pricing contributed to the financial collapse. (Thanks to Ole Hjortland for the link.) As I summarized things back in October 2009, the derivation of the central partial differential equation is quite accessible, and involves the sorts of idealizations that we'd be happy to make in most other areas of science. In my book I discuss the case of Long-Term Capital Management (LTCM) and the ways in which its trading strategies appear to have been misled by the mathematical model itself. One dimension of the problem is noted by Stewart:

Any mathematical model of reality relies on simplifications and assumptions. The Black-Scholes equation was based on arbitrage pricing theory, in which both drift and volatility are constant. This assumption is common in financial theory, but it is often false for real markets. The equation also assumes that there are no transaction costs, no limits on short-selling and that money can always be lent and borrowed at a known, fixed, risk-free interest rate. Again, reality is often very different.

In particular, the volatility estimate based on recent trading history will be reliably too low when a market enters a new period of instability and resulting higher volatility. If traders miss this change, then they will see what look like ideal arbitrage opportunities. This is what mostly what sunk LTCM and seems to underlie many more recent failures as well.

How Widely Known is Broad's Anticipation of Jackson's Knowledge Argument?

As part of my seminar on emergence and reduction we spent two weeks reviewing the classic discussions of Mill and Broad, along with McLaughlin's helpful paper "The Rise and Fall of British Emergentism." One interesting feature of these early discussions that McLaughlin relegates to his interesting footnotes is the perennial appeal to qualia. In particular, it is striking to come across the following passage from Broad's 1925 The Mind and its Place in Nature:

We have no difficulty in conceiving and adequately describing determinate possible motions which we have never witnessed and which we never shall witness. We have merely to assign a determinate direction and a determinate velocity. But we could not possibly have formed the concept of such a colour as blue or such a shade as sky-blue unless we had perceived instances of it, no matter how much we had reflected on the concept of Colour in general or on the instances of other colours and shades which we had seen. It follows that, even when we know that a certain kind of secondary quality (e.g., colour) pervades or seems to pervade a region when and only when such and such a kind of microscopic event (e.g., vibrations) is going on within the region, we still could not possibly predict that such and such a determinate event of the kind (e.g., a circular movement of a certain period) would be connected with such and such a determinate shade of colour (e.g., sky-blue). The trans-physical laws are then necessarily of the emergent type.

This should remind anyone of Jackson's famous Knowledge argument involving the physicist Mary who knows the correct physical theory of color, but who lacks color experiences. I would not say that the arguments are identical, of course. Jackson is arguing against physicalism, while Broad is arguing against what he calls mechanism. But both physicalism and mechanism have reductive implications, and the appeal to color experience in both cases to block this sort of reduction is quite similar.
This made me wonder how widely known this sort of overlap is, and if there are obvious antecedents that Broad is drawing on. Brie Gertler notes in her Encyclopedia of Philosophy article on the Knowledge argument that "Arguments in the same spirit had appeared earlier (Broad 1925, Robinson 1982)". And one finds a section on the Knowledge argument in Kent Gustavsson's entry on Broad in the Stanford Encyclopedia of Philosophy. Broad is also noted in the entry on the Knowledge argument by Martine Nida-Rümelin. So, maybe it is well-known.
It appears to me that Broad is drawing on the obvious chapter in Mill's Logic, especially Mill's remark that "from no knowledge of the properties of those substances could we ever predict that it [the tongue] could taste, unless gelatine or fibrin could themselves taste; for no elementary fact can be in the conclusion, which was not in the premises" (Bk. III, ch. vi, section 1). Indeed this style of argument could perhaps be traced back to Locke's Essay and God's power to superadd the power of thinking to matter (Bk. IV, ch. III, section 6).
Update (Feb. 13): Chalmers has drawn my attention to two prominent discussions of Broad's knowledge argument: Stoljar's introduction to There's Something About Mary and Chalmers' own "Consciousness and its Place in Nature".

Babies are Newtonians?

Following an earlier post noting the apparent Bayesian tendencies of babies, we now have word for fellow University of Missouri professor Kristy vanMarle that babies have innate knowledge of Newtonian physics.
From the Yahoo News summary "Infants Grasp Gravity with Innate Sense of Physics":

"We believe that infants are born with expectations about the objects around them, even though that knowledge is a skill that's never been taught," Kristy vanMarle, an assistant professor of psychological sciences at the University of Missouri, said in a statement. "As the child develops, this knowledge is refined and eventually leads to the abilities we use as adults."
To come to this conclusion, vanMarle and her colleague, Susan Hespos, a psychologist at Northwestern University, reviewed infant cognition research conducted over the last 30 years. They found that infants already have an intuitive understanding of certain physical laws by 2 months of age, when they start to track moving objects with both eyes consistently and can be tested with eye-tracking technology.
For instance, at this age they understand that unsupported objects will fall (gravity) and hidden objects don't cease to exist. In one test, researchers placed an object inside of a container and moved the container; 2-month-old infants knew that the hidden object moved with the container.
This innate "physics" knowledge only grows as the infants experience their surroundings and interact more with the world. By 5 months of age, babies understand that solid objects have different properties than noncohesive substances, such as water, the researchers found.

Note: Regular readers will notice that I have given into the Google/Blogger renovations and opted for the white background. Also, I have enabled mobile formatting for easy access to this blog on mobile devices.

Journal for the History of Analytical Philosophy: Update

About a year ago I posted an announcement of the launch of a new, open-access, peer-reviewed journal devoted to the history of analytic philosophy. I am pleased to report that 2 articles and 1 substantial book review have already appeared:
James Pearson, Distinguishing WV Quine and Donald Davidson
Francesco Orsi, David Ross, Ideal Utilitarianism, and the Intrinsic Value of Acts
Kevin Klement, Review: Gregory Landini, Russell. London and New York, Routledge 2011.
Interested readers are encouraged to subscribe to the journal's Facebook page for news and updates on new articles. Our goal is to publish articles as soon as possible after they have been through our review process.
Update (Feb. 19): The journal also has an RSS feed that will list recent articles.