some considerations on Williamson ‘view about the tension between non-classical logic and applicability of mathematics

classical logic has had some problems in explaining issues such as semantic paradoxes, vagueness problem, and quantum phenomena and have led logicians to seek non-classical logical formulations in which such problems do not arise. However, the undeniable growth of mathematics and its widespread influence in other disciplines has often led non-classical logicians to emphasize adherence to mathematical reasoning with the principles of classical logic by separating mathematical reasoning from non-mathematical. Against this approach, Williamson shows that the strategy of separating mathematics from non-mathematics and adhering to non-classical logic in non-mathematical fields disrupts the applicability of mathematics, and non-classical logicians need to think about solving this problem. In this essay, while expressing Williamson's arguments on the tension between advocating non-classical logic and the applicability of mathematics and emphasizing some of them, we show that, unlike Williamson, scientific activity based on deductive inference does not follow classical logic completely and therefor the tension sometimes subsides.