Pesky Truth-Tables

One of the blog posts on the new Philosopher's Carnival considers how to teach the truth-table for the material conditional to students:

http://www.soulphysics.org/2009/12/where-material-conditional-gets-its.html

I tried to comment, but it didn't work for some reason. Here's how I explain the troublesome cases (where P is false, but (P -> Q) is true).

Suppose Q is true, and P false. All we really need is that Q is true:

1. Q / Q

Monotonicity gets us:

2. P, Q / Q

And then by conditional proof we derive:

3. Q / P -> Q

One final application of monotonicity:

4. ~P, Q / P -> Q

So to reject (P -> Q) when P is false an Q true, the student must reject either conditional proof or monotonicity.

Now suppose P is false and Q is also false. All we really need is that P is false:

1. ~P / ~P

Again, by monotonicity, and conditional proof:

2. ~Q, ~P / ~P
3. ~P / ~Q -> ~P

Here there are several ways to proceed (contraposition being the most obvious). Let's try Modus Tollens:

4. P / P (assumption for CP)
5. P / ~~P (double negation, 4)
6. P, ~P / ~~Q (modus tollens, 3, 5)
7. P, ~P / Q (double negation, 6)
8. ~P / P -> Q (conditional proof, 7)
9. ~P, ~Q / P -> Q (monotonicity, 8)

So to reject (P -> Q) when P and Q are both false, the student must reject conditional proof, double negation, monotonicity, or modus tollens (alternatively, the student must reject conditional proof, monotonicity, or contraposition).

Of course, as pointed out last time, modus tollens, contraposition, disjunctive syllogism, and reductio are all inter-derivable. So my explanation is really of the form: everything follows from a false premise, so get used to it.

Independence of Reductio

The other day I was wondering whether one can have a complete propositional calculus with only the introduction and elimination rules for each connective. So you have modus ponens and conditional proof, but not modus tollens and contraposition; or-introduction and or-elimination, but not disjunctive syllogism; &-intro and &-elim, but not "modus ponendo tollens", i.e. from ~(A & B) and A to infer ~B. In particular, you don't have reductio ad absurdum, from A & ~A to infer B.

Such a system seems simple and intuitive, but I don't see how to do it. At a minimum, we should be able to prove p & ~p -> q from the introduction and elimination rules alone, but I haven't been able to prove it. You can get it assuming any of the principles we've ruled out, e.g. modus tollens, contraposition, or disjunctive syllogism. For example (using / as a turnstile):

1. {p & ~p} / p & ~p (Assumption)
2. {p & ~p} / p (&-elim, 1)
3. {p & ~p} / ~p (&-elim, 1)
4. {~q} / ~q (Assumption)
5. {p & ~p, ~q} / p & ~q (&-intro, 2, 4)
6. {p & ~p, ~q} / p (&-elim, 5)
7. {p & ~p} / ~q -> p (->-intro, 6)
8. {p & ~p} / ~~q (MODUS TOLLENS, 3, 7)
9. {p & ~p} / q (~-elim, 8)
10. / (p & ~p) -> q (->-intro, 9)

The proof assuming contraposition is similar, but instead we show ~p -> ~q (using ~p where we have p in lines 5-7), contrapose, and use p and ->-elim to conclude q (rather than ~p and modus tollens). For disjunctive syllogism, the proof is even simpler:

1. {p & ~p} / p & ~p (Assumption)
2. {p & ~p} / p (&-elim, 1)
3. {p & ~p} / p v q (v-intro, 2)
4. {p & ~p} / ~p (&-elim, 1)
5. {p & ~p} / q (DISJUNCTIVE SYLLOGISM, 3, 4)
6. / (p & ~p) -> q (->-intro, 5)

What's more, we can prove any of these rules (modus tollens, contraposition, disjunctive syllogism) by assuming reductio (it's an easy exercise). So it follows that if we can prove any of these four rules from Assumption and the intro and elimination rules, our system is complete (well, it doesn't follow per se, but I could show you, if asked).

So, here's what I want to know from my readers, few though they may be. Can you prove reductio, modus tollens, contraposition, or disjunctive syllogism from just the intro and elimination rules? And if not, why not? Why does a complete propositional calculus need something other than the intro and elimination rules? I feel like this is something I should've learned in logic, but never did.

(Aside: yes, I know this post is going to make me look foolish when someone presents the answer, whatever it is. So be it.)

Acupuncture: Evidence

So the other day I was at a friend’s house and the topic of acupuncture came up. Now, I’m one of those hard-line skeptics about “alternative” medicine, and I happened to have read several credible sources stating that acupuncture doesn’t work (is no better than a placebo treatment). But not everyone wanted to take me on my word, so I promised to produce the evidence. Here we go.

First, a caveat for those who want to do their own internet research: there are a large number of biased websites out there, on both sides. If you go to the websites of people who practice acupuncture, you’ll find links to many articles which indicate that acupuncture is beneficial. Don’t trust them! For example, on this website:

The Fertile Soul

You’ll find the oft-cited claim that acupuncture helps with in-vitro fertilization. Yet, the study linked is a poor one, and the most systematic review to date on the subject, here:

Cochrane Collective

Concludes: “Acupuncture performed on the day of ET [Embryo Transfer] shows a beneficial effect on the live birth rate; however, with the present evidence this could be attributed to placebo effect and the small number of women included in the trials. Acupuncture should not be offered during the luteal phase in routine clinical practice until further evidence is available from sufficiently powered RCTs [Randomized Clinical Trials].”

Translation: poorly conducted studies are inconclusive. Internet researchers should also be warned about overzealous skeptic sites, which will publicize the negative results that suit them, but not take the time to consider studies which seem at-odds with their views.

The best place to get your scientific evidence concerning medicine is, of course, from recent, systematic meta-analyses of randomized clinical trials published in leading medical journals. Here is one such meta-analysis, published in BMJ. The article is: “Acupuncture treatment for pain: systematic review of randomized clinical trials with acupuncture, placebo acupuncture, and no acupuncture groups” by Matias Vested Madsen, Peter C Gøtzsche and Asbjørn Hróbjartsson and it is available for free here:

Meta Analysis

This article is recent, being published in 2009.

It is also systematic. A systematic meta-analysis looks at all the articles in a large database(s) that meet the inclusion criteria. According to the study’s authors: “We searched the Cochrane Library, Medline, Embase, Biological Abstracts, and PsycLIT. The last search included all trials published before 1 January 2008.”

Furthermore, it is published in a leading medical journal. According to wikipedia: “BMJ is considered to be one of the ‘core’ general medical journals; the others being the New England Journal of Medicine, (N Engl J Med), the JAMA, and The Lancet.”

The authors reached the following conclusions: “A small analgesic effect of acupuncture was found, which seems to lack clinical relevance and cannot be clearly distinguished from bias. Whether needling at acupuncture points, or at any site, reduces pain independently of the psychological impact of the treatment ritual is unclear.”

To sum up: acupuncture treatments for pain are not clinically significant, and they may not even be statistically significant, once bias is accounted for. That seems pretty damning to me.

Still not convinced? I knew you wouldn’t be. So I direct you to one of my favorite science bloggers, Orac, over at Respectful Insolence.

Acupuncture 1

Acupuncture 2

Acupuncture 3

Acupuncture 4

Orac is a medical doctor, and much more knowledgeable than me. In the above blog posts, he dissects a number of studies and meta-analyses. He testifies:

“When I first became interested in ‘alternative medicine’--excuse me, I mean ‘complementary and alternative medicine’ (CAM)--I viewed acupuncture somewhat differently. No, I never bought the traditional explanation that sticking thin needles into the skin somehow alters the flow of qi in order to induce a therapeutic effect. That is no more plausible than reiki or therapeutic touch. However, there are needles breaking the skin in acupuncture. It was, at least to me, not entirely implausible that that might have some sort of physiologic effect. Then I had to go and ruin that lovely kumbaya feeling towards CAM by actually going and looking at the scientific literature on acupuncture… When I actually bothered to do that, I soon realized that the evidence that acupuncture is anything more than a highly elaborate placebo is shockingly thin. More like nonexistent, actually.”

You should read his posts, or the articles he links to, and see if you aren’t equally converted.

Finally, here’s a press article to stew on:

AP Report

It begins: “Ten years ago the [U.S.] government set out to test herbal and other alternative health remedies to find the ones that work. After spending $2.5 billion, the disappointing answer seems to be that almost none of them do.”

Your tax dollars at work!

Accommodationism II

Joshua Rosenau over at Thoughts from Kansas has a new post up about the accommodationist debate.

http://scienceblogs.com/tfk/2009/06/more_on_accomodationism.php

It’s typical of the accommodationist genre: reinterpret Coyne so that he’s saying something he repeatedly says he’s not saying, and then have an irrelevant and one-sided debate. Here’s a taste. First, the old (old, old, getting very old) canard that: look! there are religious scientists, so science and faith are compatible:

“Fr. George Coyne is an astronomer. He was, for many years, the director of the Vatican Observatory, and was a Jesuit priest for even longer. Does he see any conflict between his study of the heavens and his belief in heaven? Not at all”

[Note: this is confusing. JERRY Coyne is the anti-accommodationist; GEORGE Coyne is the catholic astronomer.]

Yes, yes, we get it. One and the same person can say both “I believe in the divinity of Jesus” and “I believe in contemporary evolutionary biology.” That was news, like, never and a half ago. So what’s supposed to be the upshot of Fr. G. Coyne-style accommodationism?

“Theology responds to new scientific discoveries, just as it reacts to cultural shifts. Claims about theology are tested in a different way than scientific claims, indeed cannot be tested as scientific claims, but that does not mean they are invalid. He sees science and religion as connected, as informing one another in certain ways, and as rooted in the same reality, therefore incapable of contradiction. Apparent contradictions must be addressed by further study.”

What does it mean for science and religion to be “incapable of contradiction”? And what is an “apparent contradiction”? I take it the view is this: suppose current science supports theory T1, which entails that p; and current theology supports theory T2, which entails that not-p. Then science and religion are in “apparent contradiction.” But the contradiction is only apparent, because “further study” ultimately resolves the contradiction, by replacing either T1 with another theory that doesn’t entail p; or by replacing T2 with another theory that doesn’t entail not-p; or by replacing both theories in such a way to bring them into consistency.

But here’s where things get interesting. Forget whether science and religion are capable of contradiction, and focus on the question of whether they can be in conflict. I take it that some method of inquiry is in conflict with science if when science supports T1 and the other method T2, where T1 and T2 are inconsistent, it is (always or sometimes) science (that is, T1) that must be abandoned or revised. Surely we cannot tolerate methods of inquiry that conflict with science, so the real question is not whether apparent contradictions can always be resolved, but whether they are always resolved in such a way that science wins, and religion loses.

But this isn’t what we actually see from accommodationists:

“If Jesus lived, he walked the same world I do. If he was divine, the words he spoke struck ears like mine. His miracles were either sleight of hand, embellishments by later storytellers, or suspensions of natural laws. If I could take James Randi back a couple thousand years, I could figure that out, but as it is, all I can do is believe what I believe and let Christians believe what they do.”

Please, for the love of God, can’t one single accommodationist read Jerry Coyne’s New Republic piece? Let me state the argument. Among the basic principles of science is the uniformity principle (UP) as articulated by, among others, Harlequin, Emperor of the Moon: things are always and everywhere exactly as they are here*. That is, if the universal law of gravitation holds on Earth, it holds on the Moon, and the superlunary realm, and a million years ago, and a billion years ago, and a billion years hence. The assumption that nature is uniform is just the assumption that induction works, or that science is possible. And we use UP all the time to argue against creationist nonsense. We say, for instance, that the Earth is more than 6,000 years old, because we know (for instance) that radioisotope carbon-14 decays at a certain rate now and thus must always have done so, and thus some things have been around far longer than 6,000 years. Coyne’s argument, if anyone would bother to read it, is that one must reject UP to hold on to statements like “Jesus came back from the dead,” and “Mary was a virgin when she gave birth.” But if you abandon UP when it suits you, you have no principled grounds for rejecting the young Earth creationist’s claim that carbon-14 used to decay at a much faster rate. So accommodationism is on a par with young Earth creationism, at least so far as it rejects, without principle, fundamental aspects of scientific methodology.

Now, I don’t want to weigh in in favor of Jerry Coyne’s argument (here, at any rate). It certainly excited me when I first read it, and that’s what I hoped to get out of the accommodation debate: whether J. Coyne was right. But it seems that literally no-one has read the argument, or no-one has the intellectual honesty to reply to it. You can’t just baldly assert, in the face of compelling counterarguments, that there’s just nothing one ought to believe in these cases, and that accommodationist Christians are just as rational as atheists. That’s precisely the claim at issue! At least say something about the counterarguments.

Rosenau does try to place some religious doctrines even beyond the bounds of the UP:

“Randi and I could surely figure out what the score is with the loaves and the fishes and the wine. I don't know any way that we could test Jesus' divinity, or whether Mary was born with or without original sin.”

I’m thoroughly unconvinced. It’s like saying we can never know whether there are ionizing particles in a cloud chamber, because we can’t see tiny little particles. Yes, but physical theory predicts a mist around such particles, if present, and we can see the mist. Similarly, divine people can, I don’t know, perform miracles; or their predictions are never false; or they never lie, cheat, or steal. Can’t I observe Jesus to see whether he fits the bill? Does ‘divine’ mean so little nowadays? I’ll readily admit that some claims can’t be tested—e.g. “Mr. X has special property Y, which is in principle undetectable by anyone in anyway”—but most religious claims don’t seem to be of this form.

Alright, final quote:

“[Fr. G. Coyne] believes what he believes, he doesn't impose it on others, and it would be as wrong for others to impose their beliefs about science and religion on him as it would be for him to impose his beliefs on me.”

Arg! Since when did anyone advocate imposing atheism on anyone? Let me just make this very clear: as far as I see the accommadationist debate, there are two fundamental issues: (a) are science and religion in conflict? (b) ought we to say so, if that’s true? No anti-accommodationist has ever asked the question “Ought we to force others to be atheists?” and certainly none has or would answer it affirmatively. So STOP PRETENDING THEY DO.

I leave you with Hume, from the end of On Miracles (in the Enquiries):

“No testimony is sufficient to establish a miracle, unless the testimony be of such a kind, that its falsehood would be more miraculous than the fact which it endeavors to establish… When anyone tells me that he saw a dead man restored to life, I immediately consider with myself whether it be more probable that this person should either deceive or be deceived, or the fact which he relates should really have happened. I weigh one miracle against the other; and according to the superiority which I discover, I pronounce my decision and always reject the greater miracle. If the falsehood of his testimony would be more miraculous than the event which he relates then, and not till then, can he pretend to command my belief or opinion.”

*Check Leibniz, New Essays, for the reference.

Science's Claim to Truth

Here's a common trope: science is not warranted in claiming that its deliverances are true. Science doesn't "get at" the truth; rather, it "gets at" what the evidence most supports. So scientists shouldn't claim that their theories are true; rather, they should claim that their theories are what the evidence most supports.

I see this on blogs now and again (I got on someone's case just the other day for saying it), and I think here's a place where a little simple philosophy can help the non-philosopher out.

1. First objection. If anyone's warranted in asserting certain matters of empirical fact, such as that chiropractic is bogus, scientists are. Some people are warranted in asserting such matters; therefore, scientists are. Anyone warranted in asserting that p is warranted in asserting that "p" is true, because "p" is true when and only when p. Therefore, scientists are warranted in asserting, for example, that it is true that chiropractic is bogus.

2. Second objection. To be warranted in asserting that p, one must know that p. This is why it is infelicitous to say "p, but I don't know whether p" (for example: "it's raining, but I don't know whether it is or not"). So if a scientist is ever warranted in asserting anything, she must know it. But scientists are sometimes warranted in asserting things; therefore scientists sometimes know things. But knowledge is factive: if S knows p, then "p" is true. So to be warranted in asserting something, it must be true; provided scientists know this (and if they didn't before, now they do), they may infer from the fact that their assertions are warranted that what they say is true.

3. Third objection. A standard scientific reasoning pattern is abduction. Thus, we argue from the correlation between a rise in man-made greenhouse gasses and a rise in global temperatures, to the best explanation: the conclusion that humans are causing global warming. But on equally good footing is the inference from "the evidence supports p" to "'p' is true"-- for what better explanation could there be of the evidence supporting p, than "p"s truth?

So there it is, blogospheric soldiers of science: lay your claims to truth.

Accommodationism

The atheist blogs are abuzz with the accommodationist debate: are science and religion compatible, and if we think that they aren’t, ought we to say so? Jerry Coyne has a listing of all the main posts here:

http://whyevolutionistrue.wordpress.com/2009/06/12/the-big-accommodatinism-debate-all-relevant-posts/

Right now I just want to consider this one post by Chris Mooney:

http://blogs.discovermagazine.com/intersection/2009/05/31/civility-and-the-new-atheists/

In it, Mooney outlines 3 reasons he attributes to Barbara Forrest for why we should not criticize the accommodationists:

1. Etiquette. Or as Forrest put it, “be nice.” Religion is a very private matter, and given that liberal religionists support church-state separation, we really have no business questioning their personal way of making meaning of the world. After all, they are not trying to force it on anybody else.

2. Diversity. There are so many religions out there, and so much variation even within particular sects or faiths. So why would we want to criticize liberal Christians, who have not sacrificed scientific accuracy, who are pro-evolution, when there are so many fundamentalists out there attacking science and trying to translate their beliefs into public policy?

3. Humility. Science can’t prove a negative: Saying there is no God is saying more than we can ever really know empirically, or based on data and evidence. So why drive a wedge between religious and non-religious defenders of evolution when it is not even possible to definitively prove the former wrong about metaphysics?

[Note, all three reasons are copied directly, and are not summaries of mine.]

I want to take these reasons in turn.

1. Etiquette. I don’t feel the force of this reason at all. Suppose I believe that accommodationism is false, and I base my belief on a certain array of reasons and evidence. If I write up my position and give my defenses, I will have criticized the accommodationists, because any criticism of accommodationism is ipso facto a criticism of accommodationists. So the “etiquette” principle entails I must shut up. But why should I have to shut up, while the accommodationists run around presenting their reasons and their evidence for the truth of accommodationism? That’s a sorry state for a public debate to be in, where one side is allowed to marshal its defenses and the other has to just be quiet and put up with it.

Maybe the alternative is that I’m allowed to present my case, but I must do it far away from where any accommodationist is, to avoid offense. But why? We’re told that “religion is a very private matter.” I don’t really know what that’s supposed to mean, but I imagine it’s something like: people cherish their religious beliefs, and are very upset when those beliefs are taken to task. If that’s what it means, then I can think of some other things that are very private matters: morality and well-being. But surely no-one thinks that we should just let the anti-abortionists, or the vaccine denialists and conspiracy theorists have the only say on those issues, because morality and well-being are “private matters.” And if religion is so freaking private and Ken Miller is after a “personal way of making meaning in the world” why does he have so many high profile books on accommodationism? This seems like nonsense.

Elsewhere Mooney & Co. argue that we need accommodationists like Miller as allies in the battle against religious fundie anti-science wackaloonery. I agree, and I’m all for accommodationist allies. But I say this: no-one is an ally of mine who is so afraid of any reasons or evidence that runs contrary to their view, that if presented with such would turn tail and run to the other side. That’s not an ally, that’s a passive-aggressive control freak with reality issues. Anybody who actually has respect for science and the scientific method will not be turned off but rather invigorated by critical scrutiny of their positions.

2. Diversity. I find the claims under the “diversity” heading staggeringly silly. If you read Coyne’s New Republic piece, here:

http://www.tnr.com/story_print.html?id=1e3851a3-bdf7-438a-ac2a-a5e381a70472

You’ll find that Coyne’s charge is precisely that the accommodationists do sacrifice scientific accuracy. He presents three specific charges (probably more, I haven’t read the piece for months): Miller-style accommodationism violates (a) the law of biology that says dead people don’t come back to life (b) the law of biology that says virgin births in mammals are impossible and (c) the (admittedly contestable) claim that human-like intelligent creatures are not inevitable products of evolution by natural selection. (a) is presumably necessary for natural selection at all, because death is the method of selection precisely because of its finality; (b) is a precondition of Fischer’s demonstration of the sex ratios; and (c), though it could be false, is certainly worth looking into and it would be absurd to suppress arguments for it on the grounds that otherwise Ken Miller is going to cry.

In fact, I don’t even know what Forrest and Mooney are thinking here. How could there be a scientific critique of accommodationism that wasn’t of the form: accommodationism sacrifices scientific accuracy?

3. Humility. Allow me to me non-humble for a moment, but what Forrest/ Mooney says here is literally stupid. Of course science can prove negatives. Here’s a go: it’s not the case that vaccines cause autism. Or, if negative existentials are your bag: it’s not the case that there exists matter at the top of a mercury barometer. Does Forrest think that it’s impossible to prove the existence of vacuums? Who is she, the Catholic Church circa 1200? What’s more, even in intuitionistic logic, you get the theorem: p → not-not-p, so a proof of anything is a proof of a negative. Suck on that!

I suspect the heart of the issue is that it’s not possible to prove the non-existence of God. But again, I think Forrest/ Mooney is trotting out methodological claims without thinking about them. It’s impossible to prove the non-existence of a deistic God; but one can certainly prove the non-existence of the accommodationist God. The accommodationist God by definition has causal traffickings with the physical world. He’s a watered down Christian God. I mean, Coyne’s whole point, again, is that science (in his opinion) tells against accommodationism. If it tells against accommodationism, it tells against the accommodationist God. Now, Coyne may be wrong in the end, but you don’t get that result for free by saying “humility.”

Just to head off one bit of criticism: yes, I know, I’ve been using “scientific proof” as a standard that delivers less than 100% credence, so it is always conceivable that accommodationism is true. But (a) if Coyne is right about the evidence, then this conceivability is on a par with, say, the conceivable propositions that the Flying Spaghetti Monster or the Invisible Pink Unicorn created the world; and (b) if Forrest/ Mooney is really saying we shouldn’t make scientific cases for claims we can’t establish beyond any doubt whatsoever, then they’re saying we shouldn’t make scientific cases at all.

OK, that’s the end. I’m sure all of these points have been made by posters and commenters elsewhere. But I plan to post more on accommodationism as the debate develops, and I thought a good first start was deconstructing this Forrest/ Mooney crap in detail.

P.S. Sorry I never got around to posting every Friday. This is difficult!

Armchair Evolutionary Psychology is Quackery

I haven't read the entirety of this piece of stupidity in (Pseudo)Scientific-American, it was just too painful:

http://www.scientificamerican.com/article.cfm?id=skeptic-agenticity

Now, I guess I shouldn't expect much from someone who uses the words "patternicity" and "agenticity", but this was linked over at RichardDawkins.net, and people there seemed to like it. So I think there's some merit in spelling out why armchair evolutionary psychology is woo, plain and simple. Here's a quote:

"[W]e make two types of errors: a type I error, or false positive, is believing a pattern is real when it is not; a type II error, or false negative, is not believing a pattern is real when it is. If you believe that the rustle in the grass is a dangerous predator when it is just the wind (a type I error), you are more likely to survive than if you believe that the rustle in the grass is just the wind when it is a dangerous predator (a type II error). Because the cost of making a type I error is less than the cost of making a type II error and because there is no time for careful deliberation between patternicities in the split-second world of predator-prey interactions, natural selection would have favored those animals most likely to assume that all patterns are real."

The reasoning is silly. Suppose I said: "If you believe the rustle in the grass is an indication of food when it is just the wind (a type I error), you are LESS likely to survive than if you believe the rustle in the grass is just the wind, when it's actually food (A type II error). Both times you get no food, but the in the first case you spent energy and effort that could've been used to look elsewhere. Because the cost of making a type II error is less than the cost of making a type I error, natural selection would have favored those animals most likely to assume that NO patterns are real."

Or, a parody more to the point: "Because I can think of one case where thinking X is better than thinking Y, and the thought that X has property F and the thought that Y has property not-F, it follows that evolution makes it the case that having thoughts with property F is always better and evolution made us prefer them in all cases."

Yes, people say this sort of crap. And get published in Scientific American. And fawned over at RichardDawkins.net. It's unsettling.

Let's set the record straight. The argument assumes (in particular, provides *no* evidence) that pattern-forming is in general better or less costly. We know this to be false, because Bayesianism is the true account of ideal rationality. If you don't set your present credences equal to your prior subjective probability distribution conditional on your evidence, and you don't act so as to maximize expected utility, you will be more likely to die. That's a theorem. Sometimes your evidence confirms a correlation, sometimes it doesn't. But picking "all patterns, all the time" as your update rule is not optimal, and therefore we've no reason to *a priori* expect it.

Now maybe we do form patterns more than it is rational to. It would be nice to have an explanation for that. Presumably it's because cobbling together agents that can survive for more than a few seconds is difficult, and evolution had to jury-rig some aspects of our psychology from non-optimal other bits. But pursuing any particular theory of what went on requires looking at the damn facts. We need to know what psychological traits are heritable (if any), we need to know which among them were available in the ancestral population to be selected for, which competed with which, what the selection pressures were, etc. And we don't freaking know any of that.

All right. End of rant. FYI I plan to update the blog on Fridays this summer. And I do genuinely plan on blogging, so check in, say, every Saturday

Concept-Script

Here's some rap I wrote as my alter-ego Gottlob Frege on Facebook (all-new rap at the end):

No condition-stroke, this ain't no joke, my rhymes is categorical, I'm a metaphorical soldier, inventing logic like I told ya, granting my thought access to eternal, mind-independent mathematical objects, bringin pain down on the haterz, neo-Kantians and fakerz, formalists like Hilbert get cubicle jobs like Dilbert. Russell's paradox set? I ain't finished yet. When I come back alive, I'll fix my axiom five. Word.

Yo yo yo Frege's puzzle can't be solved by Russell, introducing quantification and skipping modes of presentation, you need the bedeutung like dung-beatles need dung, need the sinn like my po ass needs twenny twen twen-- dollaz, holla I be on a roll, taught Carnap all he know, put Husserl on the flo, he used to be a psycho-logicist but not no mo, I put his ass in place while oppressing the Jewish race (sorry about that, btw) got the competition scared stiff like funktion und begriff, now my rhymes bear interpretations like the higher-order calculus of relations. Beeotch!

Frege's gonna shake ya, I know youz a hater, I'll show you who's a mensch with my infinite hierarchy of sense, your objections lost and now your thoughts denote the false, the concept of my skillz is not a concept, it's fo realz. It's presupposed I'm best, just try the negation test, I'll redefine your punkness as the set of all individuals with the same punk chumpness, hit you with the ancestral, befo you got successor, Gottlob was rockin ice before yo mama let ya. You 'n all your dogs can, check the Grundlagen, get the proper foundations... and a solution to the problem of multiple relations.

You Have No Rights. Now Stop Worrying and Get on with Your Life.

I count myself among the “New Athiests,” and I don’t even object to the label, as some do. But let’s forget labels for a second. The particular beliefs I share with, say, PZ, Dawkins, Coyne, etc. are (a) science tells against religion and (b) religion, in being anti-reason, makes the world a worse place.

How does science tell against religion? Well, either God’s existence and activity are supposed to have something to do with the events that occur in the natural world, or they aren’t. If they are, then we can directly falsify religion. If God caused a worldwide flood, we can check the geological record for evidence. If God made the earth stand still, we can use physics to tell us what that would entail and look for evidence. And whenever and wherever we look for evidence, revealed religion will lose. It won’t even be accidentally right, because now we (materialists) are in an excellent position to explain every phenomenon by adverting solely to natural laws.

So if God exists either (a) he* is causally inert (b) he causes natural phenomena, but always in a way that was overdetermined—that is, the world would have gone the same even without God (c) he caused the initial conditions or (d) he did the initial conditions and some overdetermined causation. But (a) and (b) both meet the edge of Occam’s Razor: don’t multiply entities beyond necessity. Occam’s Razor is part of scientific practice, so it’s science itself that rules out these options. And (c) and (d) meet with what I take to be Dawkins’ master argument (though I haven’t read his book, so I just picked up on this somewhere): if the initial conditions need a cause, because everything does, then God too needs a cause; if they don’t need a cause, then postulating God as their cause again violates Occam’s Razor.

I believe something like this, but I don’t want to defend it in this post. Here I won’t be pointing the finger at Believers and saying “ye fools!” Instead, I’ll be pointing the finger at my fellow New Athiests and saying “ye hypocrites!” Why are we hypocrites? Because we accept that science tells against God, but not that it tells against inalienable natural rights. But it tells against them too!

The argument against God goes: we have a complete story of the world, and it doesn’t involve God; and sticking him in is irrelevant and unnecessary. And my argument against inalienable natural rights is that we have a complete story of the world, and it doesn’t involve rights; and sticking them in is irrelevant and unnecessary.

We’re told that we have a fundamental right to believe whatsoever we want to believe, to not be coerced in matters epistemic. But how do we know we have this right? Do we train our rightometers on the oppressed, and notice a spike when they’re forced to keep silent? The other day I read a discussion regarding some individuals’ claims that they had a right to not be offended. Predictably, people said they didn’t have such a right. But how did they know that? How could they know that? It seems as though they couldn’t. This is because rights don’t have effects. They are causally inert. If you have a right to free speech and I make you shut up, the situation is exactly the same as if you don’t have the right and I make you shut up.

Inalienable natural rights are magic. Jefferson thought that God gave them to us, in a magic ceremony one might suppose, and that we can know about them through ‘the light of reason’ or some other equally spooky faculty. But we don’t have spooky faculties that tell us about magic, because magic doesn’t exist. In particular, rights don’t exist.

You might think I’m joking, but I’m not. I’ll give you the alternative proposal: the only morally relevant features of any situation are human happiness and human suffering**. Notice that whether someone is happy or is suffering is determinable by scientific investigation. We can tell whether an action mitigates suffering or increases happiness. There is no magic here.

You might think that talk of rights can be cashed out in terms of suffering and happiness. But I don’t think so. The other day I was reading about a woman in Afghanistan who had had acid thrown in her face by a scorned suitor. Normally, men who throw acid in women’s faces in Afghanistan can get out of jail by merely paying the woman’s family some compensatory sum. This is not a great deterrent, and that’s why so many women are disfigured by misogynist monsters. Now, the law allows for the woman to ask for an “eye for an eye,” that is, that acid be used to blind her attacker. In this particular case, the woman was demanding just that punishment. The interest of the story was that “human rights groups” were up-in-arms. Somehow there is a magical right people have not to be cruelly and unusually punished. Again, I have yet to be presented with the evidence for this.

Now my thinking goes as follows. Some men in some parts of the Arabic world believe that it is not morally abhorrent to throw acid at women. Because this is the case, women must walk down the street in constant fear that these idiots will disfigure them permanently, with little to fear from the law. And many women must live having been permanently disfigured by idiots. If a law allowing these women to demand an eye for an eye were on the books and were applied when applicable, there would be overall less suffering. So it is moral to enact such a law and to apply it, at least until overturning it would bring about a decrease in suffering and an increase in happiness—presumably when men stopped thinking disfiguring women was all in good fun. So please take your human rights elsewhere; I care about people, not about magic.

I think that we’ve become bogged down in nonsensical ‘rights’-talk. Consider the case of abortion. The debate often revolves around what rights fetuses have and what rights women have, etc. But these debates are intractable precisely because there’s no way of determining who has a right to what. One side says “I imagine such-and-such” and the other says “I imagine so-and-so.” But you can keep your imaginings, and you can keep your rights. Fetuses don’t have a right to life, because no-one does; and women don’t have a right to choose, because no-one does. There’s only one morally relevant question here: will there be an overall decrease in suffering if abortion is allowed, as opposed to if it is not allowed? And you don’t have to be a rocket scientist, or even a social scientist, to know that the answer is yes.

One more: Do homosexuals have the ‘right’ to get married? Of course not: no-one does. The question before us is clear: will there be an increase in happy lives if gay marriage is allowed? Yes. Case closed.

I’ve been a little polemic in this post. Good, maybe you’ll comment. But I want to end by pointing out a few things. First, my case against rights does not rest on the truth of act utilitarianism. Rights don’t exist because they’re magic, and they lie beyond the realm of evidence or even fruitful speculation.

Second, you might reply “oh, but there are sophisticated deontological theories of rights that look into both the metaphysical and epistemological issues you’re raising.” Perhaps. But this is a version of the Courtier’s Reply. Your man on the street whining about his right-to-this and his right-to-that does not gain his knowledge of rights by discovering a contradiction in universalizing maxims. There also would not be much in common between what rights he said he had and what rights a scrupulous application of the Categorical Imperative said he had. I am calling him out. I’m saying “what allows you to know that these claims you’re making are true? What makes you think these rights even exist?” I’ll save my battles with the sophisticated deontologists for another day.

Finally, I haven’t given any arguments for utilitarianism. I held it up as an example of a moral theory that does not quantify over magic. Happiness and suffering are real, and measurable. Thus, they are potential candidates for morally-relevant properties. They are not the only potential candidates, and it is a deep question how we determine what matters for ethics. But I know what doesn’t matter. Invisible, undetectable, inalienable natural rights.

Conclusion: the Enemies of Reason™ aren’t limited to those who persist in believing bronze-age myths. Some persist in believing enlightenment-era myths. These myths were important and helpful to our forebears, and they brought about many positive changes in politics and law. But it is time to kick away the latter of myth we climbed in on, and embrace the one obviously true moral principle: nothing cramps your moral powers like not existing!

[* Yes I know God isn’t supposed to have genitals. But that’s what they call it: ‘he.’]

[** I should add animal happiness and animal suffering, but for rhetorical force I’ll ignore animals for the moment. This should not be taken to indicate that I think animal happiness or animal suffering is not morally relevant.]

Comments

Apparently I hadn't enabled comments for anonymous users, and so some people were having trouble commenting. Fixed!

The Ondenotingiad

Sorry about the lengths of the posts. It looks too tech-y to hide them under a fold. But here's something meaty and philosophical for you to chew on, after all that light Fodor reading:

The Ondenotingiad

In “On Denoting” Russell tries
To establish his position
That unique existentials hide
In definite descriptions.

This 1905 paper starts
By criticizing Meinong
A guy whose non-subsistent smarts
Had led him rather wrong:

He thought that a denoting phrase
Could never fail to name;
The present king of France, he says,
Is as real as Charlemagne.

The reasoning that Russell faults
Is that the king is able
To be both bald and not—results
More suitable for Hegel.

Frege’s treatment of that great
Is crueler even yet:
He takes away his wigless pate
And equates him with a set!

Meaning comes in twos you see:
There’s “referent” or “denotation”
And on the other hand is the
Thing’s mode of presentation.

Sure, there is no fallacy—
Or none that I can tell—
But still there is that talk of C:
‘The curfew tolls the knell…’

We must distinguish ‘C’ and C:
The first denotes the second
But this it does mysteriously
Not by compositional method.

So, that “senses” are not sensible
Is the first insight of Russell’s,
An insight that makes tractable
Three philosophical puzzles.

The first of these is Leibniz’s law
Where identicals may be switched
Salva veritate in all
Propositions they exist.

If we apply this logical rule
To the thoughts of George IV
In thinking of the author who
Wrote Waverly and so forth,

And switch him for himself, viz Scott,
We find that we have blundered:
For whether Walter Scott is Scott
Is not what George had wondered.

To exonerate the wise old king
Russell states his view
In notation where ‘C(everything)’
Means ‘C(x)’ is always true.

An occurrence of the article ‘the’
Indicates uniqueness;
So let ‘author of Waverly’
Be our function C(x):

Then “it’s not the case that C(no x)
“And it is that if C(y)
“It follows y is equal to x”
Renders ‘C(the guy).’

So when King George IV once said
“Is Walter Scott the man?”
He had inside his singular head
A general proposition.

The logical law lets us switch names
Provided they co-denote;
It never said we could do the same
For improper parts of thoughts.

The second puzzle Russell solves
Is existence-claims’ negations:
He shows us that the case revolves
Round the tilda-sign’s location.

The claim that there’s a round square
Doesn’t name a thing
But says of at least one object there
It is round-squarizing.

When we say the king of France ain’t bald
There’s an ambiguity of note:
If we’re saying there’s no king at all
The ‘not’ must take wide scope;

But if we’re saying that he does exist,
And has a hirsute head,
The ‘not’ precedes the predicate
To negate the ‘bald’ instead.

The final puzzle that I’ll sing
May be stated as a riddle:
If neither ‘bald’ nor ‘not’ is the king
How to exclude the middle?

If thus far you’ve followed all,
You can see where this is leading:
‘The king of France ain’t bald’
Is false on the wide-scope reading!

O Musae, help me paint this
The grandeur of Russell’s vision:
Sometimes your knowledge ain’t acquaintance,
It’s knowledge by description.

Darwin was wrong?

This past Wednesday witnessed a debate between Rutgers’ own Jerry Fodor and Philip Kitcher on the merits of the theory of evolution by natural selection. What was unusual about this debate, as compared to others on the same topic, was that neither participant was anti-science, anti-reason, or pro-God. However, Jerry holds the iconoclastic (for a materialist) view that “the theory of evolution by natural selection is either false or vacuous, depending on how you read it.” Them, as they say, is fightin’ words.

I don’t want to resurrect that debate here. I went to the debate not to see arguments, but to watch people yell at Jerry (Tim Maudlin memorably said “Jerry, you accuse adaptationists of committing the intentional fallacy, while you yourself commit the fallacy of saying something is false when it’s been demonstrated right in front of you!”) However, I think it’s sad that no-one gives Jerry a sympathetic ear, because he’s a smart guy and even if he’s wrong, I think it would be a big advance in human inquiry just to know exactly why he’s wrong. So I want to explain what Jerry didn’t explain in the debate, though often adverted to: the analogy that Jerry sees between Chomsky’s argument against Skinner and Jerry’s argument against Darwin.

Part I of the analogy: Chomsky vs. Skinner

Most people, I imagine, have no idea what Jerry means when he says his argument more or less is Chomsky’s argument. We all thought that Skinner was wrong because, I don’t know, natural language syntax is recursive. But that’s not what Chomsky says in his review of Verbal Behavior (at least not in the selections reprinted in the Block anthology), so it’s worth taking a look at what Jerry sees in the review.

Simplifying a little, Skinner’s theory of learning by operant conditioning is that if an animal’s behavior B in situation S is reinforced (let’s just say “rewarded” for the time being), then the animal will learn to do B in S. For example, if a rat is rewarded for bar-pressing when shown a red thing, the rat will learn to press the bar when shown a red thing.

It’s an interesting fact that every finite set of red stimuli will share (that is, the members of the set will share) infinitely many properties other than being red. For instance, suppose the rat is presented with a series of bright red triangles in the bar-pressing experiment, when we want to enforce the behavior of bar-pressing given a red stimulus. The red stimuli here are not only red, but also closed figures; triangles; bright things; isosceles triangles; Granny’s favorite shape; triangles in a cage; things in a cage; etc. In addition, some infinite subset of these properties will be locally correlated with redness. That is, it might be true, in the rat’s environment (the cage), that something is red if and only if it’s a triangle; that something is red if and only if it’s an isosceles triangle; etc. Of course, not all the properties shared by the stimuli will be locally correlated with redness: ‘thing in a cage’ is true of both the red stimulus and the white rat. But an infinite amount of correlations is correlations enough. Call this “the ubiquity of local correlation.”

Now suppose we condition the rat in the way proposed. A bright red triangle is flashed, and when the rat presses the bar, it is rewarded with a food pellet. Question: can we use Skinner’s theory of learning by operant conditioning to tell us what the rat has learned? Answer: no—the theory construed in one way is false; in another way, it’s vacuous. Let’s investigate why.

A Skinnerian might be tempted to say: the rat has learned to press the bar when presented with a red stimulus. But in saying this, we need to ask her a further question, namely: is ‘learn’ here an intensional or an extensional verb? We (philosophers) say that ‘learn’ is extensional, if it follows from ‘Rat R learned to perform action A given a stimulus that is S’ and ‘S is locally correlated with F’ that ‘Rat R learned to perform action A given a stimulus that is F.’ That is, is it equally true to say that the rat learned to press the bar when presented with a red stimulus AND learned to press the bar when presented with a triangular stimulus AND learned to press the bar when presented with a stimulus that is an isosceles triangle AND…?

Let’s suppose the behaviorist says ‘yes,’ that ‘learn’ is extensional as used in her theory. Then the theory is clearly false. In order to show that the theory is false, we need only decouple two correlated variables and try the experiment again. Suppose we train the rat as described and then present it with a dull blue circle. Since ‘closed regular geometric figure’ had been locally correlated with ‘is red’ during conditioning, the rat, we are supposing, has learned to press the bar given a stimulus that is a closed regular geometric figure. A dull blue circle is a closed regular geometric figure, so the behaviorist predicts bar-pressing behavior. Now, maybe the rat will and maybe the rat won’t press the bar. If it doesn’t, behaviorism is falsified. If it does, behaviorism is left standing. But it won’t take long for a clever graduate student to find some or other local correlation the rat isn’t sensitive to (unless the rat learned ‘press the bar given any stimulus at all’), and we would all be well-advised to just abandon behaviorism now.

Horn II of the dilemma: suppose the behaviorist says ‘no,’ that ‘learn’ is not extensional as used in her theory. That is, the behaviorist asserts that the rat has learned to press the bar given a red stimulus, but that it does not follow from this and the fact that redness is locally correlated with property P that the rat has learned to press the bar given a P-stimulus. We ask: is the theory of learning by operant conditioning capable of predicting what the rat has learned, in the non-extensional sense of ‘learn’? NB. By this question we do not mean ‘is it possible to determine what the rat has learned?’ for if the rat has indeed learned anything, of course this is possible. We want to know what the theory in question has to say about what the rat learned.

Well, again, suppose we condition the rat as described, by rewarding it for pressing a bar in the presence of a bright red triangle. Has the rat learned (in the non-extensional sense) to press the bar given a red stimulus, a bright stimulus, a triangular stimulus, or some other kind of stimulus? Notice that the theory of learning by operant conditioning does not give us any guidance. The stimuli were all of these things. The experimenter receives no helpful advice from the theory about what hypothesis to hold.

Now suppose we test some hypothesis, say, the hypothesis that the rat learned to press the bar given a red stimulus. We present the rat with a blue triangle. If the rat does not press the bar, we have some confirmation of our hypothesis; if it does press the bar, perhaps we will be led to instead propose that the rat learned to press the bar given a triangular stimulus. This is how science goes. But the question is: is Skinnerian learning theory confirmed by any of this? And the answer is: vacuously, yes. If the rat does not press the bar, the Skinnerian will say ‘look, we were right: the rat’s bar-pressing behavior was rewarded when the rat was given a red stimulus, and it learned to press the bar when given a red stimulus.’ If the rat does press the bar, the Skinnerian will say: ‘look, we were right: the rat’s bar-pressing behavior was rewarded when the rat was given a triangular stimulus, and it learned to press the bar when given a triangular stimulus.’

We can go on. After the first decoupling experiment, the experimenter will have ruled out a certain hypothesis, say, that the rat learned to press the bar when presented with a red stimulus. But there will still be infinitely many properties locally correlated with triangularity, so it will not follow that the rat learned to press the bar when presented with a triangular stimulus. Here again, Skinnerian learning theory is of no help whatsoever in constructing hypotheses about what the rat learned. It cannot predict, it can only incorporate empirical findings post-hoc into the behaviorist model.

So the theory of learning by operant conditioning (a) makes no predictions (b) does not guide researchers in formulating hypotheses about learning and (c) is trivially compatible with any outcome whatsoever. That is not how science goes.

This is how I’ve heard Fodor present Chomsky’s case against Skinner. And I think it’s a compelling case. The claim is that the theory of learning by operant condition is false, if ‘learn’ is read extensionally and trivially true if ‘learn’ is read intensionally. And I take it that no-one wants to defend Skinner at this point. So without further ado:

Part II of the analogy: Fodor vs. Darwin

[Every sentence of this section should really begin with ‘According to Fodor, as I understand him.’ Please don’t attack me for attacking Darwin; I am not attacking Darwin. I am presenting Fodor’s views, as I understand them.]

Simplifying a little, Darwin’s theory of evolution by natural selection is that if two heritable traits T and T’ are possessed by some ancestral population in some ecological environment, and T is more fit than T’, then T will increase in prevalence in the population over time, eventually moving to fixation (except in certain cases where the fitness of T depends on prevalence of T’). For example, suppose there is a population of brown bears that live in the arctic wastes. At some point a mutant white bear arises. Since coat color is heritable, and a white coat is more fit than a brown one, whiteness moves to fixation in the bear population.

It’s an interesting fact that every finite set of whiteness phenotypes will share (that is, the members of the set will share) infinitely many phenotypic properties other than whiteness. For instance, suppose that at present 20% of the bear population possesses the whiteness phenotype (and for simplicity’s sake, suppose the bear head-count is 100 total individuals, so that 20 of them are white). The white bears will not only be white, but also bears; four-legged; the same color as snow; the same color as paper; more closely related to one another than to any non-white non-parental bear (assuming that whiteness is a dominant trait); located in some perhaps-disjoint spatio-temporal region; etc. In addition, some infinite subset of these properties will be locally correlated with the whiteness phenotype. That is, it might be true, in the bears’ environment (the arctic), that something is a white bear if and only if it’s a bear the same color as snow; that something is a white bear if and only if it’s more closely related to white bears or its parents than non-white non-parental bears; etc. Of course, not all the properties shared by the whiteness phenotype will be locally correlated with it: ‘bear’ is true both of white bears and of brown ones. But an infinite amount of correlations is correlations enough. This is another instance of the ubiquity of local correlation.

So suppose a mutant white bear arises in the population. Question: can we use Darwin’s theory of evolution by natural selection to tell us why the phenotype moves to fixation in the population? Answer [again, Fodor’s answer, not mine]: no—the theory construed in one way is false; in another way, it’s vacuous. Let’s see why one might think this is so.

An adaptationist might be tempted to say: the whiteness phenotype moved to fixation because being white increased the probability that a bear would produce viable offspring as compared to the probability that a brown bear would produce viable offspring. But in saying this, we need to ask her a further question, namely: is ‘phenotype P increases fitness relative to competing phenotypes C’ an intensional or extensional context at position P? It’s an extensional context if it follows from ‘phenotype P increases fitness relative to competing phenotypes C’ and ‘phenotype P is locally correlated with phenotype Q’ that ‘phenotype Q increases fitness relative to competing phenotypes C.’ That is, if it’s an extensional context, it should be equally true to say that the whiteness phenotype increases fitness AND the same-color-as-snow phenotype increases fitness AND the being-located-in-region-R (where R is the region containing all and only white bears) phenotype increases fitness AND...

So let’s suppose that the adaptationist does indeed say that ‘phenotype P increases fitness relative to competing phenotypes C’ is extensional at the P-position. Then the theory is clearly false. In order to show that the theory is false, we need only decouple two correlated variable and see what happens in the population. Suppose, to take a flight of fancy, that we’re super-scientists capable of making snow brown (we’re already capable of making it yellow, so this shouldn’t require too much of a technical advance). The adaptationist told us that ‘the same-color-as-snow phenotype increases fitness’ and by this she also meant that ‘the white phenotype increases fitness.’ Now we change the color of the snow to brown. Suppose the brownness phenotype now goes to fixation. It looks like we’ve falsified adaptationism, for it is not true after all that whiteness increases fitness.

[If you don’t like the example, because you’re worried we’ve changed the ecology, which is a free variable we’d been suppressing, you should realize that I could have run the example with any of the local correlates of the whiteness phenotype. For example: the phenotype of being a bear with exactly 19 other individuals of the same color. We don’t have to even intervene at all to watch adaptationism get falsified, we can just let whiteness go to fixation. And if you think I’m cheating by using extended phenotypes, talk to Dawkins.]

Horn II of the dilemma: suppose instead that the adaptationist says that ‘phenotype P increases fitness relative to competing phenotypes C’ is not extensional (is intensional) at the P-position. That is, the adaptationist asserts that the same-color-as-snow phenotype in bears in their present ecology increases fitness, but it does not follow from this and the fact that the same-color-as-snow phenotype is locally correlated with the whiteness phenotype that the whiteness phenotype increases fitness in bears in their present ecology. We ask: is the theory of evolution by natural selection capable of predicting what heritable traits increase fitness among bears in their present ecology? NB. By this question we do not mean ‘is it possible to determine what heritable traits increase fitness’ for if some traits do and others do not, of course this is possible. We want to know what the theory in question has to say about the relative fitness of bear phenotypes.

So suppose the whiteness phenotype has gone to fixation and there are now, say, 200 white bears. Did the whiteness phenotype increase the fitness (in the intensional sense) of the ancestral white bears or was it rather the same-color-as-snow phenotype, the same-color-as-paper phenotype, or any other phenotype that the white bears happen contingently to share with one another and not brown bears? Notice that the theory of evolution by natural selection does not give us any guidance. The ancestral bears (and the present bears) were all of these things. The evolutionary scientist receives no helpful advice from the theory about what hypothesis to hold (though of course the scientist has a helpful set of priors, and is likely to latch on to the correct hypothesis, without invoking Darwin’s theory).

Now suppose the field scientist actually runs some controlled tests on the population of bears in order to test the hypothesis that it was the same-color-as-snow phenotype that increased the fitness of the bears in their ecology, relative to the competing different-color-from-snow phenotype. Perhaps she isolates some of the bears in an area where the snow has been made artificially brown, along with some other conspecific brown bears taken from a different population. If the brownness phenotype goes to fixation in this new population, we will have some confirmation for our hypothesis; if whiteness goes to fixation, we may be led to instead propose that the whiteness phenotype (rather than the same-color-as-snow phenotype) increased fitness (maybe females prefer white bears or something). This is how science goes. But the question is: is Darwinian evolutionary theory confirmed by any of this? And the answer is [again, Fodor’s answer, not mine]: vacuously, yes. If brownness goes to fixation, the Darwinian will say: ‘look, we were right: the same-color-as-snow phenotype was more fit than the whiteness phenotype, and it went to fixation.’ Similarly, if whiteness goes to fixation, the Darwinian will say: ‘look, we were right: the whiteness phenotype was more fit than the same-color-as-snow phenotype, and it went to fixation.’

We can go on. After the first decoupling experiment, the experimenter will have ruled out a certain hypothesis, say, that the same-color-as-snow phenotype was not fitter than its competitors. But there will still be infinitely many properties locally correlated with the whiteness phenotype, so it will not follow that that phenotype was fitter. Here again, Darwinian evolutionary theory is of no help whatsoever in constructing hypotheses about which traits increase fitness. It cannot predict, it can only incorporate empirical findings post-hoc into the adaptationist model.

So the theory of evolution by natural selection (a) makes no predictions (b) does not guide researchers in formulating hypotheses about evolution and (c) is trivially compatible with any outcome. That is not how science goes [or so says Fodor].

This, I take it, is an intriguing argument. It has nothing to do with God. The claim is that the theory of natural selection read extensionally is false, and read intensionally is vacuously true. Nothing about the tree of life is questioned, nothing about inheritance through genes, nothing about the physical basis of all observable phenomena. The hard work of evolutionary biologists in the field is not ignored, nor is it taken to be irrelevant. Fodor is merely arguing that for biologists to attribute their scientific findings on evolution to The Law of Natural Selection is rather like contemporary computational psychologists attributing their findings to Behaviorism. The findings are still there, and still correct: they’re just neither suggested nor explained by natural selection. Or again, so says Fodor.

Conclusion

I don’t know whether Fodor’s right or not. Maybe that makes me an idiot, because maybe he’s as obviously wrong as Randy (Gallistel) and Tim say he is. So be it. But I’d like to be very clear on why Fodor is wrong, if he is. I used to think he was just arguing: there are no biological laws; explanation is subsumption under a law; therefore there are no biological explanations. And I used to think the response should be: that’s an exceedingly narrow conception of explanation. But now I take his argument to be what I presented above: it’s about whether the theory of natural selection itself has any content whatsoever. And one can’t answer that challenge by modifying what one counts as explanation. I invite civil discussion in the comments. No Godbotting, plz.

Metablogicon

This feels a little silly. I have a blog. It's about philosophy, but it's not one of those "here's a paper I'm writing blah blah blah" philosophy blogs. It's supposed to be about one modern materialist's struggles to understand the world he inhabits and all that's in it. I've got some posts planned on Fodor vs. Darwin, abortion, art, meaning, that sort of thing. I don't plan to update with much greater frequency than weekly. But you're invited to join the conversation anytime.