In this article, we try to show the limits of formalism based on Gödel's incompleteness theorems. The most fundamental debate at the our work is shaped by the tension between provability and truth. The studies that started with Frege's project to reduce arithmetic to logic and continued with Hilbert's formalism project aimed to establish a solid foundation for mathematics. But when Gödel proved that some propositions cannot be decided formally, the containment of Hilbert's formalism project took a hit. On the other hand, Gödel's theorems started the discussion of provability and truth, as it showed that there were propositions whose proof could not be given, but whose truth was mentioned. In our study, we aim to illuminate the argument between provability and truth in a formal language based on Gödel's theorems.
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