Information AboutInquiry |
| CATEGORIES ABOUT INQUIRY | |
| logic | |
| philosophical logic | |
| philosophy of science | |
| evaluation methods | |
| thought | |
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CLASSICAL SOURCES Deduction =] Induction
Abduction The ''locus classicus'' for the study of Abductive Reasoning is found in Aristotle 's '' Prior Analytics '', Book 2, Chapt. 25. It begins this way:
By way of explanation, Aristotle supplies two very instructive examples, one for each of the two varieties of abductive inference steps that he has just described in the abstract:
Aristotle's latter variety of abductive reasoning, though it will take some explaining in the sequel, is well worth our contemplation, since it hints already at streams of inquiry that course well beyond the syllogistic source from which they spring, and into regions that Peirce will explore more broadly and deeply. INQUIRY IN THE PRAGMATIC PARADIGM In the pragmatic philosophies of Charles Sanders Peirce , William James , John Dewey , and others, inquiry is closely associated with the Normative Science of Logic . In its inception, the pragmatic model or theory of inquiry was extracted by Peirce from its raw materials in classical logic, with a little bit of help from Kant , and refined in parallel with the early development of symbolic logic by Boole , De Morgan , and Peirce himself to address problems about the nature and conduct of scientific reasoning. Borrowing a brace of concepts from Aristotle , Peirce examined three fundamental modes of reasoning that play a role in inquiry, commonly known as Abductive , Deductive , and Inductive Inference . In rough terms, '' Abduction '' is what we use to generate a likely Hypothesis or an initial Diagnosis in response to a phenomenon of interest or a problem of concern, while '' Deduction '' is used to clarify, to derive, and to explicate the relevant consequences of the selected hypothesis, and '' Induction '' is used to test the sum of the predictions against the sum of the data. It needs to be observed that the classical and pragmatic treatments of the types of reasoning, dividing the generic territory of inference as they do into three special parts, arrive at a different characterization of the environs of reason than do those accounts that count only two. These three processes typically operate in a cyclic fashion, systematically operating to reduce the uncertainties and the difficulties that initiated the inquiry in question, and in this way, to the extent that inquiry is successful, leading to an increase in knowledge or in skills. 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 end of inquiry, we should appreciate that the three kinds of inference describe a cycle that can be understood only as a whole, and none of the three 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 that 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 proper role in the whole 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 principal components. Art and science of inquiry For our present purposes, the first feature to note in distinguishing the three principal modes of reasoning from each other is whether each of them is exact or approximate in character. In this light, deduction is the only one of the three types of reasoning that can be made exact, in essence, always deriving true conclusions from true premisses, while abduction and induction are unavoidably approximate in their modes of operation, involving elements of fallible judgment in practice 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 and problems that will no doubt continue to exceed the capacities of any finite resource, human or machine, to master. Situated in this larger reality, approximations can be judged appropriate only in relation to their context of use and can be judged fitting only with regard to a purpose in view. A parallel distinction that is often made in this connection is to call deduction a '' Demonstrative '' form of inference, while abduction and induction are classed as '' Non-demonstrative '' forms of reasoning. Strictly speaking, the latter two modes 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 as useful heuristic strategies in the repertoire of the agent. But Non-demonstrative ways of thinking are inherently subject to error, and must be constantly checked out and corrected as needed in practice. In classical terminology, forms of judgment that require attention to the context and the purpose of the judgment are said to involve an element of 'art', in a sense that is judged to distinguish them from 'science', and in their renderings as expressive judgments to implicate arbiters in styles of Rhetoric , as contrasted with Logic . In a figurative sense, this means that only deductive logic can be reduced to an exact theoretical science, while the practice of any empirical science will always remain to some degree an art. Zeroth order inquiry Many aspects of inquiry can be recognized and usefully studied in very basic logical settings, even simpler than the level of Syllogism , for example, in the realm of reasoning that is variously known as '' Boolean Algebra '', '' Propositional Calculus '', '' Sentential Calculus '', or '' Zeroth-order Logic ''. By way of approaching the learning curve on the gentlest availing slope, we may well begin at the level of '' Zeroth-order Inquiry '', in effect, taking the syllogistic approach to inquiry only so far as the propositional or sentential aspects of the associated reasoning processes are concerned. One of the bonuses of doing this in the context of Peirce's logical work is that it provides us with doubly instructive exercises in the use of his Logical Graph s, taken at the level of his so-called ' Alpha Graph s'. In the case of propositional calculus or sentential logic, deduction comes down to applications of the Transitive Law for conditional implications and the approximate forms of inference hang on the properties that derive from these. In describing the various types of inference I will employ a few old 'terms of art' from classical logic that are still of use in treating these kinds of simple problems in reasoning. : Deduction takes a Case, the Minor Premiss : and combines it with a Rule,the major premiss : to arrive at a Fact, the demonstrative Conclusion : Induction takes a Case of the form : and matches it with a Fact of the form : to infer a Rule of the form : Abduction takes a Fact of the form : and matches it with a Rule of the form : to infer a Case of the form For ease of reference, Figure 1 and the Legend beneath it summarize the classical terminology for the three types of inference and the relationships among them. o -o | ||
| Deduction Takes A Case Of The Form X | > Y, |
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| Matches It With A Rule Of The Form Y | > Z, |
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| Then Adverts To A Fact Of The Form X | > Z |
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| Induction Takes A Case Of The Form X | > Y, |
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| Matches It With A Fact Of The Form X | > Z, |
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| Then Adverts To A Rule Of The Form Y | > Z |
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| Abduction Takes A Fact Of The Form X | > Z, |
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| Matches It With A Rule Of The Form Y | > Z, |
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| Then Adverts To A Case Of The Form X | > Y |
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| { Class | wikitable cellpadding="4" |
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| A | Atrocious, Adverse to All, A bad thing |
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| B | Belligerent Battle Between Brethren |
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| C | Contest of Athens against Thebes |
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| D | Debacle of Thebes against Phocis |
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| A | the Air is cool |
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| B | just Before it rains |
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| C | the Current situation |
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| D | a Dark cloud appears |
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| { Cellspacing | "4" |
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