The precedent studies on the validity of Modus ponens and Modus tollens have been carried out with most regard to a major type of conditionals in which the conditional clause is a sufficient condition for the main clause. But we sometimes, in natural language arguments, find other types of conditionals in which the conditional clause is a necessary or necessary and sufficient condition for the main clause. In this paper I reappraise, on the basis of new definitions of Modus ponens and Modus tollens, their validity/invalidity in natural language arguments in consideration of all types of conditionals.
The logical reasoning first appeared within the Babylonian legal tradition established by the Sumerians in the law codes which were first over the world: Ur-Nammu (ca. 2047 – 2030 B.C.); Lipit-Ishtar (ca. 1900 – 1850 B.C.), and later by their successors, the Akkadians: Hammurabi (1728 – 1686 B.C.). In these codes the casuistic law formulation began first to be used: “If/when (Akkadian: šumma) this or that occurs, this or that must be done” allowed the Akkadians to build up a theory of logical connectives: “... or…”, “… and…”, “if…, then…”, “not…” that must have been applied in their jurisprudence. So, a trial decision looked like an inference by modus pones and modus tollens or by other logical rules from (i) some facts and (ii) an appropriate article in the law code represented by an ever true implication. The law code was announced by erecting a stele with the code or by engraving the code on a stone wall. It was considered a set of axioms announced for all. Then the trial decisions are regarded as claims logically inferred from the law code on the stones. The only law code of the Greeks that was excavated is the Code of Gortyn (Crete, the 5th century B.C.). It is so similar to the Babylonian codes by its law formulations; therefore, we can suppose that the Greeks developed their codes under a direct influence of the Semitic legal tradition: the code was represented as the words of the stele and the court was a logic application from these words. In this way the Greek logic was established within a Babylonian legal tradition, as well. Hence, we can conclude that, first, logic appeared in Babylonia and, second, it appeared within a unique legal tradition where all trial decisions must have been transparent, obvious, and provable. The symbolic logic appeared first not in Greece, but in Mesopotamia and this tradition was grounded in the Sumerian/Akkadian jurisprudence.
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