One way to test scientific realism

One way of formulating Scientific Realism is as follows:
What our successful scientific theories say about unobservable entities and processes is approximately true.
This is not the only way to formulate scientific realism, but it is one of the more common ones, and it does effectively separate realism from versions of anti-realism which hold that we are not justified in believing what our theories say about unboservables.

Obviously, this version of Scientific Realism cannot be directly tested using our current theories and current technology, since what is currently unobservable can't be observed now.

However, what is observable shifts over time (at least in one important sense of the word 'observable'). This can happen either because (1) we develop the ability to reach new regimes of old variables (e.g. scientists create technology to make materials colder or hotter than we previously could, or we can study bodies moving at higher and higher velocities), or because (2) scientists develop new instruments that enable new types of observation reports (e.g. telescopes, microscopes, fMRI machines, or mass spectrometers).

This suggests a way to test realism diachronically, using the historical record. First, find something that went from being unobservable to being observable. Then find theories that were (considered) genuinely successful at that earlier time, and see what claims it made about the previously-unobservable-but-now-observable world. Finally, check those claims against the now-observable reality.

Scientific Realism (at least the version stated above) predicts that the old claims about the previously-unobservable things will usually approximately match the new observations of those things. (I say 'usually' instead of 'always,' because sensible realists are fallibilists.)

I have not run this test myself. To do it in an intellectually responsible way, a large survey of past transitions from unobservable-to-observable would have to be collected, and steps would have to be taken to make that sample of transitions representative. However, at first glance, it looks like at least some cherry-picked famous examples don't bode well for the realist's prediction:

• The telescope played a significant role in the scientific revolution
• The vacuum pump played an significant role in the scientific revolution
• The ability to cool things down further and further led to the discovery of superconductivity
• The ability to study bodies at higher and higher speeds was crucial in the transition from classical mechanics to special relativity

There are historical examples that run in the realist's favor too; I think one good example is that (on the whole, i.e. usually) phylogenetic trees generated via molecular data matched previously existing phylogenetic trees fairly closely (i.e. the old trees were usually 'approximately true,' which is all the realist wants). This is why, as I said, we need a large survey to figure out which historical transitions reflect the overall, general pattern, and which cases are outliers.
{ADDED LATER (May 2022): Simon Allzen's "From Unobservable to Observable: Scientific Realism and the Discovery of Radium" is another nice, detailed example that's intended as an example in the realist's favor. Here's a representative quotation: "an entity considered to be unobservable can be inferred at one stage in the process by virtue of its role as indispensable for predictive success [i.e. via IBE -- GF-A], only to change into an observable at a later stage, thus confirming the reliability of the inference. As a case study of the conceptual changes of entities I use the discovery of radium."}

Finally, in terms of already-existing arguments, this is not really very different from the Pessimistic Induction (if at all). I think of it as a specialized version of that argument, focusing on the realist's claim that the observable/ unobservable boundary does not mark an epistemically important distinction. For this reason, I think of the above as a diachronic version of Kitcher's "Real Realism" (which potentially comes to the opposite conclusion of Kitcher's view).

Scientific Realism via the internets

I recently found out that Philosophy of Science has conditionally accepted an article I wrote on the no-miracles argument. This is a stroke of good luck, and it's also a testament to the philosophical blogosphere: basic ideas in this paper were hashed out on this blog (see especially here), and honed by readers' astute criticism. Perhaps the paper wouldn't have been good enough for acceptance otherwise.

I would greatly appreciate further help on the paper before I send away the final version; the current draft (in rich text format) is here. Here's an abbreviated abstract:

1. Scientists (usually) do not accept explanations that explain only one type of already accepted fact.
2. Scientific realism (as it appears in the no-miracles argument, or NMA) explains only one type of already accepted fact.
3. Psillos, Boyd, and other proponents of the NMA explicitly adopt a naturalism that forbids philosophy of science from using any methods not employed by science itself.
Therefore, such naturalistic philosophers of science should not accept the version of scientific realism that appears in the NMA.

And as long as I am singing the praises of the blogosphere and begging for readers, P.D. Magnus (of the excellent Footnotes on Epicycles blog) and I have a draft of a paper on another aspect of the scientific realism debate (in pdf format) here. We ask, and give a partial answer to, the question: When should two empirically equivalent theories be regarded as variants of one and the same theory? Comments large and small are appreciated!

Are there empty predicates?

Empty names are names that fail to refer, like 'Santa,' 'Pegasus,' and 'Planet Vulcan.' 'Santa Claus' fails to refer because (on most semantics for empty names) there is no entity that is assigned to 'Santa' as its referent. This is clearly distinct from another view (e.g. Frege's) that 'Santa' should be assigned e.g. the empty set as its referent. That is, there is a difference from having no referent and referring to the empty set -- for my cat has no referent, but '∅' refers to the empty set.

So are there empty predicates? That is, are there predicates that do not signify properties (or extensions, kinds, intensions (= functions from possible worlds to extensions), or whatever your preferred semantic value for predicates is). There are of course predicates whose extension is the empty set (e.g. 'is not identical with itself') -- these predicates signify uninstantiated properties (assuming you think predicates signify properties). But they still signify a property.

There is a fairly massive literature on empty names. (I can recommend Ben Caplan's 2002 dissertation as a nice survey of the empty names landscape.) But there is no talk of empty predicates -- is this because somehow every predicate, unlike names, automatically refers?

Related issue: Philosophers of science often say things like 'phlogiston' and 'caloric' fail to refer. Often, in explaining their claim "The word 'phlogiston' does not refer", these philosophers will say things like "The extension of the predicate 'is phlogiston' (or 'contains phlogiston') is empty." But having the empty set for your extension is different from failing to refer. So when we say that 'contains phlogiston' fails to refer, it seems like we should be saying that it has no (determinate?) extension, not that its extension is empty.

So are there any empty predicates? Are such things even possible? And can the usage of the philosophers of science be defended?

Can a widespread local realist be a global anti-realist?--and the preface paradox

I have been thinking about whether there might be something like the preface paradox in the scientific realism debates. There is now a distinction being drawn between local (or 'retail') realism, in which one argues for the truth of particular scientific theories (e.g. quantum mechanics) or the existence of particular scientific entities (e.g. quarks), on the one hand, and global (or 'wholesale') realism, in which one argues for the approximate truth (or referential success) of mature scientific theories in general.

What I'm wondering is whether it can be justified and/or rational to be an everywhere local realist (so QM is approximately true, and general relativity is approximately true, and population genetics is (approximately) true, etc.), but still be a global anti-realist -- say, because you place a lot of weight on the pessimistic induction on the history of science. Or, on the other hand, whether everywhere local realism really pushes us towards global realism.

I'm currently guessing that one CAN be an everywhere local realist without being a global one, for the following two reasons.
(1) One standard response to the preface paradox seems perhaps even more applicable here than in the preface case: while the author assigns a high probability to each individual assertion in her book, the probability of (p & q & r & ...) will be low.
(2) Also, although if A is true and B is true, then 'A and B' must be true, it seems to me that even if A is approximately true and B is approximately true, then 'A and B' need not be approximately true, for A and B could be contradictory (for example, the prima facie conflict between quantum mechanics and general relativity).

I'm happy to hear any reasons for the opposite view, viz. that widespread local realism pushes us towards global realism.

Azzouni and existential commitment in science

Last week Jody Azzouni was here to give a pair of talks: one about scientific theories, another about his view that English is inconsistent in a pretty radical way: Every sentence is both true and false. They were both a lot of fun, and Jody is a great interlocutor -- he kept both presentations relatively short and to the point to there'd be more time for questions and clarifications. I also have a soft spot for arguments defending unpopular ideas -- though I usually side with the orthodoxy, incredible ideas are often a bit more interesting to think about.

In the philosophy of science talk, Jody was building on his work on what he calls "thick epistemic access." His argument was that we should not (contra Quinean orthodoxy) have existential committment to all the posits of our current best scientific theory, but rather only those posits to which we have thick epistemic access. (See e.g. Kenny's post here for a quick but accurate description of thick v. thin v. ultrathin posits.)

I was wondering, however, whether the Quinean orthodoxy could be undermined in a more direct way that does not involve developing a whole epistemological apparatus to distinguish when we really do have strong evidence that such-and-such thing exists. (Such a question is certainly philosophically interesting and worthwhile, but it is likely to be complex and contentious in places.) Rather, I thought a simpler argument against the Quinean orthodoxy could go as follows:
Science is rife with idealizations -- some of which are ineliminable/ indispensible. But no one should be committed to such idealizations, since they are (almost by definition) deliberate and conscious falsifications in our theoretical account of the world. So existential commitment does not follow our best theories as well as Quine would like.

I realize that (1) there may sometimes be a legitimate question about whether a given bit of a theory is an idealization or not, but that just shows the term 'idealization' is vague -- all parties agree there is some idealization in science, even if they don't agree on every case. Also, (2) most examples of idealizations are not entities, but rather inaccurate properties (e.g., treating some body that we know to exist, like a point particle: we give an inaccurate description of the thing's dimensions). So maybe pointing out the widespread use of idealization will not create widespread problems for the Quinean orthodoxy.

Can a sentence without a truth-value ever be approximately true?

I am curious to hear people's thoughts on the question in the title. There has been a lot of philosophical work done on the idea that a sentence can be strictly speaking false, yet nonetheless approximately true (or 'truthlike' or 'verisimilar'). For example: I am 5'11", but if someone said 'Greg is 6 feet tall,' we want to say that that claim is approximately true or something like that. But what if the claim was (strictly speaking) neither true nor false? (Readers may insert their own favorite truth-valueless sentence here.)

I ask because, as I mentioned in an earlier post, I'm toying with the idea that the Pessimistic Induction over the history of science plus something like Kuhnian incommensurability (esp. untranslatability) will lead us not to the conclusion that current science is likely to be false, but rather is likely to lack a truth-value. For if we cannot translate the claims of a pre-revolutionary language into the post-revolutionary one, then the pre-revolutionary language (from our current point of view) is truth-valueless, not false.

I ask the question in the title because one common realist response to the Pessimistic induction is: "Well, yes, our current scientific theories are probably not exactly true, but they are approximately true." If truth-valueless sentences cannot be approximately true, then this response is not available to the realist.

APA wrap-up: Kyle Stanford's "New Induction"

My time at the APA last weekend was pretty good: I learned a few new things, met some new people I've been wanting to meet, and got to catch up with a couple old friends. Particularly helpful/ enlightening presentations included Angela Potochnick on how the context of inquiry shapes explanation, Ken Waters (plus commenters Jay Odenbaugh and Michael Strevens) on causes that make a difference (not, I learned, to be confused with the conception of causes as 'difference-makers'), and the Author-Meets-Critics session on Kyle Stanford's Exceeding Our Grasp.

Stanford's basic claim is that current scientific theories are underdetermined -- not because we can generate empircially equivalent rivals to our currently accepted theories, but rather because at many, many times in the past, the scientific community has been unable to conceive of good alternatives to the then-current theory. The evidence that such alternatives exist is the fact that they are proposed and accepted centuries later: thus, Newton's mechanics did not consider special relativity as an alternative hypothesis; Newton's, when he proposed his gravitation theory, did not consider the general theory of relativity as an alternative; no classical physicists before 1900 considered quantum mechanics as an alternative explanation of the data, and so on. This is what Stanford calls the "New Induction" over the history of science.

The idea, as just presented, strikes me as a promising line to take. But there is one aspect of Stanford's presentation of the problem that I don't understand. Fiona Cowie asked (in part) about this in the question and answer session, but I still didn't follow the answer. Stanford says that (e.g.) in 1700, the special theory of relativity and Newtonian mechanics were "(roughly) equally well-confirmed". Similarly for the other cases: the future theory is supposedly just as confirmed as the old one -- even in the past.

I don't understand why Stanford says this for two reasons: (1) He doesn't need the theories to be equally well-confirmed for his point to hold (viz., scientists aren't even conceiving of a hypothesis that will later be accepted as superior), and (2) it seems false to me, on any reasonable (i.e., not hardcore hypothetico-deductive)notion of confirmation. In 1700, it is true that special relativity and Newtonian mechanics agreed on all the consequences that could then be observed. But someone who, in 1700, said "Newton is approximately right, yet when something goes really, really fast its length will contract and its local time will dilate from the point of view of slower-moving observers" -- there is NO evidence at all for postulating that further bit of theory. And it's the same with GTR (what evidence would there've been for gravitation being a 10-component tensor instead of a scalar?) and especially QM (what evidence was there for thinking a body cannot have a determinate position and momentum simultaneously?). In 1700, these now-accepted alternatives were consistent with the data, but they were not equally well-confirmed.

Note: a very similar line of objection is pushed at the end of P.D. Magnus's "What's New about the New Induction?" (Synthese, 2006), though he develops it slightly differently, I think. (As I understand him, P.D. claims that in 1700, STR, GTR and QM would look like 'gruesome' hypotheses.)

On the Darwinian explanation of the success of science

I really don't have time to post now, but I'm going to anyway. Van Fraassen writes: "I claim that the success of current scientific theories is no miracle. It is not even surprising to the scientific (Darwinian) mind. For any scientific theory is born into a life of fierce competition, a jungle red in tooth and claw. Only the successful theories survive--the ones which in fact latched on to actual regularities in nature." (Scientific Image, p.40)

James Robert Brown, in "Explaining the Success of Science" (Ratio, 1985) agrees that this Darwinian explanation can account for the first two aspects of success, but not the third:
(1) The sciences "are able to organize and unift a great variety of known phenomena.
(2) This ability to systematize the empirical data is more extensive now than it was for previous theories.
(3) A statistically significant number of novel predictions pan out; that is, our theories get more predictions right than mere guessing would allow." Brown says of (3): "Here the Darwinian analogy breaks down since most species could not survive a radical change of environment, the analogue of a novel prediction."

First a small point: I don't think a novel prediction needs to be analogized to a radical change in environment -- perhaps some should be, but it's not necessary. If an organism can handle living and reproducing in any new environment, i.e., one for which its various features were not historically adapted, then that seems a decent enough analogy to a novel prediction (which makes a prediction different from the cases the thoery was originally designed to handle). A 'radical' change in environment might precipitate a scientific revolution -- i.e., the science (like the organism) might not survive.

Now, a more substantive point, and one which perhaps pushes the analogy farther than is fair. The paleobiologist David Jablonski has shown that genera that are more geographically widespread are more likely to survive mass extinction events (such as the meteor that killed off lots of the dinosaurs). The analogy would be, I suppose, to groups of related theories that 'organize and unify' a greater variety of phenomena -- which are precisely the groups of theories that we (including van Fraassen) count as most successful. So it appears that a van Fraassenite Darwinian has a nice answer to J.R. Brown: viz., the more successful groups of theories will be more likely to deliver novel predictions.

But unfortunately for the van Fraassenite, the biological story doesn't end there. What is strange about Jablonski's results is that a species' being geographically widespread has no statistical correlation with its probability of surviving a mass extinction event. The correlation only appears at the level of genera. (Side note: For the philosophers and biologists who think about group selection, this looks like an instance of it.) So, the analogy would go, the more unifying particular theories do not enjoy any advantage in novel prediction over the less unifying, but the more unifying groups of theories would. Hopefully you can see why I suggested that this may be pushing the analogy too far: I'm not sure there's anything in the domain of science that would correspond nicely to the concepts of genus and species in the evolutionary domain. Although (and now I'm really stretching), if one could be made out, perhaps the structural realists could cash out their notion of structure at the level of the genus, and thereby capture why particular theories come and go, but the structure tends to survive through revolutions.

p.s. -- Can anyone recommend a good article completely devoted to arguing for or against this Darwinian explanation of science's success? I've seen several parts of book chapters or parts of papers dealing with it, but I can't recall seeing a fine-tooth-comb analysis of it.

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.

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.

Osiander and Anti-realism

This is another post from the frontlines of the class I'm teaching on Early modern philosophy and the scientific revolution. For those who haven't ever looked at Copernicus's On the Revolutions of the Heavenly Spheres, the book's first preface is written by a man named Andreas Osiander (though this preface was left unsigned in the original work).

In this preface, Osiander advocates for (what today would be called) an anti-realist conception of astronomy: the aim of astronomy is not to arrive at "true or even probable hypotheses," but rather to construct a mathematical model that will generate accurate predictions of the observed apparent locations of the celestial bodies.*

Osiander has come in for a lot of criticism, both from his contemporaries (like Rheticus, who entrusted the publication of Copernicus's book to him) as well as current commentators. However, I think the justifications Osiander offers for his view that we should not take astronomical models as literally true are not crazy. First, he notes that, if Ptolemy's model is correct, Venus's apparent size in the sky should change a great deal more than it actually does. That is obviously an empirical argument that Ptolemaic models do not reveal the true structure of the cosmos -- even though these models do make accurate predications about the location of Venus in the nighttime sky. Second, Osiander claims that there are genuine incompatible theories that both account equally well for the phenomena: he asserts that the Sun's observed motion can be modelled using an eccentric circle as basis or using an epicycle. (Unfortunately, I don't know anything about the details of this example.) If this is a genuine example of inconsistent but observationally equivalent theories, then Osiander has as good an argument against interpreting astronomical theories as literally (approximately) true as any argument given by an anti-realist motivated by underdetermination arguments.

Finally, note that these reasons for anti-realism are specific to astronomy. Thus we should not take Osiander to be advocating a general anti-realism towards all of science. To borrow the terminology of Magnus and Callander's recent "Realist Ennui" paper in Philosophy of Science, Osiander is not offering a "wholesale" argument for anti-realism, but a "retail" one, i.e., one specific to our pretensions to knowledge of the true physical structure of the universe.

________
* Tagging Osiander with various forms of anti-realism has been contested; see Barker and Goldstein's 1998 "Realism and Instrumentalism in Sixteenth Century Astronomy: A Reappraisal," in Perspectives on Science. They do agree, however, that Osiander considers knowledge of the true physical characteristics of the cosmos to be forever beyond human reach -- which strikes me as something a modern anti-realist might say. They also make the last point in the above post -- Osiander's skepticism is restricted to astronomy.

Underdetermination and equivalence modulo p

Since the description of this blog states that it deals with "issues in logic" related to philosophy of science, I figure that, for the sake of truth in advertising, I should post something logical. (Though I don't feel particularly rushed: there are already a fair number of smart logicians actively participating in the blogosphere -- check my blogroll. For reasons I don't understand, the situation is different in philosophy of science. Any armchair anthropologists have an explanation?)

Underdetermination arguments occur in many quarters of philosophy: Descartes' demon is perhaps the most famous, but they have also played a leading role in discussions about scientific realism during the last few decades. In this post I want to characterize a particular sort of underdetermination using elementary logical notions. (This form of underdetermination either is -- or is closest to -- the Quine-Duhem variety, I'm not sure which at the moment.)

Consider two sets of sentences, A, B such that neither set is a logical consequence of the other. Now suppose there is a third set of sentences C such that:
If C then (A iff B).
That is, if we assume that C is true, then A and B are logically equivalent. (In all models where C is true, either both A and B are true, or both are false).
Then we say A and B are equivalent modulo C.

How does this relate to underdetermination? We can have two theories that are not logically equivalent (and thus are not 'the same theory'), but do become logically equivalent if we make some further assumptions (C above) -- and these further assumptions can be taken to be "auxiliary hypotheses" or "background knowledge" (or whatever one wishes to call the other claims a theory uses, besides its own, to make predictions). If we are committed to the truth of the background knowledge, then we cannot decide between the two theories.
(If this is a bit abstract, here's a toy example:
A = M and (if p then q) [assume M says nothing about p or q]
B = M and (if p then not-q)
C includes the sentence 'not-p';
so neither of A and B implies the other; if C is true then A and B are logically equivalent, while if C is false then A and B are inconsistent.)

My question: is anything philosophically interesting going on here? If we hold r to be true, do we really need to choose between (r or s) and (r or not-s)? I think not -- though they differ in logical content, they are not rivals (or are they?). At least, if we take r to be true, then they are definitely not rivals, though they might be considered rivals ‘on their own’. They certainly are genuine competitors when we hold r false -- though then they are no longer equivalent in any sense.

Comments:
1. This is not the usual sort of underdetermination situation. First, the notion of "empirical content" (or "empirical equivalence," i.e. identity of empirical content) does not appear, so the much-maligned observable/ unobservable distinction is never mentioned. Second, and more importantly, the two theories A and B are not incompatible: the Cartesian demon, on the other hand, is either deceiving us or not (at least on the usual interpretation). The demon-hypothesis is incompatible with the 'real-world' hypothesis. On the other hand, 'if p then q' and 'if p then not-q' are not inconsistent -- we need simply hold that 'not-p' is true.

2. How does this relate to a ‘real’ example, e.g. Bohmian mechanics? It is empirically equivalent to standard quantum mechanics as long as absolute position is undetectable -- but not if absolute position is detectable. In other words, the standard theory and the Bohmian theory are empirically equivalent modulo the claim that absolute position is undetectable. And that is structurally similar to the toy example above. (Of course, there is the difference in this case that the two theories are 'empirically equivalent modulo p,' not 'logically.')

3. Lastly, it is probably considerations akin if not identical to the above that prompted philosophers to move to ‘total theories’ (i.e. theories PLUS all their auxiliary assumptions) as the proper objects of epistemic evaluation. See e.g. (Leplin, Erkenntnis, 1997).