Frege: Life and Main Philosophical Ideas

Biographical Background

Gottlob Frege lived from 1848 to 1925. A German mathematician, logician, and philosopher, he spent most of his career at the University of Jena. He was little recognized during his lifetime, but later became a founder of modern logic and analytic philosophy.

His major works include Begriffsschrift, The Foundations of Arithmetic, Basic Laws of Arithmetic, and the essay "On Sense and Reference."

Philosophical Thought

Frege created modern predicate logic. Unlike Aristotelian syllogistic, his logic could handle quantifiers, variables, functions, and relations. This transformed logic and made possible later developments in analytic philosophy, mathematics, and computer science.

In the philosophy of mathematics, Frege defended logicism: arithmetic can be grounded in logic. He rejected psychologism, the view that logic and mathematics are about mental processes. Mathematical truths are objective, not psychological habits.

His system was damaged by Russell's paradox, which showed inconsistency in his Basic Laws. Yet the failure generated major developments in set theory, type theory, and mathematical logic.

Frege's distinction between sense and reference is foundational in philosophy of language. "Morning Star" and "Evening Star" have the same reference, Venus, but different senses, or modes of presentation. This explains why "The Morning Star is the Evening Star" can be informative.

Frege also held that the reference of a sentence is its truth-value and its sense is a thought. Thoughts are not private mental images but objective contents that different people can grasp.

Frege's importance lies in founding the logical and linguistic turn in philosophy. He showed that many philosophical problems require precise analysis of language, meaning, reference, and logical form.