نوع مقاله : پژوهشی
نویسنده
عضو هیات علمی گروه فلسفه علم پژوهشگاه علوم انسانی و مطالعات فرهنگی
کلیدواژهها
موضوعات
عنوان مقاله English
نویسنده English
The study of the certainty and inexorability of mathematical theorems is one of the important topics in the philosophy of mathematics. Various schools such as logicism, intuitionism, Platonism and naturalism have tried to present theories on this subject. These schools usually seek the foundation for mathematics in order to justify the certainty of mathematical theorems and logic. This has always been accompanied by numerous failures. In this article, we try to examine this issue from Wittgenstein's point of view. That is, instead of asking "What is the foundation of logic and mathematics?" we ask "Why does mathematics need the foundation?". Therefore, we first examine foundationalism. Then we show that mathematics is a language-game. In this regard, we examine geometry and logic as two language-games in mathematics. Finally, we show that, according to Wittgenstein's philosophy, the certainty and inexorability of a valid inference or a correct calculation comes from the practical procedure of inference and calculation.
کلیدواژهها English
