Nonetheless, the scientists seem to feel that the creation of an elegant mathematical model, at least one that is consistent with observed empirical phenomena and that is testable empirically, at least in theory (that is, one could imagine an empirical test of the theory or model even if current technology does not permit one to perform it), constitutes an explanation of the phenomena under investigation. In other words, these scientists appear to believe that mathematical representation constitutes understanding. However, as discussed below in our examination of mathematics, we do not have a very satisfactory theory of the relationship between mathematics and reality. In fact, the successes may be little more than coincidences that are not necessarily extendable to other areas.
The Requirement of Falsifiability
There have been serious debates as to whether a theory that provides a sense or feeling of understanding is adequate to qualify as scientific or whether other criteria must also be met. Of course, the theory must be internally consistent (not lead to two conflicting predictions or conclusions). See, e.g., Alfred Tarski, Introduction to Logic (1946), pp.108–9. (More precisely, the axioms or initial premises must be logically consistent and the rules of manipulation must be constructed so as not to allow the introduction or creation of inconsistencies in the propositions derived from the axioms. See, e.g., Barrow, Theories of Everything, p.32.) And, there are often suggestions that certain aesthetic criteria be met concerning generality, simplicity and elegance.23
Probably the most frequent additional requirement for a scientific theory has been that the theory be testable by experimentation or observation. To start, a theory or hypothesis should enable one to make predictions about observable facts or events beyond the elements contained in the hypothesis itself. If one successfully observes the occurrence of such predicted consequences, then there is a basis for considering that hypothesis or theory to be supported.
One might consider that the successful predictions constitute a “verification” of the theory involved; but, during the second half of the twentieth century, the concept of verification or verifiability came under increasing attack as a matter of logic. The issue was not about how scientists engaged in the process of scientific discovery, but the philosophical issue of what was logically defensible.24
Verification by successful prediction has the same logical problems as inference by induction (or, for that matter, deduction): there are many reasons why a prediction might come true that are not supportive of the theory by which the prediction was made (coincidence, a common underlying cause, etc.). Generally, a successful empirical test will not provide substantial confirmation of the theory, because there are likely to be multiple alternative theories that could generate the same empirical prediction. This challenge to the concept of verification came about largely as a result of the writings of Sir Karl Popper.
Among philosophers of science (and, subsequently, generally among scientist who expressly address the issue), following the lead of Karl Popper, the testability of a theory has come to mean not that the theory can be confirmed by successful predictions, but that the theory is susceptible to being disproved by an imaginable and identifiable test or set of observations—in other words, that it is falsifiable. See Popper, The Logic of Scientific Discovery; Objective Knowledge: An Evolutionary Approach (1972). That means that the testing of a theory for the philosophers of science was formulated in terms of a possible experimental result that would be viewed as inconsistent with the theory and, if achieved, would demand that the theory be rejected. This may seem to be a rather odd concept of proof, and it had implications for the nature of the process of doing science.
Falsifiability
The idea that theories should be subject to assessment and testing should not seem strange. Otherwise, one could hardly claim that theories are relevant to knowledge or understanding. Indeed, it would seem unscientific for a proponent of a theory to declare that it is unfair to require that the theory be subject to testing and possible disconfirmation. The position Karl Popper took was that the theory had to be capable of falsification for it to be a truly scientific theory. If, over time, experimental efforts to falsify the theory fail, one can increasingly become more confident that the theory is correct. However, this philosophical approach stresses the central role of criticism of and challenges to established theories and portrays the proper scientist as fully objective and psychologically prepared to reject his or her own theory in the face of falsification.
This characterization of science and scientific methodology has become widespread among philosophers of science and at least some scientists, especially physicists who have expressly addressed these methodological questions while touting their open-mindedness and objectivity. For example, as stated by Cox and Forshaw in their book in 2009: “In science, there are no universal truths, just views of the world that have yet to be shown to be false.” Brian Cox and Jeff Forshaw, Why Does E=mc2? (And why should we care?) (2009), p.xi. Or, as Deutsch puts it: “[T]he nature of science would be better understood if we called theories ‘misconceptions’ from the outset, instead of only after we have discovered their successors. Thus we could say that Einstein’s Misconception of Gravity was an improvement on Newton’s Misconception, which was an improvement on Kepler’s. The neo-Darwinian Misconception of Evolution is an improvement on Darwin’s Misconception, and his on Lamarck’s. If people thought of it like that, perhaps no one would need to be reminded that science claims neither infallibility nor finality.” The Beginning of Infinity, p.446. It is much less clear the extent to which working scientists (or, perhaps, it is more accurate to say scientists while working as scientists) really embrace and incorporate this methodological approach in the process of their work.
A strict Popperian approach might suggest that the scientist must be prepared to commit to reject a theory based upon obtaining an empirical result inconsistent with the theory’s prediction. In real life, of course, most scientists will be reluctant to quickly abandon an accepted theory, and rightly so. At a minimum, one would want to check carefully for errors in the experiment and would attempt to reproduce the results. If the inconsistent result still obtained, one would want to examine the theory with care to see if the result was truly inconsistent. Then, one would consider whether there was some minor adjustment that could be made in the theory, or in the theories upon which the test instrumentation or the test methodology were constructed, that would accommodate the inconsistent result without undermining the central elements of the theory.
Testing and verification
As suggested above, increasingly in modern physics and related subjects, the efforts to find testable, empirical propositions that are predicted by the theories has led to hypotheses that are distant, minor implications of the theory, not matters at the core, or that are themselves heavily theory-laden and not directly observable. That is, the potentially observable or measurable aspect of the prediction is a theory driven implication from the prediction. Thus, a failure of the test is susceptible to many potential explanations that preserve the central core of the theory, in other words, the central theory is not really falsifiable by that test. See, e.g., Imre Lakatos, “Science and Pseudoscience,” Philosophical Papers, vol. 1 (1977), pp.1–7.25
There is another type of problem. Economists regularly make predictions based upon their theories. The “problem” is that economists seem always to have explanations for why their predictions did not come true—explanations that often are quite consistent with the theory. The typical explanation will invoke the ceteris paribus condition or assumption. As discussed at some length below, the question then arises as to whether such theories could ever satisfy (or purport to satisfy) the falsifiability requirement. One aspect of the problem arises from the difficulties with respect to the specification of the initial conditions as a prelude to making predictions.
The laws