Should a naturalist be a realist or not?

Unsurprisingly, the answer to the question in the title of this post depends on the details of what one takes 'naturalism' about science to mean. The shared conception of naturalism is something like 'There is no first philosophy' (I think Penny Maddy explicitly calls this her version of naturalism) -- that is, philosophy does not stand above or outside the sciences. "As in science, so in philosophy" is (one of) Bas van Fraassen's formulations.

Each of the following two quotes comes from a naturalist, but the first appeals to naturalism to justify realism (about mathematics), while the second appeals to naturalism in support of anti-realism (about science).

In his review of Charles Chihara's A Structuralist Account of Mathematics in Philosophia Mathematica 13 (2005), John Burgess writes:

"If you can't think how we could come justifiably to believe anything implying
(1) There are numbers.
then 'Don't think, look!' Look at how mathematicians come to accept
(2) There are numbers greater than 10^10 that are prime.
That's how one can come justifiably to believe something implying (1)." (p.87)

Compare van Fraassen, in The Empirical Stance (2002):

But [empiricism's] admiring attitude [towards science] is not directed so much to the content of the sciences as to their forms and practices of inquiry. Science is a paradigm of rational inquiry. ... But one may take it so while showing little deference to the content of any science per se.(p.63)

Both Burgess and van Fraassen are naturalists about their respective disciplines (mathematics and empirical sciences) -- but they disagree on what the properly scientific reaction to questions like "Are there numbers?" and "Does science aim at truth or merely empirical adequacy?" is.

The mathematician deals in proof. And proof is (at least a large part of) the source of mathematics' epistemic force. The number theorist (e.g.) assumes the existence of the integers and proves things about them; that's what she does qua mathematician. People with the proclivities of Burgess and van Fraassen would agree thus far, I think. But they part ways when we reach the question "Are there integers?" A Burgessite (if not John B. himslef) could say "If you're really going to defer to number theorists and their practice, they clearly take for granted the existence of the integers." A van-Fraassen-ite could instead say: "What gives mathematics its epistemic force and evidential weight is proof, and the number theorist has no proof of the existence of integers (or the set theorist of sets, etc.). Since there is no proof of the integers' existence forthcoming, asserting the existence of the integers (in some sense) goes beyond the evidential force of mathematics. Thus, a naturalist about mathematics should remain agnostic about the existence of numbers (unless there are other arguments forthcoming, not directly based on naturalism)."

Is there any way to decide between these forms of naturalism -- one which defers (for the most part) to the form and content of the sciences, and the other which defers only to the form? (Note: van Fraassen's Empirical Stance takes up this question, but this post is too long already to dig into his suggestions.)

Pessimistic induction + incommensurability = instrumentalism?

One popular formulation of Scientific Realism is: Mature scientific theories are (approximately) true.
One of the two main arguments against this claim is the so-called 'Pessimistic (Meta-)induction,' which is a very simple inductive argument from the history of science: Most (or even almost all) previously accepted, (apparently) mature scientific theories have been false -- even ones that were very predictively successful. Ptolemy's theory yielded very good predictions, but I think most people would shy away from saying 'It is approximately true that the Sun, other planets, and stars all rotate around a completely stationary Earth. So, since most previous scientific theories over the past centuries turned out to be false, our current theories will also probably turn out to be false. (There are many more niceties which I won't delve into here; an updated and sophisticated version of this kind of argument has been run by P. Kyle Stanford over the last few years.)

The kind of anti-realism suggested by the above argument is that the fundamental laws and claims of our scientific theories are (probably) false. But we could conceivably read the history of science differently. Many fundamental or revolutionary changes in science generate what Kuhn calls 'incommensurability': the fundamental worldview of the new theory is in some sense incompatible with that of the older theory -- the changes from the classical theories of space, time, and matter to the relativistic and quantum theories are supposed to be examples of such changes. Communication breaks down (in places) across the two worldviews, so that each side cannot fully understand what the other claims.

Cases of incommensurability (if any exist) could result in each side thinking the other is speaking incomprehensibly(or something like it), not merely that what the other side is saying is false in an ordinary, everyday way. An example from the transition from Newtonian to (special) relativistic mechanics may illustrate this: Suppose a Newtonian says 'The absolute velocity of particle p is 100 meters per second.' The relativistic physicist would (if she is a Strawsonian instead of a Russellian about definite descriptions) say such a sentence is neither true nor false -- because there is no such thing as absolute velocity. [A Russellian would judge it false.] If she merely said "That's false," the Newtonian physicist would (presumably) interpret that comment as 'Oh, she thinks p has some other absolute velocity besides 100 m/s; perhaps I should go back and re-measure.' To put the point in philosophical jargon: presuppositions differ between pre- and post-revolutionary science, and so the later science will view some claims of the earlier group as exhibiting presupposition failure, and therefore as lacking a truth-value, like the absolute velocity claim above. (Def.: A presupposes B = If B is false, then A is neither true nor false)

This leads us to a different kind of pessimistic induction: (many of) the fundamental theoretical claims of our current sciences probably lack a truth-value altogether, since past theories (such as Newtonian mechanics) have that feature. (If you want to call claims lacking truth-values 'meaningless,' feel free, but it is not necessary.) This is hard-core instrumentalism, a very unpopular view today; most modern anti-realists, following van Fraassen, think that all our scientific discourse is truth-valued (though we should be agnostic about the truth-value of claims about unobservable entities and processes). But this instrumentalism seems to be a natural outcome of (1) taking the graveyard of historical scientific theories seriously, (2) believing there is something like Kuhnian incommensurability, and (3) holding that incommensurability involves presupposition failure. And none of those three strike me as crazy.

Disclaimer: This argument has probably been suggested before, but I cannot recall seeing it anywhere.

Want a job? Come to Pitt HPS

As some of you know, I am in the last stages (throes?) of my PhD program at the University of Pittsburgh, in the History and Philosophy of Science (HPS) department. For those who are not familiar with it, the department is relatively small: there are usually about 8-9 faculty whose primary appointment is in HPS, and about 30 or so graduate students.

In an average year, 1 to 3 people from my department go on the job market, and the department has had a very good placement record since I've been here: everyone who graduated from the program has gotten a tenure-track job, either straight out of grad school or after a 1-2 year post-doc. But this year, we had ten people go on the market, eight of them (myself included) for the first time. There was a lot of hand-wringing and worry, by students and faculty alike, about having so many HPS people on the market at one time. The demand for folks like us, who prove theorems in the foundations of quantum gravity or trace out the technical development of Galileo's kinematic theory, is just not as high as for people who work in ethics or epistemology.

I am now happy to report that all ten people have found good positions: 8 people are beginning tenure-track jobs, and the other two are taking enviable post-doc positions (including filling fellow-blogger Gillian Russell's old spot as Killiam fellow). I won't give the list of where everyone is headed, since I haven't asked their permission to broadcast that information to the three people who read this blog. But I grant myself permission to announce that I will be starting next fall as an assistant professor at UNLV (the University of Nevada-Las Vegas). It's a great position for me, in a department full of smart, sensible, and funny people. I'll probably blog in more detail soon about why I'm so excited about it -- but for starters, it was 70 degrees when I visited in January!

UPDATE: The Killam Fellow mentioned above will have a tenure-track position, though it is not yet determined where he will be yet. So 9 of 10 will start tenure-track jobs.

Quantum logic question

I've been thinking about quantum logic (QL) recently, and in particular about the usual semantics for 'or' in QL. I've become puzzled, and hopefully someone out there in the blogosphere can help me clear up my confusion.

For the uninitiated: In QL, propositions are represented by/ interpreted as subspaces in a Hilbert space -- including one-dimensional subspaces, i.e. rays. There are multiple ways of formulating in colloquial language what these subspaces are to represent (see final paragraph below), but (atomic) sentences are usually taken to have the form:
'The value of observable O is o1'
where 'observable' just means any physical quantity (e.g., position, momentum, energy, spin), and o1 is just a particular value (or range of values) of that observable. (E.g. 'The energy of this system is between 4 and 6 Joules.') Such sentences are true iff the state-vector of the system lies within the subspace.

Now, think of a particle P in a superposition of spin up and spin down along the y-axis. This particle's state is of course represented by a different vector (call it V_s) than particles in the spin-up state (represented by V_up), or particles in the spin-down (V_down) state. However, because the usual QL semantics assigns to 'p or q' the linear span, instead of the union, of the rays associated with p and q, the claim 'P is spin-up or P is spin-down' will be true -- because V_s is in the linear span of the spin-up ray and the spin-down ray. Each of the disjuncts is false, but the whole disjunction is true. (To me, this feature of QL is even more striking than the failure of the so-called distributive law, i.e., [p&(q or r)] iff [(p&q) or (p&r)], which commentators on QL tend to focus on.)

This seems intuitively wrong to me (or at least as 'wrong' as something can be in formal semantics). In 2-D Euclidean space, suppose we have a unit vector V at a 45-degree angle to the x-axis. I don't think anyone would consider the sentence 'V lies along the x-axis or V lies along the y-axis' to be true. V is not a unit vector on the x-axis or on the y-axis, but a distinct third thing. I don't see why we would change policies in the quantum case, which appears analogous to me.

So now I can ask my question: could we change the semantics for 'or' to avoid these apparent problems? In particular, in the usual semantics for quantum logic, why must all propositions be represented as subspaces on a Hilbert space? -- why not also allow subsets (which might not be closed under linear combinations)? For then we could allow 'or' to mean the union of rays, and 'P is spin-up or P is spin-down' will come out false.

One further note: some people (e.g. R.I.G. Hughes, "Quantum Logic and the Interpretation of Quantum Mechanics," PSA 1980) take the atomic QL propositions to have a different correlate in colloquial language. Instead of
'The value of observable O in system S is within o1,'
they take the subsets of Hilbert space to mean
'The result of a measurement operation for observable O in system S is within o1.'
Under this understanding, my above worries disappear -- for the result of a spin-y measurement surely will be either spin-up or spin-down. However, QL then becomes much less interesting, because it is just about measurement outcomes, instead of about these supremely odd things, superpositions.

realism and the limits of scientific explanation

Long time, no blog. I finally got back a few days ago from the last of my visits to schools for final job interviews. It was very interesting and instructive to observe non-Pittsburgh philosophers in their native habitats. I should know by the end of this week where I'll be next year.

In lieu of an actual post, I am putting up the handout I used at a couple of my job talks. As a result, it looks programmatic/ bullet-pointy; but I tried condensing this into a normal post, and it was just far too long. If you can make out what's going on, I would really appreciate any feedback/ comments/ eviscerations from readers.

REALISM AND THE LIMITS OF SCIENTIFIC EXPLANATION

The argument

(P1) Scientists do not accept explanations that explain only one (type of) already accepted fact.
(P2) Scientific realism, as it appears in the no-miracles argument, explains only one type of already accepted fact (namely, the empirical adequacy or instrumental success of mature scientific theories).
(P3) Naturalistic philosophers of science “should employ no methods other than those used by the scientists themselves” (Psillos 1999, 78).

Therefore, naturalistic philosophers of science should not accept scientific realism as it appears in the no-miracles argument.

Explanation and defense of (P1)

Explanations that explain only one type of already accepted fact
(i) generate no new predictive content, even when conjoined with all relevant available background information [‘already accepted fact’], and
(ii) do not unify facts previously considered unrelated [‘only one type’].

Evidence for (P1): Scientists reject
- Virtus dormativa-style explanations
- ‘Vital forces’/ entelechies as explanations of developmental regularities
- Kepler’s explanation of the number of planets, and the ratios of distances between them, via the five perfect geometrical solids
- ‘Just-so stories’ in evolutionary biology

The no-miracles argument for scientific realism

Abductive inference schema
(1) p
(2) q is the best explanation of p
Therefore, q

No-miracles argument for scientific realism
(1) Mature scientific theories are predictively successful.
(2) The (approximate) truth of mature scientific theories best explains their predictive success.
Therefore, Mature scientific theories are (approximately) true.

Proponents of the no-miracles argument (Putnam, Boyd, Psillos) accept (P3), appealing to naturalism to justify their abductive inference to scientific realism. Putnam claims that scientific realism is “the only scientific explanation of the success of science” (1975, 73).

The argument for (P2): Scientific realism (i.e., the claim that mature scientific theories are approximately true)
(i) generates no new predictions,
(ii) unifies no apparently disparate facts, and
(iii) explains only one previously accepted fact, viz., science’s predictive success.

philosophy of science in the blogosphere

I've recently noticed two new philosophy of science blogs on the internets worth following:

(1) Brains, by Gualtiero Piccinini, a recent grad of my department. As the title indicates, this leans towards cognitive science issues. This is the area of philosophy of science I know the least about, so I'm hoping keeping up with Gualtiero's blog will show me at least the tip of the iceberg.

(2) Words of Mass Dissemination, by Mickael Dickson, the current editor of the journal Philosophy of Science (which, from what I can tell, is widely agreed to be the leading North American periodical on philosophy of science). I have no idea how he'll have time to keep up with his editorial duties and make blog posts, but I certainly hope he does manage to juggle them both. (Though, it looks like posting has slowed down a bit recently.)

I apologize that it has been so long since my last real/ philosophically substantive post. Virtually all of my brain waves are currently dedicated to the job search, but I am working on a post about quantum logic (which, coincidentally, the above-mentioned Prof. Dickson has written on recently) that I hope will be up soon, once I figure out a couple more things.

A job candidate at the APA

I just returned to Pittsburgh from the American Philosophical Association meeting, where I had job interviews and gave a talk. This was my first trip to the APA, and many people had painted for me a picture of it as red in tooth and claw. There was a fair amount of anxiety in the air, but that's to be expected when 600 or so job-seekers are stuffed into a cage (I'm making up the number 600; there may have been more). But the whole affair was less psychologically traumatic than I had expected -- it was good to see old friends, all my interviews led to interesting and enlightening conversations (I never felt like I was being 'grilled,' much less attacked), and I met people I had only previously known in blogospheric form.

There was one difficulty with the conference that I did not expect: it was physically exhausting. I remember one faculty member who, a few months ago, advised job-seekers not to apply to every single job that they could, on the grounds that you don't want to have too many interviews at the APA. "Too many interviews?" -- I thought -- "How can you have too many?" Well, that person was right. I had a hard time keeping up my energy and focus for the interviews I had, and some people in my department had many more than me... I don't know how they did it.

I expect blogging to remain light here for the next couple of months, since I'm now entering the final stage of the job search process.

promotion of self and others

If any readers are going to be at the American Philosophical Association meeting this week in NYC, and want to see some obscure and confused ideas incarnate, I'll be presenting Friday morning (the 30th) at 9AM. It's a philosophical logic paper; you can preview it here.

Also, I noticed two brand-new blogs of potential interest: The Hedgehog Review, covering the early modern period, and Boundaries of Language, dealing with (you guessed it) philosophy of language.

A "Gourmet Report" for grad school mentoring

Most (if not all) of the readers here are familiar with Brian Leiter's Philosophical Gourmet Report, which ranks graduate programs by the research quality of each department's members. The PGR's primary goal is to help clueless undergraduates (such as myself 6 years ago) figure out which programs are strongest -- both overall and in particular sub-fields of philosophy. Leiter has consistently pointed out that the quality of a faculty's published books and articles is only one determinant or indicator of what kind of graduate school experience to expect at a given program: quality of faculty mentoring of students, for example, makes a huge difference in one's graduate school career -- but that does not show up at all in the Gourmet Report.

Happily, Jonathan Feagle is now trying to fill that lacuna for prospective grad students in philosophy. He is in the planning stages of what he's calling The Athena Project. He is planning to send out surveys to graduate students in philosophy in March 2006. Right now, Jonathan is requesting feedback on his current slate of survey questions, as well as suggestions for other survey questions and/or for the mechanics of administering the survey when the time comes. Hopefully, enough people will be interested in this clearly worthwhile project to generate an excellent questionnaire and, subsequently, some statistically significant data. (Note: the survey is explicitly avoiding more 'personal' issues: there will be no place for anything in the neighborhood of "My dissertation advisor is an inconsiderate jerk.")

The Philosophical Gourmet Report is, as Leiter himself says, not a perfect instrument. But it is much better than the other limited resources available to undergraduates considering grad school. From what I've seen, the Athena Project has similar promise to be an imperfect but nonetheless very useful tool for people picking a program.

Descartes on colors and shapes

As is well known, Descartes argues that the sensation of white in our minds when we look at snow does not resemble whatever it is in the snow that produces this sensation in us. (He puts this point in different ways in different places; e.g., sometimes he says that our sensory awareness of whiteness leaves us "wholly ignorant" of what the snow is like (Principles of Philosophy, I.68).) The same holds for many other sensory qualities: the pain we feel when we put our finger in the fire does not resemble anything in the fire, the sweet scent we have of honey does not resemble anything in honey, and so on.

But what about my sensory awareness of the shape of a snowball, a fireplace, or a honey jar? In these cases, Descartes takes a different line: "We know size, shape, and so forth in quite a different way from the way in which we know colors, pains and the like" (PP, I.69). What is this difference? Descartes writes: "there are many features, such as size, shape, and number which we clearly perceive to be actually or at least possibly present in the in objects in a way exactly corresponding to our sensory perception or understanding" (PP, I.70).

So the obvious question here is: what makes our sensory perception of shape different from our sensory perception of color, so that the former but not the latter can 'correspond to' or resemble the thing represented? Descartes' argument in the final quotation above strikes me as weak. Descartes says that we clearly perceive that our sensory perceptions of shapes either (i) actually resemble or (ii) possibly resemble something in the objects themselves. Regarding (i), I strongly doubt that we can clearly and distinctly perceive anything about the relationship between the ideas in our minds and the objects outside of us -- we would need to be able to 'step outside of our minds,' as it were, to survey and compare both the contents of our minds and objects as they really are. And if we take (ii), then it at least seems possible to me that my sensory awareness of white resembles some property in the object itself. Of course, that would be a fortunate coincidence, but coincidences are not impossible. (Perhaps Descartes' notion of possibility rules out more than our modern one(s)?)

So, is there a way to save Descartes' position that our sensory perceptions of shapes can/do resemble something in the objects themselves, whereas our sensor perceptions of colors can/ do not? Perhaps the piece of wax section in Meditation 2 could be of some help here?

Update: I had forgotten that this very problem also arises, perhaps more expiciltly, in Locke's Essay: Locke says that our ideas of primary qualities (shape, mobility, solidity, extension, and number) really do "resemble" their causes in the objects that we perceive (II.viii.15). And perhaps because this claim is more front-and-center in Locke than Descartes, commentators on the Essay from Berkeley through today have had difficulty making good sense of this claim. Berkeley brings out the problem clearly: is the idea square in my mind actually square-shaped? Is my idea of motion itself moving?