What unites Brazil and Poland? The ties between the two countries go beyond diplomatic relations and the cultural heritage brought by the migratory movements of the 1906th and 1965th centuries, which today occur in the south of the country, especially in Paraná. The logical look at the contradictions and inconsistencies of information and the search for ways to work with them within rational bases highlight the work of logicians, philosophers and mathematicians from both countries. If, in Brazil, Newton da Costa is the great exponent of paraconsistent logic, in Poland, the break with classical logic owes much to the legacy of Stanisław Jaśkowski (XNUMX-XNUMX), a Polish logician responsible for the development of discussional logic and one of the first to propose paraconsistent calculations.
Jaśkowski's legacy to Polish logic and its interface with the Brazilian school of logic are themes of the interview with Janusz Ciuciura, professor at the Department of Logic and Science Methodology at the University of Lodz and guest at the São Paulo School of Advanced Science in Contemporary Logic , Rationality and Information - SP LogIC. In conversation with Jornal da Unicamp, Ciuciura explains the concepts behind discussion logic and how new generations of Polish logicians perpetuate the country's tradition in the area.
The term “discussive logic” is an option made by most Brazilian logicians when dealing with this type of logic. According to Walter Carnielli, professor at Unicamp and member of the advisory board of SP LogIC who collaborated with the production of the series Logical Looks, two terms appear in the specialized literature of several countries, “discussive” and “discursive”. As this is a thought focused on the use of everyday language, on discussions, as will be explained throughout the conversation, we chose to use “discussive”, a translation that will be used in editing this interview.
Unicamp Newspaper - In your master class at SP LogIC, you addressed the concept of discussion logic and Stanisław Jaśkowski's legacy in the area. What caught my attention was the fact that he developed this concept from the observation of natural language, something different from the approach of other logicians, which starts from mathematics. Could you explain a little about Jaskowski's idea?
Janusz Ciuciura - I will explain with an example given by Jaśkowski himself. Imagine a group of people discussing a topic. The terms they use may be vague or imprecise. And each of these inaccuracies can lead to apparent contradictions, which are not non-contradictions in fact. This means that people tend to understand things in different ways. In general, this does not generate disagreements, but sometimes there are differences in the values attributed to words, which depend on the context. For example, if we say that a person is tall or short, we know who is tall or short from the context, but there is no clear distinction between these two predicates. Some may say that a person is tall, and others that they are short, it depends on the context, so there is no logical contradiction in this, it is a contradiction in communication, there is a debate about words. From this perspective, Jaskowski's discussion logic tries to understand the nature of this type of contradiction. But it is not a contradiction as in the case of dialetheism. I personally disagree with the dialetheist perspective. It is a question similar to reflection on the origin of truth. There is a famous thought, written by a Polish philosopher, founder of the Lviv-Warsaw School (Lwów-Warsaw School, known by the acronym LWS), Kazimierz Twardowski. He wrote treatises on the origin of truth, according to which truth is singular, there are no relative truths. If there is room for some relativization, it is because some information has been lost. For example, if there are different sources of information, and you tell one person that something is true and another that it is not. If you put this information together, in the end, it's like you're talking about different things. If we include information about time and place, we may reflect that there are no logically extracted truths. It's the same thing that happens with contradictions. In my opinion, they are abstract objects. In essence, if there is a language rich enough for us to express our intuition, through symbols, you can do it. This is a problem that goes back to Platonism, the idea that you don't discover logical principles, they exist in some form. If you have an idea of contradiction, these contradictions exist in reality. But this is philosophical, nothing more. If we start from different premises and accept them, perhaps we will reach different conclusions. It's a matter of points of view. This is Jaśkowski's idea: if there is a contradiction between two ideas, or two people, it is because some information is missing.
JU - This reminds me a little of the idea of Newton da Costa's Quasi-Truth Theory. Is there any relationship between them?
Janusz Ciuciura - Are you referring to the criterion according to which everything non-trivial in mathematics is possible? Well, I'm not a mathematician, my focus is on philosophical logic. I think it is one of the possible approaches to the issue, people have different perceptions. Professor Newton da Costa developed a great idea, something very original for the non-classical logics of that period, and gained a lot of respect within this area for it. But, for me, it is another possible perspective within the list of non-classical logics that we can accept or not. It is a question that involves accepted criteria. The Brazilian school of logic is more interested, for example, in monotonic logics, which can be paraconsistent, as well as others. Which one is correct? For some, just classical logic and its variations, because they need the principles of classical logic. I think we lose our intuition when we work this way. We have several perspectives that live in harmony and are open to discussion.
JU - Stanisław Jaśkowski and Newton da Costa developed ideas of paraconsistency, but with different approaches and in different periods. Jaskowski died in 1965, a time when Newton published his first works. Was there any kind of cooperation between them?
Janusz Ciuciura - No. There were some collaborations, not between Jaśkowski and Newton da Costa, but between him and Jaśkowski's students. Lech Dubikajtis was Jaskowski's student and assistant and was supervised by him in his doctorate. He specialized in geometry, because Jaśkowski was a mathematician and logician. There was this cooperation between Jaśkowski's Polish students, like Dubikajtis, and Professor da Costa. They co-authored articles on discussion logic. Another person who contributed to Newton da Costa and was a student of Jaśkowski was Jerzy Kotas. He was also a professor, but specialized in algebra and proposed an algebraic perspective on discussion logic. These were the main ones who worked in partnership with Newton da Costa, in the sense of having worked personally.
JU - And did Newton da Costa's work influence the logical panorama of Poland?
Janusz Ciuciura - This is a complicated question, because in Poland we have our own tradition, of the Lviv-Warsaw School. We have many famous logicians, not just the founder of the school, and we prefer to focus on this tradition. I believe it's a little similar to what happens here in Brazil, you have your own masters, which is the case of Newton da Costa. Even so, some Polish logicians ignore paraconsistent logic because they have no experience with the topic, or because they are not interested in this perspective, they are interested in others, such as deontic logic and temporal logic. There are no great examples of Newton da Costa's influence in Poland, because we already have the influence of our great names, we are inspired by our own logicians. It's a kind of consensus among Polish logicians, they have contact with Brazilian production and its contributions, but that's it, it was just another contribution in the development of non-classical logics.
JU - Is Jaśkowski's perspective of applying logic to the study of everyday language still a current approach in Poland? Are there new phenomena or applications that attract the attention of Polish logicians?
Janusz Ciuciura - The number of logicians has grown in recent years, but they are people who work with a purer, more internal logic. The applications are more focused on computer science, artificial intelligence, linguistics. Some people focus on these applications, just as in social sciences, where there are pure and applied sciences. There may be some people with this objective, but it is not so common that we seek to apply logic to solve non-logical problems. There may be some kind of cooperation, but in other cases there may not be. Some cooperate with IT, in the preparation of some programs, in the development of their structures. There are also cooperations with linguistics, in this case logic becomes an apparatus to reach the origin of language, in the use of some expressions, etc. I'm interested in pure logic, even without the philosophical context, when it is a part of mathematics. I don't focus much on applications.
JU - But do you believe there can be more application of logic in our daily lives? Can logic contribute to our lives?
Janusz Ciuciura - I think this is going to be a slightly personal answer, I'll give you an example: the internet is everywhere, at least today you need to be connected everywhere. Is this good for the user? I think not. The same happens with logic, we work with it, but it doesn't mean that logic should be everywhere. Sure, for some people it might work, logic might be like a religion. Religious people tend to see connections with God everywhere. Likewise, some people who work with logic tend to see it in everything. In part, this is right, we can see logical structures in everyday reasoning, we deal with premises, we notice mistakes that people make in communication. It depends on the person's perspective. If logic helps people survive in the chaos of the world, that's fine. But maybe that won't happen. It depends on the philosophical assumptions people make, as well as how familiar they are with logic.
JU - Throughout our interview, you emphasize the Polish tradition in logic and philosophy. What is the current situation in the country? Is this tradition continuing among new generations?
Janusz Ciuciura - There is continuity in several aspects, firstly because we need to respect our tradition. All the famous names in logic, members of the Polish school, are always mentioned. Many Polish philosophers have brilliant intuitions that have been rediscovered by others. For example, Jaśkowski is considered the father of natural deduction. He presented the first results on this in 1927 at a conference in the city of Lviv. At the time, it was a city in Poland, today it is on Ukrainian territory. But he saved this idea to publish it only in 1944. In the meantime, (Gerhard) Gentzen published his work on natural deduction. Because of this, in many countries, especially in the West, Gentzen is considered the father of natural deduction, but it was Jaśkowski who developed the idea first. The same thing happens with paraconsistency, Jaśkowski published his work in 1948, while Newton da Costa did so in the early 1960s. Of course, in this case there is a noticeable difference, because they are different concepts of paraconsistency. Newton da Costa rejected the principle of non-contradiction, while Jaśkowski adopted it as a thesis. So there's always this question of who was first. From a historical point of view, this is simple, but from a scientific perspective, things are different.
