Page 9 - A Fortiori Logic: Innovations, History and Assessments
P. 9


AVI SION / A FORTIORI LOGIC 3





Contents in detail
Abstract ............................................................................................................................................. 1 
Foreword ............................................................................................................................................. 8 
1.  Innovations .............................................................................................................................. 8 
2.  History ..................................................................................................................................... 9 
3.  Assessments ............................................................................................................................. 9 
PART I - FORMALITIES ............................................................................................................. 10 
1.  The standard forms .................................................................................................................... 10 
1.  Copulative a fortiori arguments ............................................................................................. 10 
2.  Implicational a fortiori arguments ......................................................................................... 15 
3.  Validations ............................................................................................................................. 17 
4.  Ranging from zero or less ..................................................................................................... 26 
5.  Secondary moods .................................................................................................................. 30 
2.  More formalities ........................................................................................................................ 35 
1.  Species and Genera ............................................................................................................... 35 
2.  Proportionality ....................................................................................................................... 37 
3.  A crescendo argument ........................................................................................................... 40 
4.  Hermeneutics ......................................................................................................................... 45 
5.  Relative middle terms ............................................................................................................ 47 
3.  Still more formalities ................................................................................................................. 54 
1.  Understanding the laws of thought ........................................................................................ 54 
2.  Quantification ........................................................................................................................ 56 
3.  A fortiori through induction .................................................................................................. 60 
4.  Antithetical items .................................................................................................................. 67 
5.  Traductions ............................................................................................................................ 72 
4.  Apparently variant forms ........................................................................................................... 79 
1.  Variations in form and content .............................................................................................. 79 
2.  Logical-epistemic a fortiori ................................................................................................... 81 
3.  Ethical-legal a fortiori ........................................................................................................... 83 
4.  There are no really hybrid forms ........................................................................................... 84 
5.  Probable inferences ............................................................................................................... 86 
6.  Correlating ontical and probabilistic forms ........................................................................... 89 
5.  Comparisons and correlations ................................................................................................... 92 
1.  Analogical argument ............................................................................................................. 92 
2.  Is a fortiori argument syllogism? ........................................................................................... 98 
3.  Correlating arguments ........................................................................................................... 99 
4.  Structural comparisons ........................................................................................................ 100 
5.  From syllogism to a fortiori argument ................................................................................. 101 
6.  From a fortiori argument to syllogism ................................................................................. 105 
7.  Reiterating translations ........................................................................................................ 107 
8.  Lessons learned ................................................................................................................... 109 
PART II – ANCIENT AND MEDIEVAL HISTORY ............................................................... 110 
6.  A fortiori in Greece and Rome ................................................................................................ 110 
1.  Aristotle’s observations ....................................................................................................... 110 
2.  The Kneales’ list .................................................................................................................. 116 
3.  Aristotle in practice ............................................................................................................. 118 
4.  Relation to syllogism ........................................................................................................... 120 
5.  Cicero .................................................................................................................................. 122 
6.  Alexander of Aphrodisias .................................................................................................... 125 
7.  Historical questions ............................................................................................................. 127 

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