An inquiry (also spelled as enquiry in British English) is any process that has the aim of augmenting knowledge, resolving doubt, or solving a problem. A theory of inquiry is an account of the various types of inquiry and a treatment of the ways that each type of inquiry achieves its aim.
Inquiry theories
Deduction
When three terms are so related to one another that the last is wholly contained in the middle and the middle is wholly contained in or excluded from the first, the extremes must admit of perfect syllogism. By 'middle term' I mean that which both is contained in another and contains another in itself, and which is the middle by its position also; and by 'extremes' (a) that which is contained in another, and (b) that in which another is contained. For if A is predicated of all B, and B of all C, A must necessarily be predicated of all C. ... I call this kind of figure the First. (Aristotle, Prior Analytics, 1.4)
Induction Inductive reasoning consists in establishing a relation between one extreme term and the middle term by means of the other extreme; for example, if B is the middle term of A and C, in proving by means of C that A applies to B; for this is how we effect inductions. (Aristotle, Prior Analytics, 2.23)
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: We have Reduction (απαγωγη, abduction): When it is obvious that the first term applies to the middle, but that the middle applies to the last term is not obvious, yet is nevertheless more probable or not less probable than the conclusion; Or if there are not many intermediate terms between the last and the middle; For in all such cases the effect is to bring us nearer to knowledge.
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: For example, let A stand for "that which can be taught", B for "knowledge", and C for "morality". Then that knowledge can be taught is evident; but whether virtue is knowledge is not clear. Then if BC is not less probable or is more probable than AC, we have reduction; for we are nearer to knowledge for having introduced an additional term, whereas before we had no knowledge that AC is true. Or again we have reduction if there are not many intermediate terms between B and C; for in this case too we are brought nearer to knowledge. For example, suppose that D is "to square", E "rectilinear figure", and F "circle". Assuming that between E and F there is only one intermediate term — that the circle becomes equal to a rectilinear figure by means of lunules — we should approximate to knowledge. (Aristotle, "Prior Analytics", 2.25, with minor alterations)
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.Rescher, N. (2012). Pragmatism: The Restoration of its Scientific Roots. New Brunswick, NJ: Transaction Press. 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.
In Logic: The Theory of Inquiry, John Dewey defined inquiry as "the controlled or directed transformation of an indeterminate situation into one that is so determinate in its constituent distinctions and relations as to convert the elements of the original situation into a unified whole".Dewey, John (1938). Logic: The Theory of Inquiry. New York:NY: D.C. Heath & Co.<http://www2.sunysuffolk.edu/osullis/spring07/courses/page0/history/documents_files/Dewey_pattern%20of%20inquiry.pdf > Dewey and Peirce's conception of inquiry extended beyond a system of thinking and incorporated the social nature of inquiry. These ideas are summarize in the notion Community of inquiry.Wikisource:The Fixation of Belief
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 premises, 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.
Limits to inquiry C. S. Peirce argued that inquiry reaches a logical limit, or "approximate[s] indefinitely toward that limit", which he regarded as "truth".Legg, C., Charles Peirce’s Limit Concept of Truth, Philosophy Compass 9 (3):204-213, published 5 March 2014, accessed 26 May 2024
Jewish rabbinical writers used the text of Deuteronomy 4:32 in the Hebrew Bible, or ask now concerning the days that are past, which were before you, since the day that God created man on the earth, and ask from one end of heaven to the other, whether any great thing like this has happened, or anything like it has been heard,: New King James Version to impose ethical limits on inquiry, forbidding inquiry into the work of creation in the presence of two people, reading the words "for ask now of the days past" to indicate that one may inquire, but not two. The Rabbis reasoned that the words "since the day that God created man upon the earth" in this verse taught that one must not inquire concerning the time before creation, but that the words "the days past that were before you" meant that one may inquire about the six days of creation. They further reasoned that the words "from the one end of heaven to the other" indicated that one must not inquire about what is beyond the universe, what is above and what is below, what is before and what is after.Babylonian Talmud Chagigah 11b
Zeroth order inquiry Many aspects of inquiry can be studied in very simple logical settings, even simpler than the level of syllogism. The sorts of reasoning used by Boolean algebra, propositional logic, or zeroth-order logic can be taken as examples of this. 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 graphs, taken at the level of his so-called "alpha graphs".
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 the following employs 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 premise and combines it with a Rule, the major premise 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