Category Philosophy

Frege’s Logicism: A Short Portrait

In 1893, Gottlob Frege published the first volume of Gottlob Frege: Basic Laws of Arithmetic.Using the logical notation, logical axioms, and axiomatic predicate logic (first- and second-level quantification, which he himself had invented!), from his earlier works (the Begriffsschrift and The Foundations of Arithmetic: A Logico-Mathematical Enquiry into the Concept of Number), he meticulously laid out his ontology, rules […]

Hilbert’s Second Problem and Gödel’s Incompleteness Theorems

In a talk given at the Second International Congress of Mathematicians in the year 1900, David Hilbert (one of the greatest mathematicians of his day) outlined what he considered to be ten of the unsolved problems of mathematics, believing that by pointing to the unsolved problems in mathematics, he would be able to give direction to the mathematical […]