Functional Logic • Inquiry and Analogy • 6

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.

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

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