Judaic Logic

Judaic reasoning is discussed from the standpoint of modern logic. Andrew Schumann defines Judaic logic, traces Aristotelian influence on developing Jewish studies in Judaic reasoning, and shows the non-Aristotelian core of fundamentals of Judaic logic. Further, Schumann proposes some modern approaches to understanding and formalizing Judaic reasoning, including Judaic semantics and (non-Aristotelian) syllogistics.

Contenu

Table of Contents (page 5) Preface (page 7) Transliterations of Hebrew Letters and Their Numeric Values (page 9) Introduction (page 11)

• Appendix: The main hermeneutic rules used in theTalmud (page 24) In Search of the Logic of Judaism: From Talmudic Chaos to Halakhic Linearity (page 35)

• 1. Introduction (page 35)
• 2. The linear logic of the Halakhah according to Urbach, Roth, Sanders et. al. (page 37)
• 3. The term Halakhah in the early literature (page 44)
• 4. Two metaphors of logic: linearity or chaos (page 47)
• 5. Fractal conclusions (page 53)

• References (page 54) Maimonides' Use of Logic in The Guide of the Perplexed (page 57)

• 1. Introduction (page 57)
• 2. Logical terms and distinctions (page 59)
• 3. Logical distinctions in the Guide (page 66)
• 4. Demonstratons and knowledge of God (page 69)
• 5. Critical challenges (page 78)
• 6. Conclusion (page 82)

• References (page 83) Structure and Sources of the Hebrew Commentary on Petrus Hispanus's Summulae Logicales by Hezekiah Bar Halafta, Alias Bonenfant De Millau (page 87)

• 1. Introduction (page 87)

• References (page 124) Aristotelian Logic and Talmudic Methodology: The Commentaries on the 13 Hermeneutic Principles and their Application of Logic (page 127)

• 1. Introduction (page 127)
• 2. The commentaries on the thirteen principles (page 130)
• 3. The material commentaries vs. the formal ones (page 131)
• 4. Other manners by which logic influenced the interpretation of the principles (page 133)
• 5. Remonstrations to the incorporation of logic in the interpretation of the principles (page 138)
• 6. The affinities of the medieval methods to the modern research (page 140)
• 7. The neutral attitude of logic to the realm of religious tradition (page 143)
• 8. Halakhah's mindedness and the principles of logic: creativity, artificiality and educational ends (page 146)
• 9. Conclusion (page 149)

• References (page 150) A Fortiori Reasoning in Judaic Logic (page 155)

• 1. Historical background (page 155)
• 2. The valid moods of a fortiori (page 161)
• 3. Samples in the Torah (page 167)
• 4. The dayo principle (page 173)
• 5. Objections! (page 176)
• 6. Rabbinic formulations (page 179)
• 7. Conclusions (page 182)

• References (page 184) The A Fortiori Argument in the Talmud (page 187) 1. Introduction (page 187) 2. What is an a fortiori argument? (page 189) 3. Theories of a fortiori arguments (page 191)

• 3.1. Topical theory of a fortiori (page 192)
• 3.2. Logical theory of a fortiori (page 193)

• 3.3. Two-dimensional theory of a fortiori (page 193) 4. Talmudic theory of a fortiori (page 196) 5. Conclusion (page 197) References (page 198) Sense in Making: Hermeneutical Practices of the Babylonian Talmud Against the Background of Medieval and Contemporary Views (page 199) 1. Introduction (page 200) 2. From Russell and Austin to the Talmud (page 201) 3. From Medieval Methodologies to the Talmud (page 206) 4. Two Aramaic speakers (page 211)

• The first Aramaic speaker (page 211)
• The second Aramaic speaker (page 213)
• All branches are cut (page 214)
• The first speaker again (page 218)
• The speakers' shadows (page 220)

• The open protocol (page 223) 4. Conclusion (page 227) 5. Methodological postscript (page 227) References (page 237) Judaic Syllogistics: The Baba Qama from the Logical Point of View (page 239)

• References (page 253) Symbolic Computation and Digital Philosophy in Early Ashkenazic Kabbalah (page 255) 1. Introduction (page 255) 2. Beyond Gematria (page 257)

• 2.1. Set partitions (page 257)
• 2.2. Automata theory (page 259) 3. Conclusion (page 265) References (page 266) Index (page 267)