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Mathematical logic is mathematical only in so far as it makes use of mathematical tools. In this sense, mathematical logic is mathematical to the same extent that, say; Newtonian mechanics. Despite using mathematical tools, neither science has become a branch of mathematics properly. They both aim at explaining and describing an external realm of reality. In the case of logic, its mathematical tools -both its symbolism and its calculus- are formal, because they allow for formal calculation. These tools were developed in early modern times with the purpose of giving an algebraic treatment to geometry. Nevertheless, they soon became the main tools for all mathematics and mathematical science.

¿Qué tan matemática es la lógica matemática?