{"title":"机会组合:被历史遗忘的理论","authors":"John D. Norton","doi":"10.1162/posc_a_00621","DOIUrl":null,"url":null,"abstract":"Abstract Seventeenth-century “chance combinatorics” was a self-contained theory. It had an objective notion of chance derived from physical devices with chance properties, such as casts of dice, combinatorics to count chances and, to interpret their significance, a rule for converting these counts into fair wagers. It lacked a notion of chance as a measure of belief, a precise way to connect chance counts with frequencies and a way to compare chances across different games. These omissions were not needed for the theory’s interpretation of chance counts: determining which are fair wagers. The theory provided a model for how indefinitenesses could be treated with mathematical precision in a special case and stimulated efforts to seek a broader theory.","PeriodicalId":19867,"journal":{"name":"Perspectives on Science","volume":"3 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2023-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Chance Combinatorics: The Theory that History Forgot\",\"authors\":\"John D. Norton\",\"doi\":\"10.1162/posc_a_00621\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Abstract Seventeenth-century “chance combinatorics” was a self-contained theory. It had an objective notion of chance derived from physical devices with chance properties, such as casts of dice, combinatorics to count chances and, to interpret their significance, a rule for converting these counts into fair wagers. It lacked a notion of chance as a measure of belief, a precise way to connect chance counts with frequencies and a way to compare chances across different games. These omissions were not needed for the theory’s interpretation of chance counts: determining which are fair wagers. The theory provided a model for how indefinitenesses could be treated with mathematical precision in a special case and stimulated efforts to seek a broader theory.\",\"PeriodicalId\":19867,\"journal\":{\"name\":\"Perspectives on Science\",\"volume\":\"3 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2023-10-17\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Perspectives on Science\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1162/posc_a_00621\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"Arts and Humanities\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Perspectives on Science","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1162/posc_a_00621","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"Arts and Humanities","Score":null,"Total":0}
Chance Combinatorics: The Theory that History Forgot
Abstract Seventeenth-century “chance combinatorics” was a self-contained theory. It had an objective notion of chance derived from physical devices with chance properties, such as casts of dice, combinatorics to count chances and, to interpret their significance, a rule for converting these counts into fair wagers. It lacked a notion of chance as a measure of belief, a precise way to connect chance counts with frequencies and a way to compare chances across different games. These omissions were not needed for the theory’s interpretation of chance counts: determining which are fair wagers. The theory provided a model for how indefinitenesses could be treated with mathematical precision in a special case and stimulated efforts to seek a broader theory.