Functional Logic • Inquiry and Analogy • 7

Inquiry and AnalogyPeirce’s Formulation of AnalogyVersion 2

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.

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

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 • 7

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

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