An Ottoman Philosopher’s Attempt For Philosophy of Mathematics: “Wroński’s Mathematical Philosophy” by Husnu Hamid

Abstract

With the impact of the axiomatic method revealed by Euclides in his book of Elements, mathematics was regarded as the reflection of absolute truth until the 19th century. For a long time mathematicians have tried to prove the fifth postulate that Euclides mentioned in his book. The fact that the fifth postulate, which is also called problematic postulate in the history of mathematics, could not be confirmed for a long time brought about some doubts. Islamic scholars such as Ibn al- Haytham, Omar Khayyam, Nasiruddin-i Tûsî have made considerable progress in the proof of the fifth postulate, but have not been successful in their work. In the late 18th century, Giovanni Girolamo Saccheri and Johann Lambert advanced the work of Islamic mathematicians. Later, at the beginning of the 19th century, Carl Friedrich Gauss, Janos Bolyai, Nikolai Ivanovich Lobachevsky and Bernhard Riemann were able to formulate non-Euclidean geometries. With the emergence of non-Euclidean geometries, the foundations of mathematics have started to be discussed. Thus the absolute truth of the propositions of mathematics has become doubtful. These unusual developments in mathematics have expanded the field of study of the philosophy of mathematics. In the 19th century, schools of Logic, Formalism, and Intuitionism emerged in the philosophy of mathematics to re- foundation of mathematics. Apart from these schools, there were some scientists who have worked on this subject but whose ideas have not turned into a school. One of them was Jósef Maria Hoene-Wroński.

Hüsnü Hamid, one of the late Ottoman intellectuals, examined Josef Maria Hoene- Wroński's understanding of mathematical philosophy. Hüsnü Hamid tackled the subject in his articles titled respectively "Hoene Wroński's Tawabi-i Elfiye", "Hoene Wroński's Tawabi-i Elfiye (cont.)" and "Wroński's Mathematical Philosophy" published in the Journal of the Faculty of Science in Daru'l-Fünun. Hüsnü Hamid asserted that he wrote his first two articles in order to lay the groundwork for his third article on Wroński's mathematical philosophy.

What Wroński aims to do in philosophy of mathematics is to put forward a mathematical formula, which he might call "the highest law" from which all mathematics can be derived. Hüsnü Hamid not only emphasized Wroński's this line of understanding in his articles, but also tried to confirm Wroński mathematically in his search for the formula in question.

In his first two articles, Hüsnü Hamid approached Wroński's thoughts in a distance, while in his last article he confirmed that Wroński's methods yielded very approximate results in the solution of equations of higher degree than 4, as Wroński puts it. It is valuable for our history of science that the fact that Hüsnü Hamid was interested in the mathematical philosophy of Wroński, which was not very popular during his time, and that it was revealed.