Medieval vs Contemporary Metaphysics and Logic of Intentionality MSc Thesis (Afstudeerscriptie) written by Andrzej Bułeczka (born April 24th, 1989 in Zdu´nskaWola, Poland) under the supervision of Prof. Francesco Berto, and submitted to the Board of Examiners in partial fulfillment of the requirements for the degree of MSc in Logic at the Universiteit van Amsterdam. Date of the public defense: Members of the Thesis Committee: June 23, 2017 Prof. Francesco Berto Prof. Catarina Dutilh Novaes Prof. Benedikt Löwe Dr Jaap Maat Prof. Robert van Rooij Prof. Frank Veltman Andrzej Bułeczka: Medieval vs Contemporary Metaphysics and Logic of Intentionality, , © June 2017 Breviary Lord, grant me the ability to compose a long sentence, whose line, customarily from breath to breath, is a line spanned like a suspension bridge like a rainbow the alpha and omega of the ocean Lord, grant me the strength and agility of those who build sentences long and expansive as a spreading oak tree, like a great valley; may they contain worlds, shadows of worlds, and worlds of dreams may the main clause rule confidently over dependent claus- es, control their course, a circuitous but expressive basso continuo, endure unmoved above the elements in motion, draw them to itself like nucleus draws electrons by unseen laws of gravitation I pray then for a long sentence, sculptured by the sweat of my brow, extending so far that in each there might be reflected the mirror image of a cathedral, a great oratorio, a triptych, and also animals mighty and minuscule, train stations, the heart brimming with sorrow, rocky cliffs, and the furrow of the fate in the hand — Zbigniew Herbert Ad maiorem Dei gloriam. iv ABSTRACT This thesis addresses three challenges posed by intentionality - the ability of our mental states and language to be about something - to a logician: an apparent reference to non-existent objects, intentional indeterminacy and the failure of substitutivity of coextensive terms in an intentional context. Since intentionality plays an important role in our everyday reasoning, a proper formal account of it is highly desirable, yet it requires a departure from classical logic. One can modify classical logic and adapt the formal apparatus to account for the aforementioned problems (Graham Priest’s logic for intentional- ity serves as an example of such an approach in this work) or one can make an even more radical shift and seek for inspiration in a different logical tradition like the terminist logic developed in the Late Middle Ages by figures like William of Ockham or John Buridan. The sec- ond path is explored here as a modest attempt to show that once we abandon the bias against the history of logic as irrelevant, we can ac- tually get access to firm logical solutions inaccessible from a classical perspective, while still practicing logic proper. v Among all worldly things there is nothing which seems worthy to be preferred to friendship. Friendship unites good men and preserves and promotes virtue. Friendship is needed by all men in whatsoever occupations they engage. — Thomas Aquinas ACKNOWLEDGMENTS Logicians are not usually concerned with miracles. Yet, for the author of the present work it seems a bit like a miracle that this thesis is written. Be it as it may, it would definitely not happen without the help of others. First, special thanks are due to my supervisor Francesco Berto, who was not afraid of my obscure ideas, patiently guided me through the whole long process and taught me how to express my thoughts in a more explicit and precise way. I also benefited a lot from the helpful comments on the earlier draft by Magali Roques and Ernesto Perini Santos, discussions about Ockham’s semantics with Claude Panaccio, encouragement to work on medieval logic as logic from Sara Uckel- man, discussions with amazing people who participated in the win- ter school on medieval logic in Geneva last December. I want to thank Gyula Klima for writing papers on medieval logic which sparkled my interest in it and motivated me to do the Master of Logic Program in general, and to pick the very subject of my thesis in particular. I am very grateful to Zbigniew Zdziarski for his invaluable help with cor- recting the English of the thesis. I also need to thank my friends without whom I would not be where I am now. Thanks to other MoL students who helped me so many times and from whom I have learned so many things, not only about logic. Thanks to my friends from the Leidenhoven College who supported me in so many ways over the last three years in Amster- dam and always encouraged me to be a better man. Many thanks are also due to my friends in Poland - it is so great to have people on whom you can always count. Last but not least, I want to thank my family for supporting me through all ups and downs of my stay in the Netherlands uncondi- tionally. Deo gratias! vii CONTENTS introduction xi i informal exposition1 1 intentionality: easy for a kid, hard for a logi- cian3 1.1 Intentionality: a mental bow 3 1.2 Non-existent objects 6 1.3 Intentional indeterminacy 8 1.4 Substitutivity of identicals 12 1.5 Noneist solutions informally 13 1.5.1 Non-existent Objects 13 1.5.2 Intentional Indeterminacy 15 1.5.3 Substitutivity of Identicals 16 2 medieval logic and semantics: ockham and buri- dan 19 2.1 Medieval Theories of Intentionality 19 2.1.1 Brentano on Intentionality 20 2.1.2 Preliminaries: Intention and Imposition 21 2.1.3 Intentionality in Ockham 24 2.1.4 Intentionality in Buridan 27 2.2 Medieval Logic.. What? 29 2.2.1 Important thus negligible 29 2.2.2 Medieval Logic: Formal yet not Formalised 30 2.3 Signification 33 2.3.1 General overview 33 2.3.2 Signification in Ockham and Buridan 34 2.4 Supposition 40 2.4.1 Ockham’s Theory of Supposition 41 2.4.2 Buridan’s Theory of Supposition 48 2.5 Ampliation and Restriction. Appellation 50 2.5.1 Ampliation and Restriction 50 2.5.2 Appellation 53 2.6 Ockham’s and Buridan’s solutions 57 2.6.1 Non-existence: medieval noneism 57 2.6.2 Intentional Indeterminacy 70 2.6.3 Substitutivity of Identicals 74 ii formalisation 83 3 ockham’s semantics formalised 85 3.1 Few remarks about the idea of formalisation 85 3.2 Formalisation of Ockham’s Supposition Theory 85 3.2.1 Preliminaries 86 ix x contents 3.2.2 Personal, Simple and Material Supposition 89 3.2.3 Modes of Personal Supposition 90 3.2.4 Quasi-Syntactical Rules for the Modes of Per- sonal Supposition 96 3.3 Ockham’s Solutions Formally 99 3.3.1 Non-existent Objects 99 3.3.2 Intentional Indeterminacy 100 3.3.3 Substitutivity of Identicals 102 4 conclusions 107 4.1 Medievals and Noneists: How Far from Each Other? 108 4.2 Philosophia et Logica Perennis 109 bibliography 113 INTRODUCTION This thesis is an attempt towards the practice of the philosophical logic in an historically self-conscious way. The main focus is on the three major challenges posed by intentionality to logic: an apparent reference to non-existent objects, the phenomenon of intentional in- determinacy and the failure of substitutivity of coextensive terms in intentional context. Such problems might not worry someone inter- ested just in the classical, pure mathematical logic. However, if a logi- cian attempts to give an account of human reasoning outside of this well defined, safe zone, sooner or later she or he would have to face at least one of the above mentioned problems. As a matter of fact, these issues where discussed from the very beginnings of logic as a discipline. Already Aristotle discussed the first and the last problem in his logical writings. Each of them re- ceived even more attention in the late Middle Ages, among others from logicians such as Ockham and Buridan. Not surprisingly, also contemporary logicians such as Graham Priest, while developing the logic of intentionality, discuss exactly these old problems. A brief look at the contemporary examples of the logic of intention- ality shows that solutions to the challenges posed by intentionality require a rather sophisticated formal tools. Moreover, it seems to be necessary that the classical logic is abandoned, since some crucial assumptions behind it have to be dropped (e.g. an assumption that each name has a referent). At the same time, these very issues where discussed by Medieval logicians without the powerful resources of a (fully) formalised language. One could wonder how they were able to handle it. Things get even more intriguing when one observes that contemporary attempts to formalise Medieval Logic also require very sophisticated formal tools and departure from the classical logic. This thesis is build around this link, connecting the relevant ideas from the history of logic with the advantages of contemporary formalisation. In the first chapter the basic characterisation of intentionality and related concepts, like intentional operators or the de re/de dicto distinc- tion is given. Also the three above mentioned challenges are described in more detail. Finally, an example of a contemporary solution to each of them as given by Graham Priest from a noneist (neo-Meinongian) perspective is presented. In the second chapter we take a step back to the Middle Ages, specifically to the works of two chief nominalists and logicians of the fourteenth century, William Ockham and John Buridan. Their respective views on intentionality are given, followed by an exposition of their logic based on the semantical properties of terms such as signification, supposition, ampiliation and appellation.