Wednesday, January 31, 2007

The Scientific Method, part 2

In my previous post, we found we had a method (perception) of generating statements which so many people "mysteriously" (in the sense that the statements were not logical necessities) agreed upon that we are forced to consider these statements to be "true".

We also found a method (logical deduction) that relates true statements together. Again, so many people "mysteriously" (in the sense that one cannot directly perceive these relationships) agreed that deductive relationships were valid that we're forced to consider this way of relating statements to be "true".

Two great tastes. Maybe they'd taste great together [1]?

The biggest problem with logical deduction is where to start: How do we justify our premises? If intuition is sufficient justification, then why use deduction at all--especially when (as notoriously with probability theory) our deductive conclusions are in conflict with our intuition? If intuition is reliable enough for our premises, why isn't it reliable enough to reject counterintuitive conclusions?

How about statements of perception? We have this great process--deduction--but we're running into trouble justifying our premises. And here we have this great process--perception--that seems to satisfactorily justify statements without deduction. The blindingly obvious course is to use perception to justify our premises and then use deduction to acquire more knowledge from those premises.

It's so blindingly obvious that philosophers have at least spoken about the relationship between perception and deduction since the time of Socrates (if not before), even if, as Plato did in his early days, to simply dismiss perception as unreliable. Still, a contingent of philosophers, "Empiricists", labored for millennia to get statements of perception to work well with deduction.

As blindingly obvious as is the seemingly "right" way to merge perception and deduction--that is to use perception to justify premises from which we can deduce knowledge--this task turned out to be frustratingly difficult, for a number of reasons.

The first reason is that our statements of perception, while usually uncontroversial, in some cases yield what appear to be puzzling contradictions. Place a pencil, a usually rigid object, halfway into a bowl of water and it appears to be bent; take it out again, and it appears to be straight. Eat certain foods (like grain contaminated by ergot, or psilocybin) and suddenly one has all of these perceptual experiences that just don't cohere with anything. Most people can differentiate objects on the basis of color, but certain people--who appear normal in every other respect--simply cannot do so. Statements of perception, while "mysteriously" reliable, do not appear to give us the certainty we need to construct a purely deductive edifice of knowledge.

The second reason, as Hume noted, was that it seems impossibly difficult, even uncritically accepting statements of perception, to deduce something as basic and seemingly obvious as causality.

The next reason (which I alluded to in part 1), as Quine noted, is that it's not so easy to understand at a fundamental level what statements of perception actually mean. Yes, everyone assents to, "The cat is on the mat" (when they're looking at the cat, which is, of course, on the mat), but what precisely are they assenting to? Quine and the other "linguistic wholists" make a powerful case that one's entire linguistic apparatus (or at least a non-trivially large portion of it) contributes to establishing the meaning of statements of perception. The meaning of statements of perception is very complicated. Worse yet, since each person's overall linguistic apparatus is different, it becomes almost ridiculous to assert that two people who assent to the same statement are assenting to the exact same meaning.

Yet another reason, which Quine also noted, is that statements of perception are not really statements of perception. The "fanciful fanciless medium of unvarnished news" [2] is a myth. When we assent to "The cat is on the mat," we are assenting to an ontological statement, a statement about how the world is--or how we conceive it to be--not strictly about what we see. We need only a little introspection to realize that what we are consciously aware of is not the "raw footage" of our senses, but rather a stream of conclusions about how the world is, heavily processed and interpreted by our subconscious and preconscious minds. We can support this conclusion further by noting that even animals--devoid of linguistic capability--appear to have some sort of model of the world in their brains. It's implausible to suggest that an ontological attitude--a model of how the world is--can be formed only by the sort of language-dependent rational deduction which is philosophers' stock in trade.

(I'm going to only briefly mention a couple of red herrings which have diverted the project of unifying perception and deduction: The analytic/synthetic dichotomy, which Quine also spoke on, and that the core project of most philosophers has been to justify ethics, which is not (as I'll write on in the future) susceptible to even scientific investigation, much less the sort of axiomatic foundationalism which Empiricism has foundered on.)

How frustrating! We have all these great statements of perception, but they're just useless as an axiomatic foundation for any process of deduction. And we have this great tool--deduction--but we just can't find any sort of axiomatic foundation for it.

There is a way out. But to open this door, we have to abandon some philosophical baggage. Specifically, we're going to have to discard the notion that we can ever be certain about anything we have to say about the world, and similarly, we have to discard the notion that anything we can say with certainty is directly about the world. As Einstein put it, "As far as the laws of mathematics refer to reality, they are not certain, as far as they are certain, they do not refer to reality." Although some philosophers are not willing to give up on the notion of establishing real truth about the world with absolute deductive certainty (and more power to them), I think that after two thousand years of banging our heads against the brick wall of deductivism sheer desperation compels us to consider alternatives.

If we look at mathematical axioms and theorems, such as ordinary arithmetic, we notice two things: One is that the axioms are both simple, in the sense of not being composed of very many parts, and precise, in the sense of saying exactly one thing. For example, the axioms of Peano's Arithmetic [3] are:
  1. 1 is a natural number.

  2. Every natural number is equal to itself.

  3. For all natural numbers a and b, a=b if and only if b=a.

  4. For all natural numbers a, b, and c, if a=b and b=c then a=c.

  5. If a = b and b is a natural number then a is a natural number.

  6. If a is a natural number then Sa is a natural number. Here Sa denotes the successor of a, otherwise known as a+1.

  7. If a and b are natural numbers then a=b if and only if Sa=Sb.

  8. If a is a natural number then Sa is not equal to 1.

  9. For every set K, if 1 is in K and for every natural number x in K, Sx is also in K, then every natural number is in K.

The other thing that we notice is that the derived theorems, i.e. conclusions, of arithmetic are complex (composed of many parts) and rest on an enormous chain of reasoning. For instance, the basis for establishing the "occasionally useful" proposition that 1+1=2 does not occur until page three hundred seventy nine of volume I of Principia Mathematica, and isn't actually completed until well into volume II!

"Well, hmm..." says the philosopher, stroking his beard [4]. "These mathematical conclusions look suspiciously similar to our statements of perception." And indeed they do, at least in terms of their complexity and depth. "What if we go in the other direction?" What if we treat statements of perception as a more-or-less arbitrary collection of true theorems, and see if we can figure out the premises which would allow us to derive these statements of perception? And thus was born the hypothetico-deductive model of science, the third and penultimate piece of the puzzle.

We're going to throw out the need to directly justify our premises. Instead, we'll take the philosophically outrageous step of just making premises up. Since we're just making up premises, we can make them as simple, precise, unequivocal and definite as we please. But, since we're explicitly and intentionally making them up, instead of just taking them on faith (unlike others *cough* theologians *cough*), we're going to be a little more skeptical about them, and call them "hypotheses".

Since our hypotheses are simple and precise, we can deduce conclusions from them. More importantly, we can draw conclusions that correspond to statements about perception in natural language--without having to make very many assumptions about the intrinsic neurological or psychological meaning of these statements. Quine's objections no longer become fundamentally important; we don't need to know precisely what "the cat is on the mat" means. Rather, we're going to construct some hypotheses and deduce from them whether or not people will in fact assent to "the cat is on the mat," whatever that might mean.

We're not quite out of the woods yet; there's still one more piece of the puzzle.

We're going to make our arbitrary hypotheses, deduce statements of perception from them (thus forming an empirical theory), and see how well our deductions match our perceptions. But what precisely do we mean by "match"? It seems obvious that a theory should be "good" if it matches a lot of statements of perception, if it is verifiable.

But again we have a problem with an apparently "obvious" criterion: We can construct theories which match any and all statements of perception! Your friendly neighborhood psychic, for instance, predicts that you will take a long journey. Well, sooner or later, you probably will take a long journey. And even if you don't actually get on a plane and fly to Pago Pago, you can interpret this prediction metaphorically; perhaps the "long journey" refers to the difficult time you're having cutting through the bullshit understanding philosophy. In short, no matter what happens, the psychic's predictions will be "verified".

Professor Altemeyer gives us another excellent example of a Freudian explanation for authoritarian aggression.
Supposedly the future authoritarian follower was severely punished as a child by his cold, distant parents for any signs of independence or rebellion. So such urges were repressed. Instead through a reaction-formation the child became obedient, loyal, even adoring of his parents. But deep down inside he hated them. However the Freudian “deep down inside” doesn’t have a shredder or burn-basket, so ultimately the repressed hostility has to come out some way. Thus the authoritarian follower projected his hostility onto safe targets, such as groups whom the parents disliked or people who couldn’t fight back, and decided they were out to get him. That projection provided the rationalization for attacking them and, voila, you have authoritarian aggression--thanks to just about all the ego defense mechanisms in Freud’s book.[5]
The problem is that this "theory" doesn't predict how a patient will act. Anything you see is consistent with this theory:
Suppose you did a study of dreams and concluded that authoritarians greatly love their parents. “Ah ha,”the theory would say with goose bumps breaking out, “there’s that reaction-formation I told you about.” Suppose you found, on the other hand, that authoritarians seemed to hate their parents. “Ah ha,” the Freudians would remark, “Just as we said; their unconscious mind is so filled with dislike for dad and mom, it can’t be held back any more.” Suppose you found that authoritarians dream both good things and bad things about their parents. “Ah ha,” goes the explanation. “You see both repression and the true feelings are at work.”


Basically, Freud's hypothesis says, "If a person has repressed hostility towards his parents, his dreams about his parents will be positive (reaction-formation), negative (repression failure), or mixed." But this sort of statement is just a trivial restatement of the operation of logical implication. We could easily say that "If the moon were made of green cheese then either Superman exists or Superman does not exist." We can even rob the individual predicates of any referent whatsoever and say, "If toves are slithy then borogroves are mimsy or borogroves are not mimsy." That's a valid mathematical theorem of logic, but it doesn't tell us anything about the world.

The whole reason we're looking to science is that we actually do want to predict things in just the same way that Freud's theory doesn't predict what sort of dreams a person with repressed hostility will have.

Karl Popper rides to the rescue to put the last piece of the puzzle in place: falsifiability. In order for a hypothesis to be relevant, there must be some logically possible statement of perception such that the truth or falsity of that statement would render the hypothesis false through modus tollens (proof by contradiction). In other words, if your hypothetico-deductive construct says that, "If this hypothesis is true, then that statement of perception will be assented to," then it follows logically that if that statement of perception is dissented from, then either the conditional or the antecedent is somehow false.[7] If a construct does not meet this test, if it says instead that, "If this hypothesis is true then that statement will either be assented to or dissented from," then "this hypothesis" is not falsifiable; it's not logically connected to "that statement".

We'll throw in Occam's Razor (more in part 3) and put all the pieces together to give a concise definition of the scientific method:

The Scientific Method is the construction of a parsimonious falsifiable explanation from hypothetical premises which logically implies some set of verifiable facts.

In part 3, I'll talk about some of the philosophical objections, alternatives and refinements to the scientific method as presented here, including parsimony (Occam's Razor), coherentism, Pirsig's infinite-hypotheses objection and Metaphysics of Quality, some of Popper's relatively minor "mistakes", and perhaps about the difference between universal and historical/forensic sciences.

I'm pretty busy today, so I don't have time to go over this essay with a fine-tooth comb. I apologize in advance for any mistakes in grammar, spelling, and composition.

[1] With apologies to The Hershey Company.

[2] Word and Object, W. V. O. Quine, The MIT Press, 1960, p. 2

[3] I'll spare you (and myself!) the intricacies of set theory, which are not necessary to make my point about the simplicity of mathematical premises.

[4] Everyone knows that all philosophers are male, have beards, smoke pipes and wear threadbare corduroy jackets with leather elbow-patches. I still don't know how such luminaries as Elizabeth Anscombe or Iris Murdoch pulled this look off.

[5] The Authoritarians, Bob Altemeyer[6], University of Manitoba, 2006-2007, http://home.cc.umanitoba.ca/~altemey/, accessed 1/31/07, Chapter 2, p. 53

[6] Whom, despite never having seen a picture of him, and despite the fact that he's a psychologist, not a philosopher, I cannot help but imagine as having a beard, a pipe and a threadbare corduroy jacket with leather elbow-patches.

[7] It doesn't matter which, something is wrong.

9 comments:

  1. Popper's demarcation criterion for the sciences -- falsifiability -- is vulnerable to a number of objections related to some of the things you mentioned earlier.

    Quine has argued that no individual sentence has a distinctive verification or falsification condition, except relative to a mass of background theory against which observation takes place. All experimental observations are theory laden. If we were studying a astronomical phenomon, we would be working with observations made with telescopes (of one sort or another). However, in using such telescopes (and interpreting what we see through them) we assume an understanding, if only an intuitive one, of optics.

    Plus, using Popper to establish a general epistemology is vulnerable to another objection. Falsification can only tell you what not believe, but not what is true. Even a well-tested theory that has not yet been falsified may turn out to be wrong. It leaves the question: what makes it justified for you to believe it?

    Not all of our beliefs have to be understood on the model of scientific beliefs. Scientific theories about imperceptible entities, such as atoms, may simply be epistemologically different from our perceptually-justified beliefs about garden variety middle-sized objects. The most natural account here is an externalist one, according to which a belief is justified if it is produced by a reliable cognitive process. It is not necessary, then, to produce an argument for the reliability of sense perception, or memory, or whatever else to be warranted in believing what they issue. (Knowing something is true is not the same as being able to prove it is true to a skeptic.)

    You might want to read Bertrand Russell's The Philosophy of Logical Atomism, where he says that epistemological order of things is not necessarily the same as their logical order. The mathematical beliefs which are most easily justified are about the mathematical objects with which we are more readily acquainted. (Incidentally, not many philophers and mathematicians subscribe the logic of Russell and Whitehead's Principia Mathematics, and there is good reason not to believe it is right!)

    Maybe I'm jumping the gun on the third part of you posts on the Scientific Method, but I thought I'd make some comments all the same.

    Cheers!

    ReplyDelete
  2. I thought I would add one more comment to prevent my being cut down by Russell scholars out there on the web!

    Strictly speaking, Russell does not think there are any "mathematical" objects with which can be "acquainted". Acquaintance is a relation between a perceiver and an individual sense-datum, but not with the subject matter of mathematics. For Russell, terms purporting to refer to mathematical objects, such as classes, are incomplete symbols and can be "analyzed away". There is a paraphrase which, using the ramified theory of types, eliminates references to classes in every context.

    ReplyDelete
  3. Timmo,

    Thanks for your comments! They're much appreciated. I always prefer to address the objections of sincere skeptics; I've always found it dodgy to try to construct arguments objecting to my own conclusions.

    Addressing objections such as yours will indeed be the focus of the next part (possibly the next several parts) of this theme, so I hope you'll understand if I simply acknowledge the value and incisive nature of your objections and promise to do them what justice I can in my next essay.

    What would really make me jump for joy would be for you to write up your objections to falsificationism in essay form and publish it on your own blog, let me publish it here, or both.

    ReplyDelete
  4. Let me add this... My invocation of Principia Mathematica was not to indicate any sort of metaphysical or epistemological commitment to the work, but merely to give a striking example of the elaborate complexity of even s seemingly simple mathematical theorem and to relate that complexity to that of "theory laden" statements of observation.

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  5. After your next post, I can try to squeeze in a short essay on Popper's philosophy of science. The exchange, I expect, will be interesting, and I look forward to it.

    I should qualify what I said earlier about skeptics. We can distinguish between ordinary and extraordinary skepticism. An ordinary skeptic is just the sort of opponent we fact in day-to-day discussions. If a scientist asserts that he, say, discovered a new state of matter, then the appropriate response would be ordinary skepticism: doubt his assertion until he could produce compelling evidence for his contention. On the other hand, a philosophical skeptic might have doubts about the trustworthiness of our cognitive faculties, demanding evidence for trusting them.

    What I mean to say is that we ought to address the ordinary skeptic, but that we cannot, and need not, address the concerns of the philosophical skeptic. (Their doubts go, as it were, too far to be reasonable.) I suspect that only the former could be genuinely "sincere" about their skepticism. Even classical skeptics, like Pyhrro's followers, believed what their senses revealed.

    ReplyDelete
  6. Timmo,

    When I used the word "skeptic", I was referring to you personally; you appear justly skeptical (in the ordinary sense) of the persuasive value of my arguments.

    I'm very much looking forward to reading your thoughts about Popper and the concept of falsificationism in general.

    ReplyDelete
  7. parsimonious?

    ReplyDelete
  8. <a href="http://jroller.com/phentermine">Phentermine</a>8/13/07, 1:17 PM

    Nice design of blog.

    ReplyDelete
  9. Phentermine: Thanks, but I can't take credit. It's a stock Blogger.com template.

    ReplyDelete

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