No mathematical background is necessary to appreciate this classic of probability theory, which remains unsurpassed in its clarity, readability, and sheer charm. Its author, British logician John Venn (1834-1923), popularized the famous Venn Diagrams that are commonly used in teaching elementary mathematics.

SYMBOLIC LOGIC. CHAPTER I. ON THE FORMS OF LOGICAL PROPOSITION. IT has been mentioned in the Introduction that the System of Logic which this work is ...

Schemes of diagrammatic representation have been so familiarly introduced into logical treatises during the last century or so, that many readers, even of those who have made no professional study of logic, may be supposed to be acquainted with the general nature and object of such devices. Of these schemes one only, viz. that commonly called "Eulerian circles," has met with any general acceptance. A variety of others indeed have been proposed by ingenious and celebrated logicians, several of which would (...) claim notice in a historical treatment of the subject; but they mostly do not seem to me to differ in any essential respect from that of Euler. They rest upon the same leading principle, and are subject all alike to the same restrictions and defects. We must therefore cast about for some new scheme of diagrammatic representation which shall be competent to indicate imperfect knowledge on our part; for this will at once enable us to appeal to it step by step in the process of working out our conclusions. I have never seen any hint at such a scheme, though the want seems so evident that one would suppose that something of the kind must have been proposed before. (shrink)

This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work. This work is in the public domain (...) in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant. (shrink)

This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work.This work is in the public domain in (...) the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant. (shrink)

CHAPTER I. THE FOUNDATIONS OF LOGIC :— THE UNIVERSE AS THE MATERIAL LOGICIAN REGARDS IT. SINCE Logic, as conceived and expounded in this work, ...

John Grote struggled to construct an intelligible account of philosophy at a time when radical change and sectarian conflict made understanding and clarity a rarity. This book answers three questions: * How did John Grote develop and contribute to modern Cambridge and British philosophy? * What is the significance of these contributions to modern philosophy in general and British Idealism and language philosophy in particular? * How were his ideas and his idealism incorporated into the modern philosophical tradition? (...) Grote influenced his contemporaries, such as his students Henry Sidgwick and John Venn, in both style and content; he forged a brilliantly original philosophy of knowledge, ethics, politics and language, from a synthesis of the major British and European philosophies of his day; his social and political theory provide the origins of the 'new liberal' ideas later to reach their zenith in the writings of Green, Sidgwick, and Collingwood; he founded the ‘Cambridge style’ associated with Moore, Russell, Broad, McTaggart and Wittgenstein; and he was also a major influence on Oakeshott. (shrink)

The duality of truth and falsity in a Boolean algebra of propositions is used to generate a duality of belief and disbelief. To each additive probability measure that represents belief there corresponds a dual additive measure that represents disbelief. The dual measure has its own peculiar calculus, in which, for example, measures are added when propositions are combined under conjunction. A Venn diagram of the measure has the contradiction as its total space. While additive measures are not self-dual, the (...) epistemic state of complete ignorance is represented by the unique, monotonic, non-additive measure that is self-dual in its contingent propositions. Convex sets of additive measures fail to represent complete ignorance since they are not self-dual. (shrink)

Investigamos a lógica de Leonhard Euler com ênfase no papel dos “diagramas de Euler”. Concluímos que os referidos diagramas constituem um instrumento intuitivo, embora não sistemático, para determinar validade na silogística tradicional, isto é, a silogística munida de implicações conversacionais. Nisto, contrastam-se com os diagramas de Venn que constituem um instrumento sistemático, porém menos intuitivo, para determinar validade numa silogística mais voltada para os fundamentos da matemática moderna.: We investigate the logic of Leonhard Euler, giving emphasis to the role (...) of “Euler diagrams”. We conclude that these diagrams are an intuitive, non-systematic instrument for determining validity in the traditional syllogistic, that is, the syllogistic furnished with conversational implications. In this regard, they contrast with Venn diagrams which are a systematic, less intuitive instrument for determining validity in a syllogistic more appropriate for the foundation of modern mathematics. Keywords: History of Logic. Leonhard Euler. Euler Diagrams. Venn Diagrams. (shrink)

Spider diagrams are based on Euler and Venn/Peirce diagrams, forming a system which is as expressive as monadic first order logic with equality. Rather than being primarily intended for logicians, spider diagrams were developed at the end of the 1990s in the context of visual modelling and software specification. We examine the original goals of the designers, the ways in which the notation has evolved and its connection with the philosophical origins of the logical diagrams of Euler, Venn (...) and Peirce on which spider diagrams are based. Using Peirce’s concepts and classification of signs, we analyse the ways in which different sign types are exploited in the notation. Our hope is that this analysis may be of interest beyond those readers particularly interested in spider diagrams, and act as a case study in deconstructing a simple visual logic. Along the way, we discuss the need for a deeper semiotic engagement in visual modelling. (shrink)

John Venn is remembered today as the inventor of the famous "Venn diagram." The postmortem fame of the namesake diagram has until now eclipsed Venn's own status as one of the most accomplished logicians in his day. Praised by John Stuart Mill as a "highly successful thinker" with much "power of original thought," Venn profoundly influenced nineteenth-century philosophers, ranging from Mill and Henry Sidgwick to Charles Sanders Peirce. Venn was heir to a clerical, (...) Evangelical dynasty but religious doubts led him to resign Holy Orders and instead turn to an academic life, writing influential textbooks on probability theory and logic and advocating for education reform, including for women's education. Venn also collaborated with Francis Galton in the unofficial Anthropometrical Laboratory, and, through his writing and teaching, a direct line can be traced from Venn and his circle to the development of analytic philosophy in the work of W. E. Johnson, G. E. Moore, Bertrand Russell, and C. D. Broad. Through family descent, Venn was connected to eminent Victorians like Leslie Stephen and Virginia Woolf. This essential book explores Venn's life and work in context, taking readers on his journey from Evangelical son to Cambridge don. The picture that emerges of Venn, the person, is of a man with many sympathies-sometimes mutually reinforcing and at other times outwardly contradictory. (shrink)

John Venn is known as one of the clearest expounders of the interpretation of probability as the frequency of a particular outcome in a potentially unlimited series of possible events. This view he held to be incompatible with the alternate interpretation of probability as a measure of the degree of belief that would rationally be held about a certain outcome based upon the reliability of testimony and other prior information. This paper explores the reasons why Venn may (...) have been so opposed to the degree-of-belief interpretation and suggests that it may have been a way for him to resolve a conflict in his own mind between his ideas of proper scientific methods of inference and the religious beliefs that he held as a young man. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:John Venn. A Life in Logic by Lukas M. VerburgtClaudia CristalliLukas M. VerburgtJohn Venn. A Life in Logic Chicago and London: The University of Chicago Press, 2022. 411 pp., incl. indexThis is the first intellectual biography of John Venn (1834–1923), British logician, “philosopher and antiquarian” (DNB). Until now, Venn had not been studied as a philosophical figure in its own right. He (...) is mostly remembered today for the “Venn Diagrams,” a graphical device illustrating logical relations such as inclusion, exclusion, conjunction, disjunction, and for having systematically articulated a frequentist theory of probability. Together with an in-depth account of Venn’s logical developments, of his studies in probability theory, and of its applications to history and to anthropometry, Lukas M. Verburgt brings to life Venn’s spiritual struggles within—and eventually out of— his family’s religion, evangelicalism. Verburgt’s reconstruction is substantiated by many extracts from Venn’s correspondence and private notes, which add substantially to the value of this biography. (Of note is Verburgt’s 2022 editon of Venn’s unpublished writings and slected correspondence, which can be considered a companion to this biography).While showing the connections of epistemology, religion and academic politics in Victorian Cambridge, Verburgt contributes an important chapter in the history of logic and of empiricist philosophy.The book opens with a chapter on Venn’s childhood and early youth (1834–53), largely drawn from manuscript material of the Venn family—the “Parentalia”—and from Venn’s Annals of a Clerical Family, where he included “autobiographical recollections” (p. 2). The chapter introduces the reader to the values of a prominent evangelical family and to their peculiar way of understanding Christianity as a faith to be embedded in habit and to be taught by example. The following two [End Page 385] chapters follow Venn’s development, first as a student at Caius college, Cambridge (1853–57) and then as a country curate; the chapters elaborate on the institutional history of the college and on parish life from the perspective of evangelical orthodoxy. Chapter 4 is still chronologically situated within Venn’s early clerical service but is arranged thematically around his first publication (1862), “Science of History,” which contains some elements of the fundamental ideas elaborated in the Logic of Chance (1866): namely, that probability theory could only make predictions about long-run frequencies of events, and never about individual cases (p. 77). The core of Venn’s argument in 1862 revolved around possible atheistic implications of a science of history. If at some point it would be possible to predict future events, would there still be free will? Or a God? In his reply, Venn maintained that any prediction concerning individual agents could be defeated by assuming that the agent gets to know the prediction and changes her actions accordingly (pp. 74–76).After the publication of the “Science of History” essay, Venn left the parish for Cambridge, where he worked first as a Catechist (1862– 1867) and then as a moral sciences lecturer. Verburgt devotes chapter 5 to that and to the Cambridge milieu, where Venn sides for university reforms and engages with the Grote Club, all while drifting away from evangelical orthodoxy. After laying out Venn’s theory of probability (Chapter 6), Verburgt returns to an integrated analysis of Venn’s scientific and religious thought in chapter 7. This chapter may be particularly relevant for pragmatist readers, since here Verburgt highlights the commonalities between Venn’s “religious logic” and the notion of belief that will be expressed in more detail by pragmatism. Verburgt focuses on Venn’s logic in three subsequent chapters (Chapters 8, 9 and 11). Considered together, they provide a comprehensive history of Venn’s logical development, which Verburgt proudly announces as the first of this kind (p. xx). The last chapter on Venn’s logic (Chapter 11) also includes Verburgt’s argument for “includ[ing] Venn in the local history of early analytic philosophy at Cambridge” (p. 262). Chapters 10 and 12 recount Venn’s last years with particular emphasis on his interests in natural and historical sciences; they provide relevant material for scholars interested in the history and philosophy of... (shrink)

The goal of this paper is to provide a detailed reading of John Venn's Logic of Chance as a work of logic or, more specifically, as a specific portion of the general system of so-called ‘material’ logic developed in his Principles of Empirical or Inductive Logic and to discuss it against the background of his Boolean-inspired views on the connection between logic and mathematics. It is by means of this situating of Venn 1866 [The Logic of Chance. (...) An Essay on the Foundations and Province of the Theory of Probability. With Especial Reference to Its Application to Moral and Social Science, London: Macmillan] within the entirety of his oeuvre that it becomes both possible to revisit and necessary to re-articulate its place in the history of the frequency interpretation of probability. For it is clear that if Venn's approach to logic not only allowed him to establish its foundations on the basis of a process of idealization and define it as consisting of so-called hypothetical infinite series, bu.. (shrink)

In 1897, Cambridge University created a professorship in Mental Philosophy and Logic; despite the double name it was filled by a “mental philosopher,” James Ward, who did no work in logic. The chief logician candidate, John Venn, then turned his attention elsewhere, leaving Cambridge without senior leadership in logic. Ward himself turned to other philosophical issues, doing little further original work in mental philosophy. Cambridge became a center for a fresh interpretation of logic in the early 20th century, (...) but with no help from Venn. Psychology split off from mental philosophy, and what remained, the “philosophy of mind,” was developed elsewhere until after Ward’s tenure. (shrink)

A short characterization is given of the contents and origin of the collection of books on logic donated by John Venn to the Cambridge University Library and of its relation to the bibliography in...

In 1866, the young John Venn published The Logic of Chance, motivated largely by the desire to correct what he saw as deep fallacies in the reasoning of historical determinists such as Henry Buckle and in the optimistic heralding of a true social science by Adolphe Quetelet. Venn accepted the inevitable determinism implied by the physical sciences, but denied that the stable social statistics cited by Buckle and Quetelet implied a similar determinism in human actions. Venn (...) maintained that probability statements were intelligible solely as projections of the ultimate frequency of an outcome in an unlimited series of trials and therefore led to no inferences about free will. An issue here was Venn's claim that although the aggregate probability may be stable, the individual events were completely irregular and, in fact, displayed randomness. Venn's concept of randomness was really apparent, or pseudo-, randomness, which could be totally determined. Ironically, Venn's frequentist position was very useful to the growing field of statistics, which could develop correlations and predictive models empirically without having to address implications for personal freedom or fatalism. (shrink)

The goal of this paper is to correct a widespread misconception about the work of Robert Leslie Ellis and John Venn, namely that it can be considered as the ‘British empiricist’ reaction against the traditional theory of probability. It is argued, instead, that there was no unified ‘British school’ of frequentism during the nineteenth century. Where Ellis arrived at frequentism from a metaphysical idealist transformation of probability theory’s mathematical calculations, Venn did so on the basis of an (...) empiricist critique of its ‘inverse application’. (shrink)

John Venn w Formal Logic zbudował pewien system sylogistyki, będący jedną z realizacji idei kwantyfikacji orzeczników. Interesującą rekonstrukcję tego systemu zaproponował V.I. Markin. Markin posługuje się pięcioma funktorami pierwotnymi {aa,ai,ia,ii,e}. Wyrażenia elementarne SaaP,SaiP,SiaP,SiiP oraz SeP są czytane odpowiednio: wszelkie S są wszelkimi P, wszelkie S są pewnymi P, pewne S są wszelkimi P, pewne S są pewnymi P oraz żadne S nie są P.Markin podaje aksjomatykę dla tego systemu. Proponuje też reguły translacji jego formuł na język sylogistyki klasycznej, (...) o aksjomatyce Łukasiewicza {SaS, SiS, MaP/\SaM ε SaP, MaP/\MiS ε SiP} oraz reguły translacji odwrotnej.To sformułowanie sylogistyki Venna można uprościć przez przyjęcie konwencji notacyjnej:SφΨP / SφP/\PΨS SφP/\PΨS / SφΨP dla φ,Ψε{a,ι}.Proponowana jest nowa aksjomatyka dla sylogistyki Venna z mocnym rozumieniem zdań szczegółowo-twierdzących. Badane są związki logiczne między sylogistyką Venna i systemem Łulasiewicza. Zostaje sformułowany system z mocnym rozumieniem zdań szczegółowo-twierdzących. Podany jest dowód, że systemy SI i SL są równowane. (shrink)

In this paper we argue that there were several currents, ideas and problems in 19th-century logic that motivated John Venn to develop his famous logic diagrams. To this end, we first examine the problem of uncertainty or over-specification in syllogistic that became obvious in Euler diagrams. In the 19th century, numerous logicians tried to solve this problem. The most famous was the attempt to introduce dashed circles into Euler diagrams. The solution that John Venn developed for (...) this problem, however, came from a completely different area of logic: instead of orienting to syllogistic like Euler diagrams, Venn applied Boolean algebra to improve visual reasoning. Venn’s contribution to solving the problem of elimination also played an important role. The result of this development is still known today as the ‘Venn Diagram’. (shrink)

The attempt to find usable diagrams fornterms of the sort devised by John Venn seems to have originated with Venn himself, who published diagrams for up to five classes (the fifth class, however, was shaped like a doughnut, and contained an area outside itself — like the hole in the doughnut). Venn then suggested that “if we wanted to use a diagram forsixterms (x, y, z, w, v, u) the best plan would probably be to taketwofive-term (...) figures, one for theupart and one for the non-upart of all the other combinations …” Such a method would, as Venn admits, be somewhat confusing to the eye, and thus fail to fulfil one of the major purposes of the diagram; nevertheless, it is a method which could be extended to covernclasses.Venn also suggests (but without illustration) another method for drawing diagrams fornterms: “… the rule of formation would be very simple. We should merely have to begin by drawing any closed figure, and then proceed to draw others subject to the one condition that each intersect once, and once only, all the existing subdivisions produced by those which had gone before.” Then, in a rather surprising footnote, he adds: “It will be found that when we adhere to continuous figures, instead of the discontinuous five-term figure given above, there is a tendency for the resultant outlines thus successively drawn to assume a comb-like shape after the first four or five. If we begin by circles or other rounded figures the teeth are curved, if by parallelograms then they are straight. (shrink)

It is of common use in modern Venn diagrams to mark a compartment with a cross to express its non-emptiness. Modern scholars seem to derive this convention from Charles S. Peirce, with the assumption that it was unknown to John Venn. This paper demonstrates that Venn actually introduced several methods to represent existentials but felt uneasy with them. The resistance to formalize existentials was not limited to diagrammatic systems, as George Boole and his followers also failed (...) to provide a satisfactory symbolic representation for them. This difficulty points out issues that are inherent to the very nature of existentials. This paper assesses the various methods designed for the representation of existential statements with Venn diagrams. First, Venn’s own attempts are discussed and compared with other solutions proposed by his contemporaries and successors, notably Lewis Carroll and Peirce. Since disjunctives hold an important role in an effective representation of existentials, their representation is also discussed. Finally, recent methods for the diagrammatic representation of existing individuals, rather than mere existence, are surveyed. (shrink)

It is not rare to meet in scientific literature with a figure made of three circles, intersecting in such a way as to delineate all the combinations of the components that they stand for. This figure is commonly known as a ‘Venn diagram’ or ‘Venn’s three circles’. In this paper, we argue that many so-called Venn diagrams found in modern scientific literature do not truly depict intersections, and hence, are not true Venn diagrams.

During 1881, the British logicians John Venn and Hugh MacColl engaged in a brief dispute in Nature about ‘symbolical logic’. The letters to the editor shed interesting light on the early reception of MacColl’s contributions to logic and his position in the logical community of the Victorian era. Drawing on the correspondence between Venn and William Stanley Jevons, this paper analyzes the background and context of these letters, adding to the recent interest in the social dimensions of (...) the development of British algebraic logic in the confusing intermediary period between the 1870s and 1890s. (shrink)

Though the revised edition of A Theory of Justice, published in 1999, is the definitive statement of Rawls's view, so much of the extensive literature on Rawls's theory refers to the first edition. This reissue makes the first edition once again available for scholars and serious students of Rawls's work.

Though the revised edition of A Theory of Justice, published in 1999, is the definitive statement of Rawls's view, so much of the extensive literature on Rawls's theory refers to the first edition.

John MacFarlane explores how we might make sense of the idea that truth is relative. He provides new, satisfying accounts of parts of our thought and talk that have resisted traditional methods of analysis, including what we mean when we talk about what is tasty, what we know, what will happen, what might be the case, and what we ought to do.