THREE QUESTIONS TO
THREE QUESTIONS TO
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- When and how did you hear about paraconsistent logic and start your work?
I heard about paraconsistent logics for the first time when I was enrolled in the Master of Epistemology program at the National University of San Marcos in Peru. I was in Luis Piscoya’s first-order logic course, which wasn’t a typical logic intro. It felt more like a seminar on philosophical logic, deeply diving into topics such as Tarski’s truth definition and Gödel’s incompleteness theorems.
I heard about paraconsistent logics for the first time when I was enrolled in the Master of Epistemology program at the National University of San Marcos in Peru. I was in Luis Piscoya’s first-order logic course, which wasn’t a typical logic intro. It felt more like a seminar on philosophical logic, deeply diving into topics such as Tarski’s truth definition and Gödel’s incompleteness theorems.
One day, Piscoya mentioned da Costa’s Cn systems, describing them as inference systems where the rules of non-contradiction and explosion don’t hold in general. Up to that time, I regarded logic as this source of certainty that pulled me away from scepticism. Because of paraconsistent logics, it seemed now that some logical systems played by their own rules. Instead of sending me back to my old sceptical self, this discovery sparked a real interest in logic and the philosophy behind it.
One day, Piscoya mentioned da Costa’s Cn systems, describing them as inference systems where the rules of non-contradiction and explosion don’t hold in general. Up to that time, I regarded logic as this source of certainty that pulled me away from scepticism. Because of paraconsistent logics, it seemed now that some logical systems played by their own rules. Instead of sending me back to my old sceptical self, this discovery sparked a real interest in logic and the philosophy behind it.
This led me to explore the works of paraconsistent systems pioneers like da Costa himself, Jaśkowski, Batens, Priest, D’Ottaviano, among others. My interest in logic became so strong that I changed not only my thesis subject but also its whole research area: from the philosophy of language to the logic of science. More precisely, I moved away from a study of proper names to investigate the logical criterion to be used in testing inconsistent empirical theories, which required me to get acquainted with paraconsistent logics.
This led me to explore the works of paraconsistent systems pioneers like da Costa himself, Jaśkowski, Batens, Priest, D’Ottaviano, among others. My interest in logic became so strong that I changed not only my thesis subject but also its whole research area: from the philosophy of language to the logic of science. More precisely, I moved away from a study of proper names to investigate the logical criterion to be used in testing inconsistent empirical theories, which required me to get acquainted with paraconsistent logics.
Furthermore, I decided to organise a workshop called Inconsistency in Factual Science at the First World Congress of the Brazilian Academy of Philosophy. It was a big deal because so many heavyweights in paraconsistent logics were there, like Batens, D’Ottaviano, Coniglio, Béziau, Bobenrieth, Mundici, and many others. I even bumped into a fellow Peruvian paraconsistent logic enthusiast based in Brazil, Jose Carlos Cifuentes. We even teamed up to edit a special issue of the South American Journal of Logic (SAJL) and organised an event dedicated to Peru’s most important philosopher of logic: Francisco Miró Quesada Cantuarias, who, incidentally, was the one who coined the term ‘paraconsistent logic’.
Furthermore, I decided to organise a workshop called Inconsistency in Factual Science at the First World Congress of the Brazilian Academy of Philosophy. It was a big deal because so many heavyweights in paraconsistent logics were there, like Batens, D’Ottaviano, Coniglio, Béziau, Bobenrieth, Mundici, and many others. I even bumped into a fellow Peruvian paraconsistent logic enthusiast based in Brazil, Jose Carlos Cifuentes. We even teamed up to edit a special issue of the South American Journal of Logic (SAJL) and organised an event dedicated to Peru’s most important philosopher of logic: Francisco Miró Quesada Cantuarias, who, incidentally, was the one who coined the term ‘paraconsistent logic’.
Right after all these events, I defended my master’s thesis with Luis Piscoya as my advisor and Cifuentes in the audience, the latter visiting Peru during those days. The experience in Brazil was a game-changer: helped me polish my presentation, discover more relevant works for my research, argue my points with experts, and really get a better gras of the spirit of paraconsistent logics.
Right after all these events, I defended my master’s thesis with Luis Piscoya as my advisor and Cifuentes in the audience, the latter visiting Peru during those days. The experience in Brazil was a game-changer: helped me polish my presentation, discover more relevant works for my research, argue my points with experts, and really get a better gras of the spirit of paraconsistent logics.
Born May 15, 1988, Lima, Peru.
Born May 15, 1988, Lima, Peru.
2. How did you further develop your work on paraconsistent logic ?
2. How did you further develop your work on paraconsistent logic ?
During the exploration of various paraconsistent and non-classical logic systems that I did during the research of my master’s thesis, a fundamental question emerged at the forefront of my philosophical inquiries: are the laws of logic immutable set in stone, or are they just somewhat arbitrary guiding principles?
During the exploration of various paraconsistent and non-classical logic systems that I did during the research of my master’s thesis, a fundamental question emerged at the forefront of my philosophical inquiries: are the laws of logic immutable set in stone, or are they just somewhat arbitrary guiding principles?
This question, though not immediately apparent, had been subtly leading my academic interests. It started to crystallise into a research subject when I delved deeper into the works of Francisco Miró Quesada. Prior to my master’s dissertation, my exposure to Miró Quesada’s ideas had been limited. In fact, I only quoted one of his works in the final version of my thesis. It was only during my editorial role in SAJL that I engaged with his writings more comprehensively.
This question, though not immediately apparent, had been subtly leading my academic interests. It started to crystallise into a research subject when I delved deeper into the works of Francisco Miró Quesada. Prior to my master’s dissertation, my exposure to Miró Quesada’s ideas had been limited. In fact, I only quoted one of his works in the final version of my thesis. It was only during my editorial role in SAJL that I engaged with his writings more comprehensively.
Miró Quesada’s scholarly pursuits were partly dedicated to unraveling the implications of the existence of multiple non-classical systems for the theory of reason. His seminal talk titled ‘Heterodox logics and the problem of the unity of reason’ expressed concerns about the potential threat non-classical logics posed to the unity of reason itself. In sum, although Miró Quesada enthusiastically accepted the plurality of logic systems, reason had to remain one.
Miró Quesada’s scholarly pursuits were partly dedicated to unraveling the implications of the existence of multiple non-classical systems for the theory of reason. His seminal talk titled ‘Heterodox logics and the problem of the unity of reason’ expressed concerns about the potential threat non-classical logics posed to the unity of reason itself. In sum, although Miró Quesada enthusiastically accepted the plurality of logic systems, reason had to remain one.
This problem is the inspiration of the Ph.D. research I’m currently doing at the Munich Center for Mathematical Philosophy, supported by a DAAD funding. My research question is whether we can find criteria to decide which logical system is better suited for a given context or purpose. In this pursuit, my initial objective is to construct a comprehensive framework facilitating the organisation of logic systems. Miró Quesada had attempted a similar task in his aforementioned article, primarily centered around classifying non-classical systems. In contrast, my aim is to develop a neutral classification framework, i.e., not centred around classical logic or any specific logical system.
This problem is the inspiration of the Ph.D. research I’m currently doing at the Munich Center for Mathematical Philosophy, supported by a DAAD funding. My research question is whether we can find criteria to decide which logical system is better suited for a given context or purpose. In this pursuit, my initial objective is to construct a comprehensive framework facilitating the organisation of logic systems. Miró Quesada had attempted a similar task in his aforementioned article, primarily centered around classifying non-classical systems. In contrast, my aim is to develop a neutral classification framework, i.e., not centred around classical logic or any specific logical system.
In addition to my academic pursuits, my passion for logic extends to organising events that foster intellectual exchange and collaboration within the logic community. In 2022, María del Rosario Martínez-Ordaz and I organised the workshop Logic(s) in Defective Science, at UNILOG 7, which took place in Greece. This workshop featured some talks exploring the paraconsistent approach in scientific contexts. Furthermore, as the current president of Peru’s Society for Epistemology and Logic (SEPLO), I have actively organised logic-related events. These include the First Peruvian Logic Prize and three online events in celebration of the World Logic Day.
In addition to my academic pursuits, my passion for logic extends to organising events that foster intellectual exchange and collaboration within the logic community. In 2022, María del Rosario Martínez-Ordaz and I organised the workshop Logic(s) in Defective Science, at UNILOG 7, which took place in Greece. This workshop featured some talks exploring the paraconsistent approach in scientific contexts. Furthermore, as the current president of Peru’s Society for Epistemology and Logic (SEPLO), I have actively organised logic-related events. These include the First Peruvian Logic Prize and three online events in celebration of the World Logic Day.
Looking ahead to 2024, our fourth World Logic Day event will be an in-person congress: the First South American Logic Meeting (SALOME 1), which is being co-organised with SAJL. This event will take place in the UNSAAC, Cusco, and will bring together logicians from South America and around the world. Notably, a significant part of the participants will be paraconsistent logicians, which highlights the importance of paraconsistent logic in the broader logical community.
Looking ahead to 2024, our fourth World Logic Day event will be an in-person congress: the First South American Logic Meeting (SALOME 1), which is being co-organised with SAJL. This event will take place in the UNSAAC, Cusco, and will bring together logicians from South America and around the world. Notably, a significant part of the participants will be paraconsistent logicians, which highlights the importance of paraconsistent logic in the broader logical community.
3. How do you see the evolution and further challenges for paraconsistent logic ?
3. How do you see the evolution and further challenges for paraconsistent logic ?
I think the main challenge of paraconsistent logic today is that establishing itself as part of mainstream science. Unlike some non-classical logics, such as fuzzy logics with their well-established applications in artificial intelligence, decision-making processes, and fuzzy databases, paraconsistent logics have yet to gain widespread recognition for their scientific and technical utility.
I think the main challenge of paraconsistent logic today is that establishing itself as part of mainstream science. Unlike some non-classical logics, such as fuzzy logics with their well-established applications in artificial intelligence, decision-making processes, and fuzzy databases, paraconsistent logics have yet to gain widespread recognition for their scientific and technical utility.
While paraconsistent logics have found some applications in addressing issues like the management of inconsistent databases, these applications have not garnered the same level of popularity as those associated with other non-classical logics. At present, paraconsistent logics seem to predominantly occupy the realm of philosophical interest and mathematical exploration. There’s nothing wrong with this. Nevertheless, good ‘heretic science’, to use a concept by Isaac Asimov, must become mainstream science at some point, otherwise it might raise suspicions.
While paraconsistent logics have found some applications in addressing issues like the management of inconsistent databases, these applications have not garnered the same level of popularity as those associated with other non-classical logics. At present, paraconsistent logics seem to predominantly occupy the realm of philosophical interest and mathematical exploration. There’s nothing wrong with this. Nevertheless, good ‘heretic science’, to use a concept by Isaac Asimov, must become mainstream science at some point, otherwise it might raise suspicions.
Now, I’m not saying there are no such applications, but their recognition by the scientific community remains a hurdle. To be regarded as a legitimate scientific research program, paraconsistent logics must overcome the barrier of being perceived primarily as a mathematical curiosity which is mainly applicable to formalise some unorthodox philosophical views. The path forward involves showcasing how paraconsistent logics are well-suited to tackle particular scientific or technical problems, thereby bridging the gap between theoretical interest and practical relevance.
Now, I’m not saying there are no such applications, but their recognition by the scientific community remains a hurdle. To be regarded as a legitimate scientific research program, paraconsistent logics must overcome the barrier of being perceived primarily as a mathematical curiosity which is mainly applicable to formalise some unorthodox philosophical views. The path forward involves showcasing how paraconsistent logics are well-suited to tackle particular scientific or technical problems, thereby bridging the gap between theoretical interest and practical relevance.
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