Functional Logic • Inquiry and Analogy • 9

Inquiry and Analogy • Dewey’s “Sign of Rain” • An Example of Inquiry

We turn again to Dewey’s vignette, tracing figures of logic on grounds of semiotic.

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.

(John Dewey, How We Think, 6–7)

Inquiry and Inference

If we follow Dewey’s “Sign of Rain” example far enough to consider the import of thought for action, we realize the subsequent conduct of the interpreter, progressing up through the natural conclusion of the episode — the quickening steps, seeking shelter in time to escape the rain — all those acts form a series of further interpretants, contingent on the active causes of the individual, for the originally recognized signs of rain and the first impressions of the actual case.  Just as critical reflection develops the associated and alternative signs which gather about an idea, pragmatic interpretation explores the consequential and contrasting actions which give effective and testable meaning to a person’s belief in it.

Figure 10 charts the progress of inquiry in Dewey’s “Sign of Rain” example according to the stages of reasoning identified by Peirce, focusing on the compound or mixed form of inference formed by the first two steps.

$\text{Figure 10. Cycle of Inquiry}$

• Step 1 is Abductive, abstracting a Case from the consideration of a Fact and a Rule.
• $\begin{array}{lll} \textsc{Fact} & : & {C \Rightarrow A}, \end{array}$     In the Current situation the Air is cool.
• $\begin{array}{lll} \textsc{Rule} & : & {B \Rightarrow A}, \end{array}$     Just Before it rains, the Air is cool.
• $\begin{array}{lll} \textsc{Case} & : & {C \Rightarrow B}, \end{array}$     The Current situation is just Before it rains.
• Step 2 is Deductive, admitting the Case to another Rule and arriving at a novel Fact.
• $\begin{array}{lll} \textsc{Case} & : & {C \Rightarrow B}, \end{array}$     The Current situation is just Before it rains.
• $\begin{array}{lll} \textsc{Rule} & : & {B \Rightarrow D}, \end{array}$     Just Before it rains, a Dark cloud will appear.
• $\begin{array}{lll} \textsc{Fact} & : & {C \Rightarrow D}, \end{array}$     In the Current situation, a Dark cloud will appear.

What precedes is nowhere near a complete analysis of Dewey’s example, even so far as it might be carried out within the constraints of the syllogistic framework, and it covers only the first two steps of the inquiry process, but perhaps it will do for a start.