Abductive reasoning

The epistemological concept abduction (Latin ABDUCTIO " captivity, kidnapping ."; Abduction eng ) has been introduced essentially by the American theorist Charles Sanders Peirce ( 1839-1914 ) in the scientific debate. " Abduction is the process in which an explanatory hypothesis is formed " ( Peirce: Collected Papers (CP 5.171 ) ). Among Peirce understood a closing procedure that is different from the deduction and induction in that it extends the knowledge.

Peirce designed a three-stage knowledge logic of abduction, deduction and induction. In this sense, a hypothesis by means of abduction is found in the first stage of scientific knowledge process. In the second stage predictions of the hypothesis are derived. This is a deduction. In the third stage looks for facts that " verify " the presuppositions. This is an induction. If this does not find the facts, the process begins anew, and this is repeated several times until the " matching" Facts are achieved.

This pulse was partially addressed in recent debates about the nature of science theory and methodology of scientific knowledge or controversial. The recent discussion is guided in large part related to the concept of inference to the best explanation. There have been proposed a wide variety of drafts of a methodology abductive reasoning and discuss applications in various special sciences, including in areas such as cultural studies or semiotics. Various theories about the nature of certain closing process of the "everyday logic " also use the concept of abduction.

The abductive conclusion

In the history of logic, the idea of ​​abduction or hypothesis goes back to Aristotle, who mentions the term Apagoge (First Analytics II, 25, 69a) and also an induction ( conclusio ) faces. The translation of the term Apagoge with abduction took place for the first time in 1597 by Julius Pacius, a Heidelberg law professor. Charles Sanders Peirce thus the term " abduction " is not inserted into the sciences, but picked up a long-forgotten concept and re-introduced into the language. The special power of Peirce is to have this reasoning of a closer look and made ​​fruitful for the logic of the scientific process. The term " abduction " Peirce used for the first time about 1893, he systematically put him, however, until 1901. In 1906, Peirce then increasingly used the concept of Retroduktion.

In the language of logic allows the abduction described as follows:

" The surprising fact C is observed; But if A were true, C would be a matter of course; hence there is reason to suspect that A is true. "

Not a known rule is at the beginning, but a surprising event, something which casts serious doubt on the correctness own ideas. Then there is the second step to a lower position, a pro forma assumption: if there was a rule A, then the surprising event had lost his surprise character. It is now crucial for the determination of the abduction, it is not the " elimination of surprise " the essence is to her, but the elimination of surprise by " a new rule A». Eliminate could be a surprise also, by adopting well-known rules. But that would be no abduction. The rule A has yet to be found or constructed; it was not previously known, at least not for the time that the surprising event has been perceived. If the rule already existed as knowledge, then the event would not have been surprising. In the second part of the abductive process, ie, a hitherto unknown rule is developed. The third step then yields two things: firstly, that the surprising event is a case of the constructed rule, on the other hand, that this rule has a certain persuasiveness.

Peirce characterized abduction as opposed to the inferential deduction and induction as follows:

" Abduction is the kind of argument which starts from a surprising experience, that is an experience that is contrary to an active or passive belief. This takes the form of a perceptual judgment or a proposition that refers to such a judgment, and a new form of persuasion is necessary to generalize the experience. "

" Deduction proves that something must be; Induction shows that something actually is operative; Abduction merely indicated then that something can be. "

" Deduction Proves did something must be; Induction shows did something Actually is operational; Abduction Merely Suggests did something 'may be. "

Comparison of inferential

Deductive conclusions are in the nature of if- then statements. " Each deduction has this character; it is only the application of general rules to particular cases " (CP 2.620 ). Starting from given sets apply deductive reasoning with necessity. This applies to the structure Sciences Mathematics and logic.

Inductive conclusions are based on a case and a result and determine the rule. Induction is synthetic, that is, there are observations used, from which, with sufficient frequency rules are formulated. But the conclusion is made ​​unnecessary.

The abduction is synthetic. In her closing of a result on a rule and on a case occurs. So "closes" of a known size on two unknown. The fact that the result is something Singular, abduction is the final way with the highest risk of fallibility. It is mere conjecture without evidence. The following table serves to illustrate the methodological structure of the different inferential.

" What is the purpose of an explanatory hypothesis? Their purpose is, in that it is subjected to the test of experiment, to perform any surprise to the prevention and the establishment of a behavioral habit of positive expectation, which will not be disappointed. Each hypothesis can therefore, if no special reasons for their rejection are present, may be allowed, provided that it is able to be verified experimentally, and only insofar as it is such verification accessible. This is approximately the doctrine of pragmatism "

From today's perspective is recognized that Peirce about until 1898, the term Hypothesis two quite different forms of reasoning summarized, without providing notice ( for details see Reichertz 2013). When he noticed this vague use, he worked in his later philosophy the difference between the two methods clearly out and called the operation a " qualitative induction ", the other " abduction ". Most of what Peirce had written on the subject of Hypothesis before 1898, but did not characterize the abduction, but the qualitative induction. Only later Peirce admits a: " By hypothetic inference, I mean ( ... ) on induction from qualities" ( Peirce, CP 6.145 ). Reason for the error: " But I was too busy to investigate the syllogistic form, and the doctrine of logical extension and comprehension, which I saw as fundamental as far they really are. As long as I was this conviction, mingled in my mind of the abduction required two different types of closing " ( Peirce MS 425-1902 ). In a draft letter to Paul Carus Peirce went with his views from 1883 even more sharply into court.

" In almost everything I gave into pressure before the start of this century, I blended more or less hypothesis and induction "

In later work Peirce has not been used in accordance with the formal structure of the syllogism, to characterize the abduction. He has rather then the creative moment and the originality of the incident that arises as a flash highlighted.

" The abductive suggestion comes to us like lightning, it is an act of insight, although of extremely deceptive insight. It is true that the various elements of the hypothesis were previously in our mind; but the idea that together, of which we had never dreamed of before, it can bring together, in a flash the new presumption in light of our contemplation "

Abduction as a starting point of the cognitive process

Peirce saw abduction as the starting point of the cognitive process. What man receives as sense-data, is perception. To distinguish " Nihil est in intellectu quod non prius in sensu fuerit. " (CP 5.181 ) Of which perceptual judgments are formed from where the perceived terms. In the exercise of it " really nothing more than the most extreme case of abductive judgments. " These are (CP 5185 )

The abductive character of perceptual judgments made ​​clear Peirce based optical illusions such as of the Necker cube. " In such optical illusions, of which two or three dozen are well known, the most amazing thing is that, that a particular theory of interpretation of the figure quite seems to be given in perception. If they showed us the first time, it also seems to be completely beyond the control of rational criticism, as it is every percept; but after many repetitions of the experiment, the now-familiar deception loses by being less distinct first and last completely disappears. This shows that these phenomena are real links between abductions and perceptions " (CP 5.183 ).

" This wealth of insight has at the same time the general nature of an instinct that so far the instinct of animals is like when he goes far beyond the general assets of our reason and leads us, as if we were in possession of facts that entirely outside the reach of our senses are. It is like the instinct still is that it is subject to error to a small extent; because although it often strikes the wrong as the right way, it is on the whole, but the most wonderful of all our constitution "

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Theoretical significance

In the scientific theoretical discussions between representatives of the neo-positivism (Rudolf Carnap, Carl Gustav Hempel, Hans Reichenbach and Karl Popper ), it was agreed that it is in the requirements of a scientific statement is not the context of discovery, but of the context of justification. For Hempel as for Popper the context of discovery is something subjective, irrational, that is not relevant to the question of the scientific nature of a statement / hypothesis. Any statement is allowed in science, if it meets the criteria of a rational justification, no matter how they came about. At issue was whether the criterion of verification or falsification is.

Peirce, however, who went out as Popper by a basic fallibilism, considered on the basis of its abductive interpretation of the perception that knowledge is not static, as a condition or fact, but as a process. While Popper the logic of the research was examined was the logic of discovery ( logic of discovery ) in focus at Peirce.

" The judgment of perception, in turn, is the result of a process, albeit a process that is not aware enough to be controlled or, to determine correctly which is not controllable and therefore not fully aware. If we were to submit this unconscious process of logical analysis, we would find that it ends in what would represent those measurements as an abductive conclusion, which is based on the result of a similar process, the abductive logical analysis than by a similar conclusion would represent completed and so on ad infinitum. This analysis would be exactly analogous to that applied by the sophism of Achilles and the tortoise, and they would fail for the same reason is to represent the real process. Namely, just as Achilles would not have to make a number of separate efforts so takes this process of forming perceptual judgments because it is unconscious and so the logical criticism is not accessible, no separate record of closing, but its course is taking place in a continuous process. "

Just like in the perception of the abduction is also in the scientific process in the form of closing, which is the starting point of the thought process. The scientists observed a phenomenon that he can not explain an anomaly that contradicts his previous theories. This interferes with his habit and leads to doubt he wants to eliminate. He looks for a theory ( a rule) that it provides an explanation for the cause and then performs verification at a well founded belief.

" A physicist meets a new phenomenon in his laboratory. How does he know that it is not the planetary conjunctions have something to do with it or that it might, therefore, is not so, because the Empress Dowager of China has accidentally pronounced the same time last year a word of mystical power or perhaps an invisible genie may be present? Think of the millions and millions of hypotheses that could be made ​​, of which only one is true; and yet the physicist meets after two or three or at most a dozen guesses fairly accurately the correct hypothesis. By chance, he would have not probably done all the time, since solidified the earth. "

" Someone would have to be completely insane, he would deny that science many real discoveries are managed. But every single piece of scientific theory, which stands firmly established today, is due to the abduction. "

Research is the removal of doubt by the discovery of new rules to attract new, strong convictions. For the orderly process of scientific research presented Peirce the following relationship between abduction, deduction and induction ago:

" After the abduction has given to us a theory, we use the deduction to derive from that ideal theory a mixed variety of consequences from the standpoint that if we perform certain actions, we are confronted with certain experiences. We then go on to try these experiments, and if the predictions of the theory are verified, we have a proportionate confidence that the other experiments that are still trying, to confirm the theory. I say, these three are the only modes of inference, there is. I am both a priori and a posteriori convinced. "

Whether abduction is suitable as a starting point of a scientific theory, opts for Peirce because the subsequent steps of the conversion into a general law ( deduction ) and the empirical testing ( induction) without logical contradictions can be performed. Otherwise, a new theory must be formulated with a new abductive conclusion. Since each theory is only a step to get closer to the truth, it will take any currently accepted theory to be correct for Peirce over time. " Infallibility in scientific matters is irresistibly funny for me." (CP 1.9)

Applications of abduction

Applications of abduction, in addition to science and epistemology medical diagnostics, criminal investigations, legal proceedings, technical troubleshooting, psychology, literature and social sciences, but also pedagogical and educational sciences and eventually computer-based expert systems. Examples of abductive include within the scope of the probability theory, the application of the Bayestheorems or the maximum likelihood method. Reason for this wide range is that the abduction of the "only logical operation [ is ], which introduces any new idea " (CP 5.171 ).

Different interpretations of the abduction

In the recent scientific reception of Abduktionsbegriffes repeatedly tried to condense many approaches of Peirce on the notion of abduction to a term. Since this is by Peirce did not succeed because of the sometimes conflicting requirement of Abduktionsbegriffes, many have resorted to the means, on the one hand to design several variants of the abduction ( eg Eco; Bonfantini & Proni ), on the other hand to keep the concept of contradictory or him to unilaterally grasp.

One of these interpretations is that the users of the Abduktionsbegriffes be keen to ensure that it is in abduction is a strictly logical operation, which is quite methodically to produce. Many AI researchers go after Paul Thagard this way, and also a number of social scientists prefer ( in continuation of Hanson ) this reading. Especially when it comes to the modeling of cognitive processes that AI researchers have noticed for some time that the abduction is fundamental to human thought and that therefore no simulation of human intelligence is complete if it does not have the capability of abduction. Therefore, they are especially interested to write the abduction as an algorithm.

The second interpretation of the Abduktionsbegriffs connects to formulations of Peirce, which state the abduction would explain surprising and can be understood unintelligible. In particular, the scientists who view reading, interpreting, translating, diagnosing, action, the ( criminal ) Educate and much more everyday examples as abductive reasoning, abduction essentially take on in this way. Examples of such extensions are the following remarks: " The logic of abductive inference can thus be understood as a practice, to solve puzzles [ ... ] " ( Moser ). As a particularly far (especially for literature ), the following interpretations of Umberto Eco have proved: must " Given that we are every time we hear a word, in principle, to decide which code must be obtained, seems to be an abduction to be involved in any Decodierungsakt " (Eco). " The logic of the interpretation is the logic of Peirce, abduction ' " (Eco). The statement of Eco, all interpretation is based on abduction, of course, is covered, as it just evens out the what is the specific of the abduction and what should be made ​​visible by the introduction of this concept. Abduction is not the application of a code which is not the application of a rule, but rather the invention is a control abduction, this invention of a code. On the other hand, can be made ​​on behalf Ecos, he probably wanted to just point out that interpretation of natural language is just not purely deductive, but also other, has to be considered by rules with difficulty or not detectable aspects, such as those of a cultural nature, or the perception of the context of the spokesman on. The difficulties of a purely deductive interpretation show, for example, clearly in tasks such as machine translation.

The third interpretation of the Abduktionsbegriffes emphasizes the statement of Peirce, abductive conclusions that would deliver the best and the most likely explanation. Researchers follow the following Rescher this interpretation, see the abduction of especially as a part of the " Economy of Research ". A similar argument Wirth: " Abductive reasoning is a pragmatic strategy whose goal is to minimize the risk of failure. [ ... ]. The researcher tries to optimize the likelihood and plausibility of his hypothesis. He is primarily a gambling betting partner that aligns its judgments and research results to the criteria of successful betting and the successful search for clues before they ' subsumes the standards of the scientific and paradigmatic, the criminal justice system. " (Uwe Wirth).

All three interpretations of the abduction mentioned here designate undoubtedly also features the abduction. But: All these ingredients abductive reasoning - namely their logical form, their explanatory function and its ability to provide probable readings - are necessary but not sufficient components of the abduction. These three characteristics do not indicate the specificity of the abduction, but their boundary conditions. Bluntly: abductions may or may not be logical, explanatory or economically. Understanding and explanation can be a lot also by deduction and induction - often even better, and of course the deduction provides the best explanation, and certainly the induction or even the deduction is a reliable logical conclusion. But the decisive factor in abduction is not their logical form, the explanatory function or the probability, but also the ability to find a new rule.