Professor of Philosophy of Science, Institute for Humanities and Cultural Studies
10.30465/ps.2026.53585.1809
Abstract
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.
Moghaddam Heidari,G . (2026). Mathematical certainty :Inference and calculation practice. (e10803). Philosophy of Science, 15(2), e10803 doi: 10.30465/ps.2026.53585.1809
MLA
Moghaddam Heidari,G . "Mathematical certainty :Inference and calculation practice" .e10803 , Philosophy of Science, 15, 2, 2026, e10803. doi: 10.30465/ps.2026.53585.1809
HARVARD
Moghaddam Heidari G. (2026). 'Mathematical certainty :Inference and calculation practice', Philosophy of Science, 15(2), e10803. doi: 10.30465/ps.2026.53585.1809
CHICAGO
G Moghaddam Heidari, "Mathematical certainty :Inference and calculation practice," Philosophy of Science, 15 2 (2026): e10803, doi: 10.30465/ps.2026.53585.1809
VANCOUVER
Moghaddam Heidari G. Mathematical certainty :Inference and calculation practice. Philosophy of Science. 2026;15(2):e10803 (In Persian). doi: 10.30465/ps.2026.53585.1809
