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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]]
Immanuel Kant directed philosophy of science to a new theory of empiricism in the 18th Century. He coined the distinction between analytic and synthetic propositions to provide an alternative infallible foundation for geometry and Newtonian physics. For Kant, analytic proposition predicts the containment of objects and synthetic propositions predicts contradiction or no connection between objects. In that sense, statements in arithmetic, geometry, physics and philosophy are all synthetic per Kant .[[CiteRef:: Russell (132017). ]] He also defined ‘a priori’ and ‘a posteriori’ knowledge. A priori knowledge is true independent of experience and is infallible- analytical pre-contained statements always a priori by definition. While a posteriori knowledge is based on experience and by the problem of induction and sensation cannot be absolutely certain (14). Furthermore, Kant makes a distinction between the world is it (noumena) and the world as we perceive it (phenomena), and claims that only the world of phenomena is knowable. Kant argued that the world of phenomena is structured by a priori forms such as sensibilities and cognitive faculties (15). In particular, Euclidian geometry is an a priori form that shapes how we perceive space. By working within the realm of phenomena, and structuring it by a priori form, Kant claims that synthetic propositions can be justified a priori as they are deducible from the a priori forms, and accordingly that synthetic proposition of mathematics and physical science are absolutely.
By the beginning of 20th Century Newtonian physics which was key to Kant was replaced by relativity with the introduction of special relativity in Einstein’s 1905 paper “On the Electrodynamics of Moving Bodies”, followed by a general theory of relativity by 1915. The theory was widely accepted after its corroboration in 1919 solar eclipse expeditions by Dyson and Eddington. As General relativity required the use of a non-Euclidian geometry to describe the matrix tensors of timespace it violated Kant’s fundamental transcendental a priori forms – Euclidian geometry of space (3D) and in fact even the form of time. Kantian tradition held a strong influence on German culture since its origin to Carnap’s time, and when it faced contradiction by relativity Carnap was motivated to formulate a new justification for empirical knowledge (3).
