موسی خوشخوی

ABSTRACT:

If we understand the term "Logic" to mean "Pure Logic" which is the foundation of science and thought to mankind, that logic has not changed significantly since the time of Aristotle for centuries except for better explanations and expressions. Until this legacy reached the eighteenth and nineteenth centuries, to the time of Isaac Newton, George Boole, Georg Cantor, Gottlob Frege and Bertrand Russell. The scientific works of these mathematicans and philosophers of their time have influenced each other very closely. In the meantime, the intention of George Boole and Gottlob Frege was specifically to establish pure logic used in mathematics, philosophy and other sciences. Since logic in mathematics, more than all other sciences, had paved the way for the progress of various branches of mathematics as basic principles and rules, and on the other hand, George Boole and Gottlob Frege were both renowned mathematicians, they came up with the idea of ??extracting the logic used in mathematics from that science and then applying it as a branch of mathematics that could be used for all sciences, including philosophy.

In the process of founding and developing Pure Logic, the aim of this research is to investigate the works of George Boole and his influence on the important and valuable “Concept Script” the work of Gottlob Frege, which was published about fifteen years after Boole’s death.

George Boole published his first book, “The Mathematical Analysis of Logic” in ۱۸۴۷, ۳۲ years earlier the “Concept Script” was published. He wrote this book to establish a distinct and separate pure logical system based on mathematical analysis and algebra. And to place it under the mathematical analysis. He specifically mentions the principles of symbolic algebra as his model and mentions among his goals that he intends to use this pure logic to formalize and analyze Aristotelian deductive logic and to provide solutions to the problems of philosophical logic, and that this pure logic can also be used for other sciences. George Boole wrote a total of three connected works, namely, after "The Mathematical Analysis of Logic" an article as its complimentary, and a few years later in ۱۸۵۴, he wrote his great work, "An investigation of The Laws of Thought". All these three works have been scrutinized, reviewed & analysed in this thesis reaserch paper to find out of what part of the path each has been successful or failed on.

Gottlob Frege, in his book "Concept Script", mentions that his goal is to reduce mathematics to logic. This sentence of Frege is in the same sense as what George Boole mentioned. He intended to extract pure logic from mathematics, so he had to reduce mathematics to the level of the foundations of pure logic. Both mathematicians have tried in the course of their work to redefine the three-part structure of the propositions of Aristotelian logic to the functional model in mathematics. Frege's work in the foundations of predicate logic has been distinctive. The method of both explains the use of general quantifiers and particular quantifiers. The definitions of >(FEB, ۲۰۲۵)

Key words: Pure Logic, The Laws of Thought, Axiom, Function, Truth Functional, Truth Value, Symbolic Algebra.