## JL Diagram 5

DIAGRAM 5R. Ishmael’sRule No. 8(a) – “lelamed oto hadavar”– the generalizing version of “lelamed”, may be depicted as follows, since its fourth premise is:All P2 are P1, but not all P1 are P2(predicatal premise).Diagram 5The four premises formally yield the conclusion “Some S1 are P2” (etc.), which is compatible with the two outcomes shown in [...]

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## JL Diagram 4

DIAGRAM 4We suggested a general formula for the first three (actually, four) of the hermeneutic principles which begin with the phrasekol davar shehayah bikhlal veyatsa...Given the three premises, common to the four Rules:1.Major premise:All S1 are P1.2.Minor premise:All S2 are P2.3.Subjectal premise:All S2 are S1, but not all S1 are S2.and, the fourth premise, as [...]

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## JL Diagram 3

DIAGRAM 3 Rabbi Ishmael’s Rules Nos. 8-9-10, which are some of the Talmud’s harmonization rules, are all concerned with the following logical problem, formulated with reference to the following diagram: knowing the lateral relations between four items (the terms or theses, S1, P1, S2, P2, in the four premises a, b, c, d), what are [...]

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## JL Diagram 2

DIAGRAM 2 R. Ishmael’s Rules Nos. 4 and 5, concerning the intended scope of terms, can be represented as follows. In the first case, the intent is narrow; in the second case, the intent is broad. Diagram 2

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## JL Diagram 1

DIAGRAM 1 R. Ishmael’s Rule No. 1, concerning a-fortiori argument, can be represented by a triangular star, at the center of which is the middle item (R) through which the three other items, P, Q, and S are related to each other. Diagram 1a The a-fortiori argument may also be represented, with reference to the [...]

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## JL Appendix 6

Appendix 6. In this appendix, we shall examine some examples of "kol davar shehayah bikhlal veyatsa" exegesis, which the Rabbis, in my view, misclassify. Further Notes on Harmonization Rules. 1. The goring ox. This example is given by Abitbol (quoting Mekhilta, Baba Qama 4:5), under the heading of rule No. 10, shelo kheinyano. As we [...]

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## JL Appendix 5

Appendix 5. The Hebrew Language. Logic and language are intimately bound up in Jewish thought. Interpretation of holy texts for the derivation of laws presupposes a profound acquaintance with the Hebrew language, in its every little detail; its spelling, its grammar, its etymologies, its every living nuance[1]. Judaism has for a very long time, if [...]

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## JL Appendix 3

Appendix 3. Gematria. Hebrew numerology, known as gematria[1], has to be given attention within any work on logic, inasmuch as it is, rightly or wrongly, used by many teachers in Judaism as a method of inference. However, it is rarely a process through which mitzvot or minhagim are legally established (though the interdiction against eating [...]

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## JL Appendix 2

Appendix 2.In this appendix, I want to put forward some suggestions concerning the Creation narrative, as presented in Genesis I and II and traditional Jewish commentaries thereto, and current scientific theories on the subject. (I wrote most of the text below some years ago; however, some more recent thoughts have been added in the last [...]

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## JL Appendix 1

Appendix 1. Further Notes on A-Fortiori Argument. Notes: 1. 2. 3. 4.   1. Subjectal and predicatal (or antecedental and consequental) a-fortiori are sometimes found in tandem, forming an enthymemic sorites, so that the conclusion of one implicitly serves as minor premise in the other. For instances: A is more R than B, and B [...]

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