{"title":"Geometry","authors":"Michael Potter","doi":"10.4324/9781315776187-25","DOIUrl":"https://doi.org/10.4324/9781315776187-25","url":null,"abstract":": We study the noncommutative Riemannian geometry of the alternating group A 4 = ( Z 2 × Z 2 ) >⊳ Z 3 using the recent formulation for finite groups in [2]. We find a unique ‘Levi-Civita’ connection for the invariant metric, and find that it has Ricci-flat but nonzero Riemann curvature. We show that it is the unique Ricci-flat connection on A 4 with the standard framing (we solve the vacuum Einstein’s equation). We also propose a natural Dirac operator for the associated spin connection and solve the Dirac equation. Some of our results hold for any finite group equipped with a cyclic conjugacy class of 4 elements. In this case the exterior algebra Ω( A 4 ) has dimensions 1 : 4 : 8 : 11 : 12 : 12 : 11 : 8 : 4 : 1 with top-form 9-dimensional. We also find the noncommutative cohomology H 1 ( A 4 ) = C .","PeriodicalId":368340,"journal":{"name":"The Rise of Analytic Philosophy 1879–1930","volume":"80 1-2 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-10-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126934711","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":"Acquaintance","authors":"Jessica Pepp","doi":"10.4324/9781315776187-39","DOIUrl":"https://doi.org/10.4324/9781315776187-39","url":null,"abstract":"Bertrand Russell famously distinguished between ‘Knowledge by Acquaintance’ and ‘Knowledge by Description’. For much of the latter half of the Twentieth Century, many philosophers viewed the notion of acquaintance with suspicion, associating it with Russellian ideas that they would wish to reject. However in the past decade or two the concept has undergone a striking revival in mainstream ‘analytic’ philosophy – acquaintance is, it seems, respectable again. This is the first collection of new essays devoted to the topic of acquaintance, featuring contributions from many of the world’s leading experts in this area. The volume showcases the great variety of topics in philosophy of mind, epistemology and philosophy of language for which philosophers are currently employing the notion of acquaintance. This book features an extensive introduction by one of the editors, which provides some historical background as well as summarising the main debates and issues in contemporary philosophy where appeals to acquaintance are currently being made. The remaining thirteen essays are grouped thematically into the following four sections: (1) Phenomenal Consciousness, (2) Perceptual Experience, (3) Reference, (4) Epistemology.","PeriodicalId":368340,"journal":{"name":"The Rise of Analytic Philosophy 1879–1930","volume":"63 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-10-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126342140","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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