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.
Recognizing a little more concreteness will aid understanding, let us make the following substitutions in Peirce’s example.
The converging operation of all three reasonings is shown in Figure 2.
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.
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
cc: FB | Peirce Matters • Laws of Form • Mathstodon • Ontolog • Academia.edu
cc: Conceptual Graphs • Cybernetics • Structural Modeling • Systems Science
and 
will denote a servant of every man that is a servant of every woman. So that
and we notice a triple 
where 
and 
have a character 
in common. We may quite naturally be tempted to make a further leap and suppose the sign 
precisely by virtue of the character 
I know that looks like a lot of supposing but the fact is we do the like all the time without hardly giving it a second thought. But critical reflection demands we bat an 
As long as we remain content to operate in a theoretical vacuum devoid of empirical grounding, who’s to say any number of them do not qualify?
to model an empirical system of interpretive practice, whether its agent is a single individual or a whole community of interpretation. The question is — Do the characters we mark as effective in our model actually do the job for the agent?
to describe their structures. That amounts to loose speech on my part and I may have to reform my Sprach at a later stage of the Spiel.
whose result must stay within the class of dyadic relations. We can draw that distinction by means of an adjective or a substantive term — so long as we see it we can parse the words later.
Inquiry Into Inquiry 