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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.
 
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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| We have then three different kinds of inference:
 
| We have then three different kinds of inference:
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| Deduction or inference ''à priori'',
   
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|       Deduction or inference ''à priori'',
| Induction or inference ''à particularis'',
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|       Induction or inference ''à particularis'',
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|       Hypothesis or inference ''à posteriori''.
 
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| align="right" | (Peirce, CE 1, p. 267).
| Hypothesis or inference ''à posteriori''.
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| (C.S. Peirce, CE 1, p. 267).
   
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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''.
| 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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|       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''].
| 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''.
| 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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| align="right" | (Peirce, CE 1, p. 180).
| (C.S. Peirce, CE 1, p. 180).
   
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| width=36 |   || ''A'' || = || "Wisdom",
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| width=36 |   || ''A'' || = || “Wisdom”,
 
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|   || ''B'' || = || "a certain character",
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|   || ''B'' || = || “a certain character”,
 
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|   || ''C'' || = || "a certain conduct",
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|   || ''C'' || = || “a certain conduct”,
 
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|   || ''D'' || = || "done by a wise man",
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|   || ''D'' || = || “done by a wise man”,
 
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|   || ''E'' || = || "a certain occasion".
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|   || ''E'' || = || “a certain occasion”.
 
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| width=36 |   || ''B''  || =  || "Benevolence", a certain character,
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| width=36 |   || ''B''  || =  || “Benevolence”, a certain character,
 
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|   || ''C'' || = || "Contributes to Charity", a certain conduct,
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|   || ''C'' || = || “Contributes to Charity”, a certain conduct,
 
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|   || ''E'' || = || "Earlier today", a certain occasion.
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|   || ''E'' || = || “Earlier today”, a certain occasion.
 
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