Claudio Gutierrez
Translated from Spanish by Inés Gutiérrez
Claudio Gutierrez
When studying formal fallacies we examined one, called “assertion of the antecedent”, which made us go from the premises:
We stated then that such form of argument is not valid, since the premises are not enough to assert the truth of the conclusion. Nevertheless, it is certain that if I find myself in the situation described on the premises I will feel strongly disposed to accept the truth of the conclusion. In fact, it is precisely because people who take remedies recover soon that we are driven to infer that remedies are effective. How are we to explain this discrepancy between the logical value of the argument and the faith usually placed in this deductively invalid procedure? In order to clarify this problem we should look a little more carefully into the situation described by the premises.
Let us suppose two different cases: in the first, we deal with a “remedy” prescribed by the town’s sorcerer; in the second, with a remedy prescribed at the local Health Care Center. We may very well say that, in the former case, the “deduction” is a fallacy; but, in the latter, we deal rather with a of non-deductive inference procedure, not infallible to be sure, since many things could go wrong, but in which our guarded trust is justified giving the surrounding circumstances: intervention of serious agents, application of theoretical knowledge of various sciences, accumulated medical experiences, etc. We may say that our acceptance of the conclusion is based on a probable inference. Under the conditions explained, the fact that the patient recovers soon makes it more probable than in other futures occasions that the remedy will be used with even more confidence in its effectiveness. The current experiment –we are entitled to call it such– adds some, however limited, probability to the conclusion; it even permits the doctor to report it as “another favorable case” in a control protocol kept in behalf of the manufacturing laboratory, within a research program about the effectiveness of the product. Notwithstanding, the possibility exists that the result of the application of the remedy to the next patient might be innocuous or even harmful; the doctor-researcher will then write down in the protocol one more unfavorable case, which will then lessen the probability of the remedy being effective.
What has happened here? It is evident that we are now traveling along a path much less firm than that of deductive logic, where you go necessarily from the truth of the premises to the truth of the conclusion. Nevertheless, it is also clear that through this new kind of inference procedures you are able to gain some knowledge; moreover, extremely useful knowledge, for the benefit and progress of the human species, in particular in the medical sciences. The traditional name for this important although fallible method of inference is induction, contrasting in many respects with the deduction method heretofore studied. There are many differences between both methods, and several similarities, all of which we will attempt now to present in summary fashion.
Induction and deduction are similar in that both are methods of mediate knowledge, which means that in any of them we go from certain propositions to certain others, different ones, which we accept as worthy of trust because the former are already trustworthy. Both methods have in common their being distinct from immediate knowledge, i.e. the knowledge I gain by the operation of my senses, for instance the direct knowledge I have about the things I am seeing or hearing now. They are also similar in the fact that both methods have rules, which tell us when the procedure is safe and when its application is fallacious. They differ, on the other hand, in other features. Above all, induction does not allow us to assert that the conclusion is as certainly true as the premises; it only allows the assertion that the conclusion is true with a certain degree of probability, assuming its premises. Thus, in our remedy example, a large number of favorable cases and the absolute absence of unfavorable cases produce a high degree of probability for the corresponding conclusion. We say then that the conclusion or hypothesis is sufficiently confirmed. But if there are just a few favorable cases, if the remedy has been tested only a few times, we say that the hypothesis of its being effective needs yet to be confirmed. On the other hand, unfavorable cases disconfirm the hypothesis, that is, make it less probable. If, finally, whatever the number of favorable cases may be, the appearance of enough number of unfavorable cases compensates for errors of observation, then the hypothesis is not only disconfirmed but refuted, and we must reject it.
We say then that inductive method is a procedure of inference which, as deduction, allows us to go from some propositions to others. Unlike the deductive method, it allows us to assert the conclusion with only a certain degree of probability, most of the time not specifiable in quantitative terms (we say that a hypothesis is "more or less confirmed than another," which is less confirmed; but usually we cannot say that it is "confirmed with 87 units of confirmation").
We may of course call the propositions that constitute the process of an induction, premises and conclusion; however, in order to distinguish them from their counterparts in the deductive process, it is more convenient to call the conclusion, hypothesis, and the inductive premises, its support. Likewise, we may call inference the movement that goes from the premises to the conclusion; nevertheless, we generally prefer to speak of confirmation of some propositions by others. Just as in the deduction method we say that certain premises allow the inference of certain conclusion, in the induction method we say that certain support allows the confirmation –or confirms– certain hypothesis.
The support of a hypothesis is somehow more complicated than the premises of a deductive conclusion. Above all, it generally consists of an enormous number of propositions, not two or three as in a deduction; the list of the doctor-researcher, for instance, may contain five thousand lines specifying the same amount of results of the remedy application, in the same amount of patients treated. Each favorable and unfavorable case must be conceived logically as a singular proposition, even if this proposition is only implicitly recorded in a numerical table.
On the other hand, negative support is as important as –or even more important– than the positive one. We do not call unfavorable cases negative support, which would rather be counter-support; we prefer rather calling it absence of counter-backing, which counts as strong (positive) support for the hypothesis. If there have been many favorable cases, and no unfavorable cases, then the hypothesis stands sufficiently confirmed, both by positive and negative supports. In this combined support, the presence of the negative one is paramount. Why is absence of counter-support such a powerful form of backing for an inductive conclusion? In order to understand it we must recall some of the topics in our treatment of deduction. This will allow us, besides clarifying the logical nature of induction, to better comprehend the relationship that exists between both methods of knowledge.
The effect of an unfavorable case over a hypothesis deserves special attention. Every unfavorable case disconfirms the hypothesis; but if they occur in high enough numbers, or in lower numbers but with sufficient clarity –so that human error may be discharged in assessing the soundness of the experiment– then we can say that the contrary cases refute the hypothesis; we may trust that it is false with certainty.
We have written “with certainty”. This means that we are here not facing an inductive process, which only allows us to say “with probability”, but a full-fledged deductive process. Let us see it in a concrete example:
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This problem, already familiar to our readers, is solved through the separation tactic, as the perfectly valid argument that it is. We are dealing, in fact, with a deduction problem. As usual, we rely completely in the truth of the premises, which must be true for the conclusion to be accepted also as true. It so happens in this particular case that the first premise is only probably true; however, the weakness of the premises, although does weaken the conclusion, does not weaken the argument itself, which remains undoubtedly valid.
The reason why we accept inductive conclusions is that they have been confirmed, i.e. they have accumulated considerable support in their favor. But this is only a shorter way of saying that, in spite of the careful manner in which the research has been conducted, the hypothesis has survived all the attempts made to refute it. As refutation is a strictly a deductive operation, the relationship between inference by deduction and inference by induction consists solely in this: the inductive conclusion (hypothesis) is accepted because it remains still unscathed after the considerable and premeditated efforts made by the researchers to prove that it is false.
The acute reader may at this point be inclined to object: But is this not a case of the absence-of-proof fallacy explained in section 22? Let us consider the objection carefully. If a person asks me to prove that the Boogie Man does not exist, my problem will be that I cannot even begin to do so; how would I? Would I search the whole world to find him? Could not my interlocutor forever maintain that I cannot find the Boogie Man because he is extremely skillful at changing hiding places to where I just searched a moment ago? The scientific enterprise is something else. The researcher can try out a remedy giving it precisely to the people afflicted with the illness it is supposed to cure. If they fail to recover, that would count as counter-support to its effectiveness. On the other hand, if no matter how many experiments I perform, following strictly the rules of scientific methodology, it turns out that I fail to demonstrate that the remedy is not effective, that would go a long way to dissolve reasonable doubts about its effectiveness.
It is important to observe that the trust we put on inductive conclusions is directly proportional to the trust we place on researchers. We must be reasonably certain that they do everything in their power to refute their own hypotheses, or at least those of their colleagues; that they do not try, on the contrary, to “save” them whatever the costs. Taking into account the force of human vanity and the capacity for self-deceit characteristic of human beings, it is simply extraordinary that something as trustworthy as modern science even exists among us. The explanation lies in the free intellectual competition that, in organized science, rewards with honors and material advantages the scientists who manage to stand out by refuting other people’s hypotheses. By contrast, it is hard for the scientific adventure to prosper in autocratic societies, where scientists are asked to defend and prove specific theories or doctrines and where, for political or religious reasons, their freedom for criticism is quite restrained.
Furthermore, we must underscore that the demonstrative force of the refutation scheme presented in section 116 lies in the simplicity of its first premise, for instance, “if the remedy is effective, I recover”. This premise simplicity, in fact, never happens, due to the organic or systematic nature of scientific knowledge. In fact, the premise should rather be read as: “if the remedy is effective, and the circulation of the blood proceeds as contemporary science teaches, and the nervous system is really as current neurology explains, and…, then I recover”. That is, every scientific hypothesis assumes that all other well confirmed hypotheses which constitute the state of the art in science are in fact true. If the announced prediction (“I recover”) does not happen, what is really refuted is the conjunction of the quoted particular hypothesis and all other standing scientific hypotheses. So in a strict logical analysis, we do not know which part of that enormous conjunction is false in the case of a refutation. Due to the prestige of the standing hypotheses, we blame the new one, which as yet has not enough prestige. We may not exclude in principle, however, the possibility that the experiment in question may put in jeopardy some other of the accepted scientific hypotheses or laws, demanding its rejection, rather than rejecting the new hypothesis. In fact, situations like that had occurred in the past and have provoked a whole revamping of the scientific landscape.
There is an important feature about the subject discussed that we have not yet analyzed. The remedy taken by the different patients from the doctor-researcher’s list is not really absolutely the same: the remedy taken by patient B is not the same as the remedy taken by patient A, simply because that remedy was already been ingested by patient A. The most we can say is that the remedies taken by the different patients are of the same kind, or simply that they are analogous samples of the remedy. Analogous means similar. As a matter of fact, the remedy ingested by the different patients is similar from various perspectives: they are prescriptions with the same name, manufactured in the same laboratory, by the same employees, with the same type of materials, following the same procedures, etc.
We may reinterpret our inductive argument and present it as an argument by analogy, which is another way of interpreting probable inference. The logical scheme of the premises of such argument would be the following:
Hence, the argument by analogy consists in asserting that from the conjunction of certain properties in a specific number of cases, the conjunction of the same properties may be inferred in another different case.
The argument of analogy is not always valid, as attested by the existence of the fallacy of illegitimate instantiation (see section
100). But under certain conditions and with certain precautions it may be a valuable instrument of research. The most important of these precautions consists in choosing the properties to be compared in a way that they are causally relevant to the phenomenon in question, i.e. that they relate to the production of the effect at issue. For instance, it would be totally inappropriate to choose as common qualities of several remedies the fact of their being bottled in the same kind of vial, being sold at the same drugstore, being the same color, or having the same price. The difference between these properties and those consigned previously (having been produced by means of the same procedure and from the same materials, etc.) lies precisely in the fact that some have and others do not have any relationship with the production of the curative effect of the remedy. The analysis of causal relationships requires the study of certain features of our subject matter that we have not yet covered and to which we will devote the last chapters of this work.
