The Meeting of Philosophy and Mathematics in the Station of the Mind

Radio Farda has sent questions to Mehrdad Loghmani, a mathematician and researcher residing in the United States, regarding the book "Harmony and Exchange: Toward a Legoic Society," written by Ramin Jahanbegloo, a philosophy professor and director of the Mahatma Gandhi Center for Peace Studies in India. In the book, mathematics and philosophy meet each other. Ramin Jahanbegloo states that a Legoic society is one in which citizens can autonomously shape a democratic society based on values they themselves have originated. Mehrdad Loghmani notes that mathematics has had a close connection with philosophical concepts since its inception, and the relationship between the abstract world of mathematics and the material world has always occupied the minds of philosophers. The human desire for order and finding connections among parts has been one of the most important motivations for the advancement of mathematics, while questioning from the epistemological and ontological perspectives of mathematics has led us toward philosophy. Throughout its evolution, mathematics has approached logic, although it must be acknowledged that, as Putnam has stated, mathematics is not merely logic. In the late 19th and 20th centuries, the invention of logicism by Frege and its expansion by Hilbert and Russell, along with new perspectives on mathematical concepts by Wittgenstein and Brouwer, have all transformed our understanding of mathematics and its connection to philosophy. With the rise of research on how the human mind works, the philosophy of mind has expanded, and consequently, logic and mathematics have also come into play. Inquiry into the functioning of the human mind and the expansion of artificial intelligence has increased the need for a philosophical mathematical perspective. Before we can answer the question of whether the human mind has a completely mathematical and logical structure, it is necessary to reflect on mathematical concepts from a philosophical viewpoint. The formation of mathematical understanding is based on analogy from fundamental principles, and it can be said that mathematics differs from other branches of science in the degree of certainty it has regarding its hypotheses. Now the question arises whether logic precedes mathematics; in other words, can mathematics be reduced to logic? Some 20th-century philosophers such as Frege, Russell, and Whitehead believed so. Although the shortcomings of logicism have undermined the claim that mathematics can be reduced to logic, its remarkable achievements alongside other schools of thought, such as formalism and intuitionism, have led to the growth and flourishing of many branches of mathematics. A better understanding of mathematical thinking not only clarifies mathematical concepts but also leads to a better understanding of our minds; understanding the relationship between the two has been one of the greatest philosophical projects of the 20th century. Therefore, it can be said that research on the human mind is intertwined with reflection on the foundations of mathematics. It is important to note that our minds do not form and evolve in isolation. In fact, the advancement of the human mind is a product of its social existence. Social existence itself depends on the understanding and ability for exchange. It is necessary to clarify that exchange is not only discussed in its economic aspect but also encompasses all its forms, including emotional and cognitive. In fact, exchange is the motivation for creating connections. This book creates a framework for multidimensional exchange, an exchange whose valuation is not based on binary logic but rather on the degree of conformity of the exchange (what has been exchanged with the expectations of the demander). It is important to note that this is not in competition with logic, as discussed in the philosophy of mathematics and language, but rather a model for explaining and understanding exchange structures. Since exchange, from its social aspect, is subject to time and place, understanding the context and environment of exchange is essential. In other words, only by considering the environment and conditions of exchange can we have a correct understanding of the value and conformity of the exchange. The book provides an example of the importance of a shared understanding of context among participants in an exchange, which is worth mentioning: in 2007, Joshua Bell, a famous violinist, played six pieces by Bach at a busy Washington subway station, during which only six passersby stopped to listen to his music, and twenty people in total gave him $32. No one knew he was Joshua Bell, one of the most skilled violinists. The instrument he played that day was worth $3.5 million. Interestingly, two days later, all tickets for his concert in Boston sold for $100. This is a clear example of the mismatch between participants in the exchange and the context and conditions of the exchange. This example illustrates the importance of context and the environment of exchange and creating a shared understanding among participants. Similarly, in society, without creating a shared understanding and awareness of the conditions of time, place, and context of exchange, one cannot hope for the enhancement of public awareness. In other words, even the most skilled musicians with the most expensive instruments in the world cannot, even for free, attract the attention of people who are in different exchange conditions. People who are in the right conditions to listen to the musician's music will stand in line and willingly pay for it.