Functional Logic • Inquiry and Analogy • 6

Inquiry and AnalogyPeirce’s Formulation of AnalogyVersion 1

C.S. Peirce • “On the Natural Classification of Arguments” (1867)

The formula of analogy is as follows:

S^{\prime}, S^{\prime\prime}, \text{and}~ S^{\prime\prime\prime} are taken at random from such a class that their characters at random are such as {P^{\prime}, P^{\prime\prime}, P^{\prime\prime\prime}}.

\begin{matrix}  T ~\text{is}~ P^{\prime}, P^{\prime\prime}, P^{\prime\prime\prime},  \\[4pt]  S^{\prime}, S^{\prime\prime}, S^{\prime\prime\prime} ~\text{are}~ Q;  \\[4pt]  \therefore T ~\text{is}~ Q.  \end{matrix}

Such an argument is double.  It combines the two following:

\begin{matrix}  1.  \\[4pt]  S^{\prime}, S^{\prime\prime}, S^{\prime\prime\prime} ~\text{are taken as being}~ P^{\prime}, P^{\prime\prime}, P^{\prime\prime\prime},  \\[4pt]  S^{\prime}, S^{\prime\prime}, S^{\prime\prime\prime} ~\text{are}~ Q;  \\[4pt]  \therefore ~(\text{By induction})~ P^{\prime}, P^{\prime\prime}, P^{\prime\prime\prime} ~\text{is}~ Q,  \\[4pt]  T ~\text{is}~ P^{\prime}, P^{\prime\prime}, P^{\prime\prime\prime};  \\[4pt]  \therefore ~(\text{Deductively})~ T ~\text{is}~ Q.  \end{matrix}

\begin{matrix}  2.  \\[4pt]  S^{\prime}, S^{\prime\prime}, S^{\prime\prime\prime} ~\text{are, for instance,}~ P^{\prime}, P^{\prime\prime}, P^{\prime\prime\prime},  \\[4pt]  T ~\text{is}~ P^{\prime}, P^{\prime\prime}, P^{\prime\prime\prime};  \\[4pt]  \therefore ~(\text{By hypothesis})~ T ~\text{has the common characters of}~ S^{\prime}, S^{\prime\prime}, S^{\prime\prime\prime},  \\[4pt]  S^{\prime}, S^{\prime\prime}, S^{\prime\prime\prime} ~\text{are}~ Q;  \\[4pt]  \therefore ~(\text{Deductively})~ T ~\text{is}~ Q.  \end{matrix}

Owing to its double character, analogy is very strong with only a moderate number of instances.

(Peirce, CP 2.513, CE 2, 46–47)

Figure 7 shows the logical relationships involved in the above analysis.

Peirce's Formulation of Analogy (Version 1)
\text{Figure 7. Peirce's Formulation of Analogy (Version 1)}

Resources

cc: Conceptual GraphsCyberneticsLaws of FormOntolog Forum
cc: FB | Peirce MattersStructural ModelingSystems Science

This entry was posted in Abduction, Analogy, Argument, Aristotle, C.S. Peirce, Constraint, Deduction, Determination, Diagrammatic Reasoning, Diagrams, Differential Logic, Functional Logic, Hypothesis, Indication, Induction, Inference, Information, Inquiry, Logic, Logic of Science, Mathematics, Pragmatic Semiotic Information, Probable Reasoning, Propositional Calculus, Propositions, Reasoning, Retroduction, Semiotics, Sign Relations, Syllogism, Triadic Relations, Visualization and tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , . Bookmark the permalink.

1 Response to Functional Logic • Inquiry and Analogy • 6

  1. Pingback: Survey of Abduction, Deduction, Induction, Analogy, Inquiry • 2 | Inquiry Into Inquiry

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