Qal Vachomer Arguments
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A Contemporary Examination of the A Fortiori Argument Involving Jewish Traditions by Allen Conan Wiseman A thesis presented to the University of Waterloo in fulfilment of the thesis requirement for the degree of Doctor of Philosophy in Philosophy Waterloo, Ontario, Canada, 2010 © Allen Conan Wiseman 2010 I hereby declare that I am the sole author of this thesis. This is a true copy of the thesis, including any required final revisions as accepted by my examiners. I understand that my thesis may be made electronically available to the public ii Abstract This study proposes to clarify the a fortiori argument‘s components, structure, definitions, formulations, and logical status, as well as the specific conditions under which it is to be employed, both generally and in a Jewish context. Typically, the argument claims this: if a lesser (or greater) case has a feature, a correspondingly greater (or lesser) case has that feature too. While evident in ancient thought, the argument is often central to Jewish deliberations that may continue for centuries; so this Jewish use forms the main context and material of this study. However, as general reasoning employs the argument, tracing its common forms helps to delineate its terms and relations. While the argument aspires to be true and it can be deductively valid in those cases where heritable properties recur, it is more likely to be inductively probable. In any case, the thesis presents a number of deductive formalizations, while more complex treatments are left to the appendix or further study. Inasmuch as the a fortiori is claimed to be a type of analogy, both its likenesses and its differences are set out and exemplified in a number of comparative mathematical, practical, legal, and other formats. Once the conclusion‘s feature is deductively valid or inductively likely, the amount that one accords to the feature in the new case needs to be determined. Logically, the a fortiori’s conclusion can be either limited to the same feature given in one of its premises or else proportioned to it in a way that suits both premises. Mathematically, the same outcome is just one possible ratio. However, the early Jewish stand of the Mishnah usually retains the same tradition or least onerous result as sufficient (the dayo) for the new case. A detailed analysis covers this and later Rabbinic use, and especially Maccoby‘s recent claim that the same given alone is correct, which I show to be extreme, for even in a Jewish context it generates several problems. When one includes sensible a fortiori proportions and the possibility of mercy, good moral reasoning can be reconciled with true religious values and traditional precedents. In all, the conclusion‘s amount, particularly in practical issues, involves an extra decision procedure that considers the relevant factors of the actual case. Once the a fortiori‘s informal and formal aspects are dealt with adequately and its fallacious uses avoided, the argument‘s overall reasonableness is better appreciated. iii Acknowledgements I am most grateful to all those who have assisted me with the preparation and finalization of this thesis. I wish to thank Professor James Diamond for his initial help that led to meeting Professors Menachem Fisch and David Novak. My thanks go to Professor Fisch who helped me focus on the topic and Professor D. Novak for some very useful material. I am indebted to Dr. Avi Sion for his exposition of the subject and his keen insights, many of which I have relied upon, as well as responding to several emails. Specific thanks go to Professor (Emeritus) Rolf George for assistance with the logical portions and to Dr. Greg Andres for his corrections. Most of all, my supervisor, Professor Joseph Novak, has shown me the greatest kindness in guiding me through the entire dissertation process from the beginning, especially in his careful reviews and patient editing of numerous, preliminary drafts. Any remaining errors are entirely my own. Of course, my wife deserves credit for her encouragement and for putting up with my many hours of work. Final thanks are due to my sons who taught me how to decipher (some of) the mysteries of MS Word. iv Table of Contents Author‘s Declaration……………………………………………………………………………………...ii Abstract ..................................................................................................................................................... iii Acknowledgements ................................................................................................................................... iv Table of Contents ....................................................................................................................................... v List of Diagrams ...................................................................................................................................... viii Introduction .............................................................................................................................................. 1 Thesis ..................................................................................................................................................... 1 a) General A Fortiori Argument Form and its Components .................................................................. 2 b) Some Ordinary Examples .................................................................................................................. 3 c) 1. Premises as Preliminary Principles ................................................................................................ 4 2. Preference, Choice, and Dominance .............................................................................................. 4 d) Common Thinking Process................................................................................................................ 6 e) 1. Various Argument Methods and Strengths .................................................................................... 7 2. Argument Justification and Acceptability ...................................................................................... 7 f) 1. Specific Jewish Uses ...................................................................................................................... 9 2. The Dayo Limit: the Same Feaure as Given ................................................................................. 10 g) Some Mishnaic and Amoraic Issues……………………………………………………………….11 h) Recent Jewish and General Developments of the a Fortiori ........................................................... 13 i) Importance for Study ........................................................................................................................ 15 Interim Summary ................................................................................................................................. 15 Order of Thesis Development .............................................................................................................. 16 Chapter 1: Survey of Definitions and Key Aspects of the A Fortiori ................................................. 19 1.1 Generic a Fortiori or Qal VaChomer (QC) Argument .................................................................. 19 1.2 Some Official Definitions or Representative Examples ................................................................ 19 1.3 General Comment on Above Definitions ....................................................................................... 24 1.4 Examples and Definitions from Other Sources .............................................................................. 25 1.5 Comments ...................................................................................................................................... 29 1.6 Jewish Definitions .......................................................................................................................... 30 1.7 Schwarz‘s Possible View and Probable Definition…………………………………………...31 1.8 Alternate Arrangements of QC Terms ........................................................................................... 36 1.9 Comments about the Variants ........................................................................................................ 40 1.10 Key Operative, Indicative Terms ................................................................................................. 41 1.11 Other Terms, Symbols, and Meanings ......................................................................................... 42 1.12 A General Definition .................................................................................................................... 44 Chapter 2: A Fortiori Thinking as Reasonable .................................................................................... 45 2.1 Issues about a Fortiori Reasonableness ......................................................................................... 45 2.2 Various Forms in Rational Thought: Deductive and Inductive ..................................................... 46 a) Degrees of Certainty and Limitations in Deduction and Induction ............................................. 46 b) Probabilities in Inductive Methods .............................................................................................. 47 c) Examples of Inductive Arguments .............................................................................................. 52 2.3 Potential Problems ........................................................................................................................