Thursday, December 16, 2010

New Group: Association for the Philosophy of Mathematical Practice

On the weekend I was fortunate to attend the first meeting of a new group: the Association for the Philosophy of Mathematical Practice. This group aims to promote a somewhat different approach to the philosophy of mathematics than what has become standard. As the statement of purpose of the group puts it,
Over the last few years approaches to the philosophy of mathematics that focus on mathematical practice have been thriving. Such approaches include the study of a wide variety of issues concerned with the way mathematics is done, evaluated, and applied, and in addition, or in connection therewith, with historical episodes or traditions, applications, educational problems, cognitive questions, etc. We suggest using the label “philosophy of mathematical practice” as a general term for this gamut of approaches, open to interdisciplinary work.

In 2009, a group of researchers in this field gathered to promote the creation of the Association for the Philosophy of Mathematical Practice, APMP. This association aims to become a common forum that will stimulate research in philosophy of mathematics related to mathematical activity, past and present, and foster joint actions.

The goals of APMP are:

● to foster the philosophy of mathematical practice, that is, a broad outward-looking approach to the philosophy of mathematics which engages with mathematics in practice (including issues in history of mathematics, the applications of mathematics, cognitive science, etc.);
● to gather a group of interested people that forms a coherent community, and makes us more visible to the wider communities of, e.g., philosophers of science, historians of mathematics, mathematics educationalists, etc.;
● to stimulate research in philosophy of mathematics related to mathematics in practice, and enhance our opportunities for developing research projects;
● to facilitate the exchange of information among us in all kinds of ways, and stimulate common projects, meetings, etc.
The quality of the papers of the conference was quite high and showed, I hope, the potential for fruitful cooperation in the philosophy of mathematics between philosophers, historians, cognitive scientists, sociologists, etc.

Anyone interested in joining the association can contact me or one of the organizers listed on the site above. The next planned meeting is scheduled to occur at the Nancy Congress in July. I will post more details as they become available!

Wednesday, December 15, 2010

New Journal: Journal for the History of Analytical Philosophy

This week marks the official launch of the new Journal for the History of Analytical Philosophy. I think it is a very exciting opportunity for scholars working in this field. I would emphasize the open access character of the journal. All articles will be freely available in electronic form. The hope is that the journal can provide a forum for rigorous scholarship for the broadly conceived history of analytic philosophy.

As the mission statement of the journal indicates:
JHAP aims to promote research in and discussion of the history of analytical philosophy. ‘Analytical’ is understood broadly and we aim to cover the complete history of analytical philosophy, including the most recent one. JHAP takes the history of analytical philosophy to be part of analytical philosophy. Accordingly, it publishes historical research that interacts with the ongoing concerns of analytical philosophy and with the history of other twentieth century philosophical traditions. In addition to research articles, JHAP publishes discussion notes and reviews.
This goes some way to addressing Leiter's recent skeptical remark that "I trust they will publish articles that also explain how what used to be an actual movement in philosophy ceased to exist!" I would suggest that one of the issues worth discussing in the journal itself is the sort of position that Leiter alludes to here. But of course I also hope that more ordinary scholarship directed at questions in the history of analytic philosophers, and their relations to other philosophers, can be addressed.

The editorial team is

Editor in Chief
Mark Textor, King's College London, UK

Associate Editors
Juliet Floyd, Boston University, US
Greg Frost-Arnold, University of Nevada, Las Vegas, US
Sandra Lapointe, Kansas State University, US
Douglas Patterson, Kansas State University, US
Chris Pincock, Purdue University, US
Richard Zach, University of Calgary, CAN

Assistant Editor
Ryan Hickerson, Western Oregon University, US

Review Editor
Mirja Hartimo, University of Helsinki, FI

and the advisory board is

Steve Awodey, Carnegie Mellon University, US
Michael Beaney, University of York, UK
Arianna Betti, Free University of Amsterdam, NL
Patricia Blanchette, University of Notre Dame, US
Richard Creath, Arizona State University, US
Michael Friedman, Stanford University
Leila Haaparanta, University of Tempere, FI
Tom Hurka, University of Toronto, CAN
Peter Hylton, University of Illinois, Chicago, US
Bernard Linsky, University of Alberta, CAN
Ulrich Majer, University of Göttigen, D
Paolo Mancosu, University of California, Berkeley, US
Volker Peckhaus, University of Paderborn, D
Eva Picardi, University of Bologna, IT
Ian Proops, University of Texas, Austin, US
Erich Reck, University of California, Riverside
Alan Richardson, University of British Columbia, CAN
Thomas Ricketts, Pittsburgh University, US
Peter Simons, Trinity College Dublin, IRE
Thomas Uebel, University of Mancherster, UK
Joan Weiner, Indiana University, Bloomington, US
Jan Wolenski, Jagiellonian University, PL

Thursday, December 2, 2010

Priest on Dialetheism in the NYT

Many readers of this blog have surely already seen this, but for the rest, be sure to check out Graham Priest's wonderfully accessible take on "Paradoxical Truth" in the much criticized NYT philosophy blog.

Monday, November 15, 2010

Philosophy Viral Video?

Has Roy Cook produced the first viral video for philosophers? You decide.

Sunday, November 14, 2010

Mathematics and Scientific Representation, Claim 1: Many Contributions

In the next few weeks, I hope to go through 12 of the key claims which I try to defend in my book manuscript. At its most general, the topic of the book is how mathematics helps in science. I assume to start that science is quite successful. This success is not limited to its ability to generate consensus amongst its practitioners, but extends to its predictions and contributions to technological innovations. I more or less assume some kind of scientific realism, then, although exactly how realist we should be is part of the discussion of the book.

So, what does mathematics contribute to the success of science? I argue that
1. A promising way to make sense of the way in which mathematics contributes to the success of science is by distinguishing several diff erent contributions.
Many philosophers seem to think that there is one thing which mathematics does. Perhaps the most influential view along these lines goes back (at least) to Wittgenstein's Tractatus:
In life it is never a mathematical proposition which we need, but we use mathematical propositions only in order to infer from propositions which do not belong to mathematics to others which equally do not belong to mathematics. (6.21)
But this seems too narrow. Mathematics makes any number of contributions to the success of science, and there is no straightforward way to reduce them all to a single kind.

The problems with Wittgenstein's approach are obvious. In many cases, we have no clue what the non-mathematical inputs or outputs are supposed to be. We start with mathematical descriptions and we end with equally mathematical descriptions. Either there is something defective in scientific practice, or Wittgenstein's approach is wrong. Beyond this sort of inferential or deductive contribution, there must be other kinds of contributions. But how are we to enumerate these contributions, and is there anything to be said about what they might have in common?

Monday, October 18, 2010

Workshop: The Role of Mathematics in Science

Readers of this blog in the Toronto area may want to check out a workshop this Friday at the University of Toronto, IHPST. It is on the role of mathematics in science and the speakers are me, Margaret Morrison (Toronto), Steven French (Leeds), Alex Koo (Toronto) and Alan Baker (Swarthmore). The program is online here.

Saturday, October 16, 2010

Mandelbrot (1924-2010)

The New York Times obituary gives a useful overview of his career and contributions to applications.

Thursday, October 7, 2010

Okasha Takes On The Inclusive Fitness Controversy

In a helpful commentary in the current issue of Nature Samir Okasha summarizes the recent dispute about inclusive fitness. In an article from earlier this year E. O. Wilson and two collaborators argued that inclusive fitness (or kin selection) was dispensable from an explanation of altruistic behavior. For my purposes what is most interesting about this debate is that the Wilson argument depends on an alternative mathematical treatment which seems to get rid of the need for anything to track inclusive fitness. As a result, inclusive fitness is seen merely as a book-keeping device with no further explanatory significance.

Okasha suggests that the dispute is overblown and that each of the competing camps should recognize that a divergence in mathematical treatment need not signal any underlying disagreement. As he puts it at one point
Much of the current antagonism could easily be resolved — for example, by researchers situating their work clearly in relation to existing literature; using existing terminology, conceptual frameworks and taxonomic schemes unless there is good reason to invent new ones; and avoiding unjustified claims of novelty or of the superiority of one perspective over another.

It is strange that such basic good practice is being flouted. The existence of equivalent formulations of a theory, or of alternative modelling approaches, does not usually lead to rival camps in science. The Lagrangian and Hamiltonian formulations of classical mechanics, for example, or the wave and matrix formulations of quantum mechanics, tend to be useful for tackling different problems, and physicists switch freely between them.
This point is right as far as it goes, but my impression is that some biologists and philosophers of biology over-interpret the concept of fitness. If Wilson et. al. are correct, then there is simply no need to believe that inclusive fitness tracks any real feature of biological systems. And this interpretative result would be significant for our understanding of altruism and natural selection more generally.

Thursday, September 30, 2010

Mathematics and Scientific Representation Update

As readers of this blog are already aware, for some time now I have been working on a book called Mathematics and Scientific Representation which aims to say something useful about how mathematics helps in science. This is a project which combines elements of the philosophy of mathematics with the philosophy of science and so will hopefully be of interest to both communities.

I have recently assembled the chapters into what is hopefully their final form. An outline of the project is available in a revised chapter 1. In the next few weeks, I hope to blog through the 12 key claims which I present at the end of this chapter. Comments and links to other ways of exploring these issues are especially welcome.

Thursday, September 9, 2010

More on Epimenides

As Jonathan Livengood helpfully pointed out in a comment on my last post, Bayle links Epimenides to the semantic paradoxes in his Dictionary entry for Euclid (1740, although perhaps also in an earlier edition). A modern source cited by Bayle is Gassendi, and when you track down that reference you indeed find a link between Epimenides and the semantic paradoxes:

This comes from p. 40 of the first volume of the Opera Omnia from 1658, which has been scanned and posted online here. I don't know Latin, but the reference to this case as "celebre" suggests that Gassendi does not take himself to be making a new connection.

Friday, September 3, 2010

Who First Linked Epimenides to the Semantic Paradoxes?

As part of a philosophy of logic seminar on theories of truth I have developed an amateur interest in the history of discussions of logical and semantic paradoxes. As is well known, the Liar paradox can be traced to Epimenides and appears in the New Testament:
It was one of them, their very own prophet, who said, 'Cretans are always liars, vicious brutes, lazy gluttons.' That testimony is true. (Titus 1: 10-13, NRSV)
Russell makes allusions to this passage several times, including in "Mathematical Logic as Based on a Theory of Types" (see here.)

Given the discussion of these sorts of paradoxes in by medieval logicians, I was surprised to find this passage in Spade's article on Insolubles in the Stanford Encyclopedia:
One initially plausible stimulus for the medieval discussions would appear to be the Epistle to Titus 1:12: "One of themselves, even a prophet of their own, said, The Cretians [= Cretans] are always liars, evil beasts, slow bellies." The Cretan in question is traditionally said to have been Epimenides. For this reason, the Liar Paradox is nowadays sometimes referred to as the “Epimenides." Yet, blatant as the paradox is here, and authoritative as the Epistle was taken to be, not a single medieval author is known to have discussed or even acknowledged the logical and semantic problems this text poses. When medieval authors discuss the passage at all, for instance in Scriptural commentaries, they seem to be concerned only with why St. Paul should be quoting pagan sources.[5] It is not known who was the first to link this text with the Liar Paradox.
So, was Russell the first to make this link, or was he merely drawing on other sources?

My first thought was that Hegel or some other post-Kantian must have made the link, and Russell is merely repeating it. Through the power of Google Books I was able to find a passage in the English translation of Lotze's Logic:
One dilemma nicknamed Pseudomenos dates from Epimenides, who being a Cretan himself asserted that every Cretan lies as soon as he opens his lips. If what he asserted is true, he himself lied, in which case what he said must have been false; but if it false it is still possible that the Cretans do not always lie but lie sometimes, and that Epimenides himself actually lied on this occasion in making the universal assertion. In this case there will be no incongruity between the fact asserted and the fact that it is asserted, and a way out of the dilemma is open to us (Book II, Chapter IV).
This translation dates from 1884 and seems to be from the second edition of the Logic from 1880. I have not checked the German or the first edition.

It seems likely that Russell read Lotze's Logic, either in this very translation or the original German, as he notes Lotze's Metaphysik in his readings from 1897 and of course discusses Lotze's views on geometry in the fellowship essay. Still, it seems unlikely to me that Lotze was the first person to make the link. Any other candidates or evidence to consider?

Monday, August 30, 2010

New Book: Sociological Aspects of Mathematical Practice

Benedikt Löwe and Thomas Müller have edited an interesting collection of papers from the collaborative PhiMSAMP project. They have taken the very welcome step of making all the papers freely available for download for research use at this address. As the related page makes clear, this group aims to "to bring young researchers with foundational and sociological attitudes together and discuss a unified approach towards a philosophy of mathematics that includes both sociological analyses but is able to deal with the status of an epistemic exception that mathematics forms among the sciences."

Tuesday, August 10, 2010

Bergmann and Kain receive major Templeton award

Congratulations to my Purdue colleagues Mike Bergmann and Pat Kain who have been awarded a major Templeton grant to study how knowledge works in morality and religion! The Purdue press release describes several upcoming conferences on the general theme of skepticism and disagreement and their implications for knowledge in these domains.

Thursday, July 15, 2010

New Book: Mary Leng's Mathematics and Reality

Mary Leng's book is now out! From the back cover:
Mary Leng offers a defence of mathematical fictionalism, arguing that we have no reason to believe that there are any mathematical objects. In mounting this defence, she responds to the indispensability argument for the existence of mathematical objects ... In response to this argument, Leng offers an account of the role of mathematics in empirical science that does not assume that the mathematical hypotheses used in formulating our scientific hypotheses are true.
It's great to see an extended defence of fictionalism out there. In my book manuscript I argue that fictionalism can't work, so I will be reading this quickly to see what options the fictionalist has available! There will eventually be a symposium on this book in the journal Metascience and hopefully other reviews will appear soon.

Wednesday, July 14, 2010

Gettier Cases for Mathematical Concepts

Although I noted the appearance of this book back when it came out, it is only recently that I have had the chance to read Jenkins' Grounding Concepts. I agree with the conclusion of Schechter's review that "Anyone interested in the epistemology of arithmetic or the nature of a priori knowledge would profit from reading it." But at one point Schechter asks
In supporting Jenkins' view, it would be helpful to have an intuitive case of a thinker who forms a justified true belief that is not knowledge on the basis of a competent conceptual examination of an ungrounded concept. That is to say, it would be helpful to have a clear example of a Gettier case for concepts.
Jenkins uses these sorts of cases to undermine Peacocke's account of a priori mathematical knowledge. But she often resorts to comparisons between maps and concepts in a way that makes the point less convincing.

In the last chapter of my book I discuss the issue. While I do not ultimately agree with Jenkins on all points, I think she has a very good objection to Peacocke's views. Here is how I summarize the issue in the manuscript. I have adapted Jenkins map cases to the sort of mathematical concept cases that I believe Schechter is after: Jenkins'
basic concern is that even a perfectly reliable concept is not conducive to knowledge if our possession of that concept came about in the wrong way. She compares two cases where we wind up with what is in fact a highly accurate map. In the first case, which is analogous to a Gettier case, a trustworthy friend gives you a map which, as originally drawn up by some third party, was deliberately inaccurate. The fact that the map has become highly accurate and that you have some justification to trust it is not sufficient to conclude that your true, justified beliefs based on the map are cases of knowledge. In the second case, simply finding a map which happens to be accurate and trusting it "blindly and irrationally all the same" will block any beliefs which you form from being cases of knowledge. Jenkins extends these points about maps to our mathematical concepts:
A concept could be such that its possession conditions are tied to the very conditions which individuate the reference of that concept (...), but not in the way that is conducive to our obtaining knowledge by examining the concept (Jenkins 2008, p. 61).
The first sort of problem could arise if the concept came to us via some defective chain of testimony. For example, a "crank" mathematician develops a new mathematical theory with his own foolishly devised concepts and passes them off to our credulous high school mathematics teacher, who teaches the theory to us. The mere fact that the crank mathematician has happened to pick out the right features of some mathematical domain is insufficient to confer knowledge on us. The second kind of problem would come up if I was, based on a failure of self-knowledge, like the crank mathematician myself, coming up with new mathematical concepts based on my peculiar reactions to Sudoku puzzles. Again, this approach to mathematics would not lead to knowledge even if my concepts happened to reflect genuine features of the mathematical world.
I agree with Jenkins that examples of this sort show the need for either some grounding for our concepts or some non-conceptual sources of evidence.

Saturday, June 12, 2010

Review of van Fraassen's Scientific Representation

Here is a short review of van Fraassen's 2008 book Scientific Representation: Paradoxes of Perspective. It will eventually appear in the BJPS. I found the book to be very impressive, although I had trouble understanding the way in which van Fraassen deploys indexical judgment to avoid problems like the Newman problem which have sunk some versions of structuralism. As I put it in the review,
The central unresolved issue with van Fraassen’s empiricist structuralism is what his appeal to context in the solution of his “problems of perspective” comes to. I would distinguish the weaker claim that an ability is not the same as a description of that ability (p. 83) from the stronger claim that a given indexical proposition is distinct from all the propositions expressed by any scientific theory: “Is there something that I could know to be the case, and which is not expressed by a proposition that could be part of some scientific theory? The answer is YES: something expressed only by an indexical proposition” (p. 261). The stronger point seems to link having an ability to knowing an indexical proposition. But here van Fraassen says that even though what these essentially indexical propositions express is a crucial part of any account of representation, this is outside the scope of any scientific theory. As a result, it is not possible to arrive at a scientific theory of representation. This is much less plausible than the mere distinction between an ability and a description of that ability. The weaker claim allows for the possibility of a fully naturalistic theory of how we can think and locate ourselves with respect to our representations, i.e. the abilities which underlie our knowledge of the relevant indexical propositions. While linguistics and cognitive science are not adequate at this stage of science, it is hard to see why what these indexical propositions express would be beyond their scope. It is possible that van Fraassen takes his discussion in Part IV to undermine the demand for this sort of naturalistic completion of a scientific theory of scientific representation, but if this is his intention, then I have failed to follow the argument. It also possible that van Fraassen did not intend to exclude these indexical propositions from the scope of scientific investigation, but then he owes us a clearer account of how our abilities relate to our knowledge of indexical propositions.

Monday, June 7, 2010

Discussion Note of Batterman on Mathematics and Explanation

I have written a short discussion note of Batterman's recent article on mathematical explanation in science. If you have looked at the article, you may recall that he criticizes my "mapping account" as an account of how mathematics helps in explanation, especially the sorts of explanations using asymptotic reasoning which Batterman himself has spent so much time on. The basic point I make in my reply is that I was trying to provide an account of descriptive or representational content in terms of mappings and that I agree that this approach to description is not sufficient to ground explanatory power in all cases. Still, I argue that a theory of explanatory power can build on what I offer for descriptions, and that any account of explanation must say something about how explanations differ from descriptions.

Comments are, of course, appreciated!

Wednesday, April 28, 2010

Mathematical Explanation in the NYRB

In his recent review of Dawkins' Oxford Book of Modern Science Writing Jeremy Bernstein characterizes one entry as follows:
W.D. Hamilton’s mathematical explanation of the tendency of animals to cluster when attacked by predators.
The article in question is "Geometry for the Selfish Herd", Journal of Theoretical Biology 31 (1971): 295-311. (Online here.) Given the ongoing worries about the existence and nature of mathematical explanations in science, it is worth asking what led Bernstein to characterize this explanation as mathematical?

The article summarizes two models of predation which are used to support the conclusion that the avoidance of predators "is an important factor in the gregarious tendencies of a very wide variety of animals" (p. 298). The first model considers a circular pond where frogs, the prey, are randomly scattered on the edge. The predator, a single snake, comes to the surface of the pond and strikes whichever frog is nearest. Hamilton introduces a notion of the domain of danger of a frog which is the part of the pond edge which would lead to the frog being attacked. Hamilton points out that the frogs can reduce their domains of danger by jumping together. In this diagram the black frog jumps between two other frogs:

So, "selfish avoidance of a predator can lead to aggregation."

In the slightly more realistic two-dimensional case Hamilton generalizes his domains of danger to polygons whose sides result from bisecting the lines which connect the prey:

Hamilton notes that it is not known what the general best strategy is here for a prey organism to minimize its domain of danger, but gives rough estimates to justify the conclusion that moving towards ones nearest neighbor is appropriate. This is motivated in part by the claim that "Since the average number of sides is six and triangles are rare (...), it must be a generally useful rule for a cow to approach its nearest neighbor."

So, we can explain the observed aggregation behavior using the ordinary notion of fitness and an appeal to natural selection. What is the mathematics doing here and why might we have some sort of specifically mathematical explanation? My suggestion is that the mathematical claim that strategy X minimizes (or reliably lowers) the domain of danger is a crucial part of the account. Believing this claim and seeing its relevance to the aggregation behavior is essential to having this explanation. Furthermore, this seems like a very good explanation. What implications this has for our mathematical beliefs remains, of course, a subject for debate.

Saturday, April 24, 2010

Southern Journal of Philosophy Relaunched

The Southern Journal of Philosophy has relaunched with a new publishing agreement with Wiley, a new webpage and a new editorial board (including me). As the webpage indicates
The Southern Journal of Philosophy has long provided a forum for the expression of philosophical ideas and welcomes articles written from all philosophical perspectives, including both the analytic and continental traditions, as well as the history of philosophy. This commitment to philosophical pluralism is reflected in the long list of notable figures whose work has appeared in the journal, including Hans-Georg Gadamer, Hubert Dreyfus, George Santayana, Wilfrid Sellars, and Richard Sorabji.

The jewel of each volume is the Spindel Supplement, which features the invited papers and commentaries presented at the annual Spindel Conference. Held each autumn at the University of Memphis and endowed by a generous gift from the Spindel family, each Spindel Conference centers on a philosophical topic of broad interest and provides a venue for discussion by the world's leading figures on that topic.
I hope the philosophers will take advantage of this special venue for pursuing new and exciting directions for research in philosophy.

Monday, April 12, 2010

New Entries in Internet Encyclopedia of Philosophy on the Philosophy of Mathematics

Under the editorial guidance of Roy Cook a number of new entries in philosophy of mathematics have appeared on the Internet Encyclopedia of Philosophy. As I understand it, the aim of this site is to present relatively short summaries which are accessible to a wider audience, esp. undergraduate students, than some other options.

Check out these recent entries:

Bolzano's Philosophy of Mathematical Knowledge (by Sandra Lapointe)

The Applicability of Mathematics (by me -- more shameless self-promotion!)

Mathematical Platonism (by Julian Cole)

Predicative and Impredicative Definitions (by Oystein Linnebo)

A list of the all of the philosophy of mathematics entries can be monitored here.

Tuesday, April 6, 2010

Wash Post Reminds Us That There is No Perfect Climate Model

Here. There are some useful quotations from scientists, including:
If the models are as flawed as critics say, Schmidt said, "You have to ask yourself, 'How come they work?'"
What is missing from the article, though, is any discussion of the more or less risky claims which we might derive from examining a model or computer simulation. It seems that even though the models are highly detailed, most climate scientists are comfortable drawing only highly abstract conclusions. For example, they do not take seriously the temperature predictions for Indiana, but do take seriously the predications for the global mean temperature.

Monday, April 5, 2010

Inference to the Best Explanation for Mathematical Claims

Following up my last post, I want to outline an argument for why a reasonable restriction on IBE will block the use of IBE to provide much justification for mathematical claims. The main "mathematical explanations" which are discussed by advocates of this sort of justification, like Baker and Colyvan, involve explanations of patterns observed in the physical world. These examples include the life-cycle of cicada and the shape of the cells of a honeycomb. One of the problems with these explanations is that they bring in complications associated with explanations via natural selection. Another problem is that they may involve mathematical terms in the description of what is to be explained.

To avoid these problems, I will focus on the bridges of Konigsberg case (see here for some background). The explanation could be reconstructed as
(1) The bridges of Konigsberg form a graph of type O.
(2) There is no Euler path through a graph of type O.
(3) Therefore, there is no Euler path through the bridges of Konigsberg.
An Euler path is a circuit through the graph that crosses each edge exactly once. For someone who worries that even this begs the question by using a mathematical term we can offer to extend the explanation to include "(4) Therefore, it is impossible to cross each of the bridges exactly once."

I claim that Sensitivity blocks the use of IBE to support (2). This is because an agent who was genuinely in doubt about the truth of (2) would also have as a relevant epistemic possibility that (2') There is no Euler path through a graph of type O with fewer than 100 vertices. This means that there is an alternative explanation of (3) which employs weaker mathematical assumptions:
(1’) The bridges of Konigsberg form a graph of type O with fewer than 100 vertices.
(2’) There is no Euler path through a graph of type O with fewer than 100 vertices.
(3) Therefore, there is no Euler path through the bridges of Konigsberg.
My conclusion, then, is that this puts the burden on the advocates of using IBE to justify mathematical claims to argue that Sensitivity is incorrect or that some other features of these cases have been overlooked.

Friday, April 2, 2010

Inference to the Best Explanation and Sensitivity

Philosophers of science have focused on inference to the best explanation (IBE) as the sort of inference that stands the best chance of ultimately justifying our belief in unobservable entities like atoms and electrons. More recently philosophers of mathematics like Colyvan and Baker have tried to given an explanatory indispensability argument in support some of our mathematical beliefs. The challenge for everyone, though, is to articulate a reasonable form of IBE that accords with scientific practice, but which does not overgenerate beliefs in things which we reject. Despite its clarity, Lipton's discussion of IBE seems to me overly restrictive because he focuses only on causal explanations. Are there plausible principles for the use of IBE which allow non-causal explanations?

Here is one, but it results in problems for any use of IBE to justify our mathematical beliefs. I call it "Sensitivity", although perhaps this not the best label:
Sensitivity: A claim which appears in an explanation can receive support via IBE only when the explanatory contribution tells against some relevant epistemic possibilities.
Here I am imagining an agent who is in doubt about the truth of some competing options A1, A2, A3. Suppose that A1 appears in our best explanation. Sensitivity tells us that this contribution of A1 to the explanation can only license belief in A1 when the way in which A1 contributes makes either A2 or A3 less likely.

This seems to me to be a very weak and plausible restriction on IBE. It is met by the standard atoms and electrons cases, and also by Woodward's non-causal explanation of the stability of planetary orbits. In my next post, I want to outline a case for the claim that sensitivity blocks the use of IBE to support mathematical claims.

Book Project Update

For those few readers tracking my ongoing book project on Mathematics and Scientific Representation some recent good news is that I have signed a contract with Oxford University Press. The delivery date in the contract is Nov. 2010, so over the next six months I will posting some of the key ideas, and eventually the near-final versions of the chapters, for comments and discussion.

The manuscript is projected to be 140 000 words, with twelve chapters:

1. Introduction

Part I: Epistemic Contributions

2. Content and Confirmation
3. Causes
4. Varying Interpretation
5. Scale Matters
6. Constitutive Frameworks
7. Failures

Part II: Other Contributions

8. Discovery
9. Indispensability and Explanation
10. Fictionalism
11. Facades

12. Conclusion: Pure Mathematics

Saturday, March 6, 2010

Principia Mathematica at 100 Conference Lineup

2010 marks the 100th year since the publication of the first volume of Russell and Whitehead's Principia Mathematica. A major conference on Principia is scheduled for late May at McMaster University, in conjunction with the yearly meeting of the Bertrand Russell Society. The PM at 100 abstracts were recently posted here. It looks like a great lineup and I expect a great conference!

Wednesday, February 24, 2010

Pittsburgh Announces Rescher Prize for Systematic Philosophy

Details courtesy of Soul Physics.

From the press release:
Eminent, esteemed, wide-ranging, prolific-these are adjectives that have been aptly used to describe Nicholas Rescher and his contributions to the field of philosophy in a career that spans six decades, with nearly a half century of those years devoted to teaching and research at the University of Pittsburgh. In acknowledgement of his decades-long career at Pitt, Rescher, Distinguished University Professor of Philosophy, is donating his massive collection of materials on philosophy to the University's Hillman Library. In turn, the University is honoring Rescher for his lifetime of achievement and devotion to the University with the establishment of the Dr. Nicholas Rescher Fund for the Advancement of the Department of Philosophy, which will include a prestigious biennial award, the Nicholas Rescher Prize for Contributions to Systematic Philosophy.


Income from the Rescher Fund will be used to achieve key initiatives of the Department of Philosophy and to establish the Nicholas Rescher Prize. Awarded biennially, the prize will recognize an individual “for distinguished contributions to philosophical systematization” and include a gold medal, a $25,000 award, and an invitation to the University to deliver a lecture. Currently there is no major recognition in the field of philosophy, says Rescher, that is even remotely akin to the Field Medal in mathematics; the Pulitzer Prize in journalism, letters, and the arts; or the Nobel Prize in the sciences, medicine, economics, and literature.

The prize-to be awarded for the first time in the fall of 2010-reflects the seriousness of Pitt's commitment to philosophy. “It is our aspiration that the new Rescher Prize will become recognized as the most prestigious award in the field of philosophy, emphasizing the life's work and contributions to philosophy by a preeminent, world-renowned figure,” Maher said.

Monday, February 8, 2010

The Disunity of Climate Science

While there has been a lot of misleading coverage of the stolen e-mails from East Anglia, the Guardian offers an intriguing look inside the fallout from the more significant retraction of the 2007 IPCC report claims about the Himalayan icepack:
Speaking on condition of anonymity, several lead authors of the working group one (WG1) report, which produced the high-profile scientific conclusions that global warming was unequivocal and very likely down to human activity, told the Guardian they were dismayed by the actions of their colleagues.

"Naturally the public and policy makers link all three reports together," one said. "And the blunder over the glaciers detracts from the very carefully peer-reviewed science used exclusively in the WG1 report."

Another author said: "There is no doubt that the inclusion of the glacier statement was sloppy. I find it embarrassing that working group two (WG2) would have the Himalaya statement referred to in the way it was."

Another said: "I am annoyed about this and I do think that WG1, the physical basis for climate change, should be distinguished from WG2 and WG3. The latter deal with impacts, mitigation and socioeconomics and it seems to me they might be better placed in another arm of the United Nations, or another organisation altogether."

The scientists were particularly unhappy that the flawed glacier prediction contradicted statements already published in their own report. "WG1 made a proper assessment of the state of glaciers and this should have been the source cited by the impacts people in WG2," one said. "In the final stages of finishing our own report, we as WG1 authors simply had no time to also start double-checking WG2 draft chapters."

Another said the mistake was made "not by climate scientists, but rather the social and biological scientists in WG2 ... Clearly that WWF report was an inappropriate source, [as] any glaciologist would have stumbled over that number."
As I understand the science, the climate models used to support the central claims of the report are unequivocal. But they don't always give information relevant to policy makers such as exactly how much hotter it is going to get in Indiana or what year the Himalayan icepack will melt. This creates a temptation to leap in and provide more precise predictions than the models support. What is interesting here is that the "hard scientists" are blaming the "social and biological scientists" for giving in to this temptation.

Thursday, January 21, 2010

New Book: Nasim, Bertrand Russell and the Edwardian Philosophers: Constructing the World

NDPR has an instructive review by Bernard Linsky of Omar Nasim's 2008 book on Russell and his 'Edwardian' philosophical contemporaries like Stout, Nunn and Alexander. I haven't read this book yet, but it seems to mark a new level of scholarship on Russell's external world program and its relationship to Russell's intellectual context. As Linsky summarizes things,
Nasim argues that Russell took ideas that were being debated and made them precise to formulate his own views on sense data and matter. Most importantly, Russell replaced what Nasim describes as a "socio-psychological" notion of construction with the precise method of "logical construction" modeled on the construction of numbers as equivalence classes, which he brought to the "Controversy" from his work on logic and the foundations of mathematics. Both the origins of some of the unusual aspects of Russell's theory of sense data as being non-mental, but also not material, are found in the Edwardian controversy. We also learn what new ideas Russell brought to the debate to make it his own and to come up with his distinctive project of constructing matter from sense data.
This is a very helpful contribution to our understanding of the history. Linsky raises some points about the amount of detail which Nasim is able to go into about the philosophers he discusses. For example, Linsky explains how Alexander influenced the distinctive form of realism which later flourished in Australia.

A larger question about Nasim's project concerns the extent to which we can reconstruct Russell's views by focusing on philosophers alone. It seems that we may need to look beyond the philosophical context to the scientific debates, especially in psychology and physics, concerning space and our representation of space. Gary Hatfield has made some progress in this direction and my understanding is that Alexander Klein is also pursuing some research into the links between Russell's constructions and the psychology of his day. This sort of work will hopefully complement Nasim's story by expanding what counts as Russell's intellectual context.