What is Mathematical Formalism and What Does It Mean?July 2, 2021
Mathematical logic understanding of Hilbert and his followers. German mathematician and logician David Hilbert (1862-1943), the founder of the Göttingen school of mathematics, put forward a new understanding called mathematical formalism in the field of mathematical logic. According to this understanding developed by the neo-positivist Hilbert and his followers G. Neyman, W. Ackerman, P. Bernays, mathematical facts can only be proved by non-contradiction, for this it is necessary to establish formal axioms.
This argument of Hilbert, who puts Euclidean geometry into a rigid system of axioms, is to realize in mathematics what Aristotle did centuries ago in thought, in other words, to prove mathematics with mathematics, just as Aristotle demonstrated thought with thought. In other words, it clarifies any hypothesis and tests whether it falls into mathematical contradiction. If not, that assumption is true.
This idealist understanding, like every idealist understanding, denies that truth should be verified by nature, theory should be verified by practice. This means setting aside the conformity of the subject to the object and demonstrating by the conformity of the subject to the subject. This argument of Hilbert, which also led to his meta-mathematical understanding, is also known as formalism.