{"title":"Symmetry, Invariance, and Imprecise Probability","authors":"Zachary Goodsell, Jacob M Nebel","doi":"10.1093/mind/fzae048","DOIUrl":null,"url":null,"abstract":"It is tempting to think that a process of choosing a point at random from the surface of a sphere can be probabilistically symmetric, in the sense that any two regions of the sphere which differ by a rotation are equally likely to include the chosen point. Isaacs, Hájek and Hawthorne (2022) argue from such symmetry principles and the mathematical paradoxes of measure to the existence of imprecise chances and the rationality of imprecise credences. Williamson (2007) has argued from a related symmetry principle to the failure of probabilistic regularity. We contend that these arguments fail, because they rely on auxiliary assumptions about probability which are inconsistent with symmetry to begin with. We argue, moreover, that symmetry should be rejected in light of this inconsistency, and because it has implausible decision-theoretic implications. The weaker principle of probabilistic invariance says that the probabilistic comparison of any two regions is unchanged by rotations of the sphere. This principle supports a more compelling argument for imprecise probability. We show, however, that invariance is incompatible with mundane judgements about what is probable. Ultimately, we find reason to be suspicious of the application of principles like symmetry and invariance to non-measurable regions.","PeriodicalId":48124,"journal":{"name":"MIND","volume":"76 1","pages":""},"PeriodicalIF":1.8000,"publicationDate":"2024-10-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"MIND","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1093/mind/fzae048","RegionNum":1,"RegionCategory":"哲学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"0","JCRName":"PHILOSOPHY","Score":null,"Total":0}
引用次数: 0
Abstract
It is tempting to think that a process of choosing a point at random from the surface of a sphere can be probabilistically symmetric, in the sense that any two regions of the sphere which differ by a rotation are equally likely to include the chosen point. Isaacs, Hájek and Hawthorne (2022) argue from such symmetry principles and the mathematical paradoxes of measure to the existence of imprecise chances and the rationality of imprecise credences. Williamson (2007) has argued from a related symmetry principle to the failure of probabilistic regularity. We contend that these arguments fail, because they rely on auxiliary assumptions about probability which are inconsistent with symmetry to begin with. We argue, moreover, that symmetry should be rejected in light of this inconsistency, and because it has implausible decision-theoretic implications. The weaker principle of probabilistic invariance says that the probabilistic comparison of any two regions is unchanged by rotations of the sphere. This principle supports a more compelling argument for imprecise probability. We show, however, that invariance is incompatible with mundane judgements about what is probable. Ultimately, we find reason to be suspicious of the application of principles like symmetry and invariance to non-measurable regions.
期刊介绍:
Mind has long been a leading journal in philosophy. For well over 100 years it has presented the best of cutting edge thought from epistemology, metaphysics, philosophy of language, philosophy of logic, and philosophy of mind. Mind continues its tradition of excellence today. Mind has always enjoyed a strong reputation for the high standards established by its editors and receives around 350 submissions each year. The editor seeks advice from a large number of expert referees, including members of the network of Associate Editors and his international advisers. Mind is published quarterly.