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|Historical Context=Rudolf Carnap was educated at University of Jena from 1910 to 1914 in philosophy, mathematics, and physics. In 1914, his education was interrupted by WWI due to an obligation to serve in the German army. In 1919, Carnap returns to Jena to complete his studies and commence his own independent research in philosophy.[[CiteRef::Carnap (1963c)|pp. 3-20]]
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 yet 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 [[Immanuel Kant|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 empirical knowledge, and specifically for geometry and Newtonian physics. For Per Kant, an analytic proposition predicts is a statement in which the relation between the objects is containment of objects and a synthetic propositions predicts proposition is a statement in which there is a contradiction or no connection between the objects. In that sense, statements in arithmetic, geometry, physics , and philosophy are all synthetic per Kant.[[CiteRef:: Russell (2017)]] 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.[[CiteRef::Rey (2017)]] 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.[[CiteRef::Rohlf (2016)]] 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 are absolutely certain as they are deducible from the a priori forms, and accordingly that synthetic proposition of mathematics and physical science are absolutely(missing citation).
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.[[CiteRef::Cirera (1994)|pp. 1-42]]
Carnap’s first major philosophical work- [[Carnap (1967b)|“The Logical Structure of the World” ]] (1928 German: Der logische Aufbau der Welt, English Tran. 1967)(link), also known as Aufbau, was written before he joined the Vienna Circle, yet it embodies a logical positivist view by its attempts to construct a logical system to justify empirical knowledge. By this time Carnap has had already established a strong relationship with Hans Reichenbach (also a member of the circle). The two shared an interested in discussing Einstein’s challenges to Kantianism.[[CiteRef::Cirera (1994)|pp. 1-42]]
In 1929, Carnap officially joined the Vienna Circle and became a leading member.[[CiteRef::Cirera (1994)|pp. 1-42]] The Circle, and Carnap in particular, argued for ‘logical positivism’ a new flavor of empiricism post-Kant which would replace synthetic a priori forms by structuring empirical knowledge on modern mathematics and logic as analytical statements.[[CiteRef::Friedman (2008)]] They wished to define scientific rationality that against metaphysical speculation. For members of the circle (more importantly for [[Otto Neurath(link)|Neurath]], then than Carnap) the motivation for rejecting metaphysics was to use science legitimacy as a tool to transform society, against rising nationalist movement in Vienne and Germany at that time (1930s). [[CiteRef::Cat (2017)]]
|Major Contributions====Analytic/Synthetic Distinction===
