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.)

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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.

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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.