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Originally published in 1966 On the Syllogism and Other Logical Writings assembles for the first time the five celebrated memoirs of Augustus De Morgan on the syllogism. These are collected together with the more condensed accounts of his researches given in his Syllabus of a Proposed System of Logic an article on Logic contributed to the English Cyclopaedia. De Morgan was among the most distinguished of nineteenth century British mathematicians but is chiefly remembered today as one of (...) the founders of modern mathematical logic. His writings on this subject have been little read, however since apart from his Formal Logic, they lie buried for the most part in inaccessible periodicals. De Morgan's own later amendments are inserted in the text and the editorial introduction gives a summary of the whole and traces in some detail the course of the once-famous feud with Sir William Hamilton of Edinburgh. (shrink)

Augustus De Morgan was a British mathematician and logician. He formulated De Morgan's laws and introduced the term mathematical induction, making its idea rigorousFrom the introduction:"If I had before me a fly and an elephant, having never seen more than one such magnitude of either kind; and if the fly were to endeavor to persuade me that he was larger than the elephant, I might by possibility be placed in a difficulty. The apparently little creature might use (...) such arguments about the effect of distance, and might appeal to such laws of sight and hearing as I, if unlearned in those things, might be unable wholly to reject. But if there were a thousand flies, all buzzing, to appearance, about the great creature; and, to a fly, declaring, each one for himself, that he was bigger than the quadruped; and all giving different and frequently contradictory reasons; and each one despising and opposing the reasons of the others-I should feel quite at my ease. I should certainly say, My little friends, the case of each one of you is destroyed by the rest. I intend to show flies in the swarm, with a few larger animals, for reasons to be given.In every age of the world there has been an established system, which has been opposed from time to time by isolated and dissentient reformers. The established system has sometimes fallen, slowly and gradually: it has either been upset by the rising influence of some one man, or it has been sapped by gradual change of opinion in the many.I have insisted on the isolated character of the dissentients, as an element of the a priori probabilities of the case. Show me a schism, especially a growing schism, and it is another thing. The homeopathists, for instance, shall be, if any one so think, as wrong as St. John Long; but an organized opposition, supported by the efforts of many acting in concert, appealing to common arguments and experience, with perpetual succession and a common seal, as the Queen says in the charter, is, be the merit of the schism what it may, a thing wholly different from the case of the isolated opponent in the mode of opposition to it which reason points out.During the last two centuries and a half, physical knowledge has been gradually made to rest upon a basis which it had not before. It has become mathematical. The question now is, not whether this or that hypothesis is better or worse to the pure thought, but whether it accords with observed phenomena in those consequences which can be shown necessarily to follow from it, if it be true. Even in those sciences which are not yet under the dominion of mathematics, and perhaps never will be, a working copy of the mathematical process has been made. This is not known to the followers of those sciences who are not themselves mathematicians and who very often exalt their horns against the mathematics in consequence. They might as well be squaring the circle, for any sense they show in this particular.". (shrink)

The middle years of the nineteenth century saw two crucial develop ments in the history of modern logic: George Boole's algebraic treat ment of logic and Augustus De Morgan's formulation of the logic of relations. The former episode has been studied extensively; the latter, hardly at all. This is a pity, for the most central feature of modern logic may well be its ability to handle relational inferences. De Morgan was the first person to work out an (...) extensive logic of relations, and the purpose of this book is to study this attempt in detail. Augustus De Morgan (1806-1871) was a British mathematician and logician who was Professor of Mathematics at the University of London (now, University College) from 1828 to 1866. A prolific but not highly original mathematician, De Morgan devoted much of his energies to the rather different field of logic. In his Formal Logic (1847) and a series of papers "On the Syllogism" (1846-1862), he attempted with great ingenuity to reformulate and extend the tradi tional syllogism and to systematize modes of reasoning that lie outside its boundaries. Chief among these is the logic of relations. De Mor gan's interest in relations culminated in his important memoir, "On the Syllogism: IV and on the Logic of Relations," read in 1860. (shrink)

In the early nineteenth century, Henry Brougham endeavored to improve the moral character of England through the publication of educational texts. Soon after, Brougham helped form the Society for the Diffusion of Useful Knowledge to carry his plan of moral improvement to the people. Despite its goal of improving the nation’s moral character, the Society refused to publish any treatises on explicitly moral or religious topics. Brougham instead turned to a mathematician, Augustus De Morgan, to promote mathematics as (...) a rational subject that could provide the link between the secular and religious worlds. Using specific examples gleaned from the treatises of the Society, this article explores both how mathematics was intended to promote the development of reason and morality and how mathematical content was shaped to fit this particular view of the usefulness of mathematics. In the course of these treatises De Morgan proposed a fundamentally new pedagogical approach, one which focused on the student and the role mathematics could play in moral education.Keywords: Mathematics; Education; Henry Brougham; Augustus De Morgan; Nineteenth-century England. (shrink)

De Morgan's Formal Logic, which was published on virtually the same day in 1847 as Boole's The Mathematical Analysis of Logic, contains a logic of complex terms (LCT) which has been sadly neglected. It is surprising to find that LCT contains almost a full theory of Boolean algebra. This paper will: (1) provide some background to LCT; (2) outline its main features; (3) point out some gaps in it; (4) compare it with Boole's algebra; (5) show that it is (...) a lattice-theoretical formulation of Boolean algebra; (6) discuss some issues of historical priority; and (7) conclude with the puzzle of LCT's lack of influence. (shrink)

The present paper expounds the logic notation proposed by Augustus De Morgan in 1850 from within the original context of De Morgan’s account of syllogistic logic and his approach to quantification. The notational system of 1850 is shown to be a flexible tool to state inferences, to prove their validity and to derive formulæ of the respective system by ‘blind’ application of transformation rules. These pertain to the swapping of operator signs, which are of inverse ‘character’ in (...) a two-fold sense: The signs both represent inverse operations and exemplify oppositeness due to their very shapes. Thus, while De Morgan’s initial choice of symbol shapes is due to certain diagrammatic features, his notational system of 1850 leads to an account of logical operations as effected by manipulation of symbol tokens. It is concluded that as an instantiation of what De Morgan terms a ‘calculus of opposite relations’, his notation of 1850 may also be conceived of as a ‘graphicism’ affording for the working of a ‘symbolic machine’ on ‘de-semantification’. (shrink)

This paper studies the possible influences on Boole's logic of the writings related to the controversy over the quantification of the predicate between the philosopher William Hamilton and the mathematician Augustus De Morgan. As Boole himself testified in the introduction to his book The mathematical analysis of logic , this controversy was the external agent that stimulated him into writing up his earlier thoughts about a new conception of logic. But in addition to the external role that was (...) played by the controversy, it seems that other kinds of influences on Boole of Hamilton's and De Morgan's ideas about logic, which were made explicit in writings related to the controversy, can also be traced. (shrink)

Mathematics is the most chameleon of subjects, whose meaning is differently defined in different circumstances. This essay considers the mathematics of Augustus De Morgan as an illustration of the ways that the essence of the subject, the very objects that are included within it, has been adjusted in response to cultural factors. Since these cultural factors are the same ones that shape scientific development, the argument is that the history of mathematics and the history of science are always (...) inextricably bound to one another. (shrink)

This collection of papers from the workshop serves as the initial volume in the new series Texts in Logics and Games—touching on research in logic, mathematics, computer science, and game theory. “A wonderful demonstration of ...

O objetivo do estudo foi investigar a prevalência e motivos do uso de álcool, tabaco e outras drogas por acadêmicos. A amostra foi composta por 560 estudantes, entre 17 e 74 anos ( M = 31,16, DP = 11,10). As substâncias com maior prevalência de uso na vida foram álcool e tabaco. Dentre as drogas ilí..

O climatério/menopausa é caracterizado por intensas alterações morfofisiológicas e comportamentais. O objetivo foi identificar os sinais e sintomas do climatério/menopausa e a sua relação com a Imagem corporal de mulheres ribeirinhas de uma região da Amazônia Brasileira. Estudo incluiu 100 mulheres de seis comunidades ribeirinhas de Itaituba/Pará. Os instrumentos utilizados foram: o questionário sociodemográfico, a Escala dos Sinais e Sintomas da Menopausa (MRS) e a Escala de Silhuetas de Stunkard. Para avaliar as associações entre as variáveis categóricas, o teste qui-quadrado (...) de Pearson e teste exato de Fisher foram utilizados, (p≤0,05). Os resultados indicaram que 76% das mulheres estavam insatisfeitas com a sua imagem corporal, seja porque queriam ter corpos menores ou corpos maiores. Em relação aos sintomas do climatério/menopausa, estes são percebidos de forma moderada pelas mulheres. Conclusão: Se faz necessário levar as mulheres o conhecimento desta fase da vida e assim promover saúde neste importante período da vida. (shrink)

The only complete edition in English of Baruch Spinoza's works, this volume features Samuel Shirley's preeminent translations, distinguished at once by the lucidity and fluency with which they convey the flavor and meaning of Spinoza's original texts. Michael L. Morgan provides a general introduction that places Spinoza in Western philosophy and culture and sketches the philosophical, scientific, religious, moral and political dimensions of Spinoza's thought. Morgan's brief introductions to each work give a succinct historical, biographical, and philosophical overview. (...) A chronology and index are included. (shrink)

For Ivor Grattan-Guinness on the occasion of his retirement. The work of Augustus De Morgan on symbolic logic in the mid-nineteenth century is familiar to historians of logic and mathematics alike. What is less well known is his work on probability and, more specifically, the use of probabilistic ideas and methods in his logic. The majority of De Morgan's work on probability was undertaken around 1837???1838, with his earliest publications on logic appearing from 1839, a period which (...) culminated with the publication of his Formal Logic in 1847. This article examines the overlap between his work on probability theory and logic during the earliest period of his interest in both. (shrink)