## Functional Logic • Inquiry and Analogy • 2

### Inquiry and Analogy • Three Types of Reasoning

#### Types of Reasoning in C.S. Peirce

Peirce gives one of his earliest treatments of the three types of reasoning in his Harvard Lectures of 1865 “On the Logic of Science”.  There he shows how the same proposition may be reached from three directions, as the result of an inference in each of the three modes.

We have then three different kinds of inference.

• Deduction or inference à priori,
• Induction or inference à particularis,
• Hypothesis or inference à posteriori.

(Peirce, CE 1, 267).

• If I reason that certain conduct is wise because it has a character which belongs only to wise things, I reason à priori.
• If I think it is wise because it once turned out to be wise, that is, if I infer that it is wise on this occasion because it was wise on that occasion, I reason inductively [à particularis].
• But if I think it is wise because a wise man does it, I then make the pure hypothesis that he does it because he is wise, and I reason à posteriori.

(Peirce, CE 1, 180).

Suppose we make the following assignments.

$\begin{array}{lll} \mathrm{A} & = & \text{Wisdom} \\ \mathrm{B} & = & \text{a certain character} \\ \mathrm{C} & = & \text{a certain conduct} \\ \mathrm{D} & = & \text{done by a wise man} \\ \mathrm{E} & = & \text{a certain occasion} \end{array}$

Recognizing a little more concreteness will aid understanding, let us make the following substitutions in Peirce’s example.

$\begin{array}{lllll} \mathrm{B} & = & \text{Benevolence} & = & \text{a certain character} \\ \mathrm{C} & = & \text{Contributes to Charity} & = & \text{a certain conduct} \\ \mathrm{E} & = & \text{Earlier today} & = & \text{a certain occasion} \end{array}$

The converging operation of all three reasonings is shown in Figure 2.

$\text{Figure 2. A Triply Wise Act}$

The common proposition concluding each argument is AC, contributing to charity is wise.

• Deduction could have obtained the Fact AC from the Rule AB, benevolence is wisdom, along with the Case BC, contributing to charity is benevolent.
• Induction could have gathered the Rule AC, contributing to charity is exemplary of wisdom, from the Fact AE, the act of earlier today is wise, along with the Case CE, the act of earlier today was an instance of contributing to charity.
• Abduction could have guessed the Case AC, contributing to charity is explained by wisdom, from the Fact DC, contributing to charity is done by this wise man, and the Rule DA, everything wise is done by this wise man.  Thus, a wise man, who does all the wise things there are to do, may nonetheless contribute to charity for no good reason and even be charitable to a fault.  But on seeing the wise man contribute to charity it is natural to think charity may well be the mark of his wisdom, in essence, that wisdom is the reason he contributes to charity.

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