O pojęciu prawdy w matematyce

The paper is devoted to the concept of truth in mathematics. The starting point is Tarski's definition of truth. The philosophical background of this definition is discussed, its meaning for the language of mathematics and for philosophy, its relation to various definitions of truth. The relation provability vs. truth is also considered. With use of some results of mathematical logic, it is shown that the conditions from Tarski's definition are too weak to assure the uniqueness of interpretation of truth predicate. It is also shown that semantic notions such as satisfaction and truth are not finitistic and require the concept of infinity.