Inquiry and Analogy • Peirce’s Formulation of Analogy • Version 2
C.S. Peirce • “A Theory of Probable Inference” (1883)
The formula of the analogical inference presents, therefore, three premisses, thus:
![\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}](https://s0.wp.com/latex.php?latex=%5Cbegin%7Bmatrix%7D++T+%7E%5Ctext%7Bis%7D%7E+P%5E%7B%5Cprime%7D%2C+P%5E%7B%5Cprime%5Cprime%7D%2C+P%5E%7B%5Cprime%5Cprime%5Cprime%7D%3B++%5C%5C%5B4pt%5D++S%5E%7B%5Cprime%7D%2C+S%5E%7B%5Cprime%5Cprime%7D%2C+S%5E%7B%5Cprime%5Cprime%5Cprime%7D%2C+%7E%5Ctext%7Bare%7D%7E+Q%5Ctext%7B%27s%7D%3B++%5C%5C%5B4pt%5D++%5Ctext%7BHence%2C%7D%7E+T+%7E%5Ctext%7Bis+a%7D%7E+Q.++%5Cend%7Bmatrix%7D&bg=ffffff&fg=000000&s=0&c=20201002)
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}](https://s0.wp.com/latex.php?latex=%5Cbegin%7Barray%7D%7Bl%7Cl%7D++%5Ctext%7BEvery%7D%7E+X+%7E%5Ctext%7Bis%2C+for+example%2C%7D%7E+P%5E%7B%5Cprime%7D%2C+P%5E%7B%5Cprime%5Cprime%7D%2C+P%5E%7B%5Cprime%5Cprime%5Cprime%7D%2C+%7E%5Ctext%7Betc.%7D%2C++%26++S%5E%7B%5Cprime%7D%2C+S%5E%7B%5Cprime%5Cprime%7D%2C+S%5E%7B%5Cprime%5Cprime%5Cprime%7D%2C+%7E%5Ctext%7Betc.%2C+are+samples+of+the%7D%7E+X%5Ctext%7B%27s%7D%2C++%5C%5C%5B4pt%5D++T+%7E%5Ctext%7Bis+found+to+be%7D%7E+P%5E%7B%5Cprime%7D%2C+P%5E%7B%5Cprime%5Cprime%7D%2C+P%5E%7B%5Cprime%5Cprime%5Cprime%7D%2C+%7E%5Ctext%7Betc.%7D%3B++%26++S%5E%7B%5Cprime%7D%2C+S%5E%7B%5Cprime%5Cprime%7D%2C+S%5E%7B%5Cprime%5Cprime%5Cprime%7D%2C+%7E%5Ctext%7Betc.%2C+are+found+to+be%7D%7E+Q%5Ctext%7B%27s%7D%3B++%5C%5C%5B4pt%5D++%5Ctext%7BHence%2C+hypothetically%2C%7D%7E+T+%7E%5Ctext%7Bis+an%7D%7E+X.++%26++%5Ctext%7BHence%2C+inductively%2C+every%7D%7E+X+%7E%5Ctext%7Bis+a%7D%7E+Q.++%5Cend%7Barray%7D&bg=ffffff&fg=000000&s=-1&c=20201002)
(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.
Resources
- Logic Syllabus
- Boolean Function
- Boolean-Valued Function
- Logical Conjunction
- Minimal Negation Operator
- Functional Logic • Part 1 • Part 2 • Part 3
- Cactus Language • Part 1 • Part 2 • Part 3 • References • Document History
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