Did Duhem Show That Scientific Theories Can
Be Neither True Or False Essay, Research Paper
The question as to whether scientific theories can be shown to be true or false is a complex one. The answer depends on one’s interpretation of the meaning of theory. To what does it refer? Is its role to reveal the nature of reality, or is it merely a human construct? In which case what do we mean by truth? Is it an accurate description of reality, or does it simply refer to a successful theory that produces accurate predictions? Duhem attacks this problem from a very strict non-metaphysical standpoint. As a result he shows that we can know nothing about material reality, and indeed very little about the validity of our own theories. In the end it appears that the theoretical framework within which scientists work is more a matter of convention than anything else.
In order to determine whether the claim that scientific theory cannot be proven true or otherwise we must first understand what Duhem means by scientific theory. He introduces two possibilities as to the nature of a physical (which we can equate to ’scientific’) theory. The first being that it is an explanation of the reality lying behind a group of experimental laws (those that are empirically determined). The second is that a physical theory is simply an abstract system to classify and summarize a group of laws.
Taking the first possibility (a belief still held by many today): this seeks to look beneath the sensible appearances and find the reality beneath, which is causing the sensations we experience. However, this presents us with a problem. We only have access to perceptions so how can we hope to find a physical theory that provides a certain explanation of the reality causing these sensations? A theory can only suggest a reality that would produce all those perceptions on which our experimental laws are based. In that sense it becomes just a hypothetical explanation.
A perfect physical theory, as described, aims to describe the reality of the material things whose properties we perceive. Therefore we are inexorably lead to the conclusion that in order for a physical theory to provide an explanation we must first understand the nature of material reality. This of course assumes that there is such a reality, distinct from appearances. However, this has now become a metaphysical question (the answer cannot come from empirical evidence since this deals only in sensation). So we are presented with a problem: if the value of a physical theory depends on the metaphysical system adopted then it is impossible for such a theory to achieve universal acceptance. There are many schools of metaphysics (Aristotelian, Newtonian, atomistic and Cartesian) and all hold different ideas as to the nature of reality. They are all at odds because each can find fault with properties of matter assumed by others. In their metaphysical beliefs are in conflict then by definition so would be the physical theories they adopt.
Duhem goes on to say that no single metaphysical doctrine can be sufficient to create a physical theory. All principles used in a theory must be derived from the metaphysics; otherwise the theory cannot by necessity be true. However no metaphysics gives instruction exact enough or detailed enough to derive all the elements necessary for a physical theory. Our conclusion then is that physical theory as an explanation is not possible. We cannot agree on a universal metaphysics and even if we could we would not be able to derive a physical theory from it. This implies then that if by truth we mean the nature of reality, then we can never know a physical theory to be true.
So how should we define a physical theory? We need a definition that would be acceptable to all and a method that would allow construction of a theory without the use of principles that it could not legitimately use.
Duhem defined such a theory as: ” a system of mathematical propositions, deduced from a small number of principles, which aim to represent as simply, as completely, and as exactly as possible a set of experimental laws.”
He broke down the formation of such a theory into four steps:
1) The definition and measurement of physical magnitudes. This is essentially the assigning of certain mathematical symbols to a set of simple measurable physical properties.
2) The selection of hypotheses. This is the formulation of a set of propositions that connect those measurable properties expressed in step 1. These fundamental principles do not assume to describe actual relations between the real properties. The only criterion for selection being that they are logically consistent.
3) The mathematical development of the theory. This is the combination of the principles expressed using mathematical analysis.
4) The comparison of the theory with experiment. The results predicted by the hypotheses are then compared to experiment. If they agree then the theory is good, if not then it must be modified or even rejected.
The definition Duhem has given is one in which agreement with experiment is the only criterion for truth. A physical theory as defined here does not actually describe reality; it simply is a way of condensing experimental laws into a small number of fundamental principles. This now begins to resemble the traditional scientific method employed today. Duhem goes on to emphasize how his physical theory serves to classify empirical laws; grouping them into various areas of science, creating links between them, and generally imposing an order on the multitude of laws we observe. This makes them more useful, easier to handle and, says Duhem, more beautiful. He even goes as far as to say that the incredible order and unity that the scientist finds in his system of hypotheses suggests that it is a reflection of a natural classification, in other words the relations found between observation might correspond to real relations among material things. Of course the method set out by Duhem by which theory is established means that such a natural classification can never be absolutely confirmed. However, the more successful a system of hypotheses becomes, particularly in the prediction of laws not yet observed, the greater the indication of a natural classification.
So, having defined a physical theory in Duhem’s terms, we once again ask the question of whether a theory can be shown to be true or false. As to the question of the truth of reality the answer is still no; although Duhem’s reference to natural classification hints that we might be approaching the truth of real relations even if we can never confirm it. We are therefore restricted to ‘agreement with experiment’ being the only criterion for truth.
This leads into the idea of the ‘crucial experiment’ as first proposed by Francis Bacon. The idea here being that if one doubts a theory or hypothesis then an experiment may be designed to test this doubt. This at first seems a relatively straightforward procedure. First make a prediction of an experimental observation using the theory in question, then arrange the circumstances in which this prediction may or may not be observed. If the predicted fact is produced then the theory is supported. If the fact is not observed then the hypothesis on which the prediction was based is declared false and is rejected.
Duhem finds a major flaw with this line of reasoning. He claims that it is impossible to isolate a hypothesis within a crucial experiment. When a scientist designs and performs the experiment he is assuming a whole theoretical structure to be true. The general example he uses being that of the assumptions relating to the functioning of laboratory instruments and equipment and the numerous theories involved in their use. Therefore the experiment is testing not just the hypothesis in question but the whole theoretical framework from which that hypothesis originates. A negative result therefore implies an error, but does not indicate where the error lies. It may well be in the hypothesis in doubt, but it could equally lie anywhere within the theoretical framework being used. It is therefore impossible to determine the certain falsity of a theory, only the falsity of a whole theoretical system.
Duhem has a further attack on the ‘crucial experiment’ which explains why it cannot be used to determine the truth of a hypothesis either. Putting aside the previous argument for a moment, Duhem sees the idea of the ‘crucial experiment’ as one of proof through elimination. For any one observation there are presumably a finite number of explanatory theories. Therefore to determine the correct theory one must eliminate the others through the use of the crucial experiment. However this requires a knowledge of all possible theories, which is impossible. One could always imagine the existence of another hypothesis, even if one cannot think of one. Unless all possible theories could be tested the ‘crucial experiment’, as described by Duhem, is not complete. So now it seems it is not possible to determine the absolute truth of a theory either.
The only response to this dilemma seems to be a probabilistic one. That is to say that although we cannot be sure that we know all possible hypothetical causes for a phenomenon, we can say that, based on the knowledge we have, it is unlikely that the truth lies in a theory unknown to us. Therefore we can test the theories that we are aware of in the manner described above and, by a process of elimination, determine that which is most likely to be true. This uses a less strict definition of the ‘crucial experiment’ in which the outcome is not certain truth, only probable truth.
As to the question of falsity, the response is again a probabilistic one. When we perform a crucial experiment we believe the theoretical framework in which we work to be valid because it has performed without error so frequently in the past. This is particularly true the more established the field is. Therefore if the outcome of the test is negative then we can say the error is more likely to reside in the hypothesis in question than in the rest of the theoretical system. In fact, Duhem supports this idea in his discussion of natural classification. He argues that the greater the order and unity within a theoretical framework the more we are to believe it reflects a real order in nature. Therefore in our experiment we are more likely to reject the single hypothesis than the ordered, successful (and beautiful) theoretical framework we have established.
In conclusion then, if we accept those definitions, which Duhem lays out, we are forced to accept that it is not possible to determine the absolute truth or falsity of a theory. However, science still does progress and appears to be very successful. We can only assume then that the probabilistic method of accepting those theories that seem most likely, and rejecting those that do not, is an effective one. Otherwise our theoretical frameworks would presumably rapidly deteriorate instead of progressing towards the ever more beautiful and ordered system that impressed Duhem so greatly.