No description available.

A reasoner’s beliefs can compromise or inflate the accuracy of their syllogistic judgments when syllogistic content and structure are incongruent or congruent, respectively. An integrated approach to the study of syllogistic reasoning led to the investigation of premise-based belief-content conflict and its impact on belief bias. The belief-content conflict cue attenuated belief bias in incongruent valid and invalid trials, as well as congruent invalid trials. Its efficacy was found to depend on the difficulty level of the syllogism in which it was embedded and the location of its placement. Reaction time analyses were used to guide interpretations about the relative engagement of Systems 1 and 2. The key findings suggested that belief-content conflict activated System 2 for invalid incongruent trials which would otherwise have been processed using low-cost heuristic means due to their inherent difficulty. In contrast, it appeared that in valid trials the cue led to a redirection of System 2 resources such that specialized analytic strategies were applied in incongruent trials preceded by belief-content conflict compared to those lacking this cue. Finally, belief bias was successfully offset by belief-content conflict even in cases of congruency. In congruent invalid trials without this cue participants’ intuitive awareness of the content-structure match appeared to lead to low-cost, belief-based guesses; yet when presented as the major premise this conflict cue appeared to shift System 1 processing away from content and towards structure. Albeit less diligent than System 2 analysis, the shallow consideration of structural features may have been viewed as a safer bet than any shortcut aiming to capitalize on syllogistic content. This set of findings cannot be fully accounted for by the selective scrutiny, misinterpreted necessity, mental models, verbal reasoning, selective processing, or Receiver Operating Characteristics accounts thereby highlighting the need for considering belief-content conflict in future models of belief bias.

The central topic of the thesis is the relationship between logic and the cognitive psychology of reasoning. This topic is treated in large part through a detailed examination of the recent work of P. N. Johnson-Laird, who has elaborated a widely-read and influential theory in the field. The thesis is divided into two parts, of which the first is a more general and philosophical coverage of some of the most central issues to be faced in relating psychology to logic, while the second draws upon this as introductory material for a critique of Johnson-Laird's `Mental Model' theory, particularly as it applies to syllogistic reasoning. An approach similar to Johnson-Laird's is taken to cognitive psychology, which centrally involves the notion of computation. On this view, a cognitive model presupposes an algorithm which can be seen as specifying the behaviour of a system in ideal conditions. Such behaviour is closely related to the notion of `competence' in reasoning, and this in turn is often described in terms of logic. Insofar as a logic is taken to specify the competence of reasoners in some domain, it forms a set of conditions on the 'input-output' behaviour of the system, to be accounted for by the algorithm. Cognitive models, however, must also be subjected to empirical test, and indeed are commonly built in a highly empirical manner. A strain can therefore develop between the empirical and the logical pressures on a theory of reasoning. Cognitive theories thus become entangled in a web of recently much-discussed issues concerning the rationality of human reasoners and the justification of a logic as a normative system. There has been an increased interest in the view that logic is subject to revision and development, in which there is a recognised place for the influence of psychological investigation. It is held, in this thesis, that logic and psychology are revealed by these considerations to be interdetermining in interesting ways, under the general a priori requirement that people are in an important and particular sense rational. Johnson-Laird's theory is a paradigm case of the sort of cognitive theory dealt with here. It is especially significant in view of the strong claims he makes about its relation to logic, and the role the latter plays in its justification and in its interpretation. The theory is claimed to be revealing about fundamental issues in semantics, and the nature of rationality. These claims are examined in detail, and several crucial ones refuted. Johnson- Laird's models are found to be wanting in the level of empirical support provided, and in their ability to found the considerable structure of explanation they are required to bear. They fail, most importantly, to be distinguishable from certain other kinds of models, at a level of theory where the putative differences are critical. The conclusion to be drawn is that the difficulties in this field are not yet properly appreciated. Psychological explantion requires a complexity which is hard to reconcile with the clarity and simplicity required for logical insights.

В настоящее время силлогистика, благодаря ее связи с естественным языком, занимает значимую позицию в широком спектре дисциплин: от когнитивных наук до исследований в области искусственного интеллекта. Ряд особенностей восприятия и обработки человеком силлогистических рассуждений часто приводит к ошибкам при решении данного рода задач. Применение интерактивной визуализации символьных контекстов с применением компьютерных моделей снижает вероятность возникновения подобных проблем. Кроме того, повышению эффективности на этапе обучения способствует введение игровых элементов. В силлогистике самыми распространенными вариантами графических представлений являются круговые диаграммы Эйлера и Венна. Первый подход, согласно ряду эмпирических результатов, оказывает более положительный эффект на результаты решения силлогистических задач. В качестве иллюстрации идеи визуальной поддержки освоения базовых принципов силлогистического вывода предложен проект программного решения, предоставляющего возможности интерактивного построения силлогизмов с использованием диаграмм Эйлера в качестве графической репрезентации. / Today syllogistic, due to its connection with natural language, finds broad application in a wide range of research fields: from cognitive sciences to AI. Some specific features of human perception and processing of syllogistic reasoning makes such kind of tasks prone to error. To diminish the impact of these cognitive biases visual interactive computer models are used as a representation of symbolic contexts. Moreover, to increase the effectiveness of learning various game elements could be applied. Euler and Venn diagrams are the most common methods of the syllogistic reasoning visual representation. There are some empirical proofs that Euler diagrams have better effect on the results of the syllogistic tasks solving. To illustrate the idea of a visual support system for syllogistic learning, we have proposed a project of software application that represents the environment for interactive syllogism construction, which relies on Euler diagrams as a visual representation.

This essay explores the issue of organizing mathematics education by means of syllogism. Two aspects turn out to be particularly significant. One is the syllogistic analysis while the other is the cunning of reason. Thus the exploration is directed towards gathering evidence of their existence and showing by examples their usefulness within mathematics education. The syllogistic analysis and the cunning of reason shed also new light on Chevallard's theory of didactic transposition. According to the latter, each piece of mathematical knowledge used inside school is a didactic transposition of some other knowledge produced outside school, but the theory itself does not indicate any way of transposing, and this empty space can be filled with the former. A weak prototype of syllogism considered here is Freudenthal's change of perspective. Some of the major difficulties in mathematics learning are connected with the inability of performing change of perspective. Consequently, to ease the difficulties becomes a significant issue in mathematics teaching. The syllogistic analysis and the cunning of reason developed in this essay are the contributions to the said issue.

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / This dissertation presents a reconstruction of John Venn s (1834-1923) logical theory in Symbolic Logic (1881; 1894). In his work, Venn presents an algebra of logic, and faces a number of philosophical problems underlying this symbolic logic. Firstly, Venn needs to consider the relation between symbolic logic and traditional logic, i.e., Syllogistic. Secondly, Venn needs to consider the relation between symbolic logic and Mathematics. In treating these issues, Venn will have to reflect upon a number of philosophical notions concerning the nature of symbolic knowledge. The objective of this dissertation is to present Venn s treatment to the concept of symbolic knowledge. Throughout the research, it is shown that according to Venn s point of view the algebra of logic is a formal generalization of Syllogistic. Such formal generalization is possible due to the ecthetic function algebraic symbols perform in logical representation. Furthermore, according to Venn, the logic represented by his algebraic symbolism can be precisely differentiated from Mathematics. Such differencing is possible due to the reflection upon the different modes in which algebraic symbolism performs the subrogative function of symbolic knowledge. This dissertation achieves twofold results. On the one hand, it achieves a historiographically important result, for it permits the determination of the locus of Venn s work among the efforts of logical symbolization in the Nineteenth century. On the other, it achieves a philosophical result insofar it permits, through the analysis of a historical case, to clarify key-notions of symbolic knowledge. Venn is more recognized for the creation of Venn diagrams than for his work in the algebra of logic, however, Venn doesn t elaborate much any systematic reflection upon the nature of graphic knowledge. Nevertheless, the research of Venn s work in the algebra of logic provides results concerning the nature of Venn diagrams, which are here presented as a secondary issue. / Esta dissertação apresenta uma reconstrução da teoria lógica de John Venn (1834- 1923) em Symbolic Logic (1881; 1894). Em sua obra, Venn apresenta uma álgebra da lógica, e enfrenta uma série de problemas filosóficos subjacentes a essa lógica simbólica. Em primeiro lugar, Venn precisa considerar a relação entre a lógica simbólica e a lógica tradicional, i.e., a silogística. Em segundo lugar, Venn precisa considerar a relação entre a lógica simbólica e a matemática. No tratamento dessas questões, Venn precisará refletir sobre uma série de noções filosóficas acerca da natureza do conhecimento simbólico. O objetivo dessa dissertação é apresentar o tratamento oferecido por Venn ao conceito de conhecimento simbólico. No desenvolvimento da pesquisa, verifica-se que, na opinião de Venn, sua álgebra da lógica é uma generalização formal da silogística. Tal processo de generalização formal é possível graças à função ectética que os símbolos algébricos cumprem na representação lógica. Além disso, verifica-se que, de acordo com Venn, a lógica representada pelo seu simbolismo algébrico pode ser precisamente diferenciada da matemática. Tal diferenciação é possível graças à reflexão sobre os diferentes modos em que o simbolismo algébrico cumpre a função subrogativa do conhecimento simbólico. Essa dissertação alcança, por fim, um duplo resultado. Por um lado, obtém-se um resultado de valor historiográfico, pois permite determinar o lugar do trabalho de Venn entre os esforços de simbolização da lógica do século XIX. Além disso, alcança também um resultado filosófico na medida em que permite, através de análise de um caso histórico, clarificar noções-chave do conhecimento simbólico. Venn é mais conhecido pela criação dos diagramas de Venn do que por seu trabalho em álgebra da lógica, contudo Venn pouco oferece em termos de reflexão sistemática sobre o tema filosófico da natureza do conhecimento gráfico. Apesar disso, o estudo do trabalho de Venn em álgebra da lógica oferece resultados sobre a natureza dos diagramas de Venn, resultados esses que são aqui apresentados como produto secundário da investigação.

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / The present dissertation provides a reconstruction of the categorical part of Aristotle s (384 BC 322 BC) syllogistic, from the standpoint of the theory given in Prior Analytics, a piece of the Organon. Throughout the work it will be explained the methods which Aristotle has proposed to give support to his theory, many of them suffering only occasional changes to the present days. So, on one hand, this demonstrates the relevance of syllogistic on heuristic respects, and on the other, it shows that modern logic inherited much from Aristotle s one - either by abandonment or improvement of parts of his theory, either by embedding their methods in more refined formal structures. Initially, I ll give an overview of the theory and its relation to the epistemology proposed by Aristotle, as well as the assumptions derived from his metaphysics. Next, the operation of the methods used to prove Aristotle s theory will be demonstrated. Finally, an heuristics for the theory will be outlined, also proposed by Aristotle himself. Evidently, it is not intended to argue that Aristotle's logic is suitable for scientific research nowadays, as it seems to have been conceived at the time of its emergence and rise. However, through this research it is possible to note that the simplicity behind the syllogistic theory gives us a relatively underrated power today, especially by the emergence of modern logic. / A presente dissertação traz uma reconstrução da parte categórica da silogística de Aristóteles (384 a.C. 322 a.C.), a partir da teoria presente nos Analíticos Anteriores, integrante da compilação Órganon. Ao longo do trabalho serão explicitados os métodos que Aristóteles propôs para dar sustento à sua teoria, muitos deles sofrendo apenas alterações pontuais até os dias de hoje. Por um lado, isto demonstra a atualidade da própria silogística quanto a aspectos heurísticos, e por outro, mostra o que a lógica moderna herdou de Aristóteles seja pelo abandono ou aperfeiçoamento de partes de sua teoria em detrimento de falhas, seja pela própria incorporação de seus métodos em estruturas formais mais aperfeiçoadas. Inicialmente, será dada uma visão geral da teoria, bem como sua relação com a epistemologia proposta por Aristóteles e seus pressupostos oriundos da metafísica. A seguir, serão demonstrados o funcionamento dos métodos utilizados por Aristóteles que provam a sagacidade da teoria. Finalmente, será explicitada uma heurística para a teoria, também proposta pelo próprio Aristóteles. Evidentemente, não se pretende defender que a lógica de Aristóteles seja adequada para a investigação científica, tal como ela parece ter sido pensada no momento de seu surgimento. Contudo, através da presente investigação é possível notar que a simplicidade teórica por detrás da silogística lhe confere um poder relativamente subestimado nos dias de hoje, sobretudo pelo surgimento da lógica moderna.

Kurį laiką buvo manoma, kad vaikai, kurie dar neperėjo priešoperacinės stadijos nemoka daryti tranzityvumo santykio išvadų apie kiekybę (Pears, Bryant, 1992). Pasak Schnall ir Gattis (1998), daugelis tyrinėtojų bando atsakyti į klausimą, iki kokio laipsnio ir nuo kokio amžiaus vaikai gali išspręsti tranzityvumo santykio vertinimo užduotis. Nors Piaget ir kiti (Inhelder ir Piaget, 1958; cit. pagal Schnall, Gattis, 1998) manė, kad vaikai tik apie 7-8 metus ir vyresni geba teisingai išspręsti tranzityvumo vertinimo užduotis, jaunesni vaikai (Bryant ir Trabasso, 1971; Riley ir Trabasso, 1974) (cit. pagal Schnall, Gattis, 1998) taip pat geba tranzityviai vertinti pasitreniravus. Bryant ir Trabasso (1971; cit. pagal Schnall, Gattis, 1998) padarė išvadą, kad tranzityvumo vertinimo u���duočių neišsprendimas gali būti greičiau dėl darbinės atminties ribotumo nei dėl kognityvinių trūkumų. Tyrimo objektas – 4-6 metų vaikų tranzityvumo supratimas. Tyrimo tikslas – charakterizuoti 4-6 metų vaikų tranzityvumo santykio supratimo ypatumus. Siekiant šio tikslo, išsikelti šie uždaviniai: 1. Sudaryti ir pateikti 4-6 metų am����iaus vaikams tris užduotis, kurios tiria tranzityvumo santykio supratimą. 2. Nustatyti, ar 4-6 metų vaikai geba tranzityviai samprotauti. 3. Palyginti užduotis pagal tiesioginius atsakymus. 4. Palyginti užduotis pagal kokybinius atsakymus. 5. Palyginti berniukų ir mergaičių gebėjimą tranzityviai samprotauti. Prieš atliekant tyrimą buvo išsikeltos tokios hipotezės: 1. 4-6... [toliau žr. visą tekstą] / It was believe that children which didn‘t pass preoperational stage, can‘t to do transitivity conclusions about quantity (Pears, Bryant, 1992). According Schnall and Gattis (1998), many researchers trying ask to question by what degree and from what age children are able to solve transitivity interference tasks. Though Piaget and others (Inhelder ir Piaget, 1958; cit. pagal Schnall, Gattis, 1998) thought that children only about 7-8 years and older can to solve transitivity interference tasks right, younger children (Bryant ir Trabasso, 1971; Riley ir Trabasso, 1974; by Schnall, Gattis, 1998) also are able to solve transitivity interference tasks if they are trained. Bryant and Trabasso (1971; by Schnall, Gattis, 1998) made conclusion that wrong solving of transitivity interference tasks can be rather for working memory limitation nor cognitive deficits. Object of the Study – understanding transitivity in 4-6 years old children. The aim of the study was to characterize understanding transitivity in 4-6 years old children. Goals of the study: 1. Organize and represent for 4-6 years old children three tasks which research inderstanding transitivity. 2. Find, are 4-6 years old children able to reason transitively. 3. Compare tasks by direct answers. 4. Compare tasks by qualitative ansvers. 5. Compare ability to reason transitively in boys and girls. Hyphotesis: 1. 4-6 years old children are able to reason transitively. 2. Children did more mistakes in tasks which were hard to... [to full text]

According to American philosopher W. W. Bartley, the transition from tradi- tional Aristotelian to Boolean logic is a revolutionary milestone in the history of logic. The work of George Boole which was followed by a developement of a mathematicaly oriented logic brings a shift of paradigm. In my thesis I follow the period in which the shift is said to have happened. I explicate the elements of syllogistic and its main conceptions as expounded in a textbook The Rudiments of Logic written by Henry Aldrich. Furthermore I demon- strate logical systems of three authors: Archbishop Richard Whately, George Boole and Lewis Carroll. I accent the connection of those systems and the practical aspect of logic. With this in mind I consider Bartley's statement and estimate the role of the rules in the systems and its possible use in three domains circumscribed in Aldriches book: simple apprehension, judgement and discourse. 1