This volume presents the proceedings from the Eleventh Brazilian Logic Conference on Mathematical Logic held by the Brazilian Logic Society in Salvador, Bahia, Brazil. The conference and the volume are dedicated to the memory of professor Mario Tourasse Teixeira, an educator and researcher who contributed to the formation of several generations of Brazilian logicians. Contributions were made from leading Brazilian logicians and their Latin-American and European colleagues. All papers were selected by a careful refereeing processs and were (...) revised and updated by their authors for publication in this volume. There are three sections: Advances in Logic, Advances in Theoretical Computer Science, and Advances in Philosophical Logic. Well-known specialists present original research on several aspects of model theory, proof theory, algebraic logic, category theory, connections between logic and computer science, and topics of philosophical logic of current interest. Topics interweave proof-theoretical, semantical, foundational, and philosophical aspects with algorithmic and algebraic views, offering lively high-level research results. (shrink)

In this paper I develop a cross-cultural critique of contemporary critical thinking education in the United States, the United Kingdom, and those educational systems that adopt critical thinking education from the standard model used in the US and UK. The cross-cultural critique rests on the idea that contemporary critical thinking textbooks completely ignore contributions from non-western sources, such as those found in the African, Arabic, Buddhist, Jain, Mohist and Nyāya philosophical traditions. The exclusion of these traditions leads to (...) the conclusion that critical thinking educators, by using standard textbooks are implicitly sending the message to their students that there are no important contributions to the study of logic and argumentation that derive from non-western sources. As a case study I offer a sustained analysis of the so-called Hindu Syllogism that derives from the Nyāya School of classical Indian philosophy. I close with a discussion of why contributions from non-western sources, such as the Hindu Syllogism, belong in a Critical Thinking course as opposed to an area studies course, such as Asian Philosophy. (shrink)

In this paper I develop a cross-cultural critique of contemporary critical thinking education in the United States, the United Kingdom, and those educational systems that adopt critical thinking education from the standard model used in the US and UK. The cross-cultural critique rests on the idea that contemporary critical thinking textbooks completely ignore contributions from non-western sources, such as those found in the African, Arabic, Buddhist, Jain, Mohist and Nyāya philosophical traditions. The exclusion of these traditions leads to (...) the conclusion that critical thinking educators, by using standard textbooks are implicitly sending the message to their students that there are no important contributions to the study of logic and argumentation that derive from non-western sources. As a case study I offer a sustained analysis of the so-called Hindu Syllogism that derives from the Nyāya School of classical Indian philosophy. I close with a discussion of why contributions from non-western sources, such as the Hindu Syllogism, belong in a Critical Thinking course as opposed to an area studies course, such as Asian Philosophy. (shrink)

This book responds to the need for new ways of defining the aims and forms of education, in an age that has seen the ideals of progress and growth lead the planet and its inhabitants to the brink of extinction. Arguing that contemporary ideas of performance and accountability counter 'the heart' of education, the book calls for a retuning of education that encourages the young generation to study objects and ideas for their own sake, rather than to (...) appease established and conventional notions in society - therefore stepping into a common space of reflection and study. Chapters examine exactly why and how we educate, and offer the alternative of engaging with educational questions, not determined by the logic of progress and growth but with an objective of creating a relation to the world around us. Using the works of Hannah Arendt combined with the tradition of Allgemeine Pädagogik to argue for a new conception of Bildung, the book encourages a method that emphasises outrospection over introspection. Ultimately questioning modern-day education, the book redirects and retunes education away from being wholly concerned with achievement and growth, and will therefore be of interest to students, researchers and academics in the fields of philosophy of education, education and curriculum studies, education policy and politics, and sociology of education. (shrink)

The educational aims described by educational philosophers rarely embrace the full range of differences in intellectual ability, adaptive behavior, or communication that children exhibit. Because envisioned educational aims have significant consequences for how educational practices, pedagogy, and curricula are conceptualized, the failure to acknowledge and embrace differences in ability leaves open the question of the extent to which students with intellectual disabilities are subject to the same aims as their “typically-developing” peers. In articulating and defending valued aims of education, (...) educational philosophers tacitly or expressly concede that particular aims will be ill suited to many children with intellectual disabilities, and that separate aims will therefore apply to them. This paper evaluates the philosophical reasoning behind this conclusion that some people, by necessity, must be governed by separate educational aims, to be decided separately and secondarily. The author calls this the “deferral stance.” First, the paper outlines concerns about a particular ability-biased social and epistemic context in which theorizing about educational aims takes place. The author then examines assumptions that underpin the logic of deferral, arguing that the logic proves flawed when subjected to conceptual and empirical scrutiny. The paper concludes by outlining an inclusive approach—the affirmative stance—to theorizing about educational aims that resists the logic of exclusion and deferral. (shrink)

Educating Reason: Critical Thinking, Informal logic, and the Philosophy of Education.

Over the last few decades, the idea that education should function to promote economic progress has played a major role in shaping educational policy. So far, however, philosophers of education have shown relatively little interest in analysing this notion and its implications. The present article critically examines, from a philosophical perspective, the link between education and the currently prevailing understanding of economic progress, which is grounded in human capital theory. A number of familiar philosophical objections to the (...) idea that economic progress is a worthy educational aim are raised, but it is held that many of these objections stem from a partial understanding of economic theory. The article then moves on to investigate the foundations of human capital theory's conception of economic progress. It is argued that there are inherent tensions between the philosophical foundations of the economist's conception of progress and the very essence of education. The article concludes by suggesting that in order to resolve these tensions we should consider grounding the economic theory that guides educational policy-making in an intersubjective or objective conception of welfare. (shrink)

This article disrupts the logic of the “just-a-tool” argument, a powerful rhetorical device commonly offered as a rationale for using computers in education (and health care and other areas of society). Although this argument is articulated in many ways, its essence is the contention that computers are merely instructional tools, like blackboards or pencils, that can be used to enhance learning and therefore should be used in classrooms. The just-a-tool argument is difficult to challenge because it automatically constructs (...) counterarguments as illogical; they necessarily become arguments against using technology to improve the human condition. However, an analysis of the just-a-tool argument reveals that far from being logical and unassailable, it is both invalid and unsound. This “techno-illogic,” as the author calls it, arises when wisdom is subjugated to the dictates of technological “rationality,” and it is something that people must learn to recognize and defend against. (shrink)

In the summer of 1928, Kurt Gödel (1906–1978) embarked on his logical journey that would bring him world fame in a mere three years. By early 1929, he had solved an outstanding problem in logic, namely the question of the completeness of the axioms and rules of quantificational logic. He then went on to extend the result to the axiom system of arithmetic but found, instead of completeness, his famous incompleteness theorem that got published in 1931. It belongs (...) to the most iconic achievements of 20th century science and has been instrumental in the development of theories of formal languages and algorithmic computability – two essential components in the birth of the information society. This book explores Gödel’s way from an exceptional high-school student to a firmly established young logician. Essays in Gödel’s hand from the high school show that his central philosophical and scientific convictions were formed early on, before his university studies. Particular emphasis is laid on the course that made Gödel one of the foremost logicians of all times. The scientific biography of young Gödel is followed by English translations from Gödel’s German Gabelsberger shorthand of all his early preserved notebooks on logic and related topics. (shrink)

The article presents a thought experiment aimed at indicating a possibility for thinking education beyond the logic of progress. In its first part, the argument reconstructs the entanglement of the modern idea of progress (as found in Francis Bacon and Comenius) and education, while tracking down the specific coupling of obedience and conquest at work. Through such an analysis a link between the ideas of progress and of emancipation is determined, which leads to the acknowledgement of the (...) difficulty of the task of imagining education outside of the logic of progress. In the second part an attempt is made to match this task by suggesting that when studying with a teacher, the logic of progress is deactivated. A phenomenological analysis of the practices involved in studying with a teacher points to a specific way of living together that such a collective study involves. This way of living together is formed by continual exercises in the humble equality realized through shared attention to something worthy of study: this stems from attentiveness to what exists, and it develops an attitude of care and respect for being as such. (shrink)

Moral education is a core component of ideological and political courses in primary and secondary schools and universities in China, and also an important part of contemporary Chinese Marxist educational theory and practice. In Chinese senior high schools, the main curriculum and platform for moral education is ideological and political courses. The Ideological and Political Curriculum Standards for General Senior High Schools (2017 Edition, 2020 Revised) issued by the Ministry of Education of the People’s Republic of China (...) explicitly includes a course on logical thinking in the ideological and political curriculum in general senior high schools, strengthening the importance of logic in moral education there. In this paper, the authors explain the necessity of intensifying logic training for contemporary Chinese teenagers, introduce and interpret the relevant contents in the Ideological and Political Curriculum Standards for General Senior High Schools (2017 Edition, 2020 Revised), and put forward some theoretical suggestions on how to conduct teaching on the subject of logic. (shrink)

The astronomical traditions on which Copernicus drew for his major works have been well researched. Questions about Copernicus's arguments and his education in logic have been less thoroughly treated. The arguments supplied by Copernicus in his major works are shown to rely to a large extent on well-known dialectical topics or inference warrants. Some peculiar features of his arguments, however, point to sources at Cracow that very likely inspired him to construct arguments based on the requirement of real (...) connections between antecedents and consequents as a condition for the validity of hypothetical conditionals. (shrink)

Unfortunately, Wittgenstein has entered the philosophical canon , an entrance that has served to reify interpretations of his work. In this essay I refer to recent books by Richard Eldridge (1997) and Phillip Shields (1998) which allow us again to see The Philosophical Investigations as something more than a stultifying relic. Specifically, these authors, by reading Wittgenstein's work not merely as text but also as performance, allow us to enact our own liberating performances of that work. To engage in such (...) enactments of freedom is the essence of philosophical education in the sense established by extra-canonical writers such as Socrates and the Stoics, on the one hand, and Emerson and James, on the other. At least this is so if my use of the work of classicist Pierre Hadot, on the one hand, and brief reference to literary critic Richard Poirier, on the other, is at all successful in illuminating theses from Eldridge and Shields on the nature of Wittgensteinian philosophy. (shrink)

The investigation into logical form and structure of natural sciences and mathematics covers a significant part of contemporary philosophy. In contrast to this, the metatheory of normative theories is a slowly developing research area in spite of its great predecessors, such as Aristotle, who discovered the sui generis character of practical logic, or Hume, who posed the “is-ought” problem. The intrinsic reason for this situation lies in the complex nature of practical logic. The metatheory of normative educational philosophy (...) and theory inherits all the difficulties inherent in the general metatheory but has also significantly contributed to its advancement. In particular, the discussion on its mixed normative-descriptive character and complex composition has remained an important part of research in educational philosophy and theory. The two points seem to be indisputable. First, the content of educational philosophy and theory is a complex one, connecting different disciplines. Second, these disciplines are integrated within the logical form of practical inference or means-end reasoning. On the other hand, the character of consequence relation in this field, although generally recognized as specific, represents an unresolved prob- lem, a solution of which requires a sophisticated logical theory and promises to influence the self- understanding of educational philosophy and theory. (shrink)

Undergraduate medical ethics education currently focuses on ethical concepts and reasoning. This paper uses an intern’s story of an ethically challenging situation to argue that this emphasis is problematic in terms of ensuring students’ ethical practice as junior doctors. The story suggests that it is aligning their actions with the values that they reflectively embrace that can present difficulties for junior doctors working in the pressures of the hospital environment, rather than reasoning to an ethically appropriate action. I argue (...) that junior doctors need skills for implementing their ethical decisions and that these ought to form a central component of undergraduate medical ethics education. (shrink)

Gumport chronicles the rise of "industry logic," as a departure from "social institution logic," in public higher education in the latter twentieth century. Industry logic refers to colleges restructuring for financial efficiency and developing more ties with industry. Since the 1970s, increased public scrutiny and demands for accountability have pushed colleges to become more corporatized and privatized. Gumport's sociological analysis is grounded in data from nine in-depth case studies that span three sectors of public higher (...) class='Hi'>education. (shrink)

This paper rereads John Dewey's works in the light of complexity theory and self‐organising systems. Dewey's pragmatic inquiry is posited as inspirational for developing a logic of education and learning that would incorporate novelty and creativity, these artistic elements being part and parcel of the science of complexity. Dewey's philosophical concepts are explored against the background of such founders of dynamical systems theory as Ludwig von Bertalanffy, Ervin Laszlo, and Erich Jantsch. If, in this process, Dewey's thought appears (...) to undergo some transformation, this would only confirm Jim ) belief that Dewey would welcome, in accord with his own philosophical project, the reconstruction of his own ideas so as to better respond to contingencies and challenges of new times, places and contexts. The paper introduces some elements of non‐linear dynamics, relating them to the problematic of learning and the transformation of habits. Finally, the paper addresses a delicate balance between novelty and confirmation in a self‐organised system, positing it as an issue of pedagogical significance. (shrink)

It becomes more obvious each year that the appeals of the party and government to strengthen the ties between philosophy and modern science are not being adequately implemented by the chairs of logic in the universities. In a number of institutions, a situation has persisted for a long time in which only a few professors and instructors deal with the subject area of dialectical and mathematical logic at a high professional level. Most of the teaching staff continue to (...) conduct their work essentially within the confines and at the level of the old, arbitrarily designated "traditional" formal logic, primarily in the form in which it took shape in the middle of the last century. It is clear that this does not accord with the demands of the party and of our philosophical and scientific public to raise the theoretical level of all instructional and research work in higher educational institutions. The erroneous orientation toward the old formal logic was, in particular, one of the reasons why the fundamental problems of dialectical logic have to this day not found unambiguous solutions. This is also one of the reasons why the science of logic has suffered some loss of authority among a portion of the country's students. It is not uncommon to see teachers who deal with dialectical logic giving inadequate consideration to the problems of contemporary natural and social science, while those who concern themselves with mathematical logic give inadequate attention to problems in the realm of philosophy. The appearance and persistence of this situation have made possible a sterile and erroneous approach to theoretical problems, the discussion of which is our present aim. (shrink)