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====4.3.1. Introduction====
====4.3.1. Introduction====
The pragmatic theory or model of inquiry was extracted by C.S. Peirce from basic materials in classical logic and refined in parallel with the historical development of symbolic logic to address problems about the nature of scientific reasoning. Borrowing on concepts from Aristotle, Peirce identified three fundamental modes of reasoning, called deductive, inductive, and abductive inference. In rough terms, "abduction" is what one uses to generate a likely hypothesis or initial diagnosis in response to a phenomenon or a problem of interest, while "deduction" is used to clarify and derive relevant consequences of one's hypotheses, and where "induction" is used to test the sum of one's predictions against the sum of the data that is gleaned from experience. Generally speaking, these three processes operate in a cyclic fashion, systematically reducing the uncertainties and the difficulties which initiate inquiry, and thereby leading to an increase in knowledge.
In the pragmatic way of thinking everything has a purpose, and the purpose of each thing is the first thing we should try to note about it. The purpose of inquiry is to reduce doubt and lead to a state of belief, which a person in that state will usually call knowledge or certainty. As they contribute to the purpose of inquiry, we should appreciate that the three kinds of inference form a cycle that can only be understood as a whole, and none of them makes complete sense in isolation from the others. For instance, the purpose of abduction is to generate guesses of a kind that deduction can explicate and induction can evaluate. This places a mild but meaningful constraint on the production of hypotheses, since it is not just any wild guess at explanation that submits itself to reason and bows out when defeated in a match with reality. In a similar fashion, each of the other types of inference realizes its purpose only in accord with its role in the cycle of inquiry. No matter how much it may be necessary to study these processes in abstraction from each other, the integrity of inquiry places strong limitations on the effective modularity of its components.
For our present purposes, the first feature to note in distinguishing these modes of reasoning is whether they are exact or approximate in character. Deduction is the only type of reasoning that can be made exact, always deriving true conclusions from true premisses, while induction and abduction are unavoidably approximate in their mode of operation, involving elements of fallible judgment and inescapable error in their application. The reason for this is that deduction, in the ideal limit, can be rendered a purely internal process of the reasoning agent, while the other two modes of reasoning essentially demand a constant interaction with the outside world, a source of phenomena that will no doubt keep exceeding any finite resource, human or machine. Embedded in this larger reality, approximations can only be judged appropriate in relation to a context of use and a purpose in view.
A parallel distinction made in this connection is to call deduction a demonstrative inference, while abduction and induction are classed as non demonstrative forms of reasoning. Strictly speaking, the latter types of reasoning are not properly called inferences at all. They are more like controlled associations of words or ideas that just happen to be successful often enough to be preserved. But non demonstrative ways of thinking are inherently subject to error, and must be checked out in practice.
In classical terminology, forms of judgment that require attention to context and purpose are said to involve elements of art, as compared with science, and rhetoric, as contrasted with logic. In a figurative sense, this means that only deductive logic can be reduced to an exact science, while the practice of empirical science will always remain to some degree an art. This fact has important implications for any attempt to support inquiry with automated procedures, constraining both the manner and degree of likely success. It means that inquiry software will need to be highly interactive, sensitive to run time conditions at two kinds of interfaces, those with its human users and those with the real world. Further, it means that the main effect of automation will be to speed up and strengthen deductive reasoning. The chief assistance that computation provides to induction is through measures of fit between theoretical constructs and empirical data sets. The limited guidance that formal methods can bring to hypothesis generation is restricted to checking the partly logical property of falsifiability and speeding up the subsequent evaluation process. However, because inquiry is an iterative cycle, improving the rate of performance at any bottleneck can serve to accelerate the entire process.
As far as automating induction goes, we should not expect a program to make up the data for us, no matter how sophisticated it gets! Inductive tests can provide measures of how well a theoretical construct fits a set of data, but no fit is perfect, or intended to be. An inductive concept is supposed to present a simplification of a complex reality, otherwise it would serve no function over and above just staring at the data. In gauging the slippage between concept and data, the degree of tolerance acceptable in a given situation is a matter of discretionary judgments that have to be made under field conditions.
When it comes to automating abductive reasoning, we should observe the historical circumstance that it is often the most "unlikely" set of hypotheses that turn out to form the correct conceptual framework, at least when that likelihood has been judged from the standpoint of the previous framework. Aside from their responsibilities to the inquiry process, abductive hypotheses can be freely generated in the most creative manner possible. Breaking the mind-set of the problem as stated and reformulating data descriptions from new perspectives are just some of the allowable strategies that are required for success.
Abductive reasoning is the mode of operation which is involved in shifting from one paradigm to another. In order to reduce the overall tension of uncertainty in a knowledge base, it is often necessary to restructure our perspective on the data in radical ways, to change the channel that parcels out information to us. But the true value of a new paradigm is typically not appreciated from the standpoint of another model, that is, not until it has had time to reorganize the knowledge base in ways that demonstrate clear advantages to the community of inquiry concerned.
The preceding survey has introduced a model of inquiry and charted a series of limits on the automation of inquiry. We should not be too discouraged by the acknowledgement of these limits. But we ought to notice that these constraints are not so much limits on the computational extension of human inquiry as they are limits on the instrumental nature of inquiry itself, being the specific adaptation of a finite creature to an infinite world. In other words, these are only the familiar limits of the scientific method. They are the limits that make it a method.
I now return to discussing the pragmatic theory of inquiry, treating its positive features in more depth. I will examine the theory in terms of a canonical model that illustates generic aspects of inquiry processes. My plan for the remainder of this section is to introduce basic terminology and issues.
Inquiry is a form of reasoning process, and therefore a manner of thinking. Pragmatist philosophers hold that all thought takes place in "signs", which is the word they use for the most general class of signals, messages, symbolic expressions, etc. that might be imagined. Even ideas and concepts are held to be a special class of signs, namely, internal states of the thinking agent that result from the interpretation of external signs. The subsumption of inquiry within reasoning and of thinking within sign processes allows us to approach the subject of inquiry from two perspectives. The "syllogistic approach" views inquiry as a logical species. The "sign-theoretic" approach views inquiry within a more general setting of sign processes.
The best point of departure I know for both approaches to inquiry is the following story of inquiry activities in everyday life, as told by John Dewey.
{| align="center" cellpadding="0" cellspacing="0" width="90%"
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<p>A man is walking on a warm day. The sky was clear the last time he observed it; but presently he notes, while occupied primarily with other things, that the air is cooler. It occurs to him that it is probably going to rain; looking up, he sees a dark cloud between him and the sun, and he then quickens his steps. What, if anything, in such a situation can be called thought? Neither the act of walking nor the noting of the cold is a thought. Walking is one direction of activity; looking and noting are other modes of activity. The likelihood that it will rain is, however, something ''suggested''. The pedestrian ''feels'' the cold; he ''thinks of'' clouds and a coming shower. (Dewey, 1910, 6–7)</p>
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I now proceed to analyze this example from the standpoints of the syllogistic and sign-theoretic approaches. The ultimate task before us is to understand the relation between these two perspectives as they are unified in a single, coherent subject.
====4.3.2. The Types of Reasoning====
====4.3.2. The Types of Reasoning====
