Do Scientific Theories Ever Receive Justification?

A Critique of the Principle of Falsifiability

Karl Popper states:

Now in my view there is no such thing as induction. Thus inferences to theories, from singular statements which are 'verified by experience' (whatever that may mean), is logically inadmissible. Theories are, therefore, never empirically verifiable...

But I shall certainly admit a system as empirical or scientific only if it is capable of being tested by experience. These considerations suggest that not the verifiability but the falsifiability of a system is to be taken as a criterion of demarcation. In other words: I shall not require of a scientific system that it shall be capable of being singled out, once and for all, in a positive sense; but I shall require that its logical form shall be such that it can be singled out, by means of empirical tests, in a negative sense: it must be possible for an empirical scientific sytem to be refuted by experience,

Popper, "The Logic of Scientific Discovery," 2nd ed., 40-41)

Now these statements, taken together, require some analysis. Induction, at the simplest level, is normally taken to use the truth of singular statements which are verified by experience to provide justification for general statements. And when the justification for a given general statement is regarded as sufficient, the general statement is regarded as true. This is the general nature of induction. However, Popper is opposed to this view.

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Popper states his opposition in terms of using induction to justify theories rather than individual statements, but this makes little difference. Theories are composed of statements, and to say that one cannot ever regard a theory which has stood the test of induction as true is to say that one can never regard the statements which compose the theory as being true: if all of the statements which compose the theory are true, then one would have no reason to deny the status of truth to the theory itself.

To see why, let a theory be expressed by the set of statements {h1,h2,h3,...,hn}. Assume that each of the statements in this set is true. Then the theory may expressed by the statement h1&h2&h3&...hn. The truth of this statement necessarily follows from the truth of the statements which compose it. Thus Popper's Principle of Falsifiability is wide open to a criticism stemming from what is called "Duhem's Thesis": the principle of falsification runs into problems since scientific statements are presummably never regarded as true.

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According to Duhem's Thesis, no empirical hypothesis H can be used to make empirical predictions unless it is conjoined with one or more auxilary hypotheses A. Thus when we use an experiment to test H, where H&A is used to predict an experimental outcome S, the failure to obtain S falsifies H&A. But an isolated experiment does not allow you to determine whether H is false, A is false, or whether both H and A are false. Thus no single test can falsify H by itself.

However, we can state this even more strongly in the case of the principle of falsification. Since no hypothesis is ever regarded as true, no hypothesis can ever be shown to be false. And if one takes as one's unit of meaning to be theories instead of hypotheses, one will find that present theories are generally tested by presupposing the validity of theories which have stood the test of time. Unless one assumes that one's background theories are true, one cannot falsify the theory which is in the foreground, i.e., the theory which one is presently testing. However, the above analysis calls for some examples. I will provide three.

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In my first example, I will be considering a problem involving Newton's gravitational theory. In his day, the explandatory power of his theory was considered amazing. Given the highest degree of accuracy available in the 1600s, his theory was able pin-point the trajectories of all the planets but one: there existed a minute discrepancy in rotation of the perhelion of Mercury. This one fact was not regarded as in any way falsifying Newton's theory, though. To test his theory, it had been necessary to bring in other assumptions. For example, when his theory was first checked against the orbit of Mercury, it was assumed that Mercury was the closest planet to the sun. Rather than throwing out Newton's theory, this assumption was modified.

For a while, it was thought that there existed a planet Vulcan inside Mercury's orbit which disturbed this orbit in just such a way as would account for the discrepancy between the original theoretical prediction and the experimental observation. On the basis of this hypothesis, astronomers searched the heavens for the hypothetical planet. As things happened, the additional hypothesis that Vulcan existed turned out to be wrong and Newton's gravitational theory was abandoned in favour of Einstein's gravitational theory, in part on the basis of this early experimental evidence, but also on the basis of additional experimental evidence which came after the formulation of Einstein's theory. Does this mean that Newton's gravitational theory should have been abandoned in the first place rather than being saved by means of an "ad hoc" hypothesis?

The Principle of Falsifiability not withstanding, no it does not.

A similar proceedure was used to predict and ultimately discover the existence of Neptune on the basis of how this outer planet disturbed the orbit of Uranus. Newton's gravitational theory simply proved to powerful to abandon as hastily as the Principle of Falsifiability would have required. Besides, other explanations of the failure of this one prediction were still possible even once planet Vulcan failed to turn up. For example, a hypothetical oblateness of the sun, and if measurements of the sun's profile disproved this, then one could hypothesise a rotation in the sun's interior which would give rise to an oblateness of the distribution of the sun's mass that would exist only within the sun's interior, leaving no appreciable evidence at the sun's surface. Or would it? One might have to ask a student of stellar dynamics.

When the original conflicts were discovered between Newton's gravitational theory and the experimental evidence, its discovery was the result not only of Newton's gravitational theory, but also certain implicit assumptions, assumptions which were not necessarily even stated, but were, in effect, a kind of theoretical background to Newton's theory. As a result of the predictive power of Newton's theory under a wide range of circumstances, the scientists of Newton's age thought it best to modify the background assumptions rather than abandon this powerful theory. With the hindsight made possible by our own advanced age, we may conclude that with respect to Vulcan they were wrong, but in the case of Neptune, they were right. But in both cases, their approach was most reasonable.

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Now I will begin my second example. Roughly at the time that Darwin, it was considered a recognised fact that the earth and the sun couldn't be more than a few million years old: the only fires known were chemical fires, and alternatively, the only other source of energy which we could conceive of for the sun was due energy being released as the result of gravitational collapse. On the basis of the latter, Lord Kelvin calculated that the age of the sun had to be in the range of millions of years, not thousands of millions. This required evolution to take place at a rate which seemed unlikely.

Similarly, a geologist discovered evidence that the rocks of the earth were in many cases older than the limit on the earth's age based upon the calculation involving the sun. In addition, the theory of continental drift was proposed to account for similarities in the shapes of the continents: these enormous land masses seemed to have shapes which could fit together like pieces of a puzzle, but the fit was not perfect, and once again the apparent age of the earth seemed to count against the theory. Another problem with this theory was that there existed no known engine for the hypothesised movement of the continents: as far as scientists of the time knew, the earth was essentially one giant, solid rock. Volcanos were simply a small, irrelevant side-issue.

However, special relativity, which was originally put forward to account for experimental results involving the motion of light, required an equivilence between mass and energy which suggested that chemical fires were not that efficient. The study of subatomic particles lead to the recognition that nuclear fires could exist which would be much more efficient than chemical fires. Nuclear fusion made it possible for us to recognise that the sun is much older than we originally thought it was.

Nuclear fission explained the generation of heat internal to the earth's surface, and this made it possible for us to recognised the fact that the continents are afloat on a sea of molten rock which exists beneath the earth's crust. This provided us with a means to explain continental drift. In addition, both botany and zoology discovered similar populations at just the places the theory of continental drift argued were where the continents had once been together.

New evidence and once highly-controversial theories were fitting together like the continents once had. They were providing us with a unified view of our world. Whereas Karl Popper's fallibilism viewed distinct theories as being tested against evidence independently of one-another, the history of science has shown a remarkable degree of interdependence between distinct theories existing in highly disparate areas of human knowledge.

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With my last example, I will be considering Newtionian mechanics. If one stead-fastly held to Popper's Principle of Falsifiability, one result contrary to prediction would be enough to falsify this theory. With this in mind, one could easily conclude that Newtonian mechanics has been falsified many thousands of times over in high school physics classes. Students perform experiments which quite regularly "falsify" this theory every year. But why is it that whereas this would be enough to discount the theory if the experiments were being performed by expert experimental physicists, this is not enough when the experiments are being performed by young students?

When one explains this difference in terms of the different levels of training and reliability, one is bringing in psychological considerations to explain the results of physical experiments. Thus one can argue that there is a sense in which the science of physics depends upon the science of psychology.

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I will draw from this analysis three conclusions.

First, if one accepts induction, some element of coherentialism is required: there exists an interdependence between the justification of the distinct statements which compose a theory. Second, there exists an interdependence between the justification of a foreground theory and its background theories. Third, in science, one must regard many statements as true even if the justification of these statements does not admit of absolute certainty. Much of our knowledge is corrigible.