Gottlob Frege was a German mathematician, logician, and philosopher. He is considered one of the founders of modern logic and made major contributions to the foundations of mathematics.
He was born in 1848 in Wismar, Germany. Studied mathematics at the University of Jena. He spent most of his career as a professor of mathematics at the University of Jena (1874–1918). He married Margarete Katharina Sophia Anna Lieseburg in 1887. They had no children. He died in 1925 at the age of 76.
In 1879, Frege published his landmark book Begriffsschrift ("Concept Script") which introduced his system of predicate logic. This allowed a mathematical foundation for logic by using symbols and rules of inference. It was a dramatic break from traditional Aristotelian logic.
Frege wanted to show that arithmetic could be derived from logic, hoping to put mathematics on an absolute foundation. In his 1884 book The Foundations of Arithmetic, Frege developed his logicist approach showing how cardinal numbers could be defined in terms of logical concepts.
His most famous work The Basic Laws of Arithmetic (1893) built on his logicist program. However, Bertrand Russell discovered a contradiction in Frege's logical system, now known as Russell's paradox. This dealt a major blow to Frege's logicist program.
Despite problems with his logicism, Frege's inventions of quantifiers and his work on formalizing definitions had a profound influence on subsequent mathematics and philosophy. His contributions include being a founder of analytic philosophy and pioneering modern formal logic systems.
Gottlob Frege was an extremely influential thinker who developed modern logic and made major contributions towards establishing the logical foundations of mathematics, even though his logicist program was ultimately unsuccessful. His work has had immense impact on the philosophy of language, logic, and mathematics.
Summary:
Developed predicate logic and begriffsschrift - a logical notation that opened up logic to detailed analysis. This allowed propositions to be broken into function and argument.
Pioneered analytic philosophy - influenced Ludwig Wittgenstein and Bertrand Russell. His work on sense and reference are important to analytic tradition.
Logicist program to show arithmetic as derived from logic - inspired great mathematical work even if ultimately failed.
Formalized the modern quantifier notation - fundamental to logic and mathematics.
Rigorously developed concepts of number, function, and truth in mathematics.
Notable Quotes:
"Always separate sharply the psychological from the logical, the subjective from the objective."
"The concept of number is the common property of us all."
"Never ask for the meaning of a word in isolation, but only in the context of a proposition."
"Equality gives rise to challenging questions which are not altogether easy to answer."
"It is the content of a thought that is decisive for its truth or falsity, not how it is produced in us."