A more developed version of this paper can be found in
Santaella, Lucia (2004). O método anti-cartesiano de C. S. Peirce. São Paulo: Unesp/Fapesp.
THE DEVELOPMENT OF PEIRCE'S THREE TYPES OF REASONING:
ABDUCTION, DEDUCTION, AND INDUCTION
São Paulo Catholic University
Among the current commentators there seems to be no doubt about the developmental nature of Peirce's philosophy. An extremely original thinker as he was, Peirce did not escape the confrontation with philosophical tradition, neither the consequences of his own discoveries. One of these consequences was the need of self-correction and self-criticism, which he continuously faced. If this is true with respect to the whole of his work, it is even more valid for his theory of the three types of inference or reasoning: abduction, deduction, and induction.
In 1946, Arthur Burks, the first to present an interpretation of Peirce's theory of hypothesis, retroduction or abduction, divided the development of this theory into two periods: the period before 1900 and the period after 1900. Later, this division was discussed more extensively by Fann (1970), followed by Thagard (1977, 1981) and then by Anderson (1986). In my view, ignoring the historical development of Peirce's three types of reasoning and their interrelations has been a source of misunderstanding and reductionism. The aim of this paper is to present a synthesis of Peirce's ideas in the light of his commentators' discussions.
At the beginning, Peirce considered that all forms of syllogism could be reduced to Barbara. As early as 1866, however, when he studied in detail the relation between the syllogistic figures, Peirce was able to prove that each figure involves an independent principle of inference. This led him to recognize the autonomy of each of the three forms of inference, hypothesis, induction, and deduction, as it was presented to the Academy of Arts and Sciences in 1867 (CP 2.461). According to this version, induction is the inference of the syllogism's major premise from its minor premise and conclusion. Hypothesis is the inference of the syllogism's minor premise from two propositons. The function of hypothesis is to substitute a great series of predicates, which do not form a unity, by a single one that involves all of them. Hence, similarly to induction, hypothesis reduces a multiplicity to a unity (Fann 1970: 19-20).
Peirce's ideas in the 1860's were still based on classical logic, particularly on the theory of the subject and object of the proposition. The discovery of the logic of relations, at the end of the 60's, led him to the introduction of propositions that were not reduced to the forms of subject and predicate. In 1870, Peirce had already published an essay on the logic of relations where the syllogism was described as a form of a logical relation and not as the fundamental form of any argument (ibid.: 20). It is rather odd, however, that in Peirce's famous paper of 1878 on "Deduction, Induction, and Hypothesis" (CP 2.619-2.644), his analysis did not present any substantial change in comparison to his essay of 1867. Hence, in 1878, induction was still the inference of a rule (major premise) from the case (minor premise) and the result (conclusion), while hypothesis was the inference of a case from the rule and the result. Deduction, always less problematic, was the inference of a result from a rule and a case.
We induce whenever we generalize from a number of cases of which something is true, and we infer that the same thing is true of a whole class. As Peirce states, "hypothesis is where we find some very curious circumstance, which would be explained by the supposition that it was a case of a certain general rule, and thereupon adopt that supposition. Or where we find that in certain respects two objects have a strong resemblance, and infer that they resemble one another strongly in other respects" (CP 2.624). Conceived as a process of corroboration, hypothesis is similar to induction in its task to decide favorably or contrary to a hypothesis. From the beginning, however, the function of hypothesis as a source of new hypothesis is present, as it is apparent in the above quotation. Here Peirce was close to the problem of hypothesis selection which is present in this type of inference, a topic which Peirce elaborated later on.
According to Peirce, the process of raising a hypothesis has to follow three rules in order to lead to probable results:
1. The hypothesis should be distinctly put as a question, before making the observations which are to test its truth. In other words, we must try to see what the result of the predictions from the hypothesis will be.
2. The respect in regard to which the resemblances are noted must be taken at random. We must not take a particular kind of predictions for which the hypothesis is known to be good.
3. The failures as well as the successes of the predictions must be honestly noted. The whole proceeding must be fair and unbiased. (CP 2.634)
In the first rule, Peirce almost prefigured the theory of abduction which he was to elaborate later on. Only in his later writings did he recognize that a prediction from a hypothesis is a more properly deductive function. At that time, he also recognized that the second and third of the above mentioned rules are much more related to induction than to hypothesis.
The imprecisions inherent in his theory of inferences before 1900 resulted from the fact that Peirce first interpreted inference in general as a process of probation. Although he considered induction as an inference from a series of facts to another series of similar facts, and hypothesis as an inference of one type of facts to facts of a different type, Peirce was not yet ready to distinguish clearly between these two types of reasoning. He saw both as occupying opposite sides in the continuum of ampliative inferences. Later on, the concept of induction was to be extended to include induction of characters, whereas abduction was to appear as a rather different kind of inference.
Initially, the three types of reasoning were distinguished by means of the categories of amplification and explication. Deduction was seen as purely explicative because it does not add anything new to thought. Induction and hypothesis, on the other hand, were conceived as ampliative, since both adduce probable and possible knowledge about an undetermined future. At this point, the view that logic is not a closed system of thought, but a question of alive and open human inquiry began to emerge in Peirce's mind. In order to develop this view, he needed to get rid of the reductive syllogistic frame in which his theory of inferences was confined. Within this earlier frame, induction and hypothesis shared the same function, but not the same form. When the place of hypothesis was finally substituted by abduction, induction and abduction had no longer anything in common.
Peirce's interest in the distinction between the two types of ampliative inference began to emerge very early. When he stated, both in 1866 and in 1878, that induction infers from one set of facts to a similar set of facts, while hypothesis infers from facts of one type to facts of another type, Peirce was already realizing that only hypothesis has a truly ampliative power. From 1878 on, he began to put much more emphasis on the differences than on the similarities between induction and hypothesis. That is why F. Reilly's (1970) attempt at reducing abduction to induction as well as William's (1972) attempt at reducing induction to abduction are both unacceptable (see Anderson, 1986: 151). In fact, Peirce had never entertained any doubts about considering hypothesis as a legitimate and independent mode of inference. However, a further advance was necessary to arrive at the discovery of the creative functions of hypotheses. Peirce arrived at this idea only after 1900, when his concept of abduction was fully developed. In 1902, referring to his view of 1883, Peirce declared:
Upon this subject (of abduction)..., my doctrine has been immensely improved since my essay "A Theory of Probable Inference" was published in 1883. In what I there said about "Hypothetical Inference" I was an explorer upon untrodden ground. I committed, though I half corrected, a slight positive error, which is easily set right without essentially altering my position. But my capital error was a negative one, in not perceiving that, according to my own principles, the reasoning with which I was there dealing could not be the reasoning by which we are led to adopt a hypothesis, although I all but stated as much. But I was too much taken up in considering syllogistic forms and the doctrine of logical extension and comprehension, both of which I made more fundamental then they really are. As long as a held that opinion, my conceptions of Abduction necessarily confused two different kinds of reasoning. When, after repeated attempts, I finally succeeded in clearing the matter up, the fact shone out that probability proper had nothing to do with the validity of Abduction. (CP 2.102)
Unfortunately, many interpreters of Peirce's concept of abduction have written a good number of books and essays on the subject which ignore that Peirce has given several warnings concerning the evolution of that concept in his writings. Taking as a reference only the paper of 1878 on "Deduction, Induction and Hypothesis" where these inferences are treated exclusively within the syllogistic frame, some commentators have unnecessarily limited their interpretation to this narrower frame. Others have arbitrarily gone beyond this frame, provoking unavoidable confusions in the boundaries between abduction, induction, and deduction, which Peirce was so meticulous to distinguish. The latter, for instance, is the case of Umberto Eco (1992); the former is the case of Herrero (1988), who inherited from Bonfantini's (1987) school the fascination for rules, cases, results, and their combinations (see Santaella 1991).
When Peirce stated that the question was "cleared up", he referred to his later concept of abduction as that kind of reasoning which merely leads to the adoption of a hypothesis. The function of induction is then to validate a hypothesis by testing it. Consequently, the validity of an abduction is entirely different from the validity of an induction. In fact, what had been called hypothesis in the period before 1900, was now considered as one of the many types of induction, namely, qualitative induction. What had previously been called induction became now quantitative induction. The route which led to this development is my folloowing topic.
In 1896 Peirce wrote a manuscript of notes for a projected, but never completed, "History of Science" (CP 1.43-1.125). In these notes, his earlier concept of hypothesis was now renamed as "retroduction". This corresponded to Peirce's interpretation of abduction in the sense of Aristotle's "apagogue". Peirce wrote: "Retroduction is the provisional adoption of a hypothesis, because every possible consequence of it is capable of experimental verification, so that the persevering application of the same method may be expected to reveal its disagreement with facts if it does so disagree" (CP 1.68). Under its new name of retroduction or abduction, the concept began to be extended to include a new function, namely the methodological function, as it was to be developed still later in Peirce's methodeutics. The reinterpretation of inferences as methodological stages of inquiry in addition to their proof function was predominantly characteristic of Peirce's view after 1900.
In 1901, in a manuscript "On the Logic of Drawing History from Ancient Documents", Peirce presented a clearer account of his new interpretation of Aristotle's Prior Analytic (II, 25). He now translated Aristotle's "apagogue" as abduction and defined it as accepting or creating a minor premise as a hypothetical solution for a syllogism whose major premise is known and whose conclusion we discover to be a fact (CP 7.249). Thus, it was in the context of his original reading of Aristotle that the concept of abduction first appeared before he extended it and understood abduction as the examination of a mass of facts allowing the suggestion of a theory (CP 8.209). At this point, a new idea began to emerge in Peirce's thought, the revolutionary and controversial idea of a type of reasoning which is at the same time logical and instinctive, as if there were a logical form for instict. Peirce pursued this idea until the end of his life.
Before 1890, there had not been many changes in Peirce's concepts of induction and deduction, but in 1898, deduction was reinterpreted in the sense of a process of inferring the probable and necessary consequences of a hypothesis. Induction was not yet treated as the process of testing a hypothesis. However, the radical change in the understanding of abduction, in 1901, was only possible as a consequence of the displacement of the logical character of induction. This resulted in the new conception of the three types of reasoning as three interconnected and interdependent stages of scientific inquiry, abduction, deduction and induction. It was here that Peirce's most mature explication of the method of scientific inquiry was born. Fann (1970: 31-32) has given a clear outline of this process.
When surprising facts emerge, an explanation is required. According to Peircem, this "explanation must be such a proposition as would lead to the prediction of the observed facts, either as necessary consequences or at least as very probable under the circumstances. A hypothesis then has to be adopted which is likely in itself and renders the facts likely. This step of adopting a hypothesis as being suggested by the facts, is what I call abduction" (CP 7.202). This corresponds, for Peirce, to the first stage of inquiry. "The first thing that will be done, as soon as a hypothesis has been adopted, will be to trace out its necessary and probable experimental consequences. This step is deduction" (CP 7.203).
"The next step is to test the hypothesis by making experiments and comparing the predictions drawn from the hypothesis with the actual results of the experiment. When we find that prediction after prediction is verified by experiment we begin to accord to the hypothesis a standing among scientific results" (Fann 1970: 32). "This sort of inference it is, from experiments testing predictions based on a hypothesis, that is alone properly entitled to be called induction" (CP 7.206).
After these transformations in the frontiers of the three kinds of inference, the distinctions between abduction and induction were defined more precisely in the following way. Induction has no power to add any new information to the present knowledge. At most it can correct the value of a reason or modify a hypothesis slightly in a way that had already been considered as a possibility. Abduction, in its turn, is merely preparatory. It is the first step of scientific reasoning, while induction is the last step. Both represent the opposing poles of reason. Abduction is the less effective pole, while induction is the more effective one. One is the reverse of the other. Abduction looks for a theory. Induction seeks for facts (CP 7.217-18, apud Fann 1970: 43-35).
Induction is now the only process of validation, while abduction is the process that leads to the adoption of a hypothesis as a pure "may be". Hence, probability, which is a feature of induction, can only indirectly affect abduction, namely after the process of deduction infers the consequences of a hypothesis so that an inductive test can be accomplished. As the first form of logical inference in scientific research, abduction evolved from the subsidiary role which it played for induction to occupy the privileged place where creativity occurs in science. That is why abduction is so perfectly able to fuse the logical and psychological aspects of reasoning, engendering the hypothetical foundations for deduction and induction.
There has been much controversy concerning the relation of Peirce's three phenomenological categories with the three types of inference. When we keep in mind the development of these three kinds of inference in Peirce's semiotics, there appears a way of clarifying the controversy. In fact, there is a reason for the controversy. Before 1900, the modes of inference were related to the categories according to the degree of certainty characteristic of each of these modes. Deduction belonging to thirdness was associated with the highest degree of certainty. Next came induction, as a category of secondness, and finally there was hypothesis as a category of firstness. After 1900, when these three modes were conceived as stages of scientific investigation, the relation changed to induction (thirdness), deduction (secondness), and abduction (firstness). At this point of the elaboration of Peirce's theory, not the grade of the force of each of these forms of arguments, but the order of their interdependence in the process of reasoning had moved into the foreground.
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