Thursday, February 26, 2009
Tuesday, February 24, 2009
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
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’
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
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
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.
This past Wednesday witnessed a debate between
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
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.
[Every sentence of this section should really begin with ‘According to Fodor, as I understand him.’ Please don’t attack me for attacking
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
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
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.
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.