When Newton da Costa, professor emeritus at Unicamp, developed the theory of paraconsistent logic, his ideas began to travel the world, influencing logicians, philosophers and mathematicians from different backgrounds. However, his ideas were not always understood in the way he developed them. "I visited countries like Russia and Poland, around the 1960s and 1970s, and talked about paraconsistency. They loved it, it seemed like it would be the new absolute truth. But I didn't defend that idea. Some of them understood it differently than me", recalls Newton, who defends paraconsistency not as a universal truth, but as a way of recognizing the existence of contradictions and working with them on a rational basis.
The experience is a clear example of how much science is built from concepts created by social actors, inserted in a well-defined historical context. In this case, the contradiction he pointed out sounded like music to the ears of enthusiastic theorists of dialectical logic compatible with Marxism. “This understanding of contradiction makes the theory trivial, capable of explaining anything and, therefore, capable of explaining nothing”, ponders Elena Dragalina-Chernaya, professor at the Higher School of Economics – HSE University, in Moscow, and one of the guests at the School São Paulo of Advanced Science in Contemporary Logic, Rationality and Information – SP LogIC.
In the interview given to Journal of Unicamp, Elena explains how logic was consolidated as a field of study in Russia and what contributions the sector received from the Brazilian school of logic. She also comments on the importance of logic and critical thinking for contemporary informational reality. The interview had the collaboration of Walter Carnielli, professor at Unicamp and president of the SP LogIC advisory committee.
Jornal da Unicamp: In your master class at SP LogIC, you address the theory of hylomorphism. From what I have been able to research, it goes back to the ideas of Aristotle and seems to have a metaphysical meaning, according to which every body consists of two intrinsic principles, primary matter and substantial form. Could you explain this idea and how it relates to logic?
Elena Dragalina-Chernaya - In my master class, I cover logic more than metaphysical hylomorphism. Traditionally, logical hylomorphism relates to logical form, not logical matter. However, the distinction between form and matter is not easily established. In fact, logical form is not a concept specific to logic. From a historical perspective, it is surprising that Aristotle, the founder of logic and metaphysical hylomorphism, was not the founder of logical hylomorphism. Aristotle does not apply formalism as a criterion for logic. His distinction "form versus matter" is not present in the Organon, the collection of works by Aristotle. In my class, I sketch the history of the birth of logical hylomorphism rooted in ancient commentaries by Aristotle and in medieval disputes and consequences of this idea.
JU - How does this reach today? Is there a connection between hylomorphism and contemporary logics? In fact, some of his works make reference to Kant's logical hylomorphism. Can you explain this?
Elena Dragalina-Chernaya - Kant [Immanuel Kant] occupies a prominent space in the history of logical hylomorphism. It is with him that the use of the expression "formal logic" begins. Kant himself began to apply the criterion of formalism to demarcate the boundaries between the logical discipline and those of general logic. To clarify this type of Kant's logical hylomorphism and determine the meaning of the concept for modern logic, I propose a distinction between two types of logical hylomorphism: substantial and dynamic. Substantial hylomorphism considers logic as a theory of formal, higher-order objects that turns their structural properties into formal laws of reasoning. This presupposes an interpretation of the formal and the form in such a way that they cannot be affected by the variability of matter. In modern semantic theoretical models, substantial hylomorphism is specified in terms of being invariant to non-structural transformations of the models. The variety of invariance criteria for logicality opens the door to diverse logical systems. In dynamic hylomorphism, the idea of "which type of formalism?" gives way to "how is formalism applied?". From a dynamic point of view, logic is the domain of the activity of proposing inferences based on rules and with objectives. Dynamic formalism characterizes a special way of following these rules, where the antithesis is not the material, but the informal, in the sense in which we speak of informal behavior. For Kant, logic is a body of rules and the formalism of pure logic arises from the fact that it investigates the absolutely necessary rules of thought.
Of course, in our age of logical pluralism, this sounds old-fashioned. However, modern dynamical hylomorphism is not obliged to follow Kant in recognizing the "emptiness" or the idea of "purity" of logical forms. From the moment that a strategic activity, with directed objectives, can be conceptualized as a game, dynamic hylomorphism can be thought of in terms of game theory, for example. From this perspective, logical structures appear as structures of actions performed by rational agents, who deal with truths and consequences. Various types of invariances, information dependencies and independences arise in games, so that agents can be modeled not only by classical logic systems, but also by non-classical logic, as is the case with epistemic dynamic logic, for example.
JU - We had the opportunity to interview Professor Newton da Costa and he told about his experience of taking paraconsistent logic to the countries of Eastern Europe and Russia in the 1960s and 1970s. According to him, logicians in these countries were enchanted with his ideas because they highlighted the contradictions, but, on the other hand, he was disappointed because he realized that they assumed the ideas as a new absolute truth...
Elena Dragalina-Chernaya - Hegel's [Georg Wilhelm Friedrich Hegel] dialectical logic, in opposition to Kant's logical formalism, had ideological support in official Soviet philosophy. In the 1960s and 1970s, the development of dialectical logic took on a special dimension. Some of its more reticent supporters considered it a Marxist theory of knowledge, being a methodological and ideological basis of formal logic. But there were also enthusiasts who saw it as genuine logic, legitimately supplanting the old version during the historical movement toward communism. Newton da Costa seems to be referring to these enthusiasts. In my view, their disagreement with them can be explained by the fact that logical contradiction is considered not as a problem but as a universal solution of all philosophical problems by dialectical logicians. In other words, the view that it would be a new absolute truth, which would turn Marxism into a single and irrefutable theory. In fact, this understanding of contradiction makes the theory trivial, capable of explaining anything and therefore capable of explaining nothing. This supposed trivialization is the main criticism made of paraconsistent logic. Thus, I believe that the main opposition to paraconsistent logic is not formal dialectical logic, but a vulgarized form of that logic.
JU - Based on this, how do you analyze the development of logic and philosophy in your country? Do historical and political legacies have an effect on this?
Elena Dragalina-Chernaya - There is a quote from a famous Russian philosopher of the early 19th century, Peter Chaadayev, who once said with regret: "The syllogism of the West is unknown to us." Of course this is a rhetorical exaggeration. There is no doubt that Russian philosophy has always been influenced by great Russian literature, with its existential and religious problems. However, rationalist philosophy was also very important for Russian culture. It is no coincidence that, in the 20th century, Russian philosophers participated in the origin of several non-classical logics. The imaginary, non-Aristotelian logic of Nikolai Vasiliev had a great influence on the development of paraconsistent logic. The first relevant logical axiomatization was proposed by Ivan Orlov. It is also worth mentioning the pioneering results of Russian mathematicians in the development of probabilistic logic. For me, the source of success of philosophical logic in Russia is the cooperation between philosophers and mathematicians, as well as between psychologists, linguists and other scientists. Current successful strategies for developing academic programs in philosophy presuppose their interaction with other related disciplines. Extending its methods to the field of problems of classical philosophy is the essence of formal philosophy, which develops verifiable models to be evaluated by general scientific methods. Formal philosophy appears to be the most important area of development both in Russia and in the rest of the world. It is impossible to limit philosophy within disciplinary or geographic boundaries in today's world with its modern information technologies.
JU - Are there influences from the Brazilian school of logic in Russia?
Elena Dragalina-Chernaya - My first impressions of Brazil were diversity and tolerance. To me, it seems that these are the main characteristics of Brazilian logic. It is difficult to describe a specific way in which Brazilian logic influenced Russia. However, we can say that it has a special role in the development of several non-classical logics. Initially, the achievements of the Brazilian school of paraconsistent logic. Here it makes sense to talk about a mutual influence, because the Russian philosopher Nikolai Vasiliev was one of its founders, founder of this theory whose discovery for world science is credited to Vladimir Smirnov. It is no coincidence that one of the results of joint research between Brazilian and Russian logicians in the field of paraconsistency was the text "The logical legacy of Nikolai Vasiliev and modern logic" (The logical legacy of Nikolai Vasiliev and modern logic, Vladimir Markin, Dmitry Zaitsev, Synthese Library, 2017), which includes articles by Jean-Yves Beziau, Otávio Bueno, Ítala D'Ottaviano and Evandro Luís Gomes, Juliana Bueno-Soler and Walter Carnielli and José Veríssimo Teixeira da Mata. Based on Vasilyev's ideas and using the formalism of Brazilian classics Newton da Costa and Ayda Ignez Arruda, Russian logicians Vladimir Vasyukov, Vladimir Popov and Vasily Shangin constructed original combined systems of paraconsistent logic.
The influence of the Brazilian school on Russian logic is not limited to the reconstruction of Vasiliev's ideas. Based on the approach of Newton da Costa and Walter Carnielli, Vladimir Vasyukov, for example, developed several versions of semantic categories for paraconsistent logic. As in the rest of the world, in Russia there is special attention to the research of Brazilian logicians who dedicated their efforts to translating and combining logic, logical pluralism and universal logic, such as Ítala D'Ottaviano, Jean-Yves Beziau, Walter Carnielli, Marcelo Coniglio , João Marcos, Decio Krause and Otávio Bueno, among others.
JU - What, do you believe, are the main challenges and questions facing logic today? Are there aspects of the contemporary world in which logic can help?
Elena Dragalina-Chernaya - I think the revolution that transformed traditional logic into mathematical logic and eventually evolved into an informational revolution changed the world and is not finished. Modern logic is in a process of cognitive updating. As a theory involving multiple agents and resource-limited cognitive activity, logic faces not only the traditional task of cataloging correct inferences but also the optimizing tasks of rationalizing a variety of rational interactions. The importance of this in today's world cannot be overstated when read, for example, as interactions between artificial intelligence developers or between AI systems and their users. No less interesting for modern logic are the interactions between the "ideal" agents of classical logic and also those between unlimited rational agents, whose cognitive techniques were often evaluated by classical logic as mere cognitive distortions and which are now successful models of non-monotonic, paraconsistent, dynamic-epistemic and other non-classical logics.
We can say that modern logic descended from the heavens of mathematical abstractions to the Earth of human reason, which was created in Antiquity. Their interaction appears, however, in a radically modified informational environment, which includes new ways of receiving and using information, which even involves non-human cognitive agents. The inevitable conflicts between reliable cognitive abilities and the new informational reality can lead us to technological disasters and social explosions, which modern logic, with its plurality of logical systems, can prevent or at least mitigate.
JU - Several countries, including Brazil, the United States and even Russia, are currently suffering from digital disinformation. There are groups that exploit hatred, distrust and political divisions and create new forms of irrationality that affect democracy. Do you believe that logic and rationality can be a defense against this?
Elena Dragalina-Chernaya - Logic, like philosophy, sees the world as a polycentric universe of equally thinking people. These hybrid wars unite people into irrational communities based on the imitation of rational arguments. Understanding the logical nature of argumentation, the ability to identify contradictions and the resources of rhetorical manipulation is what helps logic to develop. Charles Sanders Peirce, one of the founders of modern logic, predicted that as logic and ethics develop, a great affinity will emerge between them. He believes that the great technological and social challenges of the modern world are evidence that that time has arrived.
JU - Do you think we need more logic in our lives?
Elena Dragalina-Chernaya - Yes, I believe that modern human life has become so information-driven that we cannot help but improve our logical competence. The average person reads the news on the computer, pays their bills virtually, plays video games, engages in arguments with strangers on social media, and is not always aware that things are not as they seem. Understanding, on the one hand, the nature of algorithmic processes and virtual communications and, on the other, developing critical thinking, are vital for any modern person. This is exactly what logic can bring us.
