„The essence of mathematics lies precisely in its freedom” (Georg Cantor) Starting from Cantor’s insight into the nature of infinity and transfinite numbers, my aim is to show that, after Godel’s and Turing’s results, mathematics cannot be grounded on logic alone but rather, the essence of mathematics as the formal language of physics lies precisely in its logical empirical necessity. It is the dynamic interaction between these three realms of reality, mathematics as freedom of thought at the most abstract level, its inherent logical laws, as manifested within the unity of the classical Aristotelian and Fregean logical principles and the empirical, ontological necessity as existentially given at the most concrete level as laws of physics, which ultimately leads to genuine knowledge and deep understanding of reality.
Mihai C Panoschi