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An ARF Fellow Report by Henrique Antunes

A Report on my ARF Fellowship from August to November 2013 Henrique Antunes February 2, 2014 When I accepted the suggestion to apply for an ARF-Fellowship from Professor Walter A. Carnielli, mymaster's adviser at the State University of Campinas (Unicamp) and one of ARF senior members, I couldhardly imagine how it would be like. At that time, I knew almost nothing about Richard L. Epstein andmost the other ARF-members' work, and I didn't have enough time to get acquainted with it. Nevertheless,I was encouraged by Professor Carnielli and decided to take the chance. The ARF-Fellowship turned to beone of the most stimulating intellectual experiences of my life, changing my conception of logic andof the philosophy of logic. During the three months I spent in Dogshine, I read the essays written by Richard L. Epstein on variousthemes related to mathematical logic, the philosophy of logic, metaphysics, epistemology and linguistics,which are to be published this year in a book entitled Reasoning and Formal Logic: Essays on Logic as theArt of Reasoning Well. When my fellowship started, some of the essays for the book were completely finishedand some had already been published previously in journals or other books. I was supposed to read thoseessays carefully and report my opinion about them to the author. In the beginning, this was a very hardtask to accomplish because all of them seemed to me so different from everything else I ever read before thatI could hardly figure out what they were about. After reading and re-reading them a couple of times anddiscussing some of their parts with the author and with Esperanza Buitrago-Diaz, another ARF Fellow atDogshine at the time, I started to understand them better, though. Some of the other essays for the book were still being written at the time I arrived in Dogshine. Exceptfor one or two essays, all of them were almost complete drafts that needed only some minor changes andcompletions. When I started to read them, I was already acquainted with the big picture about logic andphilosophy they were meant to be part of, which includes a general skepticism about metaphysical issues andthe idea that the main purpose of logic is to unfold the assumptions built into our language and into ourlinguistic habits. As I could understand these ideas better than I could before, the task of reading those otheressays was much more easier than that of reading the first ones. During the discussions I had with RichardL. Epstein, I could then participate in a more active way, posing more interesting questions and sometimesdisagreeing with him. All of those discussions were friendly and fun, which turned then into a very pleasantdaily habit. Most part of the discussions Richard L. Epstein and I had together were about the very nature of logic.They represented to me one the most important aspects of my fellowship and I think it is worthwhile todescribe briefly the main lesson I learned from them on this report. Before I went to Dogshine, I was very committed to a realistic view of logic, which I inherited fromreading Aristotle and specially Frege's work during my undergraduate course on philosophy at the FederalUniversity of Minas Gerais (UFMG), in Brazil. At that time, I couldn't understand how logic could be viewedas something different from the science of the most general and ultimate laws of reality, which all beings,irrespective of their particular features, had to obey. Mathematical Logic was then just a mathematicalabstraction of this unique science called 'Logic'. Even though I was aware of the problem the existence of somany different logics posed to this view, I thought that it had to be some way out of it; perhaps, as consideringthe so-called 'non-classical logics' as describing the way we, human beings, actually reason in some specificsituations involving specific conditions. Accordingly, the non-classical logics were not to be seen as Logic, butmuch more similar in principle to linguistics or to psychology. The discussions with Richard L. Epstein andthe reading of the essays "Valid Inferences", "A General Framework for Semantics for Propositional Logics", "WhyAre There So Many Logics?", "The Timeless of Classical Predicate Logic" and especially "Truth and Reasoning",though, offered to me a much more complex and elaborate alternative to the realistic view than the onesI've seen before and which is to be understood in a general philosophical framework deeply connected toskepticism. As I think Epstein would say, we can't prove any particular metaphysical system to be correct becausemetaphysical assumptions are already built into any logic we would use to try to do it. So, there is no way wecan use logic to talk about metaphysics without entering into a vicious circle or begging the question. Thealternative proposed by Epstein is to start from those very metaphysical assumptions and then abstract someaspects of them to develop a logic that describes and rules the way we reason according to those assumptions.Under this view, formal logic is a useful tool for reasoning only after we have agreed about the assumptions aparticular system of logic codify; if we disagree about them while discussing a particular subject, this systemwould turn out to be completely useless for that discussion. Even though this new view dissociates logic and metaphysics, it opens the possibility to apply formal logicin radically different reasoning situations and banishes the distinction between classical and non-classical logic(see "Why Are There So Many Logics?"). As far as I can see, it describes logic as a local science or tool thatis to be adapted to (i) the specific purposes we want to achieve while discussing and reasoning together, (ii)to the specific conditions of these reasoning situations (e.g., their subject matter) and (iii) to the specificmetaphysical assumptions we choose to accept -- these are not unrelated. For instance, if we are discussingsome subject in which time and changes are completely irrelevant, then maybe classical predicate logic willdo, since it does not account for theses aspects (cf. "The Timelessness of Classical Predicate Logic"). On the otherhand, if we are reasoning about the objects on my desk now, then we will need some dierent kind of logicthat deals with time and changes. I don't know if I've been completely faithful to Epstein's view in the description I've made in the precedingparagraphs but it represents the main lesson I learned from our discussions and from the reading of the essayscited above: there is an alternative to the realistic view of logic that presents very interesting answers to theclassical problems the realist must deal with. I'd like thank all of ARF-members for their support and approval, especially Richard L. Epstein for hishospitality and teachings, and Professor Carnielli for all his efforts to make this trip possible. I also owemy gratitude to the other people in Brazil that helped to afford the trip: Itala D'Ottaviano, Marco Runo,Ablio Rodrigues Filho, Rofoldo Ertola, Juliana Bueno-Soler, Samir Gorsky and Mariana Matulovic.

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