Mathematical_logic

 Mathematical_logic

is a subfield of mathematics exploring the applications of formal logic to mathematics. It bears close connections to metamathematics, 

the foundations of mathematics, and theoretical computer science.

 

Logic and mathematics are two sister-disciplines, because logic is this very general theory of inference and reasoning, and inference and reasoning play 

a very big role in mathematics, because as mathematicians what we do is we prove theorems, and to do this we need to use logical principles and logical inferences.

 

Mathematics is the study of topics such as quantity (numbers), structure, space, and change. ... The field of logic ranges from core topics such as the study of 

fallacies and paradoxes, to a specialized analysis of reasoning using probability and to arguments involving causality.

 

What is mathematical logic used for?

Mathematical logic was devised to formalize precise facts and correct reasoning. Its founders, Leibniz, Boole and Frege, hoped to use it for common sense 

facts and reasoning, not realizing that the imprecision of concepts used in common sense language was often a necessary feature and not always a bug.

 

Aristotle

As the father of western logic, Aristotle was the first to develop a formal system for reasoning. He observed that the deductive validity of any argument can be 

determined by its structure rather than its content, for example, in the syllogism: All men are mortal; Socrates is a man; therefore, Socrates is mortal.



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