Gottlob Frege (1848 – 1925) was a German intellectual whose work in the fields of mathematics and logic led to the development of modern predicate logic and sowed the seeds for contemporary analytic philosophy. Frege was largely ignored by his peers, but was to become influential upon and through the next generation of popular thinkers such as Bertrand Russell and Whitehead.
The importance of Frege’s work arises from the inadequacy of Aristotelian and Stoic logic in dealing with mathematical statements, for example Euclid’s theory of the infinite amount of prime numbers. This was a problem for Frege because he contended that all the truths of arithmetic simply were truths that were both logical and analytic. In this way, Frege’s work is more in the rationalist tradition of Leibniz than in Kant’s transcendental idealism.
Frege set about clarifying logic by doing away with the typical subject/predicate analysis and replacing it with function and argument. Many will be familiar with a mathematical function such as f(x) = x + 3, where the function is equal to the numerical value of x + 3. Frege radically applied the function to arguments, such as “all cats have tails”, expressing them as f(x), where x is a cat, then x has a tail.
Fregean logic allowed the dissolution of the problem of multiple generality. For example, prior to Frege the distinction between statements such as “every person loves some city” and “every city is loved by some person” could only be represented artificially.