We show that in Kabbalah, the esoteric teaching of Judaism, there were developed ideas of unconventional automata in which operations over characters of the Hebrew alphabet can simulate all real processes producing appropriate strings in accordance with some algorithms. These ideas may be used now in a syllogistic extension of Lindenmayer systems (L-systems), where we deal also with strings in the Kabbalistic-Leibnizean meaning. This extension is illustrated by the behavior of Physarum polycephalum plasmodia which can implement, first, the Aristotelian syllogistic and, second, a Talmudic syllogistic by qal wa-homer.
In constructing the three-valued logic, Jan Łukasiewicz was highly inspirited by the Aristotelian idea of logical contingency. Nevertheless, we can construct a four-valued logic for explicating the Stoic idea of logical determinacy. In this system, we have the following truth values: 0 (‘possibly false), 1 (‘necessarily false’), 2 (‘possibly true’), 3 (‘necessarily true’), where the designated truth value is represented by the two values: 2 and 3.
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.
This volume contains the papers presented at the Philosophy and History of Talmudic Logic Affiliated Workshop of Krakow Conference on History of Logic (KHL2016), held on October 27, 2016, in Krakow, Poland.
In this paper reflexive games are defined as a way to act beyond equilibria to control our opponents by our hiding motives. The task of a reflexive game is to have the opponent’s actions become transparent for us, while our actions remain obscure for the competitor. In case a reflexive game is carried out between agents belonging to the same organisation (corporation, company, institute), success in a reflexive game can be reached by a purposeful modification of some components of a controlled system. Such a modification for the guaranteed victory in a reflexive game is called reflexive management. This kind of management uses reflexive games to control a knowledge structure of agents in a way their actions unconsciously satisfy the centre’s goals.
In the paper, a new syllogistic system is built up. This system simulates a massive-parallel behavior in the propagation of collectives of parasites. In particular, this system simulates the behavior of collectives of trematode larvae (miracidia and cercariae).
In decision making quite often we face permanently changeable and potentially infinite databases when we cannot apply conventional algorithms for choosing a solution. A decision process on infinite databases (e.g. on a database containing a contradiction) is called troubleshooting. A decision on these databases is called creative reasoning. One of the first heuristic semi-logical means for creative decision making were proposed in the theory of inventive problem solving (TIPS) by Genrich Altshuller. In this paper, I show that his approach corresponds to the so-called content-generic logic established by Soviet philosophers as an alternative to mathematical logic. The main assumption of content-genetic is that we cannot reduce our thinking to a mathematical combination of signs or to a language as such and our thought is ever cyclic and reflexive so that it contains ever a history.
It is a Preface to Volumes 7:3 and 7:4 (2018) consisting of articles presented at the International Interdisciplinary Conference Ideas and Society on the 150th anniversary of the birth of Leon Petrażycki, held on November 24, 2017, in Rzeszów, Poland.
The paper considers main features of two groups of logics for biological devices, called Physarum Chips, based on the plasmodium. Let us recall that the plasmodium is a single cell with many diploid nuclei. It propagates networks by growing pseudopodia to connect scattered nutrients (pieces of food). As a result, we deal with a kind of computing. The first group of logics for Physarum Chips formalizes the plasmodium behaviour under conditions of nutrient-poor substrate. This group can be defined as standard storage modification machines. The second group of logics for Physarum Chips covers the plasmodium computing under conditions of nutrient-rich substrate. In this case the plasmodium behaves in a massively parallel manner and propagates in all possible directions. The logics of the second group are unconventional and deal with non-well-founded data such as infinite streams.