Substructural Logics and Pragmatic Enrichment Pilar Terrés Villalonga Aquesta tesi doctoral està subjecta a la llicència Reconeixement- NoComercial 4.0. Espanya de Creative Commons. Esta tesis doctoral está sujeta a la licencia Reconocimiento - NoComercial 4.0. España de Creative Commons. This doctoral thesis is licensed under the Creative Commons Attribution-NonCommercial 4.0. Spain License. SUBSTRUCTURAL LOGICS AND PRAGMATIC ENRICHMENT PILAR TERRES´ VILLALONGA A thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy Supervisor: Prof. Dr. JOSE´ MART´INEZ FERNANDEZ´ PhD program: Cognitive Science and Language Philosophy Department Pilar Terres´ Villalonga: Substructural Logics and Pragmatic Enrichment, 2019 SUPERVISOR: Prof. Dr. Jose´ Mart´ınez Fernandez´ TUTOR: Prof. Dr. Jose´ Mart´ınez Fernandez´ Cognitive Science and Language Doctoral Program Facultat de Filosofia Universitat de Barcelona This work was supported by the grant FPI (BES 2012-056627) of the Spanish Ministry de Economy and Competitiveness; the project on Reference, Self-Reference and Empirical Data (FFI2011-25626) from the Spanish Ministry of Education; and the project on Localism and Globalism in Logics and Semantics (FFI2015-70707-P) from the Spanish Ministry of Economy and Competitiveness. Abstract In this dissertation, we argue for a Pragmatic Logical Pluralism, a pluralist thesis about logic which endorses Classical, Relevant, Linear, and Ordered logic. We justify that the formal languages of these four logics are legitimate codifications of the logical vocabulary and capture legitimate senses of logical consequence. This will be justified given a particular interpretation of the four formal languages: logical conse- quence and conditional, disjunction, and conjunction of the four dif- ferent logics codify different and legitimate senses of ‘follows from’, ‘if...then’, ‘or’ and ‘and’ which diverge in their different pragmatic en- richments. The dissertation is twofold. First, we will explore the ef- fect that the lack of structural rules has on logical connectives, in four substructural logics, and its connection with certain pragmatic enrich- ments. Second, we will defend a pluralist thesis according to which pragmatics has an important role for capturing the inferential role of logical vocabulary, both of the notions of ‘follows from’ and the logical constants, although classical logic preserves truth and captures their lit- eral meaning. In sum, we defend a version of logical pluralism based on the plurality of legitimate translations from natural language to for- mal languages, arguing that more than one translation is legitimate for logical vocabulary, which makes it possible to adopt more than one logic. iii Resum En aquesta tesi presentem el Pluralisme Logic` Pragmatic,` una tesi pluralista sobre la logica` que accepta les logiques` Classica,` Rellevant, Lineal i Ordenada. Justifiquem que els llenguatges formals d’aquestes quatre logiques` son´ codificacions leg´ıtimes del vocabulari logic` i cap- turen sentits leg´ıtims de la consequ¨ encia` logica.` Aixo` es justificara` do- nant una interpretacio´ particular dels quatre llenguatges formals: la consequ¨ encia` logica` i el condicional, la disjuncio´ i la conjuncio´ de les quatre logiques` acceptadas codifiquen diferents i leg´ıtims sentits de ‘si...llavors’, ‘o’ i ‘i’, que es distingeixen pels diferents enriquiments pragmatics` que codifiquen. La tesi te´ dues vessants. Primer, explorem l’efecte que la falta de regles estructurals te´ en les connectives logiques` de les quatre logiques` presentades, i la seva connexio´ amb certs en- riquiments pragmatics.` Segon, defensem una visio´ pluralista segons la qual la pragmatica` juga un rol important a l’hora de capturar el rol in- ferencial del vocabulari logic,` tant per la nocio´ de consequ¨ encia` logica` com per les connectives, tot i que la logica` classica` preserva la veritat i captura el seu significat literal. En resum, defensem una versio´ del pluralisme logic` basat en la pluralitat de traduccions leg´ıtimes del llen- guatge natural al llenguatge formal, argumentant que mes´ d’una tra- duccio´ es´ leg´ıtima pel vocabulari logic,` la qual cosa ens permet adoptar mes´ d’una logica.` iv Publications Some ideas presented here have been published in the following papers: ◦ Terres´ Villalonga, Pilar (2019). From Natural to Formal Language: A Case for Logi- cal Pluralism. Topoi 38 (2):333-345. ◦ Terres´ Villalonga, Pilar (forthcoming). Substructural logics, pragmatic enrichment, and the inferential role of logical constants. Inquiry: An Interdisciplinary Journal of Philosophy:1-27. v vi Acknowledgements Many people has contributed, in some way or another, in the process of developing the content of this dissertation. First and foremost, I want to express my deepest gratitude to my supervisor, Jose´ Mart´ınez Fernandez.´ I want to thank him not only for all these years in which he has supervised my work but also for his influence in my philosophical training, which starts some years before I became a PhD researcher. Being one of his undergraduate students, his insightful and rigorous treatment of different topics on philosophy of logic awaked my interest in the field. Later, during the period as a PhD researcher, this rigour and philosophical insight guided my work and shaped the preliminar ideas and intuitions with which I approached the debate on logical pluralism. Without his excellent guide this dissertation would not have reached the present form, as he has made uncountable and extremely valuable comments, corrections, and observations about different versions of this thesis, which have significantly improved the text. I have a junior member of Logos since 2012, coordinated first by Genoveva Mart´ı and later by Sven Rosenkranz. In this group I have found the perfect environment for elab- orating this thesis, and for this reason I am indebted to all the members of the group that I have had the chance to meet. Particularly important to me have been the people participating in the different reading groups which I have attended during these years, and in which I could present different parts of the dissertation: the Philosophy of Logic reading group, coordinated by Jose´ Mart´ınez, and the Graduate Reading Group. In both regular meetings I could share my ideas with actual or formers members of Logos, visit- ing students and professors, and other researchers, including Mar Alloza, Carlos Benito, Joan Bertran, Bartłomiej Czajka, Laura Delgado, Johannes Findl, Johan Gebo, John Hor- den, Carlos Jaen,´ Nasim Mahoozi, Sergi Oms, Claudia Picazo, Luc´ıa Prieto, David Rey, Gonc¸alo Santos, Sven Rosenkranz, Javier Suarez,´ Lisa Vogt, Romina Zuppone, and Elia Zardini. I could also benefit from fruitful discussions about different parts of this disser- tation with Genoveva Mart´ı and Josep Macia,` whose expertise on philosophy of language improved the core of this thesis. With Sergi Oms and Jose´ Mart´ınez I read some technical vii papers and books on substructural logics which clearly had an impact on the pluralist the- sis that is defended in this dissertation. I also met in Logos Elia Zardini with whom I had extremely fruitful conversations about both technical and philosophical consequences of my views, and in different stages of development of the research, which allowed me to improve the work. And I had innumerable conversations during the first years of this re- search with Claudia Picazo, whose insightful perspective on language had a great impact on my own views. In 2014 and 2015 I participated in an inter-university Reading Group on Logical Plu- ralism coordinated by Concha Mart´ınez Vidal, and in which I had the chance to meet and discuss a great amount of bibliography with Giuseppe Spolaore, Matteo Plebani, Concha Mart´ınez, Jose´ Mart´ınez and Pierdaniele Giaretta. Thanks to all of them too for all the fruitful discussion and shared ideas on the logical pluralism debate. During my PhD, I completed two research stays. First, in 2015 I spend one month at the University of Cagliari, working under the supervision of Francesco Paoli. I want to thank him for his dedication in reading and discussing important parts of this disserta- tion, when it was underdeveloped, and which helped me to find better arguments for my own intuitions. Some of the main claims in this dissertation are the result of answering some insightful observations which he made about my initial ideas on logical pluralism. In Cagliari I also had the chance to present my work, and I received interesting comments from Francesca Ervas. The second stay abroad was one year later, in 2016, this time visiting the University of Bergen during four months, and working under the supervision of Ole T. Hjortland. I want to thank him for his support and dedication in supervising my work during this research stay, and for his valuable comments, pieces of advice and encouragement that he gave me during that period and in other occasions in which I had the chance to meet him. His guidance gave me a necessary perspective on the whole project when it was yet underdeveloped, by suggesting different directions in which my ideas could be expanded, which is reflected on the current form of the thesis. I had the chance to present parts of this work in several universities and other institu- tions, where I could benefit from discussions and different perspectives on the topic of my research: in 2014 at the summer School on Mathematical Philosophy for Female Students (MCMP); in 2015 at the