An ARF Fellow Report by Henrique Antunes

 

 

 

When I accepted the suggestion to apply for an ARF-Fellowship from Professor Walter A. Carnielli, my

master's adviser at the State University of Campinas (Unicamp) and one of ARF senior members, I could

hardly imagine how it would be like. At that time, I knew almost nothing about Richard L. Epstein and

most 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 be

one of the most stimulating intellectual experiences of my life, changing my conception of logic and

of the philosophy of logic.

 

During the three months I spent in Dogshine, I read the essays written by Richard L. Epstein on various

themes 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 the

Art of Reasoning Well. When my fellowship started, some of the essays for the book were completely finished

and some had already been published previously in journals or other books. I was supposed to read those

essays carefully and report my opinion about them to the author. In the beginning, this was a very hard

task to accomplish because all of them seemed to me so different from everything else I ever read before that

I could hardly figure out what they were about. After reading and re-reading them a couple of times and

discussing some of their parts with the author and with Esperanza Buitrago-Diaz, another ARF Fellow at

Dogshine 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. Except

for one or two essays, all of them were almost complete drafts that needed only some minor changes and

completions. When I started to read them, I was already acquainted with the big picture about logic and

philosophy they were meant to be part of, which includes a general skepticism about metaphysical issues and

the idea that the main purpose of logic is to unfold the assumptions built into our language and into our

linguistic habits. As I could understand these ideas better than I could before, the task of reading those other

essays was much more easier than that of reading the first ones. During the discussions I had with Richard

L. Epstein, I could then participate in a more active way, posing more interesting questions and sometimes

disagreeing with him. All of those discussions were friendly and fun, which turned then into a very pleasant

daily 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 to

describe 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 from

reading Aristotle and specially Frege's work during my undergraduate course on philosophy at the Federal

University of Minas Gerais (UFMG), in Brazil. At that time, I couldn't understand how logic could be viewed

as 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 mathematical

abstraction of this unique science called 'Logic'. Even though I was aware of the problem the existence of so

many different logics posed to this view, I thought that it had to be some way out of it; perhaps, as considering

the so-called 'non-classical logics' as describing the way we, human beings, actually reason in some specific

situations involving specific conditions. Accordingly, the non-classical logics were not to be seen as Logic, but

much more similar in principle to linguistics or to psychology. The discussions with Richard L. Epstein and

the reading of the essays "Valid Inferences", "A General Framework for Semantics for Propositional Logics", "Why

Are 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 ones

I've seen before and which is to be understood in a general philosophical framework deeply connected to

skepticism.

 

As I think Epstein would say, we can't prove any particular metaphysical system to be correct because

metaphysical assumptions are already built into any logic we would use to try to do it. So, there is no way we

can use logic to talk about metaphysics without entering into a vicious circle or begging the question. The

alternative proposed by Epstein is to start from those very metaphysical assumptions and then abstract some

aspects 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 a

particular system of logic codify; if we disagree about them while discussing a particular subject, this system

would 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 logic

in 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 that

is 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 specific

metaphysical assumptions we choose to accept -- these are not unrelated. For instance, if we are discussing

some subject in which time and changes are completely irrelevant, then maybe classical predicate logic will

do, since it does not account for theses aspects (cf. "The Timelessness of Classical Predicate Logic"). On the other

hand, if we are reasoning about the objects on my desk now, then we will need some dierent kind of logic

that 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 preceding

paragraphs but it represents the main lesson I learned from our discussions and from the reading of the essays

cited above: there is an alternative to the realistic view of logic that presents very interesting answers to the

classical problems the realist must deal with.

 

I'd like thank all of ARF-members for their support and approval, especially Richard L. Epstein for his

hospitality and teachings, and Professor Carnielli for all his efforts to make this trip possible. I also owe

my 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.