Inquiry

An inquiry (also spelled as enquiry in British English)[a][b] is any process that has the aim of augmenting knowledge, resolving doubt, or solving a problem.

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.

In the pragmatic philosophies of Charles Sanders Peirce, William James, John Dewey, and others, inquiry is closely associated with the normative science of logic.

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.

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.

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 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.

In its original usage a statement of Fact has to do with a deed done or a record made, that is, a type of event that is openly observable and not riddled with speculation as to its very occurrence.

When the time comes to branch out from the syllogistic framework, we will find that propositional constraints can be discovered and represented in arbitrary syntactic forms.

Let's first give Dewey's example of inquiry in everyday life the quick once over, hitting just the high points of its analysis into Peirce's three kinds of reasoning.

In Dewey's "Rainy Day" or "Sign of Rain" story, we find our peripatetic hero presented with a surprising Fact: Responding to an intellectual reflex of puzzlement about the situation, his resource of common knowledge about the world is impelled to seize on an approximate Rule: This Rule can be recognized as having a potential relevance to the situation because it matches the surprising Fact, C → A, in its consequential feature A.

The next phase of inquiry uses deductive inference to expand the implied consequences of the abductive hypothesis, with the aim of testing its truth.

So let us imagine that our up-looker has a more deliberate purpose in mind, and that his search for additional data is driven by the new-found, determinate Rule: Contemplating the assumed Case in combination with this new Rule leads him by an immediate deduction to predict an additional Fact: The reconstructed picture of reasoning assembled in this second phase of inquiry is true to the pattern of deductive inference.

The explanation of imminent rain removes the discrepancy between observations and expectations and thereby reduces the shock of surprise that made this process of inquiry necessary.

Peirce noted similar forms of duality in many of his early writings, leading to the consummate treatment in his 1867 paper "On a New List of Categories" (CP 1.545-559, W 2, 49-59).

Inductive reasoning is involved in the learning and the transfer of these rules, both in accumulating a knowledge base and in carrying it through the times between acquisition and application.

For example, a rule like: is usually induced from a consideration of many past events, in a manner that can be rationally reconstructed as follows: However, the very same proposition could also be abduced as an explanation of a singular occurrence or deduced as a conclusion of a presumptive theory.

In these terms, the "analogy of experience" proceeds by inducing a Rule about the validity of a current knowledge base and then deducing a Fact, its applicability to a current experience, as in the following sequence: Inductive Phase: Deductive Phase: If the observer looks up and does not see dark clouds, or if he runs for shelter but it does not rain, then there is fresh occasion to question the utility or the validity of his knowledge base.