Paraconsistency in Mathematics

Paraconsistent logic is a branch of non-classical mathematics that studies inconsistent theories in a coherent way. It was developed in the mid-20th century and has evolved into an area of research known as inconsistent or paraconsistent mathematics. This Element provides an introductory survey of the field, distinguishing between moderate and radical approaches and emphasizing philosophical issues and future challenges.

Format: Paperback / softback
Length: 75 pages
Publication date: 11 August 2022
Publisher: Cambridge University Press

Paraconsistent logic is a fascinating branch of philosophy that enables us to study inconsistent theories in a coherent and systematic manner. Its origins can be traced back to the mid-20th century, when it was initially conceived with the intention of being applied in mathematics. The primary goal of paraconsistency was to provide a rigorous framework for describing abstract objects and structures that allow for certain contradictions, without resorting to incoherence.

Over the years, this initiative has evolved into a distinct field of non-classical mathematics known as inconsistent or paraconsistent mathematics. This Element serves as a selective introductory survey of this research program, distinguishing between two main approaches: "moderate" and "radical." The focus of this survey will be on philosophical issues and the potential challenges that lie ahead.

One of the key advantages of paraconsistent logic is that it allows us to explore and understand theories that are not fully coherent or consistent. By embracing the notion of paraconsistency, we can explore the boundaries of logical reasoning and gain a deeper understanding of the complexities of the world. This approach has been particularly useful in fields such as metaphysics, where inconsistencies arise due to the nature of abstract concepts and the limitations of human understanding.

However, paraconsistent logic also raises several philosophical challenges. One of the most significant is the question of whether inconsistencies can be resolved or whether they are inherent to the nature of reality. Paraconsistent logicians argue that inconsistencies can be tolerated, provided that they are not used to undermine the basic principles of logic or to make unfounded claims. However, others argue that inconsistencies are a sign of deeper philosophical problems and that they should be avoided at all costs.

Another challenge is the question of whether paraconsistent logic can be applied to practical problems. While paraconsistent logic has been used in various areas of mathematics, such as set theory and logic programming, its application to real-world problems remains a topic of ongoing research. Some argue that paraconsistent logic can provide a more nuanced and accurate understanding of complex systems, while others argue that it may be too abstract and difficult to apply in practice.

Despite these challenges, paraconsistent logic continues to be an active area of research, with many scholars working to develop new theories and applications. The field has the potential to revolutionize our understanding of logic, mathematics, and the nature of reality, and it will be interesting to see how it develops in the years to come.

In conclusion, paraconsistent logic is a fascinating and important branch of philosophy that enables us to study inconsistent theories in a coherent and systematic manner. While it raises several philosophical challenges, it also has the potential to revolutionize our understanding of logic, mathematics, and the nature of reality. As we continue to explore the boundaries of logical reasoning, it will be important to consider the ethical and practical implications of paraconsistent logic and to work towards developing a more comprehensive and coherent understanding of the world.

Weight: 144g
Dimension: 152 x 226 x 10 (mm)
ISBN-13: 9781108995412