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===1.2. Types of Reasoning in C.S. Peirce===
 
===1.2. Types of Reasoning in C.S. Peirce===
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Here we present one of Peirce's earliest treatments of the three types of reasoning, from his Harvard Lectures of 1865 "On the Logic of Science".  It illustrates how one and the same proposition might be reached from three different directions, as the end result of an inference in each of the three modes.
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{| cellpadding=2
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| width=36 |  
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| We have then three different kinds of inference:
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{| cellpadding=2
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| Deduction or inference ''à priori'',
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|-
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|  
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| Induction or inference ''à particularis'',
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|-
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|  
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| Hypothesis or inference ''à posteriori''.
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|}
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{| cellpadding=2
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| width=36 |  
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| (C.S. Peirce, CE 1, p. 267).
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{| cellpadding=2 width=50%
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| If I reason that certain conduct is wise because it has a character which belongs ''only'' to wise things, I reason ''à priori''.
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|-
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| 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''].
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| 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''.
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|-
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| (C.S. Peirce, CE 1, p. 180).
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|}
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Suppose we make the following assignments:
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{|
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| width=36 |   || ''A'' || = || "Wisdom",
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|-
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|   || ''B'' || = || "a certain character",
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|-
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|   || ''C'' || = || "a certain conduct",
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|-
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|   || ''D'' || = || "done by a wise man",
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|-
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|   || ''E'' || = || "a certain occasion".
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|}
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Recognizing that a little more concreteness will aid the understanding, let us make the following substitutions in Peirce's example:
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{|
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| width=36 |   || ''B''  || =  || "Benevolence", a certain character,
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|-
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|   || ''C'' || = || "Contributes to Charity", a certain conduct,
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|-
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|   || ''E'' || = || "Earlier today", a certain occasion.
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|}
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The converging operation of all three reasonings is shown in Figure 5.
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<pre>
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o---------------------------------------------------------------------o
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|                                                                    |
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|  D ("done by a wise man")                                          |
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|  o                                                                |
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|    \*                                                              |
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|    \ *                                                            |
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|      \  *                                                          |
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|      \  *                                                        |
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|        \    *                                                      |
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|        \    *                                                    |
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|          \      * A ("a wise act")                                  |
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|          \      o                                                |
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|            \    /| *                                              |
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|            \  / |  *                                            |
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|              \ /  |    *                                          |
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|              .  |      o B ("benevolence", a certain character)  |
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|              / \  |    *                                          |
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|            /  \ |  *                                            |
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|            /    \| *                                              |
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|          /      o                                                |
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|          /      * C ("contributes to charity", a certain conduct)  |
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|        /    *                                                    |
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|        /    *                                                      |
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|      /  *                                                        |
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|      /  *                                                          |
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|    / *                                                            |
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|    /*                                                              |
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|  o                                                                |
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|  E ("earlier today", a certain occasion)                            |
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|                                                                    |
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o---------------------------------------------------------------------o
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Figure 5.  A Thrice Wise Act
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</pre>
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The common proposition that concludes each argument is ''AC'', to wit, "contributing to charity is wise".
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Deduction could have obtained the Fact ''AC'' from the Rule ''AB'', "benevolence is wisdom", along with the Case ''BC'', "contributing to charity is benevolent".
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Induction could have gathered the Rule ''AC'', after a manner of saying that "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".
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Abduction could have guessed the Case ''AC'', in a style of expression stating that "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 that is wise is done by this wise man".  Thus, a wise man, who happens to do all of the wise things that there are to do, may nevertheless contribute to charity for no good reason, and even be known to be charitable to a fault.  But all of this notwithstanding, on seeing the wise man contribute to charity we may find it natural to conjecture, in effect, to consider it as a possibility worth examining further, that charity is indeed a mark of his wisdom, and not just the accidental trait or the immaterial peculiarity of his character — in essence, that wisdom is the "reason" that he contributes to charity.
    
===1.3. Comparison of the Analyses===
 
===1.3. Comparison of the Analyses===
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