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Ernst Mayr claimed that Darwin's theory of natural selection is now the prevailing explanation of evolutionary change, but admitted that "it has achieved this position less by the amount of irrefutable proofs it has been able to present than by the default of all the opposing theories".
Toward a New Philosophy of Biology (Belknap Press, 1988), p.192
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Scientific Theory Testing
It is sometimes* argued that, in order to prove a theory wrong, one must also supply an alternative theory (alleged to be right). I believe that this argument is invalid, as the following particular example from Newtonian Mechanics shows.

We consider two sets of phenomena:

A.  Planetary orbits are elliptical (within the accuracy of measurement).

B.  In the case of the planet Mercury, the axes of the ellipse rotate very slowly (with respect to the fixed stars).

Newtonian Mechanics describes A but not B.

Note that:-

We can state categorically that Newtonian Mechanics fails to describe B without knowing whether or not there is an alternative theory that does describe both A and B. (In fact, Einstein's General Theory of Relativity is such a theory. Of course, one can regard Newton's inverse square law of gravitational attraction as a limiting case of General Relativity Theory, but the Newtonian concept of action at a distance is incompatible with General Relativity Theory because this is a field theory which admits contiguous actions only.)

Of course, one should give a fuller statement here with a list of known heavenly bodies that have been included in the calculation. It is, strictly speaking, a complete statement of theory that is being tested, and it cannot be ruled out that an as yet undiscovered heavenly body is responsible for the Mercury anomaly, and that Newtonian Mechanics is still valid.

Lakatos (1978) considers a siimilar argument in much more detail (see below).

The fact that Newtonian Mechanics succeeds in describing A has no bearing on the question Does it describe B?


* e.g., in a debate on the validity of Neo-Darwinian Theory, Kenneth Miller criticizes Phillip Johnson for failing to provide an alternative theory:

This is as unreasonable as it would be if one were to criticize astronomers, who measured the motion of the perihelion of Mercury and made Newtonian calculations, on the grounds that they failed to produce Einstein's General Theory of Relativity.

Certainly, once a theory has been shown to be false, curiosity promotes a search for a valid theory - an important scientific activity. Premature discussion of alternative theories can, however, be used to divert attention from the weaknesses of a theory under discussion.

Can experiments be used to test theories?

It has been argued that, because techniques used in experiments depend on theories of their own, and for other reasons, one cannot in fact test theories by experiments. Thus Brady (1979, p. 611) states: "But when we see that in any particular test the congruence or incongruence of the anticipation with the result may be due to parameters external to our theory, it becomes clear that tests neither prove nor disprove theories".

Similar objections have been mentioned by Singham (2002): "The `naïve falsifiability' approach…is untenable. Its success depends on the belief that theories and experiments are two distinct and independent types of knowledge and that one can be used to test the other….Popper argues that all observations are `theory-laden'….that all ..observations need a theoretical framework in order to be  interpreted."  (p.81)

This reminds one of Aristotle's objection to experimental tests: can an outcome have more than one cause? In spite of this, the experimental method in science has proved to be extraordinarily profitable - even although certainty can seldom, if ever, be claimed, or need be claimed. Brady's objection might conceivably be applicable to certain kinds of "fundamental" theories when subjected to tests, but I believe his objection is invalid in the case of what I may call less far-reaching, down-to-earth theories. Two simple counterexamples to Brady and Popper will suffice:

First example: The molecular network theory of elastomer elasticity (cf., e.g., Lodge, 1999) has been formulated in sufficient detail to approach the scale of just such a theoretical corpus. For an elongated elastomer filament, it leads, in particular, to a particular form of relation between filament length L, stretching force f,  and temperature T. The form of this relation is compared with data for two elastomer samples which had been cross-linked by different methods (p. 97). One was consistent with the theory; the other was not. In the formalism, length and force are undefined elements to which certain properties are assigned by axioms. Temperature is a more difficult quantity, but its definition is treated in detail in the text (Chapter 3), because I consider that many textbook treatments of thermodynamics are unsatisfactory. The force- and length-measuring paradigms are so well established (at least, in the classical, non-relativistic domain that is appropriate here) that I did not consider it worth while to give them special attention.

I claim that the experiment has given a valid and illuminating test of the molecular network theory, showing that it could represent a (a) valid approximate treatment for one type of cross-linking but (b) not for another. It would be absurd to dismiss the test on the grounds that techniques used to measure force, length, and temperature also involve theories and, therefore, introduce too many uncertainties. Applying the arguments of Popper and Brady here, however, would mean that we cannot place much confidence in the claims (a) and (b) because of the uncertainties involved in our methods of measuring force, length, and temperature! What nonsense!

Second example: Medical evidence has led to the theory that blood is pumped by the heart in order to take oxygen from the lungs to all parts of the human body. This is the truth of the matter. Are we to doubt it because the means used to gather evidence are theory-laden and because there are an unlimited number of alternative theories for the same set of evidence? This is preposterous.

Feyerabend (p.3) would have us doubt these truths for another reason: "It is true that Western science now reigns supreme all over the globe; however, the reason was not insight in its 'inherent rationality' but power play (the colonizing nations imposed their ways of living) and the need for weapons..." This, too, is preposterous.

A useful introduction to four different viewpoints in the philosophy of science is given by Laudan (1990). The philosophers favor ancient scientific theories to illustrate their viewpoints. Had they used more modern theories (such as those given above), I suspect that they would have had a harder time in maintaining their positions.

Lakatos (1978, p.16...) goes much further in claiming that all scientific theories are both unprovable and undisprovable (p.19, para. 3). He starts his argument with a hypothetical newly discovered planet  p whose observed path does not agree with that calculated from Newtonian mechanics plus consideration of all other known heavenly bodies. Instead arguing that Newtonian mechanics is thereby disproved, one assumes the existence of yet another hitherto unknown planet p' whose presence perturbs the path of p. Unfortunately, p' is so small that it cannot be detected by available telescopic or other means. Lakatos continues in this vein and claims that Newtonian mechanics is therefore undisprovable. In making this extraordinary claim, he appears to me to be assuming the validity of a tacit assumption to the effect that all discrepancies between theory and experiment lie below the level of detection with existing techniquies. He does not seem to me to state or prove this contention, and so he has not, in fact, substantiated his claim. Had the calculated size of p' been above the detection threshold and had no such p' been observed, there would have been a significant disagreement with Newtonian mechanics which would, therefore, have been disproved.

I suggest that it is helpful and valid to distinguish between what I will call "strong falsifiabity" and "weak falsifiability".


References

R. H. Brady (1979) Systematic Zoology 28, 600 - 621
P. Feyerabend (1993) Against Method (3rd edition, Verso, New Left Books, 1993)
I. Lacatos (1978) The Methodology of Scientific Research Programs (Cambridge University Press, Cambridge, UK)
A. S. Lodge (1999) An Introduction to the Molecular Network Theory of Elastomer Elasticity (The Bannatek Press, Madison, WI)
L. Laudan (1990) Science and Relativism (University of Chicago Press, Chicago and London)
K. R. Popper (1963) Conjectures and Refutations (Harper & Row, New York)
M. Singham (2000): Quest for Truth (Phi Delta Kappa Educational Foundation, Bloomington, Indiana)