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?

Fantastic new Darwin resource

Today my faith in the web as an instrument of enlightenment was restored: the complete works of Darwin will soon (December 15th) be freely available online. The site, which currently has a detailed project description posted, is:

http://darwin-online.org.uk

Thanks to the Philosophy of Biology blog for the pointer. (Does anyone else wonder whether we would have this ID controversy in the US if Darwin were an American? The UK (from what I've seen) holds him up as a national hero of sorts, and this project is just the latest instance of their Darwin valorization.)

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.

Astrology, Astronomy, and the Scientific Revolution

One of the large-scale questions in academic discussions of the Scientfic Revolution concerns the relationship of the developments we today consider scientific to traditions we today consider pseudo-scientific or mystical, e.g. alchemy, astrology, and magic. People who make pronouncements like "There was no such thing as the Scientific Revolution" often justify such a claim by identifying and stressing continuities between mystical/ magical traditions and various new ideas that we now deem 'scientific.'

It is undeniable that significant continuities and similarities exist between pre-revolutionary views of nature and later ones. But I have often had the gut feeling that people sometimes overstate the case. Here is one example, from a brilliant historian of science, Allen Debus:

Some of the scholars, whose work contributed to our modern scientific age, found magic, alchemy, and astrology no less stimulating than the new interests in mathematical abstraction, observation, and experiment. Today we find it easy -- and necessary -- to separate "science" from occult interests, but many could not. (Man and Nature in the Renaissance)

This seemed overblown to me, because from Ptolemy up through Renaissance astrologer-astronomers such as Girolamo Cardano, the distinction between astrology and astronomy is explicitly drawn, and the historical figure often argues for the location of the boundary. So Debus's claim that students of nature during the Scientific Revolution 'could not separate science from occult interests' struck me as demonstrably false -- they could, and they did (at least in the case where the science is astronomy and the occult field is astrology).

But, as I have been working on my Magic, Medicine, and Science class (discussed last post), I've started thinking that there is something very right about Debus's idea, even if I would not couch the matter exactly as he does. What struck me is that, in the Ptolemy-Cardano scheme, astrology is classified as part of physics (in the Aristotelian sense, i.e. the study of nature), for it studies the physical influences of the sun, moon, planets and stars upon the Earth and its inhabitants. (Some astrologers thought the celestial bodies also had non-physical influences on us and our environs.) Astronomy, as mentioned in my last post, was classified as part of mathematics. Ptolemy, for one, states very clearly in Tetrabiblos that astrology studies physical, material causes associated with celestial bodies, whereas astronomy does not. And Cardano writes that astrology, unlike astronomy, studies "how lower things are linked to the higher ones."

So what is right about the Debus quotation? From the point of view of the Ptolemy-to-Cardano distinction between astronomy and astrology, the people working in the 17th C on a new physics of the celestial realm were apparently doing astrology, not astronomy. When Kepler is attempting to discover the physical cause of the planetary orbits, under the older taxonomy, that can't be astronomy, since astronomy does not deal with physical, material affairs. Thus what Kepler is doing (since it's still about the celestial realm) would naturally be classified as astrology. (And perhaps, though this is wild and irresponsible speculation, that partially explains why Kepler's theory, which appeals to entities like the Sun's 'motive soul,' has elements strongly reminiscient of earlier astrology.)

One possible problem with this idea: is there perhaps, in the Ptolemy-to-Cardano classification scheme, a separate heading for works like Aristotle's De Caelo, which does not appear to be straightforwardly astrological? That is, just because the old taxonomy won't count Kepler as astronomy, that doesn't imply that a celestial physics must be astrology: there could be some third category under which De Caelo and Kepler fall. Gentle reader, do you have any information to guide me here?