# Gottlob Frege Philosophy

## German philosopher, Mathematician, and Logician

Insights to philosophy of Gottlob Frege, famous for Context Principle and Sense & Reference, predecessor of Bertrand Russell.

Gottlob Frege was a German mathematician and logician. A creator of a logistic system in his day, he is best known for his book Foundations of Arithmetic which discusses how he attempted to derive arithmetic from a set of logical axioms.

### Life of Gottlob Frege in a Nutshell

Gottlob Frege (1848-1925) was born in Wismar, the modern federal state Mecklenburg-Vorpommern, Germany.

As a teenager, he studied at Wismar’s local gymnasium before pursuing studies at the University of Jena. He eventually became a professor of mathematics at Jena for almost 40 years and along with George Boole, they were among the founders of symbolic logic.

A predecessor of Bertrand Russell, Frege’s work went unnoticed in his own lifetime. However, he went on to become one of the greatest influences on 20th century philosophy mainly for his work in logic and the philosophy of mathematics.

### Frege’s Context of Principle: Expression of Sense and Reference

His philosophy began when he rejected the Aristotelian analysis of sentences as fundamentally forming a subject and a predicate. For example, in the sentence “Socrates is wise,” the subject which is “Socrates” is ascribed by “is wise.”

Frege took this away by analyzing sentences on a mathematical model of function and argument. In his view, the sentence “Socrates is wise” contains a function, “( ) is wise,” with Socrates taking the place of argument for that function.

He claimed that this view is taken directly from mathematics, where sentences such as “3 + 5” maybe analyzed in terms of function “( ) + ( )” which can only be completed by the arguments “3” and “5.”

This allowed Frege to profound developments in the philosophy of language. Since neither the functional expression nor the arguments assert anything individually, but only when they are combined to form a complete expression, it follows that the meaning of a term can only be given in the context of the sentence (Frege’s “Context Principle”), by deducing what contribution it makes to the sense of the whole expression (“the compositionality of the meaning”.)

### Frege’s Contribution to Philosophy and Logic

His invention of “quantificational” logic was the greatest development in that subject since Aristotle. It also completely replaced Aristotelian “syllogistic” logic in university courses.

When he applied a distinction in meaning between the sense and reference of an expression, in effect, he laid the concept of Context Principle – that meaning is primarily a property of sentences, and only derivatively of single words.

Since the sense of an expression determines what it refers to, succeeding philosophers picked this up as an essential connection between what people say and what there is, the very idea that philosophers Bertrand Russell and Ludwig Wittgenstein, pursued in their logical atomism.

Frege’s influence on 20th century philosophy is most significant to great thinkers like Russell and Wittgenstein.

### Books by Gottlob Frege

• Concept Notation, 1879
• The Foundations of Arithmetic, 1884
• Function and Concept, 1891
• On Sense and Reference, 1892
• On Concept and Object, 1892