## Functional Logic • Inquiry and Analogy • 7

### C.S. Peirce • “A Theory of Probable Inference” (1883)

The formula of the analogical inference presents, therefore, three premisses, thus:

$S^{\prime}, S^{\prime\prime}, S^{\prime\prime\prime},$ are a random sample of some undefined class $X,$ of whose characters $P^{\prime}, P^{\prime\prime}, P^{\prime\prime\prime},$ are samples,

$\begin{matrix} T ~\text{is}~ P^{\prime}, P^{\prime\prime}, P^{\prime\prime\prime}; \\[4pt] S^{\prime}, S^{\prime\prime}, S^{\prime\prime\prime}, ~\text{are}~ Q\text{'s}; \\[4pt] \text{Hence,}~ T ~\text{is a}~ Q. \end{matrix}$

We have evidently here an induction and an hypothesis followed by a deduction;  thus:

$\begin{array}{l|l} \text{Every}~ X ~\text{is, for example,}~ P^{\prime}, P^{\prime\prime}, P^{\prime\prime\prime}, ~\text{etc.}, & S^{\prime}, S^{\prime\prime}, S^{\prime\prime\prime}, ~\text{etc., are samples of the}~ X\text{'s}, \\[4pt] T ~\text{is found to be}~ P^{\prime}, P^{\prime\prime}, P^{\prime\prime\prime}, ~\text{etc.}; & S^{\prime}, S^{\prime\prime}, S^{\prime\prime\prime}, ~\text{etc., are found to be}~ Q\text{'s}; \\[4pt] \text{Hence, hypothetically,}~ T ~\text{is an}~ X. & \text{Hence, inductively, every}~ X ~\text{is a}~ Q. \end{array}$

$\text{Hence, deductively,}~ T ~\text{is a}~ Q.$

(Peirce, CP 2.733, with a few changes in Peirce’s notation to facilitate comparison between the two versions)

Figure 8 shows the logical relationships involved in the above analysis.

$\text{Figure 8. Peirce's Formulation of Analogy (Version 2)}$

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