This chapter evaluates the criticism of statistics. Already in the early nineteenth century, the statistical approach was attacked on the ground that mere statistical tables cannot demonstrate causality, or that mathematical probability presupposes the occurrence of events wholly by chance. The intent of these early critics was not to suggest the inadequacy of causal laws in social science, but to reject the scientific validity of statistics. The new interpretation of statistics that emerged during the 1860s and 1870s was tied to a view of society in which variation was seen as much more vital. Statistical determinism became untenable precisely when social thinkers who used numbers became unwilling to overlook the diversity of the component individuals in society, and hence denied that regularities in the collective society could justify any particular conclusions about its members. These social discussions on natural science and philosophy bore fruit in the growing interest in the analysis of variation evinced by the late-century mathematical statisticians. To be sure, Francis Galton gave little attention to the debates on human freedom, but Francis Edgeworth was closely familiar with them, and Wilhelm Lexis's important work on dispersion can only be understood in the context of this tradition.
{"title":"STATISTICAL LAW AND HUMAN FREEDOM","authors":"T. Porter","doi":"10.2307/j.ctvxcrz1v.15","DOIUrl":"https://doi.org/10.2307/j.ctvxcrz1v.15","url":null,"abstract":"This chapter evaluates the criticism of statistics. Already in the early nineteenth century, the statistical approach was attacked on the ground that mere statistical tables cannot demonstrate causality, or that mathematical probability presupposes the occurrence of events wholly by chance. The intent of these early critics was not to suggest the inadequacy of causal laws in social science, but to reject the scientific validity of statistics. The new interpretation of statistics that emerged during the 1860s and 1870s was tied to a view of society in which variation was seen as much more vital. Statistical determinism became untenable precisely when social thinkers who used numbers became unwilling to overlook the diversity of the component individuals in society, and hence denied that regularities in the collective society could justify any particular conclusions about its members. These social discussions on natural science and philosophy bore fruit in the growing interest in the analysis of variation evinced by the late-century mathematical statisticians. To be sure, Francis Galton gave little attention to the debates on human freedom, but Francis Edgeworth was closely familiar with them, and Wilhelm Lexis's important work on dispersion can only be understood in the context of this tradition.","PeriodicalId":148909,"journal":{"name":"The Rise of Statistical Thinking, 1820–1900","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-08-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114115664","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The Department of Mathematics and Statistics offers degree curricula in mathematics and in applied mathematics (with its various options), as well as minors and a minor in statistics. Majors acquire a firm foundation in mathematics preparing them for further study, or for careers in mathematics or statistics and related fields. For a minor in MATH or STAT see the “Minors” heading earlier in this section.
{"title":"THE MATHEMATICS OF STATISTICS","authors":"W. L. Bashaw","doi":"10.2307/j.ctvxcrz1v.18","DOIUrl":"https://doi.org/10.2307/j.ctvxcrz1v.18","url":null,"abstract":"The Department of Mathematics and Statistics offers degree curricula in mathematics and in applied mathematics (with its various options), as well as minors and a minor in statistics. Majors acquire a firm foundation in mathematics preparing them for further study, or for careers in mathematics or statistics and related fields. For a minor in MATH or STAT see the “Minors” heading earlier in this section.","PeriodicalId":148909,"journal":{"name":"The Rise of Statistical Thinking, 1820–1900","volume":"89 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-08-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122329295","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This chapter examines probability, which, during the eighteenth century, was customarily interpreted as the calculus of reasonableness for a world of imperfect knowledge. Enlightenment thinkers applied the mathematics of chance to an implausibly rich variety of issues. They used it to demonstrate the rationality of smallpox inoculation, to show how degrees of belief should be apportioned among testimonies of various sorts, and even to establish or preclude the wisdom of belief in biblical miracles. Probabilists also stressed the applicability of their subject to actuarial and demographic matters. Probability calculations based on mortality records had been used increasingly to set rates for life insurance and annuity purchases since Edmond Halley published the first life table in 1693. Mathematicians all over Europe, but especially in the great commercial states, the Netherlands and Great Britain, applied their skill to political arithmetic during the eighteenth century. Meanwhile, some of mathematician Pierre-Simon Laplace's most important contributions arose from his work on population estimates and other demographic problems.
{"title":"Chapter Three. FROM NATURE'S URN TO THE INSURANCE OFFICE","authors":"T. Porter","doi":"10.2307/j.ctvxcrz1v.10","DOIUrl":"https://doi.org/10.2307/j.ctvxcrz1v.10","url":null,"abstract":"This chapter examines probability, which, during the eighteenth century, was customarily interpreted as the calculus of reasonableness for a world of imperfect knowledge. Enlightenment thinkers applied the mathematics of chance to an implausibly rich variety of issues. They used it to demonstrate the rationality of smallpox inoculation, to show how degrees of belief should be apportioned among testimonies of various sorts, and even to establish or preclude the wisdom of belief in biblical miracles. Probabilists also stressed the applicability of their subject to actuarial and demographic matters. Probability calculations based on mortality records had been used increasingly to set rates for life insurance and annuity purchases since Edmond Halley published the first life table in 1693. Mathematicians all over Europe, but especially in the great commercial states, the Netherlands and Great Britain, applied their skill to political arithmetic during the eighteenth century. Meanwhile, some of mathematician Pierre-Simon Laplace's most important contributions arose from his work on population estimates and other demographic problems.","PeriodicalId":148909,"journal":{"name":"The Rise of Statistical Thinking, 1820–1900","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-08-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130476416","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This chapter explores how German economists and statisticians of the historical school viewed the idea of social or statistical law as the product of confusion between spirit and matter or, equivalently, between history and nature. That the laws of Newtonian mechanics are fully time-symmetric and hence can be equally run backwards or forwards could not easily be reconciled with the commonplace observation that heat always flows from warmer to cooler bodies. James Clerk Maxwell, responding to the apparent threat to the doctrine of free will posed by thermodynamics and statistics, pointed out that the second law of thermodynamics was only probable, and that heat could be made to flow from a cold body to a warm one by a being sufficiently quick and perceptive. Ludwig Boltzmann resisted this incursion of probabilism into physics but in the end he was obliged, largely as a result of difficulties presented by the issue of mechanical reversibility, to admit at least the theoretical possibility of chance effects in thermodynamics. Meanwhile, the American philosopher and physicist C. S. Pierce determined that progress—the production of heterogeneity and homogeneity—could never flow from rigid mechanical laws, but demanded the existence of objective chance throughout the universe.
本章探讨了德国历史学派的经济学家和统计学家如何将社会或统计规律的概念视为精神与物质之间或历史与自然之间混淆的产物。牛顿力学定律是完全时间对称的，因此可以向后或向前同样地运行，这与热总是从较热的物体流向较冷的物体这一普遍观察结果不容易调和。詹姆斯·克拉克·麦克斯韦(James Clerk Maxwell)在回应热力学和统计学对自由意志学说的明显威胁时指出，热力学第二定律只是可能的，而且热量可以通过足够快和敏锐的反应从冷的物体流向热的物体。路德维希·玻尔兹曼(Ludwig Boltzmann)反对将概率论引入物理学，但最终，主要是由于机械可逆性问题所带来的困难，他不得不承认，至少在热力学中存在机会效应的理论可能性。与此同时，美国哲学家和物理学家c·s·皮尔斯(C. S. Pierce)认为，进步——产生异质性和同质性——绝不可能来自严格的机械定律，而是要求整个宇宙存在客观的机会。
{"title":"Chapter Seven. TIME'S ARROW AND STATISTICAL UNCERTAINTY IN PHYSICS AND PHILOSOPHY","authors":"T. Porter","doi":"10.2307/j.ctvxcrz1v.16","DOIUrl":"https://doi.org/10.2307/j.ctvxcrz1v.16","url":null,"abstract":"This chapter explores how German economists and statisticians of the historical school viewed the idea of social or statistical law as the product of confusion between spirit and matter or, equivalently, between history and nature. That the laws of Newtonian mechanics are fully time-symmetric and hence can be equally run backwards or forwards could not easily be reconciled with the commonplace observation that heat always flows from warmer to cooler bodies. James Clerk Maxwell, responding to the apparent threat to the doctrine of free will posed by thermodynamics and statistics, pointed out that the second law of thermodynamics was only probable, and that heat could be made to flow from a cold body to a warm one by a being sufficiently quick and perceptive. Ludwig Boltzmann resisted this incursion of probabilism into physics but in the end he was obliged, largely as a result of difficulties presented by the issue of mechanical reversibility, to admit at least the theoretical possibility of chance effects in thermodynamics. Meanwhile, the American philosopher and physicist C. S. Pierce determined that progress—the production of heterogeneity and homogeneity—could never flow from rigid mechanical laws, but demanded the existence of objective chance throughout the universe.","PeriodicalId":148909,"journal":{"name":"The Rise of Statistical Thinking, 1820–1900","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-08-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126083847","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"THE SUPREME LAW OF UNREASON","authors":"T. Porter","doi":"10.2307/j.ctvxcrz1v.11","DOIUrl":"https://doi.org/10.2307/j.ctvxcrz1v.11","url":null,"abstract":"","PeriodicalId":148909,"journal":{"name":"The Rise of Statistical Thinking, 1820–1900","volume":"235 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-08-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127255308","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This chapter analyzes the law of facility of errors. All the early applications of the error law could be understood in terms of a binomial converging to an exponential, as in Abrahan De Moivre's original derivation. All but Joseph Fourier's law of heat, which was never explicitly tied to mathematical probability except by analogy, were compatible with the classical interpretation of probability. Just as probability was a measure of uncertainty, this exponential function governed the chances of error. It was not really an attribute of nature, but only a measure of human ignorance—of the imperfection of measurement techniques or the inaccuracy of inference from phenomena that occur in finite numbers to their underlying causes. Moreover, the mathematical operations used in conjunction with it had a single purpose: to reduce the error to the narrowest bounds possible. With Adolphe Quetelet, all that began to change, and a wider conception of statistical mathematics became possible. When Quetelet announced in 1844 that the astronomer's error law applied also to the distribution of human features such as height and girth, he did more than add one more set of objects to the domain of this probability function; he also began to break down its exclusive association with error.
{"title":"THE ERRORS OF ART AND NATURE","authors":"T. Porter","doi":"10.2307/j.ctvxcrz1v.12","DOIUrl":"https://doi.org/10.2307/j.ctvxcrz1v.12","url":null,"abstract":"This chapter analyzes the law of facility of errors. All the early applications of the error law could be understood in terms of a binomial converging to an exponential, as in Abrahan De Moivre's original derivation. All but Joseph Fourier's law of heat, which was never explicitly tied to mathematical probability except by analogy, were compatible with the classical interpretation of probability. Just as probability was a measure of uncertainty, this exponential function governed the chances of error. It was not really an attribute of nature, but only a measure of human ignorance—of the imperfection of measurement techniques or the inaccuracy of inference from phenomena that occur in finite numbers to their underlying causes. Moreover, the mathematical operations used in conjunction with it had a single purpose: to reduce the error to the narrowest bounds possible. With Adolphe Quetelet, all that began to change, and a wider conception of statistical mathematics became possible. When Quetelet announced in 1844 that the astronomer's error law applied also to the distribution of human features such as height and girth, he did more than add one more set of objects to the domain of this probability function; he also began to break down its exclusive association with error.","PeriodicalId":148909,"journal":{"name":"The Rise of Statistical Thinking, 1820–1900","volume":"142 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-08-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133768399","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"List of Abbreviations","authors":"","doi":"10.2307/j.ctvxcrz1v.3","DOIUrl":"https://doi.org/10.2307/j.ctvxcrz1v.3","url":null,"abstract":"","PeriodicalId":148909,"journal":{"name":"The Rise of Statistical Thinking, 1820–1900","volume":"72 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-08-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124573739","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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