Following up on my recent post about The Nature of Scientific Observation, I left two-thirds of Chalmers’ book What is This Thing Called Science untouched, including discussions on Bayes’ theorem and the New Experimentalism.

I left off right before Popper’s falsificationism and Kuhn’s paradigms came into view. Each of them has their own problems. Popper, for instance, introduced the falsificationist concept with simplistic examples that the actual scientist rarely encouters. Nevertheless, Popper’s Logic of Scientific Discovery does seem to reflect some of the approach that the typical scientist has been taught to apply in formulating testable hypotheses. As a result, sophisticated falsificationism takes a somewhat defendable position by reiterating falsificationism in strongly qualified statements.

Thomas Kuhn then introduced scientific revolutions as “paradigm shifts”, exposing the hard truth that science is normative. No argument there. But the problem lies in the logical conclusion that many people draw from the realization that science is normative: science is therefore more subjective and more falliable than we originally may have supposed, and pseudoscience might find comfort in the doubt sowed in science therein. Kuhn simply could not reconcile his normative description of science with what is obvious to any empirical scientist, which is that many scientific theories can explain wide ranges of natural phenomena with a high degree of precision. In other words, though science may be normative in practice, it is also grounded in high-level approximations of reality, and basic facts exist which can be said to be objective.

As a result, I characterize Kuhnsian paradigms as not a philosophy of science, but a sociology of science. That view has gotten me in some strongly-worded discussions with other scientists, but it’s a position that I stick to. It is very clear that some theories are better than other, and that science does indeed represent progress. One needs only to look to the offspring of science, technology. Advancements in biomedical, mechanical, electrical, and chemical technology are not mere paradigms.

Enter the Bayesian theorem of science and the New Experimentalism.

Thomas Bayes, an 18th-century mathematician, established a theorem that has a great deal of bearing for philosophy of science. Bayes’ theorem is about conditional probabilities, which prescribes how probabilities of truth statements are to be changed in the light of new evidence. Chalmers describes, on page 175:

In the context of science the issue is how to ascribe probabilities to theories or hypotheses in the light of evidence. Let P(h/e) denote the probability of a hypothesis h in the light of evidence e, P(e/h) denote the probability to be ascribed to the evidence e on the assumption that the hypothesis h is correct, P(h) the probability ascribed to h in the absense of knowledge of e, and P(e) the probability ascribed to e in the absense of any assumption about the truth of h. Then Bayes’ theorem can be written:

P(h/e) = P(h) x P(e/h)/P(e)

P(h) is referred to as the prior probability, since it is the probability ascribed to the hypothesis prior to consideration of the evidence, e, and P(h/e) is referred to as the posterior probability, the probability after the evidence, e, is taken into account.

So the formula tells us how to change the probability of a hypothesis to some new, revised probability in the light of some specified evidence.

This symbolic calculus serves to illustrate that any disagreements in science between proponents of rival research paradigms or programs must have their source in the prior probabilities held by those scientists, since the evidence is taken as given and the inference considered to be objective. But the prior probabilities are themselves totally subjective and not subject to a critical analysis.

Consequently, those who raise questions about the relative merits of competing theories and about the sense in which science can be said to progress will not have their questions answered by the Bayesian. Bayes’ theorem of science does, however, reflect the importance of the relevance of new data. That is, empirical evidence is not all considered equal – some evidence is strongly weighted as far as importance goes, whilst other evidence is considered irrelevant.

The New Experimentalism is an intriguing contrast. Chalmers starts off with an example (an experiment by Michael Faraday on electromagnetism) and then asks (page 195), “Is it useful or appropriate to regard this accomplishment of Faraday’s as theory-dependent and falliable?” Without question we can say that, at best, one can only refute the extreme empiricist position that facts must be established directly by the entry of sensory data into a mind that otherwise knows nothing, and that the recognition of a new experimental effect cannot be said to be falliable in any sense.

Thus, the production of controlled experimental effects can be accomplished and appreciated independently of high-level theory. Molecular biology is replete with examples of experimental observations that are tightly controlled, and the results derived therein can be considered objective. Extrapolating from those observations to theoretical implications is not always straightforward, to be sure, but possible if the experiment itself has relevance to aspects of those theories which are in contention among scientists.

Deborah Mayo offers the best articulation of the New Experimentalism in her 1996 book, Error and the Growth of Experimental Knowledge. She sides with Kuhn’s notion of normal science, reformulating it in such a way that reflects the ability for scientists to make factual statements independent of theory, even though they remain subjective and fallible to a degree.

So I found myself nodding very much through reading about Deborah Mayo and the New Experimentalism. I am surprised that I hadn’t read much about this area of the philosophy of science before.

Overall though, I think it also helpful to note that each of the major philosophers of science tackle a separate aspect of science – how hypotheses are made; how science is normative; the role of inductive and deductive logic; how experiments are formulated; how facts and theories are inter-dependent; etc. Each of them has a point, but none of them can be extrapolated to science as a whole.