Modalities in Medieval Logic Sara L. Uckelman Modalities in Medieval Logic ILLC Dissertation Series DS-2009-04 For further information about ILLC publications, please contact Institute for Logic, Language and Computation Universiteit van Amsterdam Science Park 904 1098 XH Amsterdam phone: +31-20-525 6051 fax: +31-20-525 5206 e-mail: [email protected] homepage: http://www.illc.uva.nl/ Modalities in Medieval Logic Academisch Proefschrift ter verkrijging van de graad van doctor aan de Universiteit van Amsterdam op gezag van de Rector Magnificus prof. dr. D.C. van den Boom ten overstaan van een door het college voor promoties ingestelde commissie, in het openbaar te verdedigen in de Agnietenkapel op dinsdag 1 september 2009, te 12.00 uur door Sara Liana Uckelman geboren te Waukesha, Wisconsin, Verenigde Staten van Amerika. Promotiecommissie: Promotores: Prof. dr. B. L¨owe Prof. dr. M.J.B. Stokhof Overige leden: Prof. dr. E.P. Bos Dr. J. Maat Prof. dr. S.L. Read Dr. P. van Emde Boas Prof. dr. F.J.M.M. Veltman Prof. dr. P. Øhrstrøm Faculteit der Natuurwetenschappen, Wiskunde en Informatica Universiteit van Amsterdam Copyright (cid:13)c 2009 by Sara L. Uckelman Cover art by Ursula Whitcher. Cover design by Matt Kuhns. Printed and bound by Ipskamp Drukkers. ISBN: 978-90-5776-194-2 Credo ut intelligam —Saint Anselm of Canterbury v Contents Acknowledgments xi 1 The changing scope of logic 1 1.1 Two views on the scope of logic . . . . . . . . . . . . . . . . . . . 2 1.2 ‘History of’ as an operator . . . . . . . . . . . . . . . . . . . . . . 5 1.2.1 The via antiqua and via nova . . . . . . . . . . . . . . . . 6 1.2.2 The Humanist revolution . . . . . . . . . . . . . . . . . . . 9 1.3 A modern view of medieval logic . . . . . . . . . . . . . . . . . . . 12 2 Logic and the condemnations of 1277 15 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 2.1.1 The condemnation in Paris . . . . . . . . . . . . . . . . . . 16 2.1.2 The prohibition in Oxford . . . . . . . . . . . . . . . . . . 20 2.2 Historical background . . . . . . . . . . . . . . . . . . . . . . . . . 22 2.2.1 The structure of a university . . . . . . . . . . . . . . . . . 22 2.2.2 Previous condemnations and strictures . . . . . . . . . . . 25 2.3 The propositions . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 2.4 After the condemnation . . . . . . . . . . . . . . . . . . . . . . . 33 2.4.1 Oxford . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 2.4.2 Paris . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 2.5 Modal and temporal logic in the 14th century . . . . . . . . . . . 36 2.5.1 Modal logic . . . . . . . . . . . . . . . . . . . . . . . . . . 37 2.5.2 Temporal logic . . . . . . . . . . . . . . . . . . . . . . . . 38 2.6 Concluding remarks . . . . . . . . . . . . . . . . . . . . . . . . . . 40 3 St. Anselm on agency and obligation 41 3.1 Agency as a modal notion . . . . . . . . . . . . . . . . . . . . . . 41 3.2 Anselm on facere . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 3.2.1 Philosophical and theological motivations . . . . . . . . . . 44 vii 3.2.2 The types and modes of doing . . . . . . . . . . . . . . . . 47 3.3 Semantics for non-normal modal logics . . . . . . . . . . . . . . . 51 3.4 The syntax of agency . . . . . . . . . . . . . . . . . . . . . . . . . 55 3.5 Human agency, obligation, and goodness . . . . . . . . . . . . . . 61 4 13th-century quantified modal logic 67 4.1 Modes and modal propositions . . . . . . . . . . . . . . . . . . . . 68 4.1.1 Construction . . . . . . . . . . . . . . . . . . . . . . . . . 70 4.1.2 Quantity . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 4.1.3 Quality . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 4.2 Inferential relations . . . . . . . . . . . . . . . . . . . . . . . . . . 74 4.2.1 Implications . . . . . . . . . . . . . . . . . . . . . . . . . . 74 4.2.2 Conversions . . . . . . . . . . . . . . . . . . . . . . . . . . 75 4.2.3 Modal syllogisms . . . . . . . . . . . . . . . . . . . . . . . 76 4.3 Contrasts with modern views of modal logic . . . . . . . . . . . . 78 4.3.1 The nature of modality . . . . . . . . . . . . . . . . . . . . 78 4.3.2 The truth conditions of modal sentences . . . . . . . . . . 80 4.3.3 Concluding remarks . . . . . . . . . . . . . . . . . . . . . . 83 5 A quantified predicate logic for ampliation and restriction 85 5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 5.2 Basic notions and definitions . . . . . . . . . . . . . . . . . . . . . 87 5.3 Appellation, ampliation, and restriction . . . . . . . . . . . . . . . 90 5.4 Constructing a formal model . . . . . . . . . . . . . . . . . . . . . 93 5.5 Applying the formal model . . . . . . . . . . . . . . . . . . . . . . 97 5.6 Conclusions and future work . . . . . . . . . . . . . . . . . . . . . 101 6 Swyneshed’s notion of self-falsification 103 6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103 6.2 Paradoxes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104 6.2.1 Fitch’s paradox of knowability . . . . . . . . . . . . . . . . 105 6.2.2 The Liar . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106 6.2.3 Solutions to paradoxes . . . . . . . . . . . . . . . . . . . . 107 6.3 Modern responses to Fitch’s Paradox . . . . . . . . . . . . . . . . 107 6.3.1 Dynamic epistemic logic . . . . . . . . . . . . . . . . . . . 109 6.3.2 Van Benthem’s solution . . . . . . . . . . . . . . . . . . . 111 6.4 Medieval responses to the Liar . . . . . . . . . . . . . . . . . . . . 111 6.4.1 Na¨ıve restriction strategy solutions . . . . . . . . . . . . . 112 6.4.2 Roger Swyneshed’s solution . . . . . . . . . . . . . . . . . 115 6.5 Announcement pointer semantics . . . . . . . . . . . . . . . . . . 118 6.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119 viii