Greek and Roman Logic

In ancient philosophy, there is no discipline called “logic” in the contemporary sense of “the study of formally valid arguments.” Rather, once a subfield of philosophy comes to be called “logic,” namely in Hellenistic philosophy, the field includes (among other things) epistemology, normative epistemology, philosophy of language, the theory of truth, and what we call logic today. This entry aims to examine ancient theorizing that makes contact with the contemporary conception. Thus, we will here emphasize the theories of the “syllogism” in the Aristotelian and Stoic traditions. However, because the context in which these theories were developed and discussed were deeply epistemological in nature, we will also include references to the areas of epistemological theorizing that bear directly on theories of the syllogism, particularly concerning “demonstration.” Similarly, we will include literature that discusses the principles governing logic and the components that make up arguments, which are topics that might now fall under the headings of philosophy of logic or non-classical logic. This includes discussions of problems and paradoxes that connect to contemporary logic and which historically spurred developments of logical method. For example, there is great interest among ancient philosophers in the question of whether all statements have truth-values. Relevant themes here include future contingents, paradoxes of vagueness, and semantic paradoxes like the liar. We also include discussion of the paradoxes of the infinite for similar reasons, since solutions have introduced sophisticated tools of logical analysis and there are a range of related, modern philosophical concerns about the application of some logical principles in infinite domains. Our criterion excludes, however, many of the themes that Hellenistic philosophers consider part of logic, in particular, it excludes epistemology and metaphysical questions about truth. Ancient philosophers do not write treatises “On Logic,” where the topic would be what today counts as logic. Instead, arguments and theories that count as “logic” by our criterion are found in a wide range of texts. For the most part, our entry follows chronology, tracing ancient logic from its beginnings to Late Antiquity. However, some themes are discussed in several eras of ancient logic; ancient logicians engage closely with each other’s views. Accordingly, relevant publications address several authors and periods in conjunction. These contributions are listed in three thematic sections at the end of our entry

Development of fuzzy syllogistic algorithms and applications distributed reasoning approaches

Thesis (Master)--Izmir Institute of Technology, Computer Engineering, Izmir, 2010Includes bibliographical references (leaves: 44-45)Text in English; Abstract: Turkish and Englishx, 65 leavesA syllogism, also known as a rule of inference or logical appeals, is a formal logical scheme used to draw a conclusion from a set of premises. It is a form of deductive reasoning that conclusion inferred from the stated premises. The syllogistic system consists of systematically combined premises and conclusions to so called figures and moods. The syllogistic system is a theory for reasoning, developed by Aristotle, who is known as one of the most important contributors of the western thought and logic. Since Aristotle, philosophers and sociologists have successfully modelled human thought and reasoning with syllogistic structures. However, a major lack was that the mathematical properties of the whole syllogistic system could not be fully revealed by now. To be able to calculate any syllogistic property exactly, by using a single algorithm, could indeed facilitate modelling possibly any sort of consistent, inconsistent or approximate human reasoning. In this work generic fuzzifications of sample invalid syllogisms and formal proofs of their validity with set theoretic representations are presented. Furthermore, the study discuss the mapping of sample real-world statements onto those syllogisms and some relevant statistics about the results gained from the algorithm applied onto syllogisms. By using this syllogistic framework, it can be used in various fields that can uses syllogisms as inference mechanisms such as semantic web, object oriented programming and data mining reasoning processes

Necessity, Possibility and the Search for Counterexamples in Human Reasoning

Abstract Necessity, Possibility and the Search for Counterexamples in Human Reasoning Sylvia Mary Parnell Serpell This thesis presents a series of experiments where endorsement rates, latencies and measures of cognitive ability were collected, to investigate the extent to which people search for counterexamples under necessity instructions, and alternative models under possibility instructions. The research was motivated by a syllogistic reasoning study carried out by Evans, Handley, Harper, and Johnson-Laird (1999), and predictions were derived from mental model theory (Johnson-Laird, 1983; Johnson-Laird & Byrne, 1991). With regard to the endorsement rate data: Experiment 1 failed to find evidence that a search for counterexamples or alternative models took place. In contrast experiment 2 (transitive inference) found some evidence to support the search for alternative models under possibility instructions, and following an improved training session, experiment 3 produced strong evidence to suggest that people searched for other models; which was mediated by cognitive ability. There was also strong evidence from experiments 4, 5 and 6 (abstract and everyday conditionals) to support the search for counterexamples and alternative models. Furthermore it was also found that people were more likely to find alternative causes when there were many that could be retrieved from their everyday knowledge, and that people carried out a search for counterexamples with many alternative causes under necessity instructions, and across few and many causal groups under possibility instructions. .The evidence from the latency data was limited and inconsistent, although people with higher cognitive ability were generally quicker in completing the tasks

Ancestor Worship in The Logic of Games. How foundational were Aristotle\u27s contributions?

Notwithstanding their technical virtuosity and growing presence in mainstream thinking, game theoretic logics have attracted a sceptical question: Granted that logic can be done game theoretically, but what would justify the idea that this is the preferred way to do it?\u27\u27 A recent suggestion is that at least part of the desired support might be found in the Greek dialectical writings. If so, perhaps we could say that those works possess a kind of foundational significance. The relation of being foundational for is interesting in its own right. In this paper, I explore its ancient applicability to relevant, paraconsistent and nonmonotonic logics, before returning to the question of its ancestral tie, or want of one, to the modern logics of games

Problems of communication and perception = Труды по психологии. Проблемы общения и восприятия

• P. Tulviste. On the origins of theoretic syllogistic reasoning in culture and in the child • P. Tulviste, A.Lapp. Could Margaret Mead's methods reveal animism in Manus children? A partial replication study in an European culture • T. Bасhmann. Cognitive contours: Overview and a preliminary theory • T. Bаchmann. Visual search and selective adaptation • J. Allik, M. Tepp. Spontaneous movement perception: Precision of the temporal discrimination depends on spatial separation. • M. Rauk, A. Luuk. Perceived visual direction of the brief test-flashes on the horizontal scale. • V.I. Кushpil, J. Allik, Yu.V. Alekseev, E.K. Veselоva, L.F. Petгоva, V.P. Smirnоv. Regularities of visual search in complex field • J. Valsiner, A. Tamm. Mother-infant interaction: A longitudinal study of behavioural interrelations • J. Valsiner, I. Tago, V. Lооlaid, K. Hauk. Maternal subjective culture: An experimental study of the post-partum cognitive phenomena • M. Kоtik. A method of diagnostics of a person's attitude towards an alarming event • П. Тульвисте. Опроисхождении теоретического силлогистического мышления в культуре и у ребенка (Резюме ) • П. Тульенсте, А. Лапп. Могли ли методики Маргарет Мид обнаружить анимистическое мышление у Мануских детей? Частичное повторное • Т. Бахман. Когнитивные контуры: Обзор и предварительная теория. (Резше) • Т. Бахман. Зрительный поиск и селективная адаптация. (Резюме) • D. Аялик, М. Тепп. Спонтанное восприятие движения: Точность временного различения зависит от пространственной удаленности. (Резюме) • М. Раук, А. Луук. Воспринятое направление кратковременных тестовых вспышек на горизонтальной шкале. (Резюме) • В. И. Кушпиль, Ю.К. Аллик, Ю.В. Алексеев, Е.К. Веселова , Л.Ф. Петрова, В.П. Смирнов. Закономерности зрительного поиска на слож • Я. Вальсинер, А. Тамм. Взаимодействие матери и ребенка: Лонгитудинальное исследование взаимосвязей в поведении. (Резюме ) • Я. Вальсинер, И. Таго, В. Лоолайд, К. Xаук . Материнская субъективная культура- Экспериментальное изучение послеродовых когнит (Резюме) • М. Котик. Метод диагностики отношения человека тревожной ситуации. (Резюме) • Contents. Содержаниеhttp://tartu.ester.ee/record=b1222889~S1*es

Class and conditional reasoning in children and adolescents

The development of the ability to comprehend and reason with class and conditional logic statements was examined in the light of Piaget's claim that prior to the age of 11-12 years children are limited to reasoning in terms of classes and relations but from the age of 11-12 years reasoning in terms of propositions becomes possible. Subjects from 5 years to 17.5 years were presented with several different comprehension and inference tasks with class and conditional logic statements. Evidence of differences in the ability of subjects under 12 years to verify class and conditional logic statements was consistent with Piaget's claim that the logical classification operations of the concrete subject enable him to interpret class inclusion statements but that the conditional interpretation of empirical information requires formal operational thinking. No distinction in performance between class and conditional statements was found on tasks which required an understanding of the logical consequences of the inclusion relation with subjects younger than first year secondary performing poorly on both class and conditional versions of an evaluation task and a syllogistic reasoning task. Significant changes in patterns of response at adolescence on the conditional verification task, the evaluation task and the syllogistic reasoning task supported Piaget's contention that there are qualitative changes in reasoning at adolescence although, as in other studies, errors in reasoning by adolescents indicated that Piaget overestimated the logical abilities of the formal subject and suggested that Piaget's logical model of cognition should be regarded as a model of logical competence

Deductive Systems in Traditional and Modern Logic

The book provides a contemporary view on different aspects of the deductive systems in various types of logics including term logics, propositional logics, logics of refutation, non-Fregean logics, higher order logics and arithmetic