Logic Textbooks Research Articles

Hume, Laws of Nature, and Miracles

ABSTRACT This article explores the connection between Hume’s view of “laws of nature” and his view of miracles by addressing three foci. First, it presents arguments that Hume construed “laws of nature” as merely beliefs in perfect or imperfect causal uniformity. So construed, laws of nature can be violated, so miracles are possible. Second, it shows that Hume’s criteria for evaluating human testimony are found in the popular textbooks of logic of the time. Hume explicitly used these criteria to criticize nonbiblical reports of miracles. Finally, the article shows that Hume took John Tillotson’s examination of transubstantiation to reduce scripture to apostolic testimony and to collapse the distinction between divine and human testimony. This implies that educated Christians entertain inconsistent beliefs.

Analysis and Reform of Leibniz's Law of Sufficient Reason

Since Leibniz first put forward the sufficient reason law in his philosophical work "The Monadology" (1914), the issue of the law of sufficient reason has aroused heated discussions in the field of logic in our country. The question of whether the law of sufficient reason is the basic law of formal logic was particularly heated in the domestic logic circle in 1978-1980. Since then, there has been little discussion, but from the newly compiled formal logic textbooks published one after another, no consensus has been reached. Although they didn't agree on the question of "whether or not", the two sides elaborated their arguments in detail and put forward some new opinions, thus creating new conditions for solving this problem scientifically. Firstly, this paper analyzes the different viewpoints of both sides of the argument. Secondly, it analyzes whether the law of sufficient reason is the basic law of formal logic from whether Leibniz put forward the law of sufficient reason. Finally, on this basis, a new transformation method is put forward. After this transformation, the law of sufficient reason is an important basic law of deductive logic, which can be juxtaposed with the other three logical laws, such as identity, and coordinated with the "three laws" and complement each other.

“The Critique of Pure Reason” in the Writings of P.D. Lodij

First Professor of Logic and Metaphysics at Main Pedagogical Institute and then also St. Petersburg University, Carpatho-Rusyn P. D. Lodij spent a quarter of a century teaching philosophy and law in the Russian Empire in the first third of the 19th century. His knowledge of Kant’s philosophy and his attitude to Kant’s criticism are estimated diametrically opposed in the research literature. An analysis of his main philosophical work, “Logical Precepts which Lead to Cognition and the Distinction of the True from the False” (1815), convincingly proves that Lodij was an excellent scholar of Kant’s philosophy. In Russia, he was the first thinker who spoke about the differences between the first and second editions of the “Critique of Pure Reason”. Lodij also was the first who noted both the revolutionary role of Kant’s Copernican turn, and the importance of Humeʼs causality problem for the formation of critical philosophy. In Russia, Lodij was the first who proposed a detailed description of Kant’s transcendental idealism. At the same time, Lodij’s general attitude to Kant was rather skeptical. In his own logic, he does not follow Kant’s division of logic into pure and applied, but he returns to pre-Kant’s split into theoretical and practical logics. Lodij disputes with the basic conclusions about the space derived from the transcendental aesthetic, denies synthetic judgments a priori and the rooting of the cognizing reason in illusions. Despite his unequivocal claims regarding Kant’s philosophy, “Logical Precepts” and its author were persecuted during the so-called “professorsʼ affair” of the 1820s. As a result, Lodij was suspended from teaching philosophy, and his logic textbook was withdrawn from teaching for both “disgrace” and imaginary Kantianism.

John Eliot's Logick Primer: A Bilingual English-Massachusett Logic Textbook

In 1672 John Eliot, English Puritan educator and missionary to New England, published The Logick Primer: Some Logical Notions to initiate the INDIANS in the knowledge of the Rule of Reason; and to know how to make use thereof (Eliot 1672) The Logick Primer: Some Logical Notions to Initiate the INDIANS in the Knowledge of the Rule of Reason; and to Know How to Make Use Thereof , Cambridge, MA: Marmaduke Johnson]. This roughly 80 page pamphlet introduces syllogistic vocabulary and reasoning so that syllogisms can be created from Biblical texts. The use of logic for proselytizing purposes is not distinctive: What is distinctive about Eliot's book is that it is bilingual, written in both English and Massachusett (Wôpanâak), an Algonquian language spoken in eastern coastal and southeastern Massachusetts. It is one of the earliest bilingual logic textbooks and it is the first, and perhaps only, textbook in an indigenous American language. In this paper, we (1) introduce John Eliot and the linguistic context he was working in; (2) introduce the contents of the Logick Primer – vocabulary, inference patterns, and applications; (3) discuss notions of ‘Puritan’ logic that inform this primer; and (4) address the importance of his work in documenting and expanding the Massachusett language and the problems that accompany his colonial approach to this work.

Implementation of Logic and Set Textbook with Ethnomathematics Content Oriented towards Higher-Order Thinking Skills

Higher-order thinking skills are skills that are an important aspect of teaching and learning mathematics. Mathematics and culture have a very close relationship, so the development and application of mathematical concepts in the learning process must be based on situations of daily life or local culture. In 2021, Researchers have developed a textbook of Logic and Set containing ethnomathematics oriented toward higher-order thinking skills. The textbook meets the 'Very Good' category on the validity test after being assessed by five experts. This year, the research focuses on the implementation and evaluation of the textbook in Logic and Set courses. The purpose of this research was to describe the feasibility level of the textbook. ADDIE's design research was used in this development research. The trial subjects in this research were 140 students in the Department of Mathematics Education, Faculty of Teacher Training and Education, Universitas Mataram who were taking the Logic and Set courses in the 2021/2022 academic year. Data collection techniques in this research were practicality questionnaires and higher-order thinking skills tests. The results of the data analysis for the practicality assessment of the textbook showed an average score of 81.44, which met the practical classification. Then the average value of the students in the final value of the Logic and Set courses is 81.90. In addition, the percentage of students who achieved a score of 75 was 76% or 106 students. Therefore, it can be concluded that the textbook meets the effective criteria.

Hegel’s logical instruction at the Gymnasium Illustre (1776-1778): the textbooks in context

This article is a contribution to the all too small literature which deals with G.W.F Hegel’s formal logical instruction. Specifically, it looks to clarify the nature, basis and educational context of the logical instruction that Hegel received during his time at the Gymnasium Illustre in Stuttgart (1776–1788). It begins with a brief biographical section where the account of the only other scholar to have significantly contributed to a discussion of the early Hegel’s logical instruction, Riccardo Pozzo, is corrected and updated. It then proceeds to describe the nature of the logic textbooks that Hegel encountered thanks to his early education. In addition to briefly describing the content and notion of logic operative in these textbooks the article also summarily explores the context in which Hegel encountered these particular textbooks and not others. In providing the reader with an interesting and rich documentation of the logical instruction Hegel received at the Stuttgart Gymnasium, the interested party may now explore any of these aspects in greater deal as they consider it relevant, necessary or both. Because of this limitation of scope and the still immature nature of this scholarly debate this paper makes a contribution that ought to be considered documentarian and biographical.

Language-Based Syllogistic Reasoning Using Deep Neural Networks

Abstract Syllogism is a common form of deductive reasoning that requires precisely two premises and one conclusion. It is considered as a logical method to arrive at new information. However, there has been limited research on language-based syllogistic reasoning that is not typically used in logic textbooks. In support of this new field of study, the authors created a dataset comprised of common-sense English pair sentences and named it Avicenna. The results of the binary classification task indicate that humans recognize the syllogism with 98.16% and the Avicenna-trained model with 89.19% accuracy. The present study demonstrates that aided with special datasets, deep neural networks can understand human inference to an acceptable degree. Further, these networks can be used in designing comprehensive systems for automatic decision-making based on textual resources with near human-level accuracy.

Институт научной философии в творческой биографии А.Ф. Лосева

The article reconstructs the historical and philosophical cooperation between Alexei F. Losev and the Institute of Scientific Philosophy in the early 1920s; on the basis of archival materials (Archive of the RAS, Archive of the Institute of Philosophy of the RAS, Archive of the State Academy of Art Sciences, State Archive of the Russian Federation, Central State Archive of Moscow) and per­sonal correspondence, we reconstruct the history of Alexey F. Losev’s crea­tive communication with the staff of the Institute (G.G. Shpet, I.N. Diakov, N.I. Ginkin, S.L. Frank, and others) and attempts to employ the philosopher as senior fellow researcher in 1921 and 1922. Special attention is paid to A.F. Lo­sev’s connections in the 1930s with the Institute of Philosophy of the Communist Academy, and then with the Institute of Philosophy of the Academy of Sciences of the USSR, and his participation in publishing projects initiated by the Insti­tute: preparation of the works of Nicholas of Cusa in 1937, creation of a new textbook of logic in 1941–1946, and the Encyclopedia of Philosophy in 1960–1970s. The question of the philosopher’s interaction with the staff of the Insti­tute of Philosophy of the Academy of Sciences of the USSR (V.V. Bibikhin, L.A. Gogotishvili, A.V. Gulyga, D.V. Dzhokhadze, M.F. Ovsyannikov, A.G. Spir­kin, A.A. Stolyarov, P.S. Trofimov) is touched upon, and the contribution of the Institute to the perpetuation of A.F. Losev’s memory in the 1990s and 2000s is underlined.

DIDACTICS OF LOGIC IN KEN SCHOOLS AND THE CONCEPTION OF LOGICIN THE "ENCYCLOPÉDIE OU DICTIONNAIRE UNIVERSEL RAISONNÉ"

The paper describes the conception of logic in Polish didactics authored by the Commission of National Education (KEN), an important educational institution of the European Enlightenment. Since the documents of the Commission refer to a vision of science presented by such influential works then as the Encyclopédie ou dictionnaire universel raisonné [Great French Encyclopedia], the paper compares the requirements from the Commission’s programmer with the encyclopaedic entries that entail logical problems broadly understood. It turns out that the Commission, following the Encyclopédie, not only recommended a list of textbooks of logic but also shared its eclectic vision of logic. Although it is characteristic of modernity to take a relative approach to the importance of traditional logic, transformed into science on method, or literally an outline of epistemology, understood according to É. Condillac as a specific form of metaphysics, nevertheless some elements of logic were eclectically made valid. This logic, from the times of I. Kant, has been defined as formal logic. Practical logical skills were preferred to the knowledge of logical theories. At the same time attention was paid to the meaning of natural logical skills, and drills in logical reasoningwhen studying languages and mathematics. Despite preferences for the analytical method they also noticed the importance of synthetic method. It seems also that although the documents of the Commission do not say anything about the teaching of syllogistic issues, in didactic practice inspired by the Encyclopédie in the schools controlled by the Commission, the room was made to teach these problems. Condillac’s book was preferred in the schools controlled by the Commission, nevertheless, it was not, as in the case of other textbooks, a must on the reading list, an obligatory reading matter, therefore it was not published in Poland. The conception of logic presented by the Commission as modelled on the Encyclopédie managed to avoid the one-sidedness of Condillac’s approach, the approach that in fact eliminated the teaching of logic.

The Mystery of the Fifth Logical Notion (Alice in the Wonderful Land of Logical Notions)

Abstract We discuss a theory presented in a posthumous paper by Alfred Tarski entitled “What are logical notions?”. Although the theory of these logical notions is something outside of the main stream of logic, not presented in logic textbooks, it is a very interesting theory and can easily be understood by anybody, especially studying the simplest case of the four basic logical notions. This is what we are doing here, as well as introducing a challenging fifth logical notion. We first recall the context and origin of what are here called Tarski-Lindenbaum logical notions. In the second part, we present these notions in the simple case of a binary relation. In the third part, we examine in which sense these are considered as logical notions contrasting them with an example of a nonlogical relation. In the fourth part, we discuss the formulations of the four logical notions in natural language and in first-order logic without equality, emphasizing the fact that two of the four logical notions cannot be expressed in this formal language. In the fifth part, we discuss the relations between these notions using the theory of the square of opposition. In the sixth part, we introduce the notion of variety corresponding to all non-logical notions and we argue that it can be considered as a logical notion because it is invariant, always referring to the same class of structures. In the seventh part, we present an enigma: is variety formalizable in first-order logic without equality? There follow recollections concerning Jan Woleński. This paper is dedicated to his 80th birthday. We end with the bibliography, giving some precise references for those wanting to know more about the topic.

Changes in British Logic Teaching During the Sixteenth and Seventeenth Centuries

British logic teaching in the sixteenth and seventeenth centuries was provided in England by Oxford and Cambridge, both medieval foundations, and in Scotland by the universities of St Andrews and Aberdeen, both founded in the fifteenth century, and Edinburgh, founded in 1582. Wales had no university, and high schools in England did not teach logic. This paper explores the effect that the invention of printing, along with organizational, political, and sociological changes, had on the teaching of these institutions as they affected the logic textbooks that were used and the ways in which the material was presented to students. The disappearance of important medieval developments such as supposition theory along with changes in the treatment of Aristotle’s logic are discussed in relation to selected logicians from the period under discussion. In particular, attention is paid to the Cambridge logician John Seton (d. 1567), whose popular Dialectica was published in 1545, the Frenchman Peter Ramus (d. 1572), whose influence in both England and Scotland was less than has been supposed, and the Oxford logician Robert Sanderson (d. 1662/3) whose Logicae artis compendium was reprinted as late as 1841.

ПРЕПОДАВАНИЕ ЛОГИКИ В ИМПЕРАТОРСКОМ МОСКОВСКОМ УНИВЕРСИТЕТЕ XVIII ВЕКА

Basing on the announcements of lectures and other historical documents, I reconstruct the process of logic teaching at Moscow University during its first half-century (from 1755 till 1800). Its most significant characteristics are the combination of logic and metaphysics teaching, tuition based on a textbook approved by the university’s conference, and the lack of competition among the professors. For the second half of the 18th century, there were four logic professors at Moscow University: J. H. Frommann, J. M. Schaden, D. S. Anichkov and A. M. Bryantsev. Anichkov was the first professor who taught logic in Russian. Despite there being many logic textbooks in Latin or German and their Russian translations, only three texts were used: those by J. H. Winckler, F. Chr. Baumeister and J. G. H. Feder. At university gymnasiums, logic was taught by Schaden, Ch. A. Chebotarev, E. B. Syreyshchikov, D. N. Sinkovskiy, M. I. Snegirev and M. G. Gavrilov. They exploited textbooks by Baumeister and especially by J. G. Heineccius. Except for Anichkov (“Annotationes inlogicam et metaphysicam”, 1782), nobody among the mentioned lectures left behind proper logic papers. For most of the 18th century, logic teaching at Moscow University did not rely on the best textbooks. In fact, the teaching process was at the level of gymnasiums. The situation began to improve only by the end of the 18th and the beginning of the 19th centuries. The current paper identifies the most likely reasons for choosing the mentioned books. In addition, it includes an annex detailing the list of logic classes at Moscow University and university gymnasiums from 1756 till 1800 with respect to lectures and textbooks. The annex is based on the available lecture announcements and the contents of logic textbooks used at Moscow University and university gymnasiums in the 18th century.

ВОЗНИКНОВЕНИЕ ФРОНТИСПИСОВ КАК ОСОБОГО ВИЗУАЛЬНОГО СРЕДСТВА В УЧЕБНИКАХ ЛОГИКИ НОВОГО ВРЕМЕНИ

The paper presents the main stages of frontispieces formation that are seen as special visual aids in logic textbooks of the Early Modern Period: from separate book illustrations inside the text to so-called broadsides and thesis prints, and from them to frontispieces. The main differences between these types of visual aids are demonstrated using the same image of a sailing ship on the engraved title of F. Bacon’s “Instauratio magna” (1620), in J. Cheron’s broadside (1622), in B. Kroner’s thesis print (1669) and S. Groser’s frontispiece “Pharus intellectus” (1697).

Reading by Design: The Visual Interfaces of the English Renaissance Book

Reading by Design: The Visual Interfaces of the English Renaissance Book

The Whole Truth about Partial Truth Tables

Partial truth tables have two salient virtues. First, like whole truth tables, they are algorithmic (i.e., effective). If you construct them correctly, you will get an answer to your question whether a particular argument is valid; whether a particular proposition is tautologous, self-contradictory, or contingent; or whether a particular set of propositions is consistent. Second, they are less time-consuming and tedious to construct than whole truth tables. No partial truth table has more than three rows, and many have only one. A whole truth table, by contrast, may have as many as 32, 64, 128, or 256 rows (or more). In this essay, I explain what a partial truth table is and show how such a table is constructed. I then apply the partial-truth-table technique successively to arguments, individual propositions, and sets of two or more propositions. I conclude by evaluating the most widely used logic textbooks, showing what they do well and where they fall short.

Перед лицом исторических вызовов: деятельность советских философов в годы Великой Отечественной войны

The Great Patriotic War was a decisive challenge not only for the military power and material and technical base of our country, but also for its spiritual, cultural and ideological foundations. Many Russian philosophers became participants in the hos­tilities, but the role of philosophers who continued scientific work was no less im­portant, the plans of which were adjusted and aimed at implementing projects re­lated to the strengthening of patriotism, the development of national identity, the revival of the classical forms of science and culture, consistent with historical heritage of Russia. This scientific work was in the context of the socio-cultural and spiritual processes that intensified in the USSR during the war and responded to the tasks of strengthening defense capability and the formation of a new socio-state identity. The main undertakings implemented in this connection by the Institute of Philosophy of the USSR Academy of Sciences were the development of the history of Russian philosophical thought and the creation of a new textbook of formal logic. These areas of research activity have shown their relevance in the light of the chal­lenges of wartime and prospects in terms of the long-term development of science.

American Terror: The Feeling of Thinking in Edwards, Poe, and MelvilleThe Official World

American Terror: The Feeling of Thinking in Edwards, Poe, and MelvilleThe Official World

A Bunch of Diagrammatic Methods for Syllogistic

This paper presents, assesses, and compares six diagrammatic methods for Categorical Syllogistic. Venn’s Method is widely used in logic textbooks; Carroll’s Method is a topologically indistinguishable version of Venn’s Method; and the four remaining methods are my own: the Dual of Carroll’s Method, Gardner’s Method, Gardner–Peirce’s Method, and Ladd’s Method. These methods are divided into two groups of three and the reasons for switching from a method to another within each group are discussed. Finally, a comparison between the Dual of Carroll’s Method and Ladd’s Method supports the main result of the paper, which is an approximation of the two groups of methods.

Логические пособия эпохи позднего Просвещения для женщин

In the focus of my attention there are six German-language textbooks in logic published in the second half of the eighteenth century. What distinguishes these books is that they were all written specially for women. While such works were fairly common in France and Italy during this period, they had something of an exotic character in the German-speaking world. Today these works and their authors are generally seen as secondary and marginal. Nevertheless, they may be of substantial interest in the study of the history of the formation of logic, a fundamental and still relevant discipline in university education. What is the status of logic for women? Is it a kind of publishing by-product paraphrasing classical logic textbooks under a new and unusual title or do they represent a new independent branch? To answer these questions I analyse the chosen works on logic and the reviews which they prompted. I demonstrate that logic manuals for women published in Germany in the second half of the eighteenth century constitute one of the numerous varieties of the popular philosophy genre. Simple language, dialogic or epistolary form, practical orientation and eclecticism — all this brings logic within the intellectual reach of any civilised person, providing him/her with an instrument of performing their own mission, i. e. the employment of their reason. The very fact that the content of logic for women is practically no different from the content of classical compendiums was a revolutionary development, a practical implementation of the postulate that logic is universal and can be understood by everyone, a principle formulated earlier in the works of C. Thomasius and C. Wolff.

The Revival Textbooks from the Old-fashioned Collection of the Centre Community "Nadejda-1869"

The subject of the study was 45 textbooks, published from 1835 to 1875 were preserved in the old-fashioned collection of the centre community "Nadejda-1869". Their authors are 17 teachers who wrote, translated and published first Bulgarian textbooks in the XIX-th century. They are journalists writing the first newspapers and magazines. They lead the struggle for new Bulgarian education, church independence and political freedom. They reform the education and the place of the cell, they build the secular. They are innovators, they introduce the study of new school subjects and languages according to the needs of the time. The text presents first textbooks in Bulgarian language, readings and grammar, arithmetics, geometry and physics. They are textbooks on history, geography, textbooks of natural history. Were preserved textbooks of logic, textbooks of moral and textbooks and dictionaries in French and German, sacred Orthodox catechisms. The article presents the history and development of the curriculum in Bulgarian schools in the ХIX c. Keywords: Old-Fashioned Collection, Centre Community "Nadejda-1869", Teachers, Authors, First Bulgarian Textbooks in the XIX-th, New Bulgarian Secular Education, New School Subjects and Languages, First Textbooks in Bulgarian Language, Readings, Grammar, Arithmetics, Geometry and Physics, History Textbooks, Geography, Textbooks and Dictionaries in French and German