Chautauqua: In Which Phaedrus Misunderstands the Nature of Science

In Zen & The Art, Pirsig talks quite a lot about his younger self, Phaedrus.  One of the things he wants to point out is that Phaedrus went the way that he did because he had discovered a fundamental flaw in the taproot of western rationalism, the scientific method.

Pirsig points out that Phaedrus was not into science for career reasons, but rather, for the love of the pursuit.

(This is something with which I can identify, and it’s something probably lost today, for reasons of simple economics.  When I was an undergraduate, at a Major Midwestern University (incidentally only, the same one that Phaedrus attended), you could register for as many classes as you liked for about $300.  Of course you had to pay for the books, but—I’m wandering.  The point is that for that kind of money in the mid-1970s, college was insanely affordable.  You didn’t go to school to get a career, but an education.  School was (I suspect) even more affordable when Phaedrus attended college.)

Phaedrus was also young, fifteen or so when he started college (at that same Major Midwestern University).  Being young, Pirsig was, as noted, in it for the love of the pursuit, and what he was pursuing was science and the notion of TRUTH through science.

Of course, he attached himself to the taproot, and quickly learned how scientific method works:  you have a theory about how the world works (theories, to be fair, are usually developed from past experience).  You examine a particular problem (e.g., what is fire?), state a hypothesis that is consistent with your theory (“it is the rapid oxidation of fuel”) and then you conduct an experiment to test the hypothesis.  Note that I am vulgarizing here.  For a full discussion of scientific method, see something like Wikipedia.  Phaedrus realized that there was a problem, in that science was eating its own tail; so many discoveries, so many ideas, had flourished, that there were a potentially infinite number of hypothesis to explain any one phenomenon.

This is a problem, because it means you can’t test all of the hypotheses—and new ones emerge even while you test extant ones.  Consequently, Phaedrus, for whom a search for TRUTH was everything, found himself grappling with what was (in his view) a dead taproot.  For without the ability propose and to test hypotheses, the scientific method is bankrupt. You can never discover TRUTH.

This is where I think Phaedrus went wrong, and I’m writing this Chautauqua because he isn’t the only one.  I’ve said before that I am a recovering sociologist, and my spouse is a statistician, and there’s an aspect of scientific method that gets a little more attention paid to it by such folk than by undergraduate biochemistry students.

This is the null hypothesis, what we might call the Default Truth, for lack of a better term.  This is not the same thing as TRUTH.  The null hypothesis (let’s use the standard notation, H0, to simplify things) essentially says that the world is boring, and that there is no relationship between any two variables X and Y.  Let X=whether one’s income is above or below the poverty level.  Let Y=one’s children’s educational attainment.  H0 says that there is no relationship between these two things, and that, consequently, holding everything else constant, the children of a corporate executive should have on average, the same kind of academic performance as those of an immigrant janitor.  That’s a Default Truth about the world (sort of like “any child can grow up to be president”).

The first thing you should notice about H0 is that I said it’s provisional.  It’s what we assume until we know better.  And it’s not hard to know better.  We test H0 by conducting an experiment, or the natural equivalent of an experiment—a survey.  We collect data on parental income and academic performance and we look at the relationship.  H0 tells us what to expect.  Our data tell us what the world really looks like.  If the data we collect are sufficiently convincing (and statisticians have a very rigorous set of methods to tell whether or not they are) we do not proclaim that we have the TRUTH—but we do reject H0, the Default Truth.  Generally, we substitute for H0 what we discovered (call it H1) and start looking to see if there’s anything we can do to improve on H1.  Or reject it.  So we have a new Default Truth.  But still not the TRUTH.

Because, here’s the trick—Phaedrus thought scientific method was a tool for discovering TRUTH, and it’s not.  It’s a tool for disposing of untruth, of Default Truth that doesn’t measure up.  No scientist ever claims to have TRUTH, which is why even things like evolution and relativity are called theories.  They can be challenged.  They can be tested. They’re falsifiable.

When I was an undergraduate, I could not for the life of me grasp why I would want a theory to be falsifiable.  And then I realized that what falsifiable means is not that the theory is wrong, but that if it is wrong, there is a way to show that it is wrong.  It can be tested.  Usually, this means that the theory makes predictions (hypotheses) about the way the world works.  Show that the hypotheses are wrong, and you start to cut away at the support for the theory.  Eventually, if the hypotheses keep coming up wrong, at some point you will abandon the theory.  Both good and bad theories thus lead to falsifiable hypotheses; in the case of bad theories, the hypotheses are not only falsifiable, they are falsified.

If, by the way, you run into something that claims to be a theory but which does not yield falsifiable hypotheses, it’s not a theory.  So-called creation science is an example.  Why?

Because it works like this.  Creation science claims that the world is around 7,000 years old.  If that’s the case, it should be possible to develop hypotheses that we can test, like (for example) that carbon dating will show that no evidence of human existence in more than 7,000 years old.  The problem is that creation science advocates attack the accuracy of carbon dating, because it falsifies the hypotheses derived from the theory.  In fact, any method that does validate the theory comes under attack, and since (1) there are many such methods and (2) these methods have independent validation (that is, apart from their application), it becomes impossible to falsify any hypotheses derived from creation science, and so, impossible to invalidate the theory.  And that means, in turn, that it is not a theory.  It’s a belief system.

So—scientific method cannot give you TRUTH; it can only point out that what you thought was true, isn’t.  It’s a tool for paring away falsehoods a la Sherlock Holmes’ famous dictum that “when you have eliminated the impossible, whatever remains, however improbable, must be the truth.”  Except, of course, that the world is so very complex, that TRUTH is elusive.  We can approach it, but (science says) we can never reach it.

But for Phaedrus, young and a believer in TRUTH, there were two related stumbling blocks here.  First was the connection between theory and hypothesis—that a theory could in fact generate multiple, potentially, infinitely many, hypotheses.  Second was the impossibility of testing all of these hypotheses.   Like Xeno’s paradox (I am thinking of the Arrow paradox, here)1, this reduces the system to incomprehensibility.

What Phaedrus missed is that, first, theories do not generate infinite, unbundled, discrete hypotheses.  That’s what theories are for:  they constrain bootless speculation because they have to be internally consistent.  So the hypotheses deriving from a given theory are both (a) limited in number and (b) related.  Second, he missed the notion that it is possible for a single test to eliminate not only an individual hypothesis, but an entire class of hypotheses at the same time.

Let’s take a fairly stupid hypothesis for an example.  Let Hi=”the number 4 is prime.”  It’s easy to show that Hi is false, because 4 is not only divisible by 1 and 4, it’s divisible by 2.  But the implication of this test is that we need not test the hypothesis that concerns any number that ends in 4.  1004? 123,776,304?  Mathematical theory tells us that any number that terminates in 4 is divisible by 2 (hidden assumption:  we’re talking about Base 10).  Therefore, we can know without testing that all hypotheses that suggest such numbers are prime have been falsified.   (One way to tell a mathematician is off the rails is when she conjectures that there is an unknown Base-10 prime that ends in 4; that mathematician wouldn’t be talking about a theory, but a belief system.)

More generally, if we have a well-validated tool (like carbon dating) we can automatically invalidate any hypotheses that suggest that the Earth is less than 4.5 billion years old and, what’s more, every hypothesis that takes that as one of its assumptions.

Consequently, while science cannot point us to the TRUTH, it needn’t plod along eliminating falsehoods one at a time—and since hypotheses derive from theories (see the discussion about Creation Science, earlier) they tend to come in the kind of bundles that can be dealt with by large whacks of the scientific method, rather than as an infinite number of discrete random ideas.

  1. Gino’s Paradox is related to Xeno’s.  Consider:  Socrates orders pizza for his study group.  How much pizza will he need?  One is sufficient, because any given slice can be divided to yield two slices.  Because dividing the pizza does not consume it, there is always enough to go around.   You’ve no doubt noted the problem—there will always be more slices, but the slices will always be smaller.  But philosophically, that’s not important.  Socrates only needs one.  For this understanding I am indebted to a cartoon in the Chicago Reader, c. 1983 or so.
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