Hat tip to Ralf Krömer’s “Tool and Object: a history and philosophy of category theory” where I found this bit of support for my cherished intellectual projects:

The historical investigation of the development of a science is most needful, lest the principles treasured up in it become a system of half-understood prescripts, or worse, a system of prejudices. Historical investigation not only promotes the understanding of what which now is, but also brings new possibilities before us, by showing that which exists to be in great measure conventional and accidental. From the higher point of view at which different paths of thought converge we may look about us with freer vision and discover routes before unknown.

Mach, Ernst. 1960. The Science of Mechanics: A critical and historical account of its development. La Salle (Illinois): Open Court.

Ladyman and Ross argue that only structure is real and that it is ontologically basic.  They make no distinction distinction between physical and mathematical structure, refusing to answer the question how such a distinction is grounded.  Yet, they seem to rely on the distinction no less.  After all, they distinguish empirical, physical science from mathematics.  Physics is interested in the physical structures, not any coherent mathematical structure.  Those are what mathematicians study.

One position to take would be to hold that the physical structures are just one slice of the mathematical structures.  Indeed, this modernized Pythagoreanism is suggested by Ladyman and Ross, specifically endorsed by mathematical phycicist John Baez, and is defended as plausible speculative cosmology by MIT phycisist Max Tegmark.
Disappointingly for philosophical pride, I find the physicist Tegmark clearer and more precise in stating directly what he means by structure:

A mathematical structure is precisely this: abstract entities with relations between them. Familiar examples include the integers and the real numbers. We review detailed definitions of this and related mathematical notions in Appendix A. Here, let us instead illustrate this idea of baggage-free description with simple examples. Consider the mathematical structure known as the group with two elements, i.e., addition modulo two.

Admirably clear thought this definition may be, I find it a bit problematic from the standpoint of the algebraic conception of structure.

First a point about language.  Mathematicians use the terms “concrete” and “abstract” for different purposes than philosophers.  The mathematician asks for a concrete example when she’s asking for a familiar setting to fix intuitions, typically arithmetic or geometric.  In this sense, the integers are paradigmatic concrete objects.  The philosopher is not as focused as working mathematicians’ psychological expedients, however.  To the philosopher, integers are paradigmatic abstract objects.  We shall mark the metaphysical distinction by the terms abstracta and concreta.  When the mathematician asks for a concrete example, then, we shall understand her as asking for concrete abstracta.

There has been some discussion of the blurring of the philosopher’s metaphysical distinction between abstracta and concreta in the philosophy of mathematics and science literature [concerning Field's program mostly: in Burgess/Rosen, Resnik, Shapiro].  For instance, are the points of a substantivally understood manifold abstract or concrete? We will not need to enter these disputes here, however.  I’m more interested in noting that mathematical structure is, in an important sense, doubly abstract (both mathematically and metaphysically) in a manner that should make us question the claims of neo-Pythagorean structural realism.

A natural setting for a request of a mathematically concrete example is in the algebraic study of groups.  One mathematical structure is the dihedral group D4.  A concrete interpretation of this structure is the symmetry group of the square.  The concrete interpretation involves philosophically abstract objects: the square’s symmetries.  However, the algebraist interest isn’t purely and simply geometric in considering the structure at hand.  A structure is an abstract abstracta, in the sense that it can “pop up” in more than one place.  A trivial example: the rotational symmetries of the square have the structure of the integers mod 4.  Structures, in the mathematical context, exhibit multiple-instantiability.

We may further develop our worry by consideration of the problem of multiple reductions for reductionist set theory, an argument for the view philosophers call structuralism put forth most famously by Paul Benacerraf.  According to the set-theoretical reductionist, the only abstracta are sets.  What we have been calling concrete abstracta, the natural numbers for instance, should therefor be identified with some sets.  The multiple-reductions problem is just the embarrassment of riches in deciding which interpretation (i.e., which model) of the Dedekind-Peano axioms in the realm of sets shall be identified as the natural numbers.  The structuralist philosophy of mathematics I prefer opposes the reductionist path leading to this pseudo-question.

According to my favored version of structuralism, the important topic of mathematico-logical inquiry is the structure shared by all models of the Dedekind-Peano axioms.  The important point presently is that the algebraic structuralist understanding of axioms like the Dedekind-Peano axioms considers them not as assertions about some intended domain (e.g., the natural numbers, the von Neumann sequence, the Zermelo sequence) but rather as an algebraic, logical characterization of a structure that many systems may share.  According to the platonist realist (reductionist and plenitudinist alike), systems having such structures include both systems of abstracta and systems of concreta.  According to the physicalist, there are only systems of concreta.  The physicalist thinks some structures have no instances, and for this reason bears some philosophical burdens in explaining the subject matter and objectivity of mathematics.  The platonist avoids those burdens by giving each coherent structure at least one instance, among the abstracta if not the concreta.  Both will agree that structures, which we have been calling abstract abstracta, may be multiply instantiated, however.

I may now put my objection to Tegmark succinctly.  When he says “A mathematical structure is precisely this: abstract entities with relations between them“, it begets the question which entities with what relations is the structure in question.  When he gives the integers and reals as examples of mathematical structures he’s giving us concrete abstracta, models of the abstract abstracta we call “structures”.  To the Pythagorean who tells us the physical world is a slice of mathematical structure (but not the whole structure, lest physics become empirically detached) we are now lead to inquire which concrete abstracta having the structure they have in mind.  Put another way: an algebraic structure defines an equivalence class of concrete abstracta.  When our Pythagorean interlocutors tell us that the physical world literally is this structure do they mean that the world just is the entire equivalence class?  Or what?  It isn’t at all made clear in the views I’ve encountered.

The neo-Pythagoreans that we have been discussing owe, it seems to me, a much clearer account of just what they mean when they say the world just is a structure (one of many mathematical structures) as opposed to saying that the world has a certain structure.  Surely there are philosophical maneuvers available to neo-Pythagoreans, such as appeal to the ontological category of universals from traditional metaphysics, but the views I’ve encountered do not, from what I’ve seen, avail themselves of this philosophical machinery.  Tegmark confuses structure and instance, abstract abstracta and concrete abstracta.  Ladyman and Ross, in particular, adopt a neo-positivist eagerness to avoid traditional metaphysical problems surrounding traditional ontological categories.   While I share their scientistic spirit, I won’t be lead into confusion by it and it seems to me that the neo-Pythagorean point of view that they endorse rests on confusion about structure.

Since I haven’t posted anything new in a while… how about something I wrote for a course last fall.

David Bostock’s book “Space, Time, Matter, and Form” collects essays spanning several decades of writing on Aristotle’s physical and biological theories. The collection begins with five essays on Aristotle’s theories of matter and form, followed by five more essays on topics relating to motion in Physics. Bostock notes in the preface that the first five essays arise from a failed attempt at a longer manuscript on Aristotle’s theories of matter and form. Bostock argues that while a coherent theory of matter may be attributed to Aristotle, no unified and coherent theory of form persists throughout Aristotle’s writings. In particular, Bostock finds Aristotle’s Metaphysics to be a failed and incoherent attempt to unify the theoretical roles assigned to form in Physics and the biological works.

I begin with comments on the essays contained in the latter half of the volume. Bostock’s essay on Aristotle’s response to Zeno is outstanding. He begins by sympathetically presenting the Aristotelian response to Zeno; viz., that passing through a region of space does not count as a discrete doing and does not actualize the points in that region, and that hence Achilles’ motion through space requires neither that there be an actual infinity of doings nor that there be an actual infinity of regions/points. Rightly, Bostock points out that Zeno might well have argued that just as it is impossible for Achilles to move, it is impossible for Achilles to be at rest—since before he rests a minute he must rest a half-minute, etc. Nevertheless, Aristotle would maintain that the passage of time no more actualizes moments than passage through space actualizes points, and Aristotle’s response thus has the virtue of answering both horns of the potential antinomy that nothing can be either at motion or at rest. However, Bostock proceeds to construct an example to show that Aristotle’s response will not work for all Zeno-style paradoxes. A ball may bounce to heights in the following sequence: 1 meter, ½ meter, ¼, etc. In so doing, it will, according even to Aristotle’s theory, actualize infinitely many points in a finite period of time. Bostock goes on to argue persuasively that the paradox is not, however, a logical paradox but rather a paradox relating to the deterministic conception of nature. The essay is one that I recall reading as an undergraduate, which contributed to my growing interest in mathematics and philosophy. It is a paradigm of clear argumentation illustrated by vivid examples and a pleasure to read.

The other essays on motion that make up the latter half of the collection are also strong, though not entirely unimpeachable. For instance, in “Aristotle on the Eleatics in Physics I. 2-3”, Bostock offers helpful clarifications of the arguments that Aristotle offers in opposition to Melissus and Parmenides, while claiming that in his attempted refutation of the thesis that only existence exists Aristotle relies on a premise that Parmenides clearly would not grant: viz., that if only existence exists it must have some property (e.g., pallor) accidentally. It seems to me that Aristotle is not begging the question when he makes the argument in question (at 186b, 4-12), however. In the Apostle translation from which I am working Aristotle has just finished arguing against the combined thesis that only existence exists and that only existence is predicated of existence—on the grounds that whatever may be predicated of a subject must not already be a property of the subject. The argument that begins with the supposition that existence exists and has some accidental property is in this context just the second horn of a dilemma, and if Parmenides would reject this horn outright so much the better for Aristotle’s case. I admit, though, to finding Aristotle’s passages on the Eleatics to be difficult, so I don’t say with absolute confidence that Bostock has things wrong.

In “A Note on Aristotle’s Account of Place” Bostock decisively shows that recent efforts to rehabilitate Aristotle’s theory of place through creative and generous interpretation fail even if stretched readings of the text are granted. In “The Account of Time” Bostock combines close reading of the text with keen logical acumen to yield a plausible reading that makes sense of some very difficult passages in Physics. In “Aristotle on Continuity in Physics VI” Bostock discusses a critically important topic in the history of ideas. I’m in no position to make declarations on the focus of medieval scholarship, but it seems to me that an overemphasis on Aristotle’s theological speculation over the halting progress made by Aristotle toward clarifying the concepts central to developing kinematic theory is in line with forming a palimpsest from the parchment containing Archimedes’ proto-calculus. Bostock effectively demonstrates that Aristotle’s geometric conception of continuity somewhat anticipates modern topological approaches. Here again Bostock’s strengths are shown in a close reading of difficult texts that extracts a plausible interpretation and uncovers important ideas. I take Bostock’s work on Aristotle’s theories of place and time to be important contributions to somewhat neglected topics.

As I mentioned, Bostock’s collection of essays on matter and form, those forming the first half of the book, arise from a failed attempt to produce a longer manuscript on matter and form in Aristotle’s works. The essays show intense scholarly engagement with the primary texts but only mixed engagement with classical and contemporary commentaries. Bostock notes in the preface that his more ambitious project ran aground because he could not identify a coherent notion of form, especially in Metaphysics. Bostock’s efforts may have benefitted from greater engagement with scholarship from Thomas Aquinas, whose commentaries are not cited once, to present work focusing on the notoriously difficult book Z. However, I do not say for certain that this is so. If Bostock is correct that there is no coherent and unified doctrine of form in Aristotle’s works then we should consider the possibility that the coherent and unified doctrines attributed by scholars to Aristotle tell us more about the author of the comments than the author of the primary text. An emphasis on the identification of form and soul over other theoretical roles assigned to form by Aristotle or on Aristotle’s theological speculation over his more “scientific” works, for example, would become a projection of unity onto a confused and equivocal notion of form that tells us at least as much about Aquinas as it tells us about Aristotle. This is not, of course, the place to fully defend this tentative point, and I only mention the possible implication to prepare the way for some methodological comments I would like to make contrasting Bostock’s approach to the Aristotelian doctrine or matter with his approach to the doctrine of form.

Bostock attributes to Aristotle the view that prime matter must exist as the subject of substantial change. Bostock establishes this interpretation in the essays that form the first three chapters of the book. The first essay, “Aristotle on the Principles of Change in Physics I”, argues that Aristotle achieves greater generality than his predecessors in maintaining that any account of a change will mention three principles: viz., form, privation, and ‘what underlies’ the change (either substance or matter). Aristotle is answering a different question than his predecessors when he gives an account of the “principles” of change. Aristotle does not identify anything like air, water, fire, atoms and the void, etc. Rather, Aristotle gives what me might call an account of the grammar of change (or a conceptual analysis of “becoming”), without settling on a specific theory. I find Bostock persuasive on this point, but also think that it is noteworthy that to make it he must import to the text distinctions that Aristotle himself does not explicitly draw. For instance, Aristotle never states that his project of seeking the fundamental principles of change departs from those of his predecessors in exactly the way that Bostock says that it does. Surely, the line between analysis and induction was rather blurry for Aristotle. Furthermore, Aristotle does not, in Physics I, explicitly distinguish between arguments given at a grammatical or conceptual level and empirical physical inquiry. Bostock is aware that he is actively interpreting the text in these ways and does take steps to motivate the relevance of the distinctions he draws.

In any case, first essay concludes without absolutely settling whether the ‘what underlies’ is matter or substance. Again, there is interpretative space. The phrase translated as ‘what underlies’ is used by Aristotle both in speaking of predication and in speaking of persistence through change. On the one hand, the phrase ‘what underlies’ may be taken as unequivocal between these contexts, so that whatever underlies a change must also be a subject of predication. Then, if Aristotle is to be consistent with his position on predication in Categories he must hold that only a substance may underlie a change, since he is absolutely clear in Categories that only substance is the ultimate subject of predication. In this case, if matter rather than substance is taken as the underlying subject of change then Aristotle must be abandoning his previous account of predication. On the other hand, ‘what underlies’ may be understood as having different senses in the contexts of predication and change. In this case, Aristotle may be read as maintaining his previous doctrine identifying substance as what underlies predication while introducing a new sense in which matter underlies change. Bostock indicates that he interprets ‘what underlies’ as equivocal. This, he notes, requires the abandonment of a different doctrine mentioned in Categories—that only substances persist through change. On this point, I find Bostock’s movements through interpretive space rather less graceful than those made in support of interpreting Aristotle as departing from his predecessors. The subsequent essay in the book, “Aristotle on the Transmutation of the Elements”, argues that Aristotle’s application of the grammar of change in his specific physical theory of elements and their mixing requires that prime matter be allowable as ‘what underlies’. The third essay, “Aristotle’s Theory of Matter”, further develops the account of matter and its theoretical role in Aristotle’s applied science. I don’t take issue with what Bostock says in these essays and think that Bostock has effectively shown that Aristotle uses the idea of matter as underlying change throughout his works. However, I wish to point out that Bostock is willing to make significant interpretive assumptions in his attempt to align Aristotle’s general account of change in the Physics, his claims about substances and attributes made in the Categories, and his particular scientific claims in works like De Generatione; he is less charitable in interpreting Aristotle on form. Bostock’s discussion, I believe, would have been more persuasive if it had included greater engagement with the secondary literature that has drawn out tensions and, perhaps, inconsistencies in attributing a belief in prime matter to Aristotle.

Bostock’s discussion of Aristotle’s account of form is provided in the chapters “Aristotle on Teleology in Nature” and “Aristotle’s Theory of Form”. In contrast with Bostock’s claim that Aristotle holds a coherent theory of matter throughout his major works, Bostock maintains that there is no coherent theory of form maintained throughout the biological works, the Physics, and the Metaphysics. Indeed, Bostock claims that the account of form contained in Metaphysics Z is itself an incoherent attempt to unify the theoretical roles given to form throughout the Aristotelian corpus. Bostock’s close reading and knowledge of the texts are apparent in both essays. The discussion of teleology is rich with illustrative examples from the biological works. In it Bostock questions the dual role of form as both the formal and final cause of a creature—as both providing the creature with a particular arrangement of parts (horns here, hooves there, etc.) and as determining the good for which the creature strives (in virtue of which it grows horns, hooves, etc.). The form is also identified as what is inherited from a father by a son and (to a lesser extent in Aristotle’s sexist account) the daughter. Form is also identified as soul and given a role in thought by Aristotle in De Anima. These theoretical roles for form in biological explanation are in addition to its role in the account of change in basic physical explanation, as well as the identification of form and species made, according to Bostock, in the logical works. In “Aristotle’s Theory of Form” Bostock argues that nothing could fulfill all of these roles, concluding that the notoriously muddled passages of Metaphysics are simply a contradictory morass resulting from Aristotle’s failed efforts to unify these theoretical roles.

In the Preface Bostock notes that his book is the result of a failed effort to produce a manuscript attributing a coherent and unified account of both form and matter to Aristotle. It would be unfair to Bostock not to note that the compiled essays show considerable, serious scholarly effort towards this end. However, it does seem to me that Bostock is more generous and more willing to be an active interpreter in his account of matter than in his account of form. Just as the account of matter downplayed scholarly disputes over the place of prime matter in Aristotle’s thinking, the account of form provided by Bostock downplays scholarly attempts to reconcile the tensions in the account of form; in particular, the claims made in the essay “Aristotle’s Theory of Form” seem to me to require closer engagement with both the text of Metaphysics and its commentators to be conclusive. However, it may be that Bostock is correct that there is no coherent doctrine of form in common to all of Aristotle’s works. While it does seem to me that charity is unequally applied in Bostock’s approaches to matter and form, I’m not sure which is methodologically superior. Unwittingly, in all likelihood, Bostock’s interpretation of Aristotle’s doctrine of form can be seen as the sort of history of ideas argued for by Foucault in “Archaeology of Knowledge”. I seldom find myself in agreement with Foucault, but I am sympathetic to the point that the principle of charity applied by interpreters of historical texts, which Bostock applies more liberally in interpreting Aristotle on matter, leads to an imposition of order that hides the tensions and even contradictions of the past. I have sometimes joked that the principle of charity means attributing to an author the view closest to your own, and I do think that the form that Bostock chooses to impose on the textual matter reflects at least as much on him as on Aristotle.

It’s been a busy summer. The garden has done ok thought my squash plant died from an infestation ofter giving me four fruits.  Traveling back and forth to the Chi-burbs: 3 weddings and two weeks helping Conscious Cup, the family business, run a concession stand at the MCYSA International Championships.  All very fun, but time consuming and productivity disrupting.  I’m a creature that thrives on routine and there hasn’t been enough of it lately.

As far as philosophy of math I’ve been reading articles from the collection Logicism, Intuitionism, and Formalism along with Resnik and Shapiro’s books on structuralism and Wittgenstein’s “Remarks on the Foundations of Mathematics”.  I’ve written about half of my prospectus, failing to meet the goal of finishing before the baseball tournament and having now turned to other things.

Other things: I’ve been working on a presentation I’ll be giving at the start of next month in Prague at the Foundations of Uncertainty colloquium.  I’m giving a response to a puzzle posed by Roger White at the 2008 Formal Epistemology Workshop, which is the basis for a forthcoming paper in the next Oxford Studies in Epistemology.  The response will be based mostly on this paper with some additional comments based on further research, done since I wrote the paper.  I’ve been reading A LOT, both math and philosophy texts, on the foundations of probability theory, especially on imprecise probabilities.  For a sample of the sort of thing that’s hooked my interest, check out this short piece “Imprecise Probabilistic Prediction for Categorical Data: From Bayesian Inference to the Imprecise Dirichlet-Multinomial Model”.  I take my response to White’s puzzle to be fairly orthodox from the point of view of theorists that have worked on imprecise probabilities, but it’s nevertheless nerve-racking to present before an audience that includes people who’ve been thinking about these things for decades (as opposed to about a year).

I’m pretty nervous.  Did Im mention I’m nervous?  My happy thought is that no matter how the presentation goes I’m spending a week with my lovely wife in Prague!  Mucha museum, Charles Bridge, Sedlec Ossuary (aka: “bone church”… google it), Strahov Library, the Prague Opera, and beer… lots of beer.  Anything else I shouldn’t miss?

Check out this post at Choice and Inference if you liked my earlier posts on probability puzles (here, here, and here).  The puzzle is given as a possible counterexample to reflection for credences, but is worked out nicely in the comments over there.  I was too late to the party to add what I learned from jd2718, but the solution to the second ace puzzle is pretty much the same as the solution to the dice puzzle that had initially fooled me when jd2718 presented it to me in comments.

I’ve got a few drafts of longer posts, but find myself always wanting to mull things over more and revise.  I suppose that, in thinking ahead to my dissertation, it’s right to be in a stage of thinking through a large project and that blogging lends itself to short bursts of ideas or to defending worked out positions.  Also, this still feels like launching words into the void; it’s hard to write anything if you don’t have a sure feeling of audience.

Sharing cool videos, on the other hand, is easy.

Writing at National Review Online’s “The Corner” conservative commentator Stephen Spruiell claims:

Health care is not a right, at least not according to the conception of rights upon which this country was founded. Your rights include life, liberty and the pursuit of happiness. You may not be unjustly deprived of these things. Your rights do not include things that I or anyone else must be forced to provide for you, such as a home, a car, a job, or health care.

I would be surprised to find the founders univocal on the nature of rights, but I understand that the narrow conception of “negative rights” was historically important and represents a distinct concept of “right” from the one employed in claiming that health care or education is a right.

What I don’t think that Spruiell will like to admit is that “property rights” may well be argued to fall under the broader conception of “right” that includes positive rights.  Consider what Thomas Paine said in “Agrarian Justice”:

There could be no such thing as landed property originally. Man did not make the earth, and, though he had a natural right to occupy it, he had no right to locate as his property in perpetuity any part of it; neither did the Creator of the earth open a land-office, from whence the first title-deeds should issue. Whence then, arose the idea of landed property? I answer as before, that when cultivation began the idea of landed property began with it, from the impossibility of separating the improvement made by cultivation from the earth itself, upon which that improvement was made.

The value of the improvement so far exceeded the value of the natural earth, at that time, as to absorb it; till, in the end, the common right of all became confounded into the cultivated right of the individual. But there are, nevertheless, distinct species of rights, and will continue to be, so long as the earth endures.

Individual property rights are here recognized as “of a distinct species” from the “common right of all” to benefit from natural resources.  Paine is commenting directly on the Lockean standard and fairly clearly rejects it.  Continuing, Paine writes:

Cultivation is at least one of the greatest natural improvements ever made by human invention. It has given to created earth a tenfold value. But the landed monopoly that began with it has produced the greatest evil. It has dispossessed more than half the inhabitants of every nation of their natural inheritance, without providing for them, as ought to have been done, an indemnification for that loss, and has thereby created a species of poverty and wretchedness that did not exist before.

In advocating the case of the persons thus dispossessed, it is a right, and not a charity, that I am pleading for. But it is that kind of right which, being neglected at first, could not be brought forward afterwards till heaven had opened the way by a revolution in the system of government. Let us then do honor to revolutions by justice, and give currency to their principles by blessings.

The establishment by governments and quasi-governments of a regime of individual ownership has costs and benefits.  On the one hand, it creates the incentive to make the land more productive.  On the other hand, it creates an elite class of property owners and deprives others of opportunity to use resources that are naturally held in common.  As a remedy, Paine proposes a tax on property owners to redistribute goods to those that are deprived by the system of private ownership.  Indeed, if we follow Paine, it would seem that the redistributive scheme is justified by a right more basic than the system of private ownership.  The system of private ownership has a purely utilitarian justification: viz., it creates incentive to increase land productivity.  The redistributive correction of the negative and unintended consequences, on the other hand, is justified by appeal to a fundamental natural right of common propoerty, characterized thusly by Paine:

It is a position not to be controverted that the earth, in its natural, cultivated state was, and ever would have continued to be, the common property of the human race. In that state every man would have been born to property. He would have been a joint life proprietor with rest in the property of the soil, and in all its natural productions, vegetable and animal.

It may be controverted that others of the founders did not share Paine’s outlook, one that blurs the distinction between landlord and government in ways that would discomfort contemporary American libertarians (and those conservatives that pretend to be libertarians whenever it suits them).  I can’t say that I have a terrific grasp of every one of the founders’ views on “rights” and I won’t pretend (as Spruiell does) that I do.  Nevertheless, I find much to recommend in Paine’s outlook.  On this view, individual property rights are (again) “of a distinct species” from what we might call natural rights.  They are justified by their positive consequences, but to the extent that they also have negative effects by limiting every non-owner’s natural right to freely use the earth’s resources to sustain his or her life and to pursue happiness, I am with Paine that government is not only justified but obligated to provide compensation.  Taxation supported public services like health, education, welfare, and infrastructure fulfill this obligation.

In wondering why Russell has shown well in the Leiter poll, Weatherson actually winds up making a pretty decent case for Berty, or so it seems to me.  Fitelson and Chalmers speak up on Russell’s behalf in the comments.

I wish I’d been there…  Philosophy title fight between theist Plantinga and atheist Dennett.

I’ve seen Plantinga give a talk presenting some of his arguments.  They depend essentially on sophistical fabrication of prior probabilities.  The link I’ve given takes Dennett to task for rudeness, and I would not be surprised if this is true.  I don’t see what the “new atheists” think they’re accomplishing in mocking bare theism.  To be sure, any degree of literalism about Christian mythology is absurd (talking snakes, human sacrifice, drinking blood…) , but I think that bare theism–basically deism–can be respectably held.  Anyhow, I empathize with Dennett’s impulse to rude response to some extent because in a way mockery is about all that you can do when the “argument” is just the other person insisting on a bunch of a priori probability judgments, but I also agree with this reviewer that the rudeness is likely counterproductive.  Naturalists can and should try to do better.

The reviewer to whom I linked wrote:

Post-script: It has been about ten minutes since the session ended. I spoke to Peter Van Inwagen about the talk and he said it was an expected performance and that while it was a clash of worldviews, it was an interesting clash in two styles of doing philosophy. Initially, I thought to myself, “Yeah, Plantinga thinks philosophy is about arguments; Dennett thinks it is about stories.” But on further reflection I realized that Van Inwagen had a point. Dennett believes that science can tell us many things about metaphysics and epistemology, that we work from science to these positions. Plantinga thinks of these matters rather differently.

This seems to me to be correct, and there’s much to be said in Dennett’s favor on exactly this point.  Plantinga’s “thinking philosophy is about arguments”, as I’ve said, means making lots of appeals to claims about prior probabilities.  Establishing an objective framework for assigning prior probabilities seems to me to be a hopeless project philosophically; though how knowledge is established and advanced nevertheless is a demand that is fair to press.  Dennett’s “telling stories” reminds me of WVO Quine’s insistence that we inherit and rely on the “lore of our fathers” by working within the scientific community (and mothers, I might add) and Isaac Newton’s “standing on the shoulder’s of giants”.  Plantinga is a tall man, but not so tall.

Lately I’ve been reading a lot and working things over, so not much to say on the philosophy of mathematics front. . . maybe not for a little while.  I’ve got some ideas brewing on the following topics: (1) category theory vs set theory foundations, (2) whether the application of SU(n) in physics and the discoveries derived from that application are “more surprising” than widely discussed examples in the history & philosophy of science (e.g. the discovery of Neptune), and (3) whether a wannabe-nominalist who accepts naturalized epistemology can answer Burgess and Rosen’s anti-nominalist arguments.  Even granting that a blog is a space for working through ideas in progress, I’m not sure I’m ready to say a whole lot about these things just yet, at least not until I work through at least some of the stack of books and articles I’m accumulating.

So, dear mathematically inclined readers (all three or four of you!), you’ll have to settle for something non-mathematical but hopefully interesting.  I had a very nice, intellectually stimulating evening last night in two parts.  It was a nice break from mathematical/logical slogging that lead to some free thinking about more open-ended questions.  First, Jason Hanna from U Colorado gave a colloquium titled “Ulysses Contracts and the Moral Relevance of Actual Consent”.  Second, Beth and I had dinner with a new professor in the political science department and his wife that lead to an interesting discussion of the voter paradox.  I will explain for you what these contracts are and what this paradox is, then relate the two issues and share some thoughts on them.

Ulysses contracts: Ulysses tells his crew to tie him to the mast and plug their ears.  Sail past the sirens so he can hear them sing.  Do not, under any circumstances, untie him.  Even if he begs, he insists that they not let him down.  A Ulysses “contract” (the word is a bit misleading since they need not be technically binding) is when one requests at timeA not to have one’s requests at a later timeB honored.

The philosophical issue that arises is how to deal with cases where we’re instructed by someone not to obey their future instructions.  These are not just philosopher’s fantasies.  Examples may arise in applied medical ethics.  For example, an expectant mother may tell her doctor not to administer an epidural even if she begs for it.  Suppose she does indeed beg for the epidural.  What is the ethical thing for the doctor to do?  How can the doctor best respect the woman’s autonomy?

In different cases our intuitions may be different.  We may think that Ullyses crew definitely should not let him down, but that the doctor definitely should administer the epidural.  The philosopher’s task is to see if there’s a principled way to account for all of the judgments that seem intuitive.  Here’s one suggestion: Honor the most recent request unless it’s obviously deficient.  Ullyses’ request to be let down is paradigmatically deficient because he’s under the spell of the siren song.  But the mother’s request is not obviously deficient.  It is made under the duress of pain, to be sure, but there’s a sense in which that makes it a more informed choice than her earlier decision and hence closer to the optimum.  The matter is debatable, but that implies that it’s not obvious.  This was not the account that our speaker gave.  He was pressed by Greg Landini and Richard Fumerton to come up with a “pure case”.  It seemed like all of the cases where we have the intuition to honor the earlier choice were cases where the later choice was made under the influence of addiction, delusion, mental illness, etc.  Is there any case where we are inclined to honor the earlier choice even though the latter choice is closer to optimally rational?

Which brings me to:

The voter paradox: The expected utility of voting is really, really low. After all, one vote is not going to have any impact on the election. So it is irrational to vote.

Of course, this isn’t a paradox if you accept the conclusion, but I think that a lot of people will be disinclined toward accepting that conclusion and it is at least worthwhile to explore the account of rationality that leads to the conclusion and to think about alternatives.  Before we do that, however, I want to return to the Ulysses contracts and offer what I think may be a pure case.  The relevance of the voter paradox will become clear as we proceed, so keep it in mind.

Suppose I tell my wife the following.  We’re going to the gym tomorrow before class.  I know that I’ll want to sleep in, but no matter what I say don’t listen.  Drag me out of bed if you have to.  Even if I tell you that I take everything I’m saying now back, I want you to bang on pots and pans until I get up…  Ok, you get the picture.  It’s at least plausible that my wife should honor my initial decision even though I take it back in the morning.  In a discussion of weakness of the will, Donald Davidson argues (citation not handy) that it can be irrational to brush one’s teeth if one believes one will in the future brush one’s teeth regularly.  That case is similar to this one.

But wait!  When in the morning langor rises, reaching to shut off the alarm isn’t it the case that I’m making a deficient decision, one clouded by grogginess.  So is this really a pure case?  I say that it is.  In fact, in the morning I’m more informed about how good it will feel to sleep in.  Furthermore, I’m not under the influence of addiction or mental illness or anything like that.  In particular, I reason that skipping the gym just this once maximizes my expected utility.  After all, one day skipped is not going to have any impact on my overall health. My decision to sleep in is more rational than my decision the night before to tell my wife to drag me out of bed whatever it takes!  (By the same type of reasoning that led to the voter paradox, that is).

In my gym case, the intuition to honor the earlier decision is, I maintain, at least respectable.  But it’s not a case where the later decision is over-ruled because it’s deficient in some obvious way.  I claim, in fact, that the later decision is more rational than the earlier decision by the standard of expected utility.  Yet, the voter paradox seems to point to some problems with that standard and I think so does the gym case.  After all, if every rational voter reasons that it’s irrational for them to vote then only irrational people will vote, which can’t be good.  Similarly, if I reason every morning that I should sleep in rather than go to the gym then I’ll never go to them gym, and this will have predictably rotund consequences.  Just as the voter paradox relies on the supposition that other people will not reason as you do, the gym case relies on the supposition that my future selves will not reason as I do now.

So, here is what I think is suggested.  Rationality is not a simple matter of maximizing expected utility with each individual decision taken in isolation.  If it were, the person who tells him or herself every day that tomorrow is the day that they’ll start eating healthy and working out would be rational, even if tomorrow never comes.  We need to make, as it were, Ulysses contracts with ourselves in order to consistently make decisions that have good results in aggregate, even if in each of the moments that we make them they have low expected utility.  It really is (sort of) like this for me, with a internal voice of conscience speaking: “Self, you swore to yourself that you’d go to the gym and I’m holding you to it even if you don’t like it”.  I don’t think that the voter paradox is really that different.  To be sure, it’s members of a group (i.e., citizens of a democracy) making a sort of Ulysses contract with one another to act as an aggregate in a way that everyone agrees is good in aggregate but everyone recognizes does not maximize expected utility individually.  The voice of conscience thus speaks on behalf of the shared interests of the group rather than the interests of the trans-temporal self, but I don’t see that this is a difference that makes the solution good in the gym case but bad in the voter case.

So, what’s the upshot of all of this?  Well, maybe my pure case is not so pure afterall, if voter paradox style reasoning is in fact deficient reasoning.  My discussion has suggested that it is deficient for the following reason.  The locus of rationality ought not to be thought of as the present self.  Assessments of rationality may equally well be made from the standpoint of the transtemporal self (which argues: sure that makes sense now, but what if you always thought like that) or from the standpoint of shared interests and intentions (which argue: sure that makes sense for each of us individually, but what if we all thought like that).  From these standpoints, the gym case and the voter paradox reasoning are obviously deficient since such reasoning will leave me fat and governed by morons, maybe even rotted of tooth. It is the deficiency of these decisions (not to go to the gym, brush my teeth, vote, etc.) that warrants the voice of conscience to enforce (e.g.,through guilt) the Ulysses contract.

Your thoughts?  Are there reasons to answer the gym case or the voter paradox differently than I have?  Are there relevant disanalogies?  Have I left the self too splintered into too many “voices”?  See my post on Lackey’s counterexamples to knowledge as the norm of assertion for more splintering along these lines (though not exactly the same); I worried then as I do now that the kinds of analyses I’m suggesting will leave us all with philosophical mutliple-personalities.