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:


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?


The reasonable effectiveness of mathematics... for Ptolemy

The class I am teaching this term covers the emergence of Early Modern philosophy and science. The first five weeks are devoted to a whirlwind tour of Ancient Greek natural philosophy (plus a bit of Renaissance thought), and the last 10 weeks cover 17th century philosophy and the scientific revolution.

We spent half of the past week discussing Ptolemy, and I was struck by something that I had noticed before, but never really appreciated. It is very natural for Ptolemy to use fully 'mathematized' explanations for astronomical phenomena, but not for (most) other physical processes. Why? On Ptolemy's view, astronomical objects share more properties with mathematical objects than they do with terrestrial objects. He thought that astronomical objects are eternal and their properties are unchanging -- like the number 5, but unlike terrestial ones. We give a mathematical treatment of astronomical phenomena because they exhibit properties of mathematical objects.

The application of mathematical methods in Ptolemaic astronomy helps bring into focus the so-called problem of the unreasonable effectiveness of mathematics, which some days appears to me to be an unequivocal pseudo-problem. Ptolemy's application of mathematics to physical phenomena, I think, appears extremely well-justified compared to our own: astronomical phenomena can be mathematized because they share peculiar features with mathematical objects, features that the mundane, material objects in our immediate surroundings lack. During and after the scientific revolution, we preserved and expanded Ptolemy's mathematizing proclivities, but we apparently relinquished his justification for treating the natural world mathematically.

Update (10/02/05): Kenny over at Antimeta just put up an interesting post on the (un)reasonable effectiveness of mathematics too, and it is in (small) part a comment on my post.


Einstein and the Units of Selection

No, the title of this post is not a typo. I just finished reading through the first three articles in the most recent issue of Philosophy of Science. They are an argument-response-rebuttal between Elisabeth Lloyd ("Why the Gene Will not Return"; "Pluralism without Genic Causes?") and Ken Waters ("Why Genic and Multilevel Selection Theories Are Here to Stay"), who is one of her targets in the original essay. As the biologically-inclined among you will have inferred, this is the latest installment in the long-standing units of selection debate; very roughly, the question in these debates is: Upon what does natural selection operate? Organisms? Genes? Groups of organisms?

Ken Waters' basic response to this question -- which he first articulated in "Tempered Realism about the Force of Selection" (Philosophy of Science 1991) -- is that there is no determinate fact of the matter about whether selection is really acting at the level of the gene or the organism/ genotype. Mathematical models can be constructed in terms of genes and in terms of genotypes, and both kinds of model suffice to represent the facts of dynamic changes in populations. (See "The Dimensions of Selection," P. Godfrey-Smith and R. Lewontin, Philosophy of Science 2002, for an excellent treatment of the niceties of of the situation.) Since these different models do not represent different facts, Waters concludes that we will choose between them on pragmatic grounds. In the language of his current paper, Waters says that different models "parse" the causal structure differently.

For the purposes of this post, I will assume Waters is correct to maintain that there is no fact of the matter about whether the true cause of any particular evolutionary change lies at the level of the gene or the genotype. What I want to do is to compare this situation with Einstein's reaction in (what I consider) an analogous situation.

At the beginning of Einstein's 1905 paper that introduces special relativity, he asks us to imagine a conductor and a magnet in relative motion with respect to each other. If the take the conductor to be at rest and the magnet moving, then Maxwell's theory says that an electromotive force is generated in the conductor, which gives rise to an observable electric current C. If, on the other hand, we assume the conductor is moving and the magnet is at rest, then Maxwell's theory says that no electromotive force is generated in the conductor, but an electric field is generated around the magnet -- and this field induces exactly the same electric current C as before. Einstein's conclusion is that we are not actually dealing with two physically different situations here; rather, our theoretically distinct models are representing one and the same set of facts. This is exactly Einstein's argumentative maneuver in his famous elevator thought-experiment as well: though the pre-Einsteinian theory would distinguish between the cases in which I am being uniformly accelerated through a gravitation-free region and in which I am at rest in a homogenous gravitational field, Einstein maintains that there is in fact no difference between these two cases. This is (one version of) the Principle of Equivalence.

Note that Einstein does not say is that 'we choose between the competing descriptions of the magnet-and-conductor case on pragmatic grounds,' or that 'we parse the causes differently: either as an electromotive force or as a electric field.' Rather, he re-arranges the permitted causal structures of the theory to eliminate these pseudo-differences, so that the theory no longer "leads to asymmetries which do not appear to be inherent in the phenomena." He replaces the separate categories of 'inertial effects' and 'gravitational effects' with a single category (which we could call gravitational-inertial effects) via his principle of equivalence.

What I am curious about is whether Einstein's maneuver can be carried over into the biological case. I am hoping someone better-informed than I am can tell me why this has no prayer of working, or why Einstein's cases are not analgous to the situation in evolutionary biology. Of course, I wouldn't mind hearing suggestions for how this might work, either.

Editorial note. Posting here will probably be sporadic for the next few months: I am going on the job market this year, and that process has been (and, I imagine, will continue to be) time-consuming.


Specialization and collaboration, again

Yesterday Paul Hoyningen-Huene presented a talk entitled "What is Science?" at the Center for Philosophy of Science here. He intends the question in his title to be taken in a very general way, so his target is one of those Big Questions that, in my last post, I bemoaned as a dying breed in our climate of increasing specialization.

Prof. Hoyningen-Huene pointed out a discouraging fact for anyone who wants to attempt an answer to the Big Questions in the philosophy of science and simultaneously remain reasonably close to actual scientific practice: according to Thomson ISI (the citation management company), there are 170 categories of natural science, 54 in the social sciences, and 15 in the formal sciences -- not including subdisciplines, which can vary widely. So if someone makes a general claim about science or scientific practice, and wants to check that claim thoroughly, then 239 different categories of scientific activity -- most of them complex and varigated -- must be checked.

I feel pulled in two directions by the existence of these 239 categories. On the one hand, it seems that collaboration is the only means to make headway on the Big Questions. On the (not-quite-mutually-exclusive) other, it seems likely that the Big Questions just won't admit of anything approximating a (reasonably) general answer. (Hoyningen-Huene's strategy is to describe several examples drawn from across several scientific disciplines that support his thesis, and assert that these examples are paradigmatic.)

Finally, Kieran Setiya has also recently posted about specialization in philosophy over on his blog, Ideas of Imperfection. Since he's much smarter than I am, I recommend you read his post.


Specialization and collaboration

Over the past few decades, philosophy -- and philosophy of science in particular -- has become increasingly specialized: we have philosophy of quantum field theory, philosophy of developmental biology, etc. It seems that even the so-called "generalists" in philosophy of science are becoming a more and more self-contained group. (For example, I went to a session entitled "Confirmation" at the last Philosophy of Science Association meeting, and I had a very difficult time understanding what was being discussed, at least in part because there was a lot of specialized jargon and assumptions shared by the experts used without explanation -- though my limited brainpower certainly played its part in my incomprehension.)

In general, I think this trend of specialization is a Good Thing, primarily because it has led to specific results that we might not have found otherwise. (Thus I disagree with Karl Popper's claim: "For the scientist, specialization is a great temptation, but for the philosopher, it is a mortal sin.") But I think specialization also has its costs -- in particular, we tend to bypass answers to bigger questions. The question "What is a scientific explanation?" is replaced by "What is explanation in quantum information theory?" or "What is an evolutionary explanation?" and so on. (I think both of those questions are very interesting and philosophically important ones!) The philosopher of biology is uncomfortable talking about explanation in the physical sciences, and the philosopher of physics feels likewise about explanations of biological phenomena -- and the generalist is busy worrying about 'grue'some predicates, the barometer and the thunderstorm, or the irrelevant conjunction problem to deal with explanations in particular sciences. (I think this may in part explain why philosophy of science survey classes often begin with writings of logical empiricists: they tried to give genuinely general accounts of notions central to science.)

In keeping with the generally naturalist spirit of philosophy of science and this blog, we can ask ourselves: What Would Scientists Do? Scientists these days are hyperspecialized, and publish their hyperspecialized research in increasingly specialized journals. However, they also answer bigger, broader questions as well, via collaboration with scientists outside their specialty. So I wonder whether the time is ripe now for philosophers of science, armed with the insights about their particular sub-disciplines amassed over the last few decades, to begin collaborating to answer some of the bigger questions again. And the collaborations need not end there -- philosophers of science could also collaborate more with folks working within epistemology and metaphysics proper, or other fields.

I imagine many will say that we have overthrown the logical empiricist myth that there is a single thing, explanation, or confirmation, or even science. I am open to the idea that these might be myths. But I think we should check whether this is the case -- and if they are mythical, we can at least gain clarity and specificity about what the differences are between e.g. the explanatory patterns of physics and biology.


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.

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).


Thanks to the Philosophy of Biology blog

I'd like to thank the folks over at the group blog Philosophy of Biology for kindly advertising the existence of my blog on their site. If anyone reading this has not checked out that blog, I'd strongly recommend it. Not only did they recently have a very enlightening interchange on the topic of Elisabeth Lloyd's new book, "The Case of the Female Orgasm", but they just posted a link to a Naked Mole Rat-Cam.


Galileo:Scholastic natural philosophers :: Carnap:Quine

I'm pretty sure the following has been said before, but I don't know where: Frege (and Russell, et alii) did for the study of language what Galileo (et alii) did for the study of material nature. Galileo 'mathematized' new portions of the physical world -- previous students of nature thought that (most of) nature was too messy, imprecise, or chancey to be susceptible mathematical treatment: how could the unchanging, eternal realm of mathematics model the changing and temporal material world? Analogously, Frege and other founders of modern logic turned language into a mathematical object, by treating (e.g.) subject-predicate assertions in terms of functions and their arguments.

I bring this up because I've been looking at one of Quine's arguments against Carnapian analyticity in the 1940s. This argument appears in the long 1943 letter from Quine to Carnap in Creath's Dear Carnap, Dear Van, and in print in a 1947 article in the Journal of Symbolic Logic ("The Problem of Interpreting Modal Logic"):
The class of analytic statements is broader than that of logical truths, for it contains in addition such statements as 'No bachelor is married.' This example might be assimilated to the logical truths by considering it a definitional abbreviation of 'No unmarried man is unmarried,' which is indeed a logical truth; but I should prefer not to rest analyticity thus on an unrealistic fiction of there being standard definitions of extra-logical expressions in terms of a standard set of extra-logical primitives. What is rather in point, I think, is a relation of synonymy, or sameness of meaning, which holds between expressions of real language, though there be no standard hierarchy of definitions. (p.44, italics Quine's, boldface mine)
Quine puts the point somewhat differently in different places, but the basic idea is always that the 'rational reconstruction' of language, however it is carried out, is an 'unrealistic fiction.'

Now, I can ask the question: is Quine's charge that a 'hierarchy of definitions' is an 'unrealistic fiction' any different from Galileo's scholastic critics' charge that Galileo is somehow 'falsifying' nature by rendering it thoroughly mathematically? The answer to this question will turn on what Good Things the Galilean mathematizing strategy is able to achieve (explanatory power, new predictions, etc.), and whether these Good Things (or analogues of them) also appear in the case of a Carnapian language. It would also be useful to know of other scientific cases where the analogue of the Scholastic triumphed over the analogue of Galileo, i.e., someone tries to mathematize certain phenomena, but this mathematization is rejected for good reasons by workers in the field.


Is 'p is a priori' itself a priori?

My most recent posts have been far too long by blogging standards, so I am determined here to be brief. Most philosophers (though not all, e.g., anyone who holds the Quine-Putnam indispensibility thesis) believe the following sentences are true:
(1) "'2+3=5' is true a priori"
(2) "'The earth is round' is true a posteriori"
The question is: are (1) and (2) true a priori or a posteriori? Put metaphorically, does experience teach us that logical theorems are known independently of experience? I am not sure there are any non-question-begging arguments to be given one way or the other; if there is one, I would love to hear it.

That's all I wanted to say. If you are curious about what motivated me to think about this question, keep reading. There are two motivating sources:
First, my dissertation, which deals with the academic year Carnap, Tarski, and Quine spent together at Harvard in 1940-41. In a private conversation Carnap had with Quine, one way they formulate the difference between themselves is as follows.
Carnap: 'p is analytic in language L' is itself an analytic statement.
Quine: 'p is analytic in L' is a synthetic statement, to be settled by a behavioristic investigation into the linguistic habits of L-speakers.
Granted, 'analytic' is not identical to 'a priori' -- but for Carnap, they were extensionally equivalent, and the question above is very close to this issue.
Second, for the last 10 years, van Fraassen has been suggesting that we think of empiricism not as a theory or assertion but as a stance. (See "Against Naturalized Epistemology" (1995) in On Quine and 2002's The Empirical Stance.) The primary argument he offers is that empiricism, if conceived as an assertion, is self-defeating: "All knowledge about the world is a posteriori" (or any other slogan intended to capture the empiricist's thesis) will be difficult to construe as having experience as its source. And, van Fraassen says, if the empiricist thesis cannot be justified on the basis of experience alone, then it fails to live up to its own standards, and is therefore self-defeating. But van Fraassen is assuming that "such-and-such is a posteriori" must itself be an a posteriori claim. And that is taking for granted an answer to my question above.


On Rosenberg and Kaplan's "Physicalism and Antireductionism in Biology"

I've just finished reading Alex Rosenberg and D. M. Kaplan's "How to Reconcile Physicalism and Antireductionism about Biology" in the current issue of Philosophy of Science. The title describes its contents perfectly, and I can unequivocally recommend it to anyone interested in the topic (which is more than I can say for my foray into the subject). I'll quote the key part of the introduction:
In considering the relation between the PNS [Principle of Natural Selection] and physical science, three alternatives suggest themselves:
a. The PNS is an underived law about biological systems, and is emergent from purely physical processes. ...
b. The PNS is a derived law; it is derivable from some laws of physics and/or chemistry. ...
c. The PNS is an underived law about physical systems (including non-biological ones), and from it the evolution of biological systems can be derived... This is an alternative no one has canvassed, and one which we shall defend here.
Before continuing, let me give their version of the PNS:
For all x, y, and E: If x is fitter than y in environment E at generation n, then probably there is some future generation n', after which x has more descendants than y.
Note that the domain of quantification has no restrictions.

Their basic rationale for calling the PNS a law of physical science -- in particular, of chemistry (59, 62) -- is this: if there is a kind of chemical molecule that (in some sense) replicates itself and has higher rates of 'survival' than other molecules in a given reaction (say, as a reaction moves towards equilibrium, this kind of molecule is favored), that molecule will be subject to the PNS. (It's not a law of physics simply because (sub)atomic particles cannot be construed as replicating.) Calling the PNS a law of chemistry instead of biology "is just a picturesque way of drawing attention to the fact that selection for effects only begins to operate at the level of chemical interactions... Similarly, we call the second law of thermodynamics a law of physics, even though it obtains for all systems -- physical, chemical, and biological -- since it is at the level of the physical that it begins to operate" (61). As an example of such chemical natural selection, they point to current models of origins of life research.

So far, so good. But I'm less comfortable with the other half of their claim in c. above, viz., that from the physico-chemical PNS a fully biological PNS can be derived. They rephrase this point later in the article:
According to this view, at each level of the organization of matter there turns out to be a PNS, and each one should be in principle derivable from the PNS for the immediately lower level or some other lower level(s), all the way back down to the PNS for molecules. (61)
The problem is that they do not explain how this (in principle) derivation would proceed. They phrase the point slightly differently elsewhere (the PNS's "operation at higher levels of the aggregation of matter is a consequence of the operation of the underived PNS for molecules together with the rest of physical law" (62)), but they never actually spell out the derivation beyond this -- as far as I can tell. (In one place (top of p.62: "The rest is natural history"), they appear to hint that any higher-level PNS is a 'consequence' of chemical PNS in a historical sense: because the PNS acted on the primordial soup, today's organisms came into existence -- yet that is completely unlike any sort of reduction any philosopher of science that I know of has talked about. So I assume they can't mean that.)

So the question to Rosenberg and Kaplan is: does natural selection operate on the biological realm (whether it be genes, individuals, or even groups) because it operates on the chemical-molecular level? -- where that 'because' has the same force as the one in 'This mole of gas has a higher temperature than that one because this one's molecules have a higher mean kinetic energy.' Here's one way to press this worry. Look at their definition of the PNS quoted above, and convert it into 'the PNS for molecules':
For any molecule x and molecule y, if x is fitter than y, then...
Now they say that from this (and perhaps other PNSes), we should be able to derive higher level PNSes:
For any gene x and gene y, if x is fitter than y, then...
For any organism x and organism y, if... then...

But these higher-level PNSes don't appear to follow at all. Certainly, each follows from the general PNS quoted at the beginning; but from the fact that all chemical molecules behave a certain way, you cannot infer that organisms will behave a certain way -- unless organisms are chemical molecules. Rosenberg and Kaplan might say at this point: but all we are is an aggregate of chemical molecules: that is just the physicalist thesis which we profess in the title of our paper. But 'Aggregates of As are B' does not in general follow from 'As are Bs,' even for the most determined physicalist.


This week's complaint about "Two Dogmas"

I am willing to admit that Quine's "Two Dogmas of Empiricism" has many virtues, and if I ever write anything one-tenth as intelligent or one-hundredth as widely read, I will count my philosophical career an unequivocal success. However, I find it a very frustrating piece when it is considered as a critique of Carnap's views on language circa 1950. A number of people who have considered "Two Dogmas" in this light have also felt that it does not directly rebut Carnap's views, but instead offers (to put it in Kuhnian terms) a different paradigm for understanding language (recently, see P. O'Grady's 1999 article in PPR). Interestingly, the first person to suggest this interpretation of "Two Dogmas" was apparently Carnap himself (see Howard Stein's "Was Carnap Entirely Wrong, After All?", Synthese 1992). This post is about my most recent round of frustrations in attempting to read "Two Dogmas" as a straightforward argument against Carnap.

My gripe here concerns section 4 of the paper, "Semantical Rules." Quine writes (page numbers from From a Logical Point of View):
Once we seek to explain 'S-is-analytic-for-L' for variable 'L'..., the explanation 'true according to the semantical rules for L' is unavailing; for the relative term 'semantical rule of' is as much in need of clarification, at least, as 'analytic for.' (34)
So Quine is telling us that there is no decent explanation or clarification of the term 'semantical rule of,' if we generalize away from particular languages.

It seems to me that the next question we should ask is: how does Carnap characterize these semantic rules? Is it as unclear as Quine alleges? To answer that, we have to look at an extremely underread book: Carnap's Introduction to Semantics (1942). There Carnap says:
a semantical system [is] ... a system of rules, formulated in a metalanguage and referring to an object language, of such a kind that the rules determine a truth-condition for every sentence of the object language, i.e., a sufficient and necessary condition for its truth. In this way the sentences [of the object language -GFA] are interpreted, i.e., made understandable. (22)
What are some of Carnap's examples of semantic rules? (Where English is both the object and metalanguage):
-'Chicago' designates Chicago etc.
-The truth-tables for the usual propositional connectives

Now I want to know what Quine finds unacceptable (unclear, unexplained, 'unintelligible' he says elsewhere in "Two Dogmas") about Carnap's characterization of semantic rules. This isn't just a matter of my pounding or kicking the table and saying 'I really do understand them' -- rather, it seems to me that if Quine is right that these things are unclear, then logic (at least logic that is not purely syntactic/ proof-theoretic) is unclear. In order to specify an artificial language in model-theoretic terms at all, we need to be able to say things like "Modus Ponens is an inference rule in such-and-such language" -- and if that is not clear, then logicans working in model theory are stumbling around in an unintelligible haze. If we cannot (intelligibly) lay down/ identify semantical rules such as this one and the others Carnap mentions, then the logician cannot (intelligibly) specify interpreted languages to study.

Thus concludes my main rant. A couple further things should be said before signing off, though. First: Quine, in "Notes on the Theory of Reference" and elsewhere, says that "'Chicago' designates Chicago," "'Snow is white' is true iff snow is white" and the like are basically comprehensible (p.138 in From a Logical PoV). That this is in tension with Quine's criticism in "Two Dogmas" has been pointed out (in different terms) already, by Marian David in Nous 1996. Second, there is one real difference between the semantic rules Carnap uses and the ones Quine favors and we usually use today, pertaining to hte interpretation of predicates and relation letters. Carnap sets up the following as a semantic rule: 'Blue' designates the property of being blue.
And here Quine would have a (more) direct disagreement with Carnap: Quine rejects intensional languages in general, and properties (for Carnap) are to be understood intensionally. So to generate a clean Quinean argument against semantic rules from the above quotation, we can fall back on Quine's rejection of non-extensional discourse as unclear and unintelligible. But this view of Quine's has won far fewer supporters than his rejection of the analytic-synthetic distinction.



Two days ago, the Pennsylvania House of Representatives, using the ideas and resources of David Horowitz's group Students for Academic Freedom successfully moved to create a committee to investigate the alleged liberal bias in Pennsylvania state schools -- and that includes the University of Pittsburgh. (The text of the motion can be found on their website.) One of the House members who opposed the formation of the committee has made a fairly detailed request for assistance from teachers at these schools. For those around here who would like to help the Representative (and yourself), his contact information is at the end of the linked request.


Naturalism and the alleged continuity between philosophy and science

There are probably as many varieties of naturalism as there are naturalists. Either despite or because of this variety, many philosophers today are naturalists (though noteworthy dissent also exists). Philosophers of science, in particular, seem to be uncompromising naturalists. Here is one slogan that I think does a decent job of expressing the basic naturalistic position in a minimal enough form that most naturalists would accept it:
For any question, approach and answer that question the way a scientist would approach and answer that question (leaving the particulars open at this level of abstraction).
In other words, philosophers should defer to scientists on both questions of both method and factual content.

Another tenet of many modern naturalisms is "science is continuous with philosophy," a phrase which traces back to Quine. There is certainly something right about this notion, for we can point to current thinkers whose work does not fall neatly into science or philosophy: the late, great Rob Clifton is a paradigmatic example, as well as many other technical philosophers of physics working today. There are similar cases in other sciences too: should Sober and Wilson's Unto Others be classed as biology or philosophy?

However, it seems to me that "Science is continuous with philosophy" is also in some tension with the original naturalist slogan. If you asked an interdisciplinary team of scientists to answer the questions:
"Am I a brain in a vat (or being deceived by an evil demon, etc.)?"
"Is knowledge justified true belief?"
"Is the meaning of a sentence identical with its truth-condition?"
"Is the fundamental aim of science truth or empirical adequacy?"
they would (I think) say that such questions are not scientifically tractable -- in such cases, the 'scientific approach' (whatever exactly that might be) cannot answer that question. I think this would be the scientists' answer on the grounds that none of these questions -- or the vast majority of the others that appear in The Journal of Philosophy, Nous, The Philosophical Review, etc. -- are ever addressed in Science, Nature or other leading scientific journals.

In short: scientists do not view science and philosophy as continuous (even though there are borderline cases in technical philosophy of the special sciences), so a philosopher who views them as continuous is not fulfilling the naturalist's commitment to defer to the sciences. (Though the first stirrings of this discontinuity were felt earlier in the 17th C., I would guess that it becomes explicit with Newton and his rules of philosophizing.) So what is a philosopher (who is not Rob Clifton) to do? I think part of the appeal of naturalism is that science is seen as epistemically privileged, and if we can lump philosophy in with science, then that epistemic privilege and prestige will rub off on philosophy. I think the moral to be drawn from the discontinuity is just that philosophy lacks science's epistemological privilege -- and that is a conclusion a naturalistically-inclined philosopher might happily accept anyway.


First real post: abduction from limited evidence

I am currently teaching a summer session class called "How Science Works." The aim of the class (according to the course description) is to "introduce science and scientific ways of thinking to students who have not had much contact with science." One of the big-picture themes I am trying to develop in the course is that, in many cases, scientific reasoning is just extra-careful common-sense reasoning made precise. Thus, for some of their homework assignments, I ask students for an example from their lives where they (or someone they know) have used whatever scientific strategy we are studying that day.

On their last homework assignment, I asked them to give an everyday example of an abductive inference that is supported by independent sources of evidence, a very common kind of inference in good scientific practice. There were some very clever answers; the most common one was the cheating significant other: I never see the significant other with someone else, but I do observe her staying out late, hanging up the phone immediately when I stop by unexpectedly, and various other secretive behaviors.

But, unsurprisingly, some students did not quite understand the requirement for evidence from multiple independent sources, and gave an example of an abduction from just one. (These examples often involved some sort of roommate malfeasance: "My favorite CD is no longer in its case, so my roommate must have taken it without asking.")

But this mistake raised one version of a question I've been wondering about off and on for a while now. This version of the question is:
What is the epistemological status of abductive inferences (also known as 'inferences to the best explanation') that have only one (independent) source of evidence?
To make this a slightly more well-posed question (or at least a question more amenable to philosophers of science), we can pose the question more naturalistically: how does science regard and treat such inferences?

My gut-feeling answer is that such inferences are regarded as 'merely hypothetical' or otherwise second-class citizens -- like atomic theory in the 19th C, for example (for an account of this historical episode very congenial to my point, see Penelope Maddy's "A Problem in the Foundations of Set Theory, Journal of Philosophy Nov. 1990, pp. 623-625). Often such abductions from limited evidence are pronounced ad hoc. And, in biology, this also seems to be the reason many people call certain adaptionist accounts of certain biological traits "just-so-stories": if the only evidence we have for that adaptationist account is the way the animal looks or acts now, then we just don't have strong reason to accept that account. If we found enough sources of independent evidence for our conjecture, even the strong anti-adaptationists might come around.

I think this question (of the status of abductive inferences based on only one evidential source) is an interesting one in its own right. But it seems it also has implications for philosophy proper: many philosophical positions purport to explain only one thing, and lack the kind of consilience that good abductive inferences in the sciences enjoy. To take just one example, scientific realism aims to explain the success of science -- and as far as I can tell, that's it. (At least some other realisms will definitely fall in the same boat.) Certain critics of scientific realism (van Fraassen, for one) criticize all instances of "inference to the best explanation" (IBE), and use that criticism as an argument against scientific realism (which is supposedly the result of an instance of IBE). However, we may not need to throw out all instances of IBE in order to have a good argument against the realist -- we need only act like the scientists (as I portrayed them in the previous paragraph): accept only those instances of IBE for which we have more than one independent source of evidence.


Justifying my existence

Who am I and why am I here?

I am an academic philosopher whose primary interests are in science and logic. Often, after I've read a provocative article or book, or had an interesting conversation with someone in or around my department, my mind is swarming with obscure and confused ideas. These ideas bounce around in my head for a short while, and I sometimes scratch an especially persistent one on the back of an envelope -- but usually they just lose their mental inertia and evaporate, crowded out by thoughts of dinner, my cats, or whatever.

I decided to create this blog in order to give those ideas something (very slightly) higher to aspire to than the back of the envelopes Capitol One keeps sending me. Hopefully, posting them here will force me to make them a bit more clear and distinct. And if anyone ever reads this blog, they could help me cut down on the obscurity and confusion as well.

Why the title?

For those who are not historians of philosophy: Descartes, Leibniz, Spinoza and certain other 17th C. philosophers thought large chunks of our supposed knowledge are based on "obscure and confused ideas." I don't know whether this view is true in general, but it certainly holds in my particular case.