Chapter XVIII

The System of Science

Claudio Gutierrez

Translated from Spanish by Inés Gutiérrez

129. The Hypothetical-Deductive Method

In previous chapters, we have emphasized the need to use complementary hypotheses whenever we want to make sure of the validity of the inductive method, either in the case of sampling or analogy, or even canonical induction. Within this framework, induction by itself appears deficient, only completed through the use of hypotheses about existing regularities, causal connections, or properties of the analysis. But, at the same time, it turns out to be a clear application of the deductive method. This leads us to two important conclusions: first, that induction alone is not an independent method of thought; to make it valid it has to be transformed into deduction. And second, that the employment of hypotheses is of paramount importance in the construction of science.

On the other hand, hypotheses not only play an essential role in relation to induction. In sections 92 and 93 we examined the use of assumptions or “borrowed premises” as a deductive strategy; hypothetical proof and reductio ad absurdum are remarkable instances of the use of hypotheses, conforming possibly the most powerful form of deduction: the hypothetical method, which can be applied indistinctly to deduction or induction problems. Thus, we have come to discover the common element, or bridge, that links the two brand of mediate or inferential thinking. We have shown the very essence of scientific reasoning, equally applied in all disciplines whose purpose is to substantiate information.

We must now ask ourselves why we do trust scientific statements, being a fact that, as you may recall, their nature pertain mainly to the realm of “borrowed premises” and hypothetical proof. How do we go from simple assumptions to unconditionally acceptable propositions? When and by what means are statements promoted from simple hypotheses to something stronger? We must answer these questions in two different ways. On the one hand, the truth is that –in logical purity– we never go from hypotheses to absolutely certain statements; an absolutely certain statement would have already left the field of science, since no one would ever doubt its truth again, and it is essential for scientific statements that all of them be disputable, impugnable, subject to criticism, and revisable, at any time and by whoever wishes to do so, provided compliance with the rules of openness, thoroughness and precision of the scientific profession.

On the other hand, the universal fact that our intellect eventually exhausts itself searching for hypotheses that adequately explain observed phenomena does come paradoxically to our help. Our minds and our world are such that, in order to explain certain appearances, it is not possible but to formulate a reduced number of hypotheses, which must be put on trial to eventually discover whether they come up either confirmed or refuted. This allows us to link what we have said about the refutation technique with what we know about the indirect strategy. A hypothesis is a premise we postulate with the purpose of seeing the consequences that follow, conjointly with the rest of our convictions. Assuming that the hypotheses list is limited, to formulate each different alternative one at a time and observe if contradictions arise, thus eliminating hypotheses one after another, offers itself as a good way to eventually obtain the confirmation a single one of them. This is exactly what we did in our example of the previous section. Although in science we can never be sure that all possible hypotheses explaining a phenomenon have been considered, possibilities are de facto exhausted, wherefore we can reasonably claim that we are moving on, step by step, towards ever truer scientific statements.

130. The Method Applied to the Confirmation of Singular Propositions

Let us examine the hypothetical method with an example, so as to better understand the way it works and its different components. Even though the method is mostly used in the confirmation of universal propositions, it is convenient to first study the case of singular propositions, analytically more simple. This type of inference is characteristic in the practice of criminology and medicine. In the former, the question we ask ourselves is “who committed the crime?” while in the latter, the question is “what illness afflicts the patient?” In both cases, the answer is a singular proposition: “such and such committed the crime” or “the patient suffers from such and such illness.” So, let us concentrate on the medical diagnosis problem, and consider the doctor in search of the illness as a natural science detective. Let us see how this works.

131. The Concept of Explanation

Let us consider the following diagnosis problem: a 40-year old woman calls her doctor on the phone and tells him that she has an acute abdominal pain; she adds that her temperature is normal. The doctor, consciously or through swift intuition, has to develop an inductive argument. Above all, he must select a hypothesis explaining the pain. The woman suffers a pain which needs explanation. By naming an ailment the doctor would have coined an explanation. But instead of speaking directly of phenomena, let us refer to the statements that describe them. Thus, we will say that a statement explains another when it occurs that the first serves as premise to deduce the second. When “this woman is sick of…” is premise enough to conclude “this woman has an acute abdominal pain,” we will say that the first statement explains the second. The original data cannot be false and the hypothesis true; as in any valid deductive argument.

The doctor’s training and experience supply him with a variety of diagnosis possibilities, so many more hypotheses which could explain the stated phenomenon. They all have in common the fact that they explain, in the sense indicated of being deducible, the acute abdominal pain. He could write them down in a list, like this: “acute colecystitis, acute appendicitis, pancreatitis,…” Many of these possibilities will be discarded immediately, some because of the patient’s age, others for their involving abnormal temperature in addition to other symptoms. The doctor must decide among those remaining, trusting his instinct or “clinical eye,” which in logic is equivalent to using tacit premises taken from the knowledge context of the patient. Let us say he decides that the woman is suffering from a displaced pregnancy, that is, a pregnancy that occurs outside the uterus. At that moment, the first stage of the method application will be finished; initial data has been explained (again, in the sense indicated before). But of course, the whole process does not end here. If instead of a doctor we were dealing with a sorcerer, whose prestige does not allow him to make mistakes, the process would probably end here; given the diagnosis, the prescription would follow, with great possibilities of seriously injuring the patient. Since the case is not that of an infallible sorcerer but of a doctor using the scientific method, our researcher will now take the step which most distinguishes modern science: he will try to refute his own hypothesis. He is going to be modest enough to recognize that maybe his first intuition is not, after all, that brilliant. Modern scientists have changed the premature glories of the sorcerer of yore for the gradual and prosaic, but very much secure, victories of the hypothetical method and the experimental verification.

132. Verification

The ultimate support of an inductive conclusion, as we have seen, consists in that refutation does not happen; so, the next step for our doctor-detective will be to create grounds to refute his own hypothesis. He will probably resort to a typical deductive form, the negation of the antecedent: “If A then B; it is so that no B; therefore, no A.” In this specific case we already have A, which is the hypothesis “this woman suffers from an ectopic pregnancy”; we need to find a B that cannot be false if A is true. The task is to find a logical consequence of A which could be easily checked. The doctor orders by phone that the pulse of the patient be taken. He knows that, if it really is an ectopic pregnancy, her pulse will be quick. If the returned answer would have been “normal pulse”, he would have had the hypothesis refuted; with that, the doctor would have appeared a little less brilliant to himself (he would have failed his first guess!). But nevertheless, he would have been closing in on the solution of his diagnosis problem.

However, the actual answer is: “quick pulse.” The hypothesis has not been refuted; we then say that it has become closer to be confirmed. This does not mean that it is true; we simply have not yet been able to demonstrate its falsehood. The hypothesis still stands. If it had been discarded, the doctor would have had to choose another hypothesis, but this time from a shorter list of possibilities. For instance, “simple obstruction of the small intestine.” But the hypothesis did not fall apart: he must therefore try to confirm it even more. In order to do so, he searches for other consequences of A. If it is truly a displaced pregnancy, the pain must be located in a specific place and worsen in specific positions; thus, he must proceed to a direct examination of the patient. On his way to her house, the doctor will review in his mind the different hypotheses that could explain acute abdominal pain; he will make a differential diagnosis, that is, a diagnosis of what the patient does not have, an operation more or less similar to the one we would do trying to divine the adversaries hands in a game of cards. By the time he arrives at her house, he will have clearly defined the most probable hypotheses, and will know what tests he should do to definitely assert the nature of the illness.

Let us summarize the steps taken by our doctor-detective; above all, he is presented with a problem that consists of initial data which require an explanation. A hypothesis is proposed, from where the statement of the initial data may be deduced. Other deductive consequences of the proposed hypotheses or explanation are sought and found. Different tests decide whether those consequences in fact occur. If refutation takes place instead of verification, we must begin the process again proposing another explanation, chosen now from a shorter list. Once a hypothesis has been confirmed, as an additional guarantee, we can imagine all possible explanations and prove that all but one are refutable. Only then can our doctor-detective rest satisfied.

Summing up, the steps are the following:

OBSERVATION – EXPLANATION – DEDUCTION – VERIFICATION– REFUTATION (of all possibilities but one)

133. The Method Applied to Universal Propositions

Let us try to generalize this method so that it applies to the discovering of universal regularities, that is, so called “natural laws.” The most important difference with the previous case is that here the explanations will not be singular propositions, such as “this woman suffers from an ectopic pregnancy,” but universal ones, like as “all bodies attract each other.” Let us examine an example from natural sciences to illustrate this kind of application.

Charles Darwin, famous English naturalist, traveled around the world aboard the Beagle, a ship of His British Majesty, from 1831 to 1836. During this trip he accumulated a large quantity of data that drove him to propose the hypothesis that the biological species change their characteristics through the generations. His main evidence for such hypothesis was the observation of clear differences that existed between similar birds that lived on isolated islands of the Pacific Ocean. Thus, the initial data to explain were of the kind “island X and island Y are inhabited by mutually similar birds, except for very specific differences in the shape of their beak or the size and coloring of their plumage.” The explanation formulated by Darwin about this interesting phenomenon was that the same species had originally migrated to both islands in the past and, from then on, their respective populations had evolved into actually distinct species. "Species evolve" was his explanatory hypothesis of the intriguing phenomenon. Being the case that breeding between specimens of the initial species was out of the question, the two population's characteristics drifted continuously away from each other. Thus, the universal proposition “species evolve” (plus several singular statements concerning the history of specific classes of birds) deductively explained the initial data collected by Darwin.

After conceiving the hypothesis, the researcher continued his voyage. On his hours of quite meditation, he draw from it different consequences. We can summarize them in this manner: “if what was observed in islands X and Y is not a simple coincidence (due to circumstances which I am not able to understand at present) then, in the next islands I visit, W or U, I will also find similar phenomena to those already observed.” He was in the deductive stage; at the moment of disembarking on the next islands he would enter the verification stage. In fact, Darwin was able to abundantly make the confirming observations he predicted.

134. Explanation of Hypotheses

Darwin’s findings were undoubtedly very important; his original hypothesis explained clearly and with numerous verification items the surprising phenomena observed during his travel. But his scientific curiosity was not satisfied with that. While his observations were explained by the hypothesis of species evolution, the hypotheses itself was no less surprising than the observations that had confirmed it. The statement “species evolve” was problematic, raised an issue, namely, the one expressed by the simple question “How come?” This problem deserved as much passion on his part as the problem of why mutually similar birds living on isolated islands had such clear differences between them. This hypothesis of higher degree also needed an explanation. How to produce it? By the same operation analyzed before: imagine a universal statement such that the statements to be explained could be logically deduced from it, in this case the hypotheses of the evolution of the species, repeating the same stages of explanation, deduction and verification, but at a more general level.

After reading, in 1838, the book by Thomas R. Malthus “Essay about Population,” Darwin was convinced that the environment of live beings supplies a “natural selection” analogous to the “artificial selection” techniques of farmers and domestic animal breeders. The explanation for the evolution hypotheses would then be something like the following:

This large statement, or set of statements, constitutes the explanation of the species evolution hypothesis. It constitutes nothing else than the theory of natural selection, today the paradigm or unifying principle of all the biological sciences. Its deductive power is great; many more hypotheses of these sciences may be deduced, and thus explained by it, at the same time confirming the unifying principle itself. Its degree of generality and verisimilitude are such that we could very well say that it is impossible for a naturalist today to think that this theory is not true. With its help, all hypotheses from biological sciences integrate with one another, into a single deductive system or knowledge web. Each particular hypothesis transmits its own confirmation to the others through this magnificent theory which, as an all-encompassing dome, makes all primary hypotheses fortify one another.

135. The Unity of Science

Just as biological sciences find a unifying principle in the theory of natural selection, other large scientific branches have one or several theories that also unify them. Thus, for instance, physical sciences have the relativity and quantum theories; chemistry, the combustion and atomic theories; economy, the theory of economic value. All these most general theories of the different sciences can in turn be explained –and mutually integrated– by a last great unifying principle: the principle of the regularity of nature, or, if you prefer to call it that way, the causality principle of which we have already discuss about. If we considered necessary then to postulate that principle, that is, to proceed as if it was true (see chapter XVII), we now find that the important regularities encountered in different fields of the empirical sciences powerfully confirm its universal validity. We can dare to say that we have failed in the purpose of proving that there is no regularity in the world, or –alternately– assert that we have not enough imagination to conceive a world without such regularity. Each one of the great theories that unify scientific fields can be considered as true, at least for the time being; we may rely on them as essential instruments in the prodigious task of building a world of riches and harmony, in tune with the dignity of humankind, which has had the extraordinary creative capacity of conceiving and confirming them.

Copyright © 1968-2006 Claudio Gutierrez