## Abduction, Deduction, Induction, Analogy, Inquiry • 20

In passing from a sign-relational account to a propositional analysis of Dewey’s story there is an old mathematical trick, analogous to the method of adding fractions by expressing them over a common denominator, that comes in handy.

The general idea is that we introduce a new term ${C}$ to denote the Current situation.  In the example at hand, letting ${A}$ be the proposition that the Air is cool, we can express our hero’s initial observation by means of the following premiss:

• Fact : ${C \Rightarrow A},$   In the Current situation the Air is cool.

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:

• Rule : ${B \Rightarrow A},$   Just Before it rains, the Air is cool.

This Rule can be recognized as having a potential relevance to the situation because it matches the surprising Fact, ${C \Rightarrow A},$ in its consequential feature ${A}.$

All of this suggests that the present Case may be one in which it is just about to rain:

• Case : ${C \Rightarrow B},$   The Current situation is just Before it rains.

The whole mental performance, however automatic and semi-conscious it may be, that leads from a problematic Fact and a previously settled knowledge base of Rules to the plausible suggestion of a Case description, is what we are calling an abductive inference.

The above is the first part of a “Zeroth Order” logical analysis of Dewey’s Sign of Rain story that I’ve posted a number of times around the web.  The rest of the analysis can be found at the following location.

### Reference

cc: Peirce List (1) (2) (3) (4) (5) (6) (7) (8)

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