Modeling the Six Modes of Peircean Abduction for Educational Purposes


Gary Shank

EPCSE Dept.
Northern Illinois University
DeKalb, IL 60115
815-753-8466
gshank@niu.edu

Donald J. Cunningham

School of Education
Indiana University
Bloomington, IN 47405
812-856-8316
cunningh@ucs.indiana.edu


Abstract:


In this paper, we will argue that Peirce's ten classes of signs can be used to derive six separate and qualitatively distinct modes of abduction, and that these six modes can lead to the formulation of new models of inference and learning. As examples of the use of this system, we apply these ideas to the study of informal science learning and to navigating the World Wide Web.



Introduction:


In an earlier paper, Shank (in press) has sketched out the derivation of the claim that C. S. Peirce's ten classes of signs can be used as the basis for outlining ten modes for making inferences. In that paper, Shank was only concerned with detailing the derivation per se. In this paper, we will look at some of the consequences of that particular derivation in terms of using the concept of abduction in research and practice.

In order to consider those consequences, however, we must first review the basic points of the derivation. This review will be sketchy, and we recommend reading the original article for a more complete account of this endeavor.

Deriving modes of inference from Peirce's classes of signs:


This paper will assume that the reader has some knowledge of Charles Sanders Peirce and his work in logic, semiotics, and pragmatic theory. All references to his work are in volume and paragraph notation (e.g., 2.205 is from Volume 2, paragraph 205) from the Harvard edition of the collected papers of Peirce (1931-1958). We have also made a few terminological moves. First of all, we have substituted the terms "tone," "token," and "type," for "qualisign," "sinsign," and "legisign" respectively. We feel the use of the simpler terms is justified, since Peirce used these terms as alternative terms in his writing. Also, we have replaced the terms "rheme," "dicent," and "argument," with, respectively, "open," "singular," and "formal." These replacements reflect the status of propositions which are a crucial part of the derivation process.

As a matter of review, we note that Peirce devised his ten classes of signs as part of his general theory of signs, or semiotic theory. At first glance, these classes look like a categorization scheme. The ten classes are: 1) Open Iconic Tone; 2) Open Iconic Token; 3) Open Iconic Type; 4) Open Indexical Token; 5) Open Indexical Type; 6) Open Symbolic Type; 7) Singular Indexical Token; 8) Singular Indexical Type; 9) Singular Symbolic Type; and 10) Formal Symbolic Type (2.254-264).

When using the classes as a categorization scheme, it seems as if they have only limited and even arbitrary use. After all, what real value is there in us coding a weathercock as a "singular token" (2.257) or the feeling of red as a "tone?" (2.254) While it does suggest something about the properties of the objects so encoded, it is important to note that one already had to be aware of those properties in order to make the coding in the first place. Therefore, using the ten classes of signs as a categorization scheme seems to yield nothing other than a clumsy new language.

Turning away from categorization, it makes sense to turn in the direction of inference. That is, what can the ten classes tell us about how human beings reason and make inferences about their world? Peirce was very much concerned with logic and logical inference throughout his career, and often identified himself as a logician. Therefore, it is quite feasible to approach any aspect of his work as if it were an exercise in basic or applied logic. When we do this to his ten classes of signs, it yields some fascinating, and even startling, results.

We begin by outlining the process Peirce used to derive the ten classes of signs in the first place. In summary, Peirce started with the ideas of potentiality, actuality, and regulation (2.233-242). When looked at in terms of inference, potentiality involves the use of the open propositional function (which he called the "rheme"), actuality involves the use of the singular proposition (which he called the "dicent"), and regulation involves the use of the formal proposition (which he called the "argument") (2.250-253). Peirce then used a monotonic intersection strategy where he exhausts the open proposition in terms of the other two areas of distinction (namely the use of icon, index, and symbol to deal with, respectively, potentiality, actuality, and regulation in the relation of the sign to the object (2.247-249); and the use of tone, token, and type to deal with, respectively, potentiality, actuality, and regulation in the relation of the sign to its ground) (2.243-246).

Briefly, Peirce started with potentiality in terms of its logical inferential form, i.e., the rheme. He then "ran" the rheme through all six remaining manifestations. In this fashion, he generated the first six classes. He then ran actuality, as manifested in the inferential form of the dicent, through those categories where actuality and regularity still apply. This served to generate the next three classes. Finally, he ran the logical inferential mode of regulation through the categories of regulation, yielding the final class of signs (2.264).

Since the categories governing inference were the basis for the generative strategy of the categorization system, it follows that we can then apply the system directly to the consideration of signs as the outcomes of these modes of inference. It remains only to establish that abduction is the mode dealing with potentiality, induction is the mode dealing with actuality, and deduction is the mode dealing with regulation. If we accept this last point (as derived from Shank, in press), then we conclude that the act of abduction is not a singular type of reasoning, but is a "family" of six distinct ways of dealing with potentiality as a logical inference. The same can be said about induction, except to say that its "family" consists of three distinct ways of dealing with actuality as a logical inference. Perhaps the reason we do not think of "families" of inference types is that deduction, the oldest and most understood mode of inference, is indeed a single type of inference based on regulation. Therefore, since we tend to use deduction as our model, our tendency is to look for "the" form of induction and "the" form of abduction.

Exploring the six modes of abductive inference:


Based upon the preceding argument, we claim that there are six separate and distinct ways to do abduction, and that these abductive modes are systematically related to each other. In this section, we will sketch out a brief description of each mode, building upon these descriptions to include an ongoing concrete set of examples.

The first mode leads to what Peirce identified as the Open Iconic Tone (or Omen/Hunch). This type of inference deals with the possibility of a possible resemblance. A more concrete way to characterize this type of reasoning is to describe it as reasoning in order to determine the possibility that our initial observations might serve as omens for possible evidence. An omen is a sign whose resolution is in future acts of inquiry and observation. When the inference of the omen is more implicit, we might call it a hunch. For instance, an archeologist might guess that she should examine the banks of an old stream bed, because she might possibly find something that might possibly be an artifact. This type of inference we traditionally consider to be merely a subjective act. However, it is an abduction, and one that is systematically related to other types of abductions.

The second mode leads to what Peirce identified as the Open Iconic Token (or Symptom). This type of inference deals with possible resemblances. Here we have the case where we are trying to decide whether or not some actual observation has enough properties to be considered as some case. A more concrete way to characterize this type of reasoning is to describe it as reasoning in order to determine whether our observations serve as symptoms for the presence of some more general phenomenon. A symptom is a sign whose action is ongoing in the present. For instance, our archeologist, let us say, finds a smoothed stone. It is not immediately clear whether or not the smoothness is natural or man-made, and so she has to make an inference. In these inferences, we often find a dependence on prior experience is involved.

The third mode leads to what Peirce identified as the Open Iconic Type (or Metaphor/Analogy). This type of inference deals with the manipulation of resemblance to create or discover a possible rule. A more concrete way to characterize this type of reasoning is to describe it as the mode of inference that uses analogy and metaphor to create new potential rules of order. For example, suppose our archeologist is unhappy with current theories of migration to describe the movements of the ancient tribes whose artifacts she has been collecting. She needs to generate a new conceptual frame of reference. Since most, if not all, general conceptual frames are metaphorical in nature (cf. Lakoff & Johnson, 1980), it makes sense to create a new root metaphor to guide the formation of the new frame of reference. In order to do this, she can shift her metaphorical base deliberately, using a principle that Shank (1987) has called the Method of Juxtaposition. Suppose, she decides to look at tribal migration as if it were like, say, reading behavior. What areas of investigation does this new metaphorical area of juxtaposition suggest? Notice that there is no requirement that the juxtaposition make explicit sense. We can get away with this due to the fact that human beings are compelled to render any juxtaposition as meaningful, or at least as meaningful as possible. In fact, juxtapositions which are arbitrary can be quite useful, in that they can lead to new areas of insight and understanding.

The fourth mode leads to what Peirce identified as the Open Indexical Token (or Clue). This type of inference deals with possible evidence. A more concrete way to characterize this type of reasoning is to describe it as reasoning in order to determine whether or not our observations are clues of some more general phenomenon. A clue is a sign which indicates some past state of affairs. Therefore, any act of reasoning which centers on clues is an act that tries to infer what past states of affairs or circumstances were, and is therefore an act of detection. For example, our archeologist discovers a number of pottery shards next to the smooth stone. Is there any connection between the two, or is it just a coincidence? In order to make a judgment, she looks at the shards and looks at the smooth stone, searching for evidence of some physical connection. If she finds pieces of pottery on the stone, then she has a potential clue that the stone was used, for some reason she does not know yet, to shatter the pots.

The fifth mode leads to what Peirce identified as the Open Indexical Type (or Diagnosis/Scenario). This type of inference involves the formation of a possible rule based on available evidence. A more concrete way to characterize this type of reasoning is to describe it as reasoning in order to discover possible diagnostic judgments amidst our observations. It is the act of reasoning that also finishes off the detection process by the creation of plausible scenarios from the body of clues. For instance, our archeologist notes that the shattered pots are all placed in a shallow pit, and there are other smooth stones organized around the edges of the pit. She then starts the process of assembling these individual observations no longer as observations, but now as potential scenarios. As scenarios, these patterns of clues take on a possible unity of character.

The sixth mode Peirce identified as the Open Symbolic Type (or Explanation). This type of inference deals with a possible formal rule. A more concrete way to characterize this type of reasoning is to describe it as reasoning in order to form a general plausible explanation. For example, suppose our archeologist is trying to account for a puzzling collection of artifacts. She has never seen burnt sticks with smooth stones attached to them. As tools, these implements have been weakened by having been burnt. If she shifts her mode of explanation, though, she can make better sense of them. Suppose, instead of being tools, these artifacts have religious significance? The burnt sticks might serve to illustrate some ritual point. Note that this explanation by itself carries no weight of certainty, but it might serve to simplify other explanations, and create a pattern to account for other data. This explanation, if it holds, allows us to summarize a lot of separate pieces of evidence, and a number of alternative scenarios, into a single coherent explanation that has the additional advantage of serving as the basis for meaningful insight. That is, a good explanatory hypothesis does not just explain the obvious. It directs us toward the less obvious, and sheds light on areas once seen as unclear or unconnected.

Applying the six modes of abduction to learning and instruction:


The modes of abduction we have identified offer the opportunity to researchers and theorists to take a fresh look at the role of reasoning in learning and instruction. We are in early stages of research on two areas of application of our approach: informal science learning and learning via the World Wide Web.

Informal science learning:


St. John & Shields (1988) in reviewing research from NSF Informal Science Initiatives, found that most informal science research focused on enhancing general scientific literacy or else concentrated on making science more interesting and attractive, thereby enhancing attitudinal and motivational factors. Other directions on research looked at social (e.g., Wellington, 1990; Berger, 1994), sociolinguistic ( e.g., Lemke, 1990), and/or familial ( e.g., Dierking & Falk, 1994) factors. Only a very few studies used principles of learning, and in particular, the findings of cognitive science (e.g., Resnick & Chi,1988; Claxton, 1993). In short, the study of informal science learning has been dominated by the idea that informal science learning is a relatively trivial pursuit that, at best, increases awareness and motivation for children. And yet, it has been documented (e.g., Berger, 1994), and our pilot research has also shown, that informal learning is one of the most important and significant experiences in the growth and development of actual scientists. In other words, there is a gap between theories of informal science learning, and the role that this informal learning actually played in the development of scientists.

By using ideas based on abductive modes of inference, we hope to show that informal science is qualitatively different from curricular science -- not just in terms of its content or affective dimensions, but as a form of inference-in-use. Following Hanson (1958), we hope to show that informal science is an applied version of the logic of discovery, which is another way of characterizing abduction. The dynamics of the use of the logic of discovery in informal science we also feel are oriented toward the resolution of meaning, and in particular, the act of reasoning to the best explanation (cf. Harman, 1965). In particular, we feel that a study of informal science using these conceptual tools will illustrate the complex interplay of the six modes of abductive reasoning, geared toward developing a depth of understanding not allowed for generally in the broad and shallow mode of science learning used in most curricular approaches.

Therefore, the study of informal science learning is actually the study of the ways that people, and particularly for our interests, children, use meaning- oriented reasoning and inquiry to resolve certain issues and concerns that relate to their emerging understanding of science. Such a form of inquiry will necessitate and abductive-sensitive and meaning oriented style of research, such as that outlined by Shank (1994).

Navigating the World Wide Web:


There is an embarrassing lack of research on learning from the World Wide Web. We argue that this state of affairs is due largely to a lack of fit between traditional models of learning and cognition and open-ended resources like the WWW. The learner is an information seeker, not the end point of a communicative act. As we move into the information age and are inundated by increasing volumes of information, the need for reasoning skills -- rather than mastery of a subject matter -- is ever more evident. The impact of information is multidimensional. Rapidly increasing volumes of information make it impossible to "master" any domain. Even if we could master the domain, new discoveries and new understandings are developing at such a rapid rate that one's knowledge of the domain would be inadequate in a very short time. Further, our society is becoming increasingly interdisciplinary and global such that domain specific knowledge is increasing inadequate to deal with modern, real world problems. We must learn to use knowledge from a variety of perspectives and from multiple sources. The focus of education is rapidly shifting to conceiving the learner as a reasoner and problem solver.

Traditional models of inductive and deductive inference are simply inadequate in conceptualizing the skills necessary to utilize the WWW. On the web we are seeking omens and clues, diagnosing symptoms and scenarios, etc. In other words, the inferential basis of learning from the web is largely abductive (although induction and deduction may also come to the fore at various points in the information exploration process). Using a mixture of think aloud protocols and computer archival data, we are beginning to explore abductive processes in learning from the WWW. Our eventual goal is to provide computer support tools for abductive inference.

Conclusion:


The application of this new approach to dealing with, not only abduction but Peirce's classes of signs, is much wider than even hinted at in this paper. Just for openers, we suggest that these ideas can be used to build upon our understanding of abduction in general (cf. Josephson & Josephson, 1994 for the definitive current look at abduction), the development of automatic abduction, expert systems, and other computer uses (e.g., Pearl, 1988; O'Rorke, 1990), recent thoughts on induction ( e.g., Holland, Holyoak, Nisbett, & Thagard, 1989), and the teaching and development of symbolic logic (e.g., Barwise & Etchemendy, 1993).

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