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In Jena, Carnap was a student of Gottlob Frege and through his lectures he was first introduced to modern logic. Carnap was highly impressed by Frege’s system- a formulation system built from two dimensions- propositional logic (connectives), and first-order and second-order logic (laws of mathematics). this is an extensional relation system that aims to provide a logical foundation for all mathematics.[[CiteRef:: Gottfried (2008)]]
When Carnap returned to Jena after the war, he discovered another logician- [[Bertrand Russell]]. Carnap studied Russell’s Principia Mathematica and his symbolic logic of relations. Russell’s theory offered a solution to a contradiction to Frege’s system previously revealed by Russell (“Russell’s paradox”). Carnap was also influenced by Russell’s philosophical views which centered logic as method to conduct philosophy.[[CiteRef::Carnap (1963c)|pp. 3-20]]
Carnap’s early ideas utilized logic tools provided by Frege and Russell to reconstruct a system of axioms that will give foundation not only to mathematics, but also to empirical science. The main factor stimulating Carnap to justify science was the difficulties Kantianism (link to Kant) and neo-Kantianism faced in early 20th Century- as Einstien’s theory of relativity got accepted.[[CiteRef::Cirera (1994)|pp. 1-42]]
