LEADER 09080nam 2200517 450 001 996466559703316 005 20230421142806.0 010 $a0-8176-4823-2 035 $a(CKB)4100000011867314 035 $a(MiAaPQ)EBC6533829 035 $a(Au-PeEL)EBL6533829 035 $a(OCoLC)1246576292 035 $a(PPN)255291388 035 $a(EXLCZ)994100000011867314 100 $a20211019d2021 uy 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 14$aThe legacy of Mario Pieri in foundations and philosophy of mathematics /$fElena Anne Corie Marchisotto, Francisco Rodri?guez-Consuegra, James T. Smith 210 1$aNew York, New York :$cBirkha?user,$d[2021] 210 4$d©2021 215 $a1 online resource (xxii, 603 pages) $cillustrations 311 $a0-8176-4822-4 327 $aIntro -- Foreword -- Preface -- Style and Translation -- Evolution of the Project and Acknowledgments -- Contents -- Illustrations -- 1 Pieri's Contributions to Foundations and Philosophy of Mathematics -- 1.1 Pieri, the Man, the Scholar, the Teacher -- 1.2 Philosophy of Mathematics and Mathematical Logic -- 1.3 Foundations of Geometry -- 2 Pieri's Philosophy of Deductive Sciences -- 2.1 Primitive Concepts -- 2.2 Definitions -- 2.3 Definitions by Abstraction -- 2.4 Postulates, or Primitive Propositions -- 2.5 Proofs -- 2.6 Abstract Deductive Science -- 2.7 Logic and Mathematics -- 2.8 Pieri's Letter to Russell -- 2.9 Metamathematics -- 2.10 Semantics and Model Theory -- 2.11 Nominalism -- 3 Two Paths to Logical Consequence: Pieri and the Peano School -- 3.1 Tarski's Definition of Consequence -- 3.2 Aristotle's Counterexample Method -- 3.3 Independence of the Parallel Postulate -- 3.4 Logical Consequence in a Model-Theoretic Context: The Peano School -- 3.4.1 Peano -- 3.4.2 Pieri -- 3.4.3 Padoa -- 4 Pieri's 1900 Paris Paper -- ON GEOMETRY ENVISAGED AS A PURELY LOGICAL SYSTEM -- I -- II -- III -- IV -- V -- VI -- VII -- 5 Pieri and Projective Geometry -- 5.1 Pieri's Studies, Research, and Teaching -- 5.2 Evolution of Projective Ideas and Methods -- 5.3 Synthetic Projective Geometry as an Autonomous Field -- 5.4 Geometry as a Logical System -- 5.5 The Transformational Approach -- 5.6 Multidimensional Projective Geometry -- 5.7 From Duality to Plurality -- 6 Pieri's 1898 Geometry of Position Memoir -- THE PRINCIPLES OF THE GEOMETRY OF POSITION -- LIST OF ABBREVIATIONS -- 1 The Primitive Entities -- POSTULATE I -- POSTULATE II -- POSTULATE III -- POSTULATES IV AND V -- POSTULATE VI -- POSTULATE VII -- POSTULATE VIII -- POSTULATE IX -- POSTULATE X -- 2 The Alignment Relation and the Projective Line -- POSTULATE XI. 327 $a3 The Visual of a Form and Projective Planes -- POSTULATE XII -- 4 The Plane Quadrangle and the Harmonic Relation -- POSTULATE XIII. -- POSTULATE XIV -- 5 The Projective Segment -- POSTULATE XV -- POSTULATE XVI -- POSTULATE XVII -- 6 Further Properties of Segments -- 7 Natural Orderings and Senses of a Projective Line -- 8 The Projective Triangle -- 9 Segmental Transformations -- POSTULATE XVIII -- 10 Harmonic Correspondences and STAUDT's Theorem -- 11 Projective Hyperplanes of the Third Species and Ordinary Space -- POSTULATE XIX -- 12 Projective Hyperplanes of the nth Species and Absolute Projective Space -- POSTULATE XIX' -- POSTULATE XX' -- APPENDIX -- 7 Transformational Geometry -- 7.1 Motions and Transformations -- 7.2 Isometries and Similarities -- 7.3 Transformations as Tools -- 7.4 Transformations in Foundational Studies -- 7.5 Postlude -- 8 Pieri's 1900 Point and Motion Memoir -- ON ELEMENTARY GEOMETRY -- LIST OF ABBREVIATIONS -- 1 Generalities about point and about motion. The relation of collinearity among points. Line, plane, and sphere are introduced. -- POSTULATE I -- POSTULATES II and III -- POSTULATE IV -- POSTULATE V -- POSTULATE VI -- POSTULATE VII -- POSTULATE VIII -- POSTULATE IX -- 2 Rotating a line onto itself. Midpoint of a pair of points. Rotating a plane onto itself. Orthogonality relation among three points or between two intersecting lines -- POSTULATE X -- POSTULATE XI -- POSTULATE XII -- POSTULATE XIII -- POSTULATE XIV -- 3 Rotating one plane onto another. Orthogonality of lines and planes. Various properties relating to lines, planes, and spheres. -- POSTULATE XV -- POSTULATE XVI -- 4 Points internal or external to a sphere. Segments, rays, half-planes, angles, and so on. -- POSTULATE XVII -- POSTULATE XVIII -- POSTULATE XIX. 327 $a5 Relation less than or greater than between two segments or between two angles. Triangle is introduced. Congruence of triangles and other propositions of the first and third books of Euclid. -- 6 Sum of two segments. Other properties of triangles, circles, and so on. Continuity of a line. -- POSTULATE XX -- 9 Pieri's Works on Foundations and Philosophy of Mathematics -- 9.1 Course Materials and a Translation -- 9.1.1 Higher Geometry Lectures by Riccardo De Paolis -- 1882-1883 -- 1883-1884 -- 9.1.2 Geometry of Position by G. K. C. von Staudt -- Pieri's Treatment of the Fundamental Theorem -- Pieri's Handwritten Notations -- 9.1.3 Projective Geometry: Lectures at the Military Academy -- 9.1.4 Course Records from Catania University Archives -- 9.1.5 Projective Geometry: Lectures at Parma -- Pieri 1910 -- Pieri 1911c -- 9.1.6 Descriptive Geometry: Lectures at Parma -- 9.2 Foundations of Projective Geometry -- 9.2.1 Principles That Support the Geometry of Position -- 9.2.2 Postulates for Abstract Projective Geometry of Hyperspaces -- 9.2.3 Primitive Entities of Abstract Projective Geometry -- 9.2.4 Intermezzo (1897b) -- 9.2.5 Principles of the Geometry of Position Composed into a Deductive Logical System -- 9.2.6 New Method for Developing Projective Geometry Deductively -- 9.2.7 Principles That Support the Geometry of Lines -- 9.2.8 Staudt's Fundamental Theorem and the Principles of Projective Geometry -- Introduction (1) -- Proof of the Fundamental Theorem (2) -- Results Not Dependent on Continuity Principles (3-6) -- Continuity and Archimedean Principles -- Pieri's Archimedean Postulate XVIII' (1, 7-9) -- Pieri's Postulate XVIII'' (9) -- Real Projective Geometry of Degree < -- 2 (10-11) -- Conclusion -- 9.2.9 New Principles of Complex Projective Geometry -- Background -- Axiomatic Framework -- Incidence Postulates and Dependence (1). 327 $aChains (2-4) -- Coordinates and Cross Ratios (7) -- Further Topics, from 4-7 and 1906a -- Conclusion -- 9.2.10 On the Staudtian Definition of Homography -- 9.3 Foundations of Elementary and Inversive Geometry -- 9.3.1 On Elementary Geometry as a Hypothetical Deductive System: Monograph on Point and Motion -- 9.3.2 Elementary Geometry Based on the Notions of Point and Sphere -- 9.3.3 New Principles of the Geometry of Inversions -- 9.4 Arithmetic, Logic, and Philosophy of Science -- 9.4.1 Geometry Envisioned as a Purely Logical System -- 9.4.2 On an Arithmetical Definition of the Irrationals -- 9.4.3 A Look at the New Logico-Mathematical Direction of the Deductive Sciences -- 9.4.4 On the Consistency of the Axioms of Arithmetic -- 9.4.5 On the Axioms of Arithmetic -- 10 Central Themes and Impact of Pieri's Work -- 10.1 Philosophical Themes in Pieri's Research -- 10.2 Themes in Foundations of Geometry -- Pieri's Views on Abstract Mathematics -- 10.2.1 Geometry as an Abstract Science -- 10.2.2 Geometry from a Synthetic Perspective -- 10.2.3 Geometry from a Transformational Point of View -- 10.2.4 Geometries Constructed as Autonomous Disciplines -- 10.2.5 Continuity and Archimedean Principles -- 10.2.6 Minimizing the Number of Primitive Notions -- 10.3 Pedagogical Themes -- Projective Geometry -- Inversive and Elementary Geometry -- 10.4 Pieri's Impact -- 10.4.1 Philosophy -- 10.4.2 Foundations of Geometry -- Projective Geometry -- Inversive Geometry -- Elementary Geometry -- 10.4.3 Pedagogy -- 10.5 Opportunities for Future Research -- Foundations of Geometry -- Pedagogy -- Logic and Philosophy -- Appendix -- A.1 Errata and Addenda for Marchisotto and Smith 2007 -- A.1.1 Errors and Corrections -- A.1.2 New Items for Chapter 6: Pieri's Works -- A.2 Two Letters from Louis Couturat -- A.3 Russell's Annotations on Principles of the Geometry of Position. 327 $aA.4 Pieri's 1905b letter to Oswald Veblen -- Bibliography -- Permissions and Credits -- Index of Persons -- Index of Subjects. 606 $aMathematics$xHistory 606 $aHistòria de la matemàtica$2thub 608 $aLlibres electrònics$2thub 615 0$aMathematics$xHistory. 615 7$aHistòria de la matemàtica 676 $a510.9 700 $aMarchisotto$b Elena$0252366 702 $aRodri?guez-Consuegra$b Francisco A.$f1951- 702 $aSmith$b James T. 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a996466559703316 996 $aThe legacy of Mario Pieri in foundations and philosophy of mathematics$92830640 997 $aUNISA LEADER 04585nam 2200913 450 001 9910792472403321 005 20210510213414.0 010 $a0-8122-9158-1 024 7 $a10.9783/9780812291582 035 $a(CKB)2660000000035133 035 $a(EBL)3442587 035 $a(SSID)ssj0001546114 035 $a(PQKBManifestationID)16135684 035 $a(PQKBTitleCode)TC0001546114 035 $a(PQKBWorkID)12134979 035 $a(PQKB)11084027 035 $a(OCoLC)918967464 035 $a(MdBmJHUP)muse46671 035 $a(DE-B1597)452791 035 $a(OCoLC)1013944018 035 $a(OCoLC)952803233 035 $a(DE-B1597)9780812291582 035 $a(Au-PeEL)EBL3442587 035 $a(CaPaEBR)ebr11091001 035 $a(CaONFJC)MIL823206 035 $a(OCoLC)932313298 035 $a(MiAaPQ)EBC3442587 035 $a(PPN)254125832 035 $a(EXLCZ)992660000000035133 100 $a20150429h20162016 uy| 0 101 0 $aeng 135 $aurnnu---|u||u 181 $ctxt 182 $cc 183 $acr 200 10$aThinking sex with the early moderns /$fValerie Traub 210 1$aPhiladelphia :$cUniversity of Pennsylvania Press,$d[2016] 210 4$d©2016 215 $a1 online resource (477 p.) 225 1 $aHaney Foundation series 300 $aDescription based upon print version of record. 311 $a0-8122-2389-6 311 $a0-8122-4729-9 320 $aIncludes bibliographical references and index. 327 $tFront matter --$tContents --$tPreface --$tChapter 1. Thinking Sex: Knowledge, Opacity, History --$tPart I. Making the History of Sexuality --$tChapter 2. Friendship's Loss: Alan Bray's Making of History --$tChapter 3. The New Unhistoricism in Queer Studies --$tChapter 4. The Present Future of Lesbian Historiography --$tPart II. Scenes of Instruction; or, Early Modern Sex Acts --$tChapter 5. The Joys of Martha Joyless: Queer Pedagogy and the (Early Modern) Production of Sexual Knowledge --$tChapter 6. Sex in the Interdisciplines --$tChapter 7. Talking Sex --$tPart III. The Stakes of Gender --$tChapter 8. Shakespeare's Sex --$tChapter 9. The Sign of the Lesbian --$tChapter 10. Sex Ed; or, Teach Me Tonight --$tNotes --$tBibliography --$tIndex --$tAcknowledgments 330 $aWhat do we know about early modern sex, and how do we know it? How, when, and why does sex become history? In Thinking Sex with the Early Moderns, Valerie Traub addresses these questions and, in doing so, reorients the ways in which historians and literary critics, feminists and queer theorists approach sexuality and its history. Her answers offer interdisciplinary strategies for confronting the difficulties of making sexual knowledge. Based on the premise that producing sexual knowledge is difficult because sex itself is often inscrutable, Thinking Sex with the Early Moderns leverages the notions of opacity and impasse to explore barriers to knowledge about sex in the past. Traub argues that the obstacles in making sexual history can illuminate the difficulty of knowing sexuality. She also argues that these impediments themselves can be adopted as a guiding principle of historiography: sex may be good to think with, not because it permits us access but because it doesn't. 410 0$aHaney Foundation series. 606 $aSex in literature 606 $aEnglish literature$yEarly modern, 1500-1700$xHistory and criticism 606 $aSex (Psychology)$xHistory$y16th century 606 $aSex (Psychology)$xHistory$y17th century 606 $aGender identity$zEngland$xHistory$y16th century 606 $aGender identity$zEngland$xHistory$y17th century 606 $aLanguage and sex$xHistory 606 $aRenaissance$zEngland 610 $aGay Studies. 610 $aGender Studies. 610 $aHistory. 610 $aLesbian Studies. 610 $aMedieval and Renaissance Studies. 610 $aQueer Studies. 610 $aWomen's Studies. 615 0$aSex in literature. 615 0$aEnglish literature$xHistory and criticism. 615 0$aSex (Psychology)$xHistory 615 0$aSex (Psychology)$xHistory 615 0$aGender identity$xHistory 615 0$aGender identity$xHistory 615 0$aLanguage and sex$xHistory. 615 0$aRenaissance 676 $a820.9/353809031 700 $aTraub$b Valerie$f1958-$01555216 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910792472403321 996 $aThinking sex with the early moderns$93816931 997 $aUNINA