As familiar as the form of the mathematical equation is to us, the ostensibly simple act of equating unlike things was an achievement many centuries in the making, and one that would ultimately redefine European mathematical enquiry such that its bias toward geometry and the concrete would be displaced by a bias toward algebraic abstraction. The moment of that displacement was the nineteenth century, and its broader significance is on particularly striking display in the British context, where the implications of algebraic abstraction were the object of sustained enquiry among mathematicians, logicians, and economists. This article argues that the ascendance of the algebraic equation, and the transformation in the conception of number on which it was premised, were not simply the product of evolutionary pressures internal to mathematics; the Victorian embrace of algebra was also a response to the practical and cognitive demands of Victorian economic life, which was increasingly reliant on attenuated exchange relations and merely nominal forms of ownership. This was an economy organized around the global extension of trade and characterized by the exponential growth of financial intermediation, of what Walter Bagehot called “number abstracted from reference.” Victorian economic practices thus modeled an abstraction that helped to justify the abstractions of mathematics, and that mathematics in turn was used by economic theorists to argue for the necessity and objectivity of their models. This mutually sustaining dialogue is particularly visible in the writings of William Stanley Jevons, who applied the principles of algebra to philosophy and economic theory so as to reconceive the logic of cognitive and social life in terms of equations. This logic, for which he was merely a spokesman, continues to shape our faith in the special value of abstract, theoretical knowledge.
数学等式的形式对我们来说再熟悉不过了，但将不同的事物等同起来这一看似简单的行为却是一项酝酿了许多世纪的成就，它最终将重新定义欧洲的数学研究，使其对几何和具体事物的偏爱被对代数抽象的偏爱所取代。这种转变的时刻是 19 世纪，其更广泛的意义在英国的背景下表现得尤为突出，代数抽象的含义是数学家、逻辑学家和经济学家持续探究的对象。本文认为，代数等式的兴起以及作为其前提的数概念的转变，并不仅仅是数学内部进化压力的产物；维多利亚时代对代数的拥护也是对维多利亚时代经济生活的实践和认知需求的回应，维多利亚时代的经济生活越来越依赖于弱化的交换关系和仅仅是名义上的所有权形式。这种经济是围绕贸易的全球扩展而组织起来的，其特点是金融中介的指数式增长，也就是沃尔特-贝格霍特所说的 "从参照中抽象出来的数字"。因此，维多利亚时期的经济实践以抽象为模型，帮助证明数学的抽象是合理的，而数学反过来又被经济理论家用来论证其模型的必要性和客观性。这种相互支持的对话在威廉-斯坦利-杰文斯（William Stanley Jevons）的著作中尤为明显，他将代数学原理应用于哲学和经济理论，从而用方程重新构思了认知和社会生活的逻辑。他只是这一逻辑的代言人，而这一逻辑继续塑造着我们对抽象理论知识特殊价值的信念。
{"title":"Victorian Equations","authors":"Andrea Kelly Henderson","doi":"10.1086/727657","DOIUrl":"https://doi.org/10.1086/727657","url":null,"abstract":"As familiar as the form of the mathematical equation is to us, the ostensibly simple act of equating unlike things was an achievement many centuries in the making, and one that would ultimately redefine European mathematical enquiry such that its bias toward geometry and the concrete would be displaced by a bias toward algebraic abstraction. The moment of that displacement was the nineteenth century, and its broader significance is on particularly striking display in the British context, where the implications of algebraic abstraction were the object of sustained enquiry among mathematicians, logicians, and economists. This article argues that the ascendance of the algebraic equation, and the transformation in the conception of number on which it was premised, were not simply the product of evolutionary pressures internal to mathematics; the Victorian embrace of algebra was also a response to the practical and cognitive demands of Victorian economic life, which was increasingly reliant on attenuated exchange relations and merely nominal forms of ownership. This was an economy organized around the global extension of trade and characterized by the exponential growth of financial intermediation, of what Walter Bagehot called “number abstracted from reference.” Victorian economic practices thus modeled an abstraction that helped to justify the abstractions of mathematics, and that mathematics in turn was used by economic theorists to argue for the necessity and objectivity of their models. This mutually sustaining dialogue is particularly visible in the writings of William Stanley Jevons, who applied the principles of algebra to philosophy and economic theory so as to reconceive the logic of cognitive and social life in terms of equations. This logic, for which he was merely a spokesman, continues to shape our faith in the special value of abstract, theoretical knowledge.","PeriodicalId":48130,"journal":{"name":"Critical Inquiry","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2024-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139125154","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"社会学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":":Pathologies of Motion: Historical Thinking in Medicine, Aesthetics, and Poetics","authors":"James Chandler","doi":"10.1086/727653","DOIUrl":"https://doi.org/10.1086/727653","url":null,"abstract":"","PeriodicalId":48130,"journal":{"name":"Critical Inquiry","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2024-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139128419","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"社会学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":":Nervous Systems: Art, Systems, and Politics since the 1960s","authors":"Ina Blom","doi":"10.1086/726298","DOIUrl":"https://doi.org/10.1086/726298","url":null,"abstract":"","PeriodicalId":48130,"journal":{"name":"Critical Inquiry","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45659288","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"社会学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":":What Pornography Knows: Sex and Social Protest since the Eighteenth Century","authors":"Gabriel Ojeda-Sague","doi":"10.1086/726307","DOIUrl":"https://doi.org/10.1086/726307","url":null,"abstract":"","PeriodicalId":48130,"journal":{"name":"Critical Inquiry","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44202653","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"社会学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":":Book, Text, Medium: Cross-Sectional Reading for a Digital Age","authors":"John Cayley","doi":"10.1086/726311","DOIUrl":"https://doi.org/10.1086/726311","url":null,"abstract":"","PeriodicalId":48130,"journal":{"name":"Critical Inquiry","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44684565","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"社会学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The twentieth century evolved several ways of treating literary authorship in terms of an object rather than a subject. One tradition, derived more or less distantly from late nineteenth century symbolism, identifies the source of authorship with the medium, the tradition, or language itself. Exponents of this view include writers as different as T. S. Eliot, Martin Heidegger, and Paul De Man. A second tradition, associated most closely with Michel Foucault, understands authorship in terms of impersonal social structures. Both of these traditions move the question of authorship from subject to object by bypassing the experience of the writer. I outline a third tradition, one that locates the movement from who to what within the experience of authorship itself. I enumerate key features of this model of authorship—which represents a revision of the classical concept of inspiration—through close readings of poems by Sylvia Plath and Jorie Graham.
{"title":"What Is an Author?","authors":"Michael W. Clune","doi":"10.1086/726273","DOIUrl":"https://doi.org/10.1086/726273","url":null,"abstract":"The twentieth century evolved several ways of treating literary authorship in terms of an object rather than a subject. One tradition, derived more or less distantly from late nineteenth century symbolism, identifies the source of authorship with the medium, the tradition, or language itself. Exponents of this view include writers as different as T. S. Eliot, Martin Heidegger, and Paul De Man. A second tradition, associated most closely with Michel Foucault, understands authorship in terms of impersonal social structures. Both of these traditions move the question of authorship from subject to object by bypassing the experience of the writer. I outline a third tradition, one that locates the movement from who to what within the experience of authorship itself. I enumerate key features of this model of authorship—which represents a revision of the classical concept of inspiration—through close readings of poems by Sylvia Plath and Jorie Graham.","PeriodicalId":48130,"journal":{"name":"Critical Inquiry","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41352543","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"社会学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":":Emancipation after Hegel: Achieving a Contradictory Revolution","authors":"Andrew Pendakis","doi":"10.1086/726309","DOIUrl":"https://doi.org/10.1086/726309","url":null,"abstract":"","PeriodicalId":48130,"journal":{"name":"Critical Inquiry","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41416819","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"社会学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This article, originally delivered as a lecture at the University of Chicago, is a critical reading of Ernesto Laclau and Chantal Mouffe’s Hegemony and Socialist Strategy: Towards a Radical Democratic Politics. Following Antonio Gramsci, their book reverses the meaning of the term hegemony. The traditional use of the term (for military or political leadership) shifts and gives birth to a new signification. Hegemony currently designates a privilege but a discursive one only. It is the privilege conferred to a certain word or category serving as a unifying symbol for different and even heterogeneous forms of political resistance. Hegemony thus understood retains an idea of direction but without any dominating intention. It just orients multiple revolt movements without reducing their differences. Such a unifying symbol appears as a specific signifier devoid of any content or reference, thus ready to bear any contextual meaning. Does this new understanding of hegemony succeed in providing a nondogmatic and nonbinding process of unification, or does it secretely reinstall the logic of commandment?
{"title":"Contemporary Political Adventures of Meaning: What Is Hegemony?","authors":"Catherine Malabou","doi":"10.1086/726295","DOIUrl":"https://doi.org/10.1086/726295","url":null,"abstract":"This article, originally delivered as a lecture at the University of Chicago, is a critical reading of Ernesto Laclau and Chantal Mouffe’s Hegemony and Socialist Strategy: Towards a Radical Democratic Politics. Following Antonio Gramsci, their book reverses the meaning of the term hegemony. The traditional use of the term (for military or political leadership) shifts and gives birth to a new signification. Hegemony currently designates a privilege but a discursive one only. It is the privilege conferred to a certain word or category serving as a unifying symbol for different and even heterogeneous forms of political resistance. Hegemony thus understood retains an idea of direction but without any dominating intention. It just orients multiple revolt movements without reducing their differences. Such a unifying symbol appears as a specific signifier devoid of any content or reference, thus ready to bear any contextual meaning. Does this new understanding of hegemony succeed in providing a nondogmatic and nonbinding process of unification, or does it secretely reinstall the logic of commandment?","PeriodicalId":48130,"journal":{"name":"Critical Inquiry","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46532781","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"社会学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This article sketches the emergence of visual schematisms from Immanuel Kant to Gilles Deleuze, Michel Foucault, and Jean-François Lyotard. It demonstrates the centrality of differentiation in these visual representations, as underscored by the “bar” or so-called vinculum (a mathematical term). It ultimately concludes that the weakness or dialectical contradiction of the thus differentiated entities lies in their tendency to fold back into each other, returning to the One which it was the purpose of the schematization to exclude in the first place.
{"title":"Schematizations, or How to Draw a Thought","authors":"Fredric Jameson","doi":"10.1086/726275","DOIUrl":"https://doi.org/10.1086/726275","url":null,"abstract":"This article sketches the emergence of visual schematisms from Immanuel Kant to Gilles Deleuze, Michel Foucault, and Jean-François Lyotard. It demonstrates the centrality of differentiation in these visual representations, as underscored by the “bar” or so-called vinculum (a mathematical term). It ultimately concludes that the weakness or dialectical contradiction of the thus differentiated entities lies in their tendency to fold back into each other, returning to the One which it was the purpose of the schematization to exclude in the first place.","PeriodicalId":48130,"journal":{"name":"Critical Inquiry","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43505602","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"社会学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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