Philosophy and History of Science and Technology

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Thursday, 09-07-17: Pseudoscience I

Readings:

Synopsis:

If it is the job of science (and, perhaps, mathematics and philosophy as well) to understand the world, then we must tread carefully and try as best we can to discriminate between genuine science and enterprises which seem like--perhaps very much like--science but won't in the end enable us to overcome our sorry evolutionary deficits to come to a full and final understanding of the universe--assuming such is possible.

Let us distinguish two views of science:

  1. The Naive View
  2. The Traditional View

According to the Naive View of science, scientists make observations and generalize those observations to state generalizations which, when added to other such generalizations, become scientific theories. These theories are then used to explain and predict other observed phenomena. Thus according to the Naive View a scientific theory starts its life as a kind of tabula rasa or blank slate. It is fleshed out as the scientist makes more and more observations and writes down generalizations of those observations. Think "this crow is black", "that crow is black", "that other crow is black", so write down "All crows are black." Such generalizations are proven, on the Naive View, by the particular observations that confirm them.

Even a moment's reflection reveals that the Naive View cannot be right. First, specific generalizations are at most probable to some degree given the evidence--remember, there could always be some funky white crow somewhere the scientist hasn't, or couldn't, look. So there is no sense in which a scientific theory is proven, that is, demonstrated to be true, as the Naive View asserts. Second, mere generalizations from observed phenomena cannot explain anything even if they can allow some modest form of prediction. That is, we might predict that the next crow we meet will be black given the generalization "all crows are black", but knowing that all crows are black tells us absolutely nothing about why crows are black! Hence, third and unsurprisingly, the Naive View has absolutely no resemblance to the actual practice of science.

So a scientific theory is not a collection of generalizations as the Naive View would have it. Instead, scientists in practice propose underlying mechanisms which account, say, for all crows being black. These underlying mechanisms might include hidden processes (DNA, RNA, and the complex processes of cellular biology, for instance), unobservable objects with special properties (electrons, quarks, charge, charm, spin etc.), or laws of nature (the three laws of thermodynamics, the laws of newtonian mechanics, the principles of evolution, and so on). Thus scientific theories consist of a core set of finitely many principles, laws, or axioms, together with indefinitely many implications from that core set. This much is agreed upon by everyone who has moved beyond the Naive View of science.

Further, as Popper explains and probability theory and logic bear out, the Naive View simply cannot be right. First, Popper explains that if all we do is look for confirming evidence for a theory, we can find it in anything since any observation can be construed in such a way as to confirm a favored theory. Indeed, humans are notoriously good at fitting evidence to support their pet theories and explanations. He gives three fairly damning examples of this:

  • The Marxist Theory of History
  • Freudian Psychoanalytic Theory
  • The Adlerian Theory of Personal Psychology

Popper points out that the amazingly frustrating thing about talking to devotees of any of these theories is that they explain everything. No evidence could ever count against them, since all evidence can be made out to confirm them. This, Popper thinks, is absurd. We shall talk more about why next time.

Second (and going a bit further than we did in class) we cannot say that a scientific theory so construed is probable to some degree since it and its alternatives must sum to a probability of 1, but since there are infinitely many such alternatives, their individual probabilities are always 0. Nor can we say, as one might wish, that we can establish the probability of the theory given the evidence we have for it, since Bayes theorem shows us that that probability will also always be 0. That is, the probability of a theory T given the evidence for it E, written 'P(T|E)', is,

P(T|E) = (P(E|T)*P(T))/P(E).

But since P(T) = 0, P(T|E) = 0. (If you have trouble following this, just remember that if the probability of one side of a six-sided dice is 1 out of 6, or 1/6th, then the probability will be less as we increase the number of sides. Indeed, the probability of one side of an infinite-sided dice is 1 out of infinity, or zero. Yet for any theory there are infinitely-many alternative theories.)

Third, and decisively, the logic of scientific theory demonstrates that you cannot prove a theory true by confirming any or even all of its implications. Why this should be so is where we find Popper and the Traditional View.

Though essentially Popper's position, I call it the Traditional View because his position, as articulated and defended in his magnum opus "The Logic of Scientific Discovery", has been almost universally adopted by working scientists. Indeed, many of Popper's ideas are echoed by students of the sciences, they themselves having been taught these positions from the very start of their scientific education.

What I sought to do today was not merely to articulate the Traditional View but to explain as best I could the foundations from which it is derived. Unfortunately, these arguments depend on certain features of formal logic and probability theory which are somewhat sophisticated.

Popper's insight was to recognize that while we cannot infer the truth of a law of nature from the verification of one of its entailed hypotheses, if an entailed hypothesis is refuted, we can infer that at least one of the entailing laws must be false. To wit, given an implication which has been shown by experiment to be false, we can conclude that at least one of the statements from which it is derived must be false.

So on the Traditional View, every experiment is not an attempt to prove a theory true (since that is impossible by logic) or even to show a theory more probable (since no comprehensive theory has a probability greater than 0), but to falsify a theory. Thus scientists are never seeking to show a theory true for the simple reason that they cannot do so. The notion that one could prove a theory true is conceptually incoherent. Rather, they are seeking to show it false. Every experiment is chosen as a way to show an implication of a theory false and thereby show the axioms, principles, or laws of the theory false. A single, repeatable experiment which shows a theory false justifies our discarding the theory and replacing it with another.

Repeated failed attempts to prove a scientific theory false leads scientists to provisionally accept the theory as (possibly) true.

Thus if a scientific theory is conceived as a core set of finitely many propositions (axioms, laws, principles, or what have you) surrounded by a penumbra of (infinitely many) entailed propositions (implications, hypotheses, or what have you, then,

  1. We cannot infer that the axioms, principles, or laws of a scientific theory are true even if their implications are, hence we can never say with absolute certainty that a scientific is true. Put another way, no scientific theory can ever be 'proven'.
  2. We can, however, conclude that one or more of the axioms, principles, or laws of a scientific theory is false if one of their implications turns out to be false. Thus, while we cannot prove a scientific theory true, we can prove it false. Falsification, then, is Popper's primary demarcation criteria to set science off from pseudoscience. Scientific theories can be falsified, and scientists by their experiments actively seek to do so. Pseudoscientific theories cannot be falsified, and their practitioners construe all evidence as confirmation.
  3. We cannot even say that a scientific theory is true to some probability P, since there are infinitely many alternatives to P, with the probability of any one of which thereby converging on zero.

This, as I said, is the Traditional View of science and the important distinction, Popper thinks, between science and pseudoscience. Next time we take up a serious challenge to the Traditional View.