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==1. Three Types of Reasoning==

==1. Three Types of Reasoning==

===1.1. Types of Reasoning in Aristotle===

===1.1. Types of Reasoning in Aristotle===

(See Figure 1.) …

(See Figure 1.) …

===1.2. Types of Reasoning in C.S. Peirce===

===1.2. Types of Reasoning in C.S. Peirce===

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The converging operation of all three reasonings is shown in Figure 5.

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

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{| align="center" style="text-align:center"

|                                                                    |

|                                                                    |

o---------------------------------------------------------------------o

o---------------------------------------------------------------------o

Figure 5.  A Thrice Wise Act

Figure 2.  A Thrice Wise Act

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===1.3. Comparison of the Analyses===

===1.3. Comparison of the Analyses===

&hellip;

(See Figures&nbsp;3 and 4.) &hellip;

 

 

===1.4. Aristotle's &ldquo;Apagogy&rdquo; : Abductive Reasoning as Problem Reduction===

===1.4. Aristotle's &ldquo;Apagogy&rdquo; : Abductive Reasoning as Problem Reduction===

If virtue is a form of understanding, and if we are willing to grant that understanding can be taught, then virtue can be taught.  In this way of approaching the problem, by detour and indirection, the form of abductive reasoning is used to shift the attack from the original question, whether virtue can be taught, to the hopefully easier question, whether virtue is a form of understanding.

If virtue is a form of understanding, and if we are willing to grant that understanding can be taught, then virtue can be taught.  In this way of approaching the problem, by detour and indirection, the form of abductive reasoning is used to shift the attack from the original question, whether virtue can be taught, to the hopefully easier question, whether virtue is a form of understanding.

The logical structure of the process of hypothesis formation in the first example follows the pattern of &ldquo;abduction to a case&rdquo;, whose abstract form is diagrammed and schematized in Figure&nbsp;6.

The logical structure of the process of hypothesis formation in the first example follows the pattern of &ldquo;abduction to a case&rdquo;, whose abstract form is diagrammed and schematized in Figure&nbsp;5.

{| align="center" style="text-align:center"

{| align="center" style="text-align:center"

|  Case:  V => U?                                |

|  Case:  V => U?                                |

o-------------------------------------------------o

o-------------------------------------------------o

Figure 6.  Teachability, Understanding, Virtue

Figure 5.  Teachability, Understanding, Virtue

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(See Figure 5.) &hellip;

(See Figure&nbsp;6.) &hellip;

 

Figure 6.  Aristotle's &ldquo;Paradigm&rdquo;

===1.6. Peirce's Formulation of Analogy===

===1.6. Peirce's Formulation of Analogy===