One-Day Symposium on the Philosophy of Mathematics

The philosophy of mathematics is a branch of philosophy that deals with philosophical questions arising from the science of mathematics. Among the important schools of the philosophy of mathematics, one can mention logicism, intuitionism, formalism, and realism.

In logicism, the attempt is made to reduce mathematical concepts and propositions to logical concepts and propositions. The background of this theory goes back to a critical view of Kant's opinions on mathematics. Intuitionism, however, holds that the truth of mathematical propositions can only be perceived and understood through mental constructions that prove that proposition to be true, and communication between mathematicians is merely a means that can create identical mental processes in different minds. Proponents of formalism believe that the foundations of mathematics are entirely formal and its problems can only be advanced and solved with regard to these formal foundations. Realism, with its very long history, claims that mathematical laws exist and in mathematical activity one cannot open a path except in accordance with them. They hold such a view toward the mathematical categories themselves.

Discussions in the philosophy of mathematics, despite belonging to a specialized field of knowledge like mathematics, have long been linked with most major branches of philosophy and have remained so to this day. The outcomes of many disputes in the philosophy of mathematics have ultimately determined the fate of many philosophical discussions. Perhaps Gödel's problem is considered among the most famous of these discussions.

The upcoming session is a one-day symposium on the philosophy of mathematics held on November 3, 2010, at Sharif University of Technology. In this symposium, Dr. Roozbeh Touserkani, a researcher at the IPM, first discusses his experiences and philosophical transition regarding the two important theories of formalism and intuitionism. Subsequently, Dr. Kaveh Lajevardi briefly critiques his remarks. In the second lecture, Dr. Siavash Shahshahani, a full professor of mathematics at Sharif University, opens a critical approach to the philosophy of mathematics and expands his talk on the misunderstandings and misconceptions about the philosophy of mathematics in its relation to mathematics. In the third lecture, Dr. Mehdi Nasrin, a former professor of philosophy at Sharif University, tries to delve into the old dispute about the a priori or a posteriori nature of mathematical propositions and emphasize the main points of the discussion.

After these three foundational lectures, it is time for a dialogue among the professors on the contentious issues of the philosophy of mathematics. The attachment of these professors to different philosophical schools has made the discussions among them more serious and, of course, more worth hearing. Dr. Zia Movahed, Dr. Mohammad Ardeshir, and Dr. Siavash Shahshahani have sat down for a dialogue in this symposium. The scientific secretary of the session is Dr. Kaveh Lajevardi.

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Dr. Touserkani's Lecture; Intuitionism versus Formalism: The Roots of the Dispute

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Dr. Shahshahani's Lecture; The Philosophy of Mathematics and Mathematicians

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Dr. Nasrin's Lecture; The A Priori or A Posteriori Nature of Mathematics

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Debate between Dr. Movahed, Dr. Ardeshir, and Dr. Shahshahani; Intuitionism and Formalism

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One-Day Symposium on the Philosophy of Mathematics

Sharif University, November 2010

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