[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-seo-678033-105":3,"detail-sidebar-cat-0-en-105":80,"doc-detail-678033-en":130},{"code":4,"msg":5,"data":6},0,"ok",{"site_id":7,"language":8,"slug":9,"title":10,"keywords":11,"description":12,"schema_data":13,"social_meta":73,"head_meta":75,"extra_data":77,"updated_unix":79},105,"en","the-venn-behind-the-diagram","The Venn Behind the Diagram","","John Venn is widely remembered as the inventor of the diagram that bears his name, still used to solve set-theory problems and to test syllogisms in logic. The note contrasts Venn diagrams with Euler diagrams, showing why the two forms are often confused yet fundamentally different. It traces how Venn’s diagrams emerged from adapting Euler’s approach to Boolean logic, and discusses what can and cannot be known about their origin and invention, including Cambridge influences.",{"@graph":14,"@context":72},[15,34,55],{"@type":16,"itemListElement":17},"BreadcrumbList",[18,23,27,31],{"item":19,"name":20,"@type":21,"position":22},"https://docshare.wps.com","Home","ListItem",1,{"item":24,"name":25,"@type":21,"position":26},"https://docshare.wps.com/document/","Document",2,{"item":28,"name":29,"@type":21,"position":30},"https://docshare.wps.com/document/literature/","Literature",3,{"item":32,"name":10,"@type":21,"position":33},"https://docshare.wps.com/document/the-venn-behind-the-diagram/678033/",4,{"url":32,"name":10,"@type":35,"image":36,"author":41,"headline":10,"publisher":44,"fileFormat":47,"inLanguage":8,"description":12,"dateModified":48,"datePublished":49,"encodingFormat":47,"isAccessibleForFree":50,"interactionStatistic":51},"DigitalDocument",{"url":37,"@type":38,"width":39,"height":40},"https://docshare.wps.com/thumbnails/the-venn-behind-the-diagram/678033.png","ImageObject",300,407,{"name":42,"@type":43},"Adam","Person",{"url":19,"name":45,"@type":46},"DocShare","Organization","application/pdf","2026-11-05","2026-11-04",true,{"@type":52,"interactionType":53,"userInteractionCount":33},"InteractionCounter",{"@type":54},"ViewAction",{"@type":56,"mainEntity":57},"FAQPage",[58,64,68],{"name":59,"@type":60,"acceptedAnswer":61},"Why are Venn and Euler diagrams often confused?","Question",{"text":62,"@type":63},"They both use circles and can look similar, and both summarise information. However, many Euler diagrams cannot be Venn diagrams and vice versa, so the forms are not essentially the same.","Answer",{"name":65,"@type":60,"acceptedAnswer":66},"What does the article say about how Venn diagrams were constructed?",{"text":67,"@type":63},"It describes a two-step procedure: first draw a primary diagram representing the combinations in a proposition or argument, then add syntactic signs such as shading to indicate the state of sub-classes.",{"name":69,"@type":60,"acceptedAnswer":70},"What evidence does the article give for when Venn invented the diagrams?",{"text":71,"@type":63},"It cites circumstantial evidence: Venn said the diagrams were suggested by his study of George Boole’s algebraic logic, and it notes that around 1878 he finally managed to engage with Boole’s work.","https://schema.org",{"og:url":32,"og:type":74,"og:title":10,"og:site_name":45,"og:description":12},"article",{"robots":76,"canonical":32},"index,follow",{"doc_id":78,"site_id":7},678033,1793783116,{"code":4,"msg":81,"data":82},"success",[83,87,90,94,99,104,109,114,119,122,126],{"id":22,"doc_module":4,"doc_module_name":25,"category_name":84,"show_sort_weight":85,"slug":86},"Story & Novel",90,"story-novel",{"id":26,"doc_module":4,"doc_module_name":25,"category_name":29,"show_sort_weight":88,"slug":89},80,"literature",{"id":33,"doc_module":4,"doc_module_name":25,"category_name":91,"show_sort_weight":92,"slug":93},"Exam",70,"exam",{"id":95,"doc_module":4,"doc_module_name":25,"category_name":96,"show_sort_weight":97,"slug":98},5,"Comic",60,"comic",{"id":100,"doc_module":4,"doc_module_name":25,"category_name":101,"show_sort_weight":102,"slug":103},6,"Technology",50,"technology",{"id":105,"doc_module":4,"doc_module_name":25,"category_name":106,"show_sort_weight":107,"slug":108},7,"Healthcare",40,"healthcare",{"id":110,"doc_module":4,"doc_module_name":25,"category_name":111,"show_sort_weight":112,"slug":113},8,"Research & Report",30,"research-report",{"id":115,"doc_module":4,"doc_module_name":25,"category_name":116,"show_sort_weight":117,"slug":118},9,"Religion & Spirituality",20,"religion-spirituality",{"id":117,"doc_module":4,"doc_module_name":25,"category_name":120,"show_sort_weight":117,"slug":121},"World Cup","world-cup",{"id":123,"doc_module":4,"doc_module_name":25,"category_name":124,"show_sort_weight":123,"slug":125},10,"Lifestyle","lifestyle",{"id":127,"doc_module":4,"doc_module_name":25,"category_name":128,"show_sort_weight":95,"slug":129},19,"General","general",{"code":4,"msg":81,"data":131},{"doc_id":78,"user_id":132,"nickname":42,"user_avatar":133,"doc_module":4,"category_id":26,"category_name":29,"doc_title":10,"doc_description":12,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":33,"is_deleted":4,"is_public":22,"is_downloadable":22,"audit_status":22,"page_count":30,"language":139,"language_code":8,"site_id":7,"html_lang":8,"table_of_contents":140,"faqs":141,"seo_title":142,"seo_description":12,"update_tm":79,"read_time":95},1374404737137,"https://ap-avatar.wpscdn.com/davatar_155a257f0dc6eb9ab79c44ca47cae57d","The Venn Behind the Diagram Lukas M. Verburgt, Netherlands Institute for Advanced Study  \nJ ohn Venn is mostly remembered  \nas the inventor of the famous dia  \ngram that bears his name. It is still widely used today, for instance, to solve problems in set theory and to test the validity of syllogisms in logic.  \nLike Euler diagrams or truth tables, Venn diagrams summarise and present certain information and, in the best case, they also generate new information. Given their similarities, Euler and Venn diagrams are often mentioned in the same breath or even said to be essentially one and the same. Both are formed by using circles, are intuitively understandable and sometimes look alike. The fact is, however, that they are very different. For one thing, there are many Euler diagrams that cannot be Venn diagrams, and vice versa.  \nThe long-standing confusion of Euler and Venn diagrams points to an interesting paradox – or an irony, perhaps. Venn  \nCredit: CPA Media Pte Ltd | Alamy Stock Photo  \nJohn Venn (1834–1923)  \nthem consisted of a two-step procedure: first, draw a primary diagram that represents the combinations between the terms involved in a proposition or an argument; second, add syntactic signs, like shading, onto this scheme to indicate the state of the sub-classes. Thus, ‘All x is y’ (i.e.‘The sub-class xy is empty’) would go like this: make a two-term diagram (Figure 1) to represent xy , xy , xy, and xy; and then shade (stripes in Figure 2) the compartment xy to obtain the diagram of the proposition.1  \nThe reason why almost nothing is known about the origin of Venn diagrams is as simple as it is mysterious: there is no mention of them at all in Venn’s own writings or correspondence prior to 1880, and in his autobiography, Venn dryly reports that he ‘first hit upon’ Euler diagrams in 1862 and that his own diagrams ‘did not occur to [him] till much later’ [2, p. 70] .  \nis best remembered for the Venn diagram, which, at least in its form of three overlapping circles, is of Google Doodle fame. Atthe same time, its nature is often misunderstood and almost nothing is known about its origin. There is a whole literature on the first point. In this short note, I would like to briefly reflect on the second.  \nVenn first published his diagrams in 1880 in a paper which appeared in the PhilosophicalMagazine [1] . His method for making  \nRon Weickart, [network-graphics.com](network-graphics.com) Ron Weickart, [network-graphics.com](network-graphics.com)  \nx y  \nFigure 1: Venn diagram for two terms  \nx y  \nFigure 2: Venn diagram for ‘All x is y’  \nHis description of the journey that led him to their invention is brief and hardly insightful [1, p. 4]:  \nI tried at first, as others have done, to represent the complicated propositions [of Boole] by the old [Eulerian] plan; but the representations failed altogether to answer the desired purpose; and after some consideration I hit upon the plan here described.  \nThis makes clear that Venn diagrams emerged from the attempt to adapt Euler diagrams to Boolean logic. On this basis, much can be learned about how Venn arrived at his diagrams. One can retrace the steps that opened the way to their invention, drawing together post-Eulerian developmentsin diagrammatic representation and Boolean logicians’ dealings with the so-called problem of elimination [3] . But all this says nothing about when and why Venn invented them.  \nSome people, including myself, have argued that it is likely that Venn invented his diagrams at some point in the late 1870s [4, pp. 177–208] . The circumstantial evidence is twofold. First, Venn himself wrote that they were suggested to him by his study of George Boole’s algebraic logic. Second, it was around 1878 that he finally managed to come to grips with Boole’s work.  \nThe why question is more tricky. Any answer toit will be contextual at best. It has much to do with the Cambridge tradition of mathematics in which Venn was trained as an undergraduate. Interesting","cbCaisrhNIY5iBya","https://ap.wps.com/l/cbCaisrhNIY5iBya","pdf",687601,"English","# John Venn and the diagram\n# Venn vs. Euler diagrams\n# Origins and publication history\n# From Euler diagrams to Boolean logic\n# Timing of the invention\n# Cambridge tradition and the “why”","[{\"question\":\"Why are Venn and Euler diagrams often confused?\",\"answer\":\"They both use circles and can look similar, and both summarise information. However, many Euler diagrams cannot be Venn diagrams and vice versa, so the forms are not essentially the same.\"},{\"question\":\"What does the article say about how Venn diagrams were constructed?\",\"answer\":\"It describes a two-step procedure: first draw a primary diagram representing the combinations in a proposition or argument, then add syntactic signs such as shading to indicate the state of sub-classes.\"},{\"question\":\"What evidence does the article give for when Venn invented the diagrams?\",\"answer\":\"It cites circumstantial evidence: Venn said the diagrams were suggested by his study of George Boole’s algebraic logic, and it notes that around 1878 he finally managed to engage with Boole’s work.\"}]","The Venn Behind the Diagram | PDF"]