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Carnap was a highly prolific writer that published numerous works on philosophy of science and semantic logic, including 12 books translated or published in the English language. As a fruitful philosopher, Carnap’s views have evolved and changed throughout his career. In fact, many of the arguments presented in his contributions (link to major contributions) to philosophy of science do not reflect Carnap’s final opinions on the matter. In some instances, the change in point of view, or interpretation, will be provided in Carnap’s response to criticism (link to criticism).
|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 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 (11).
In Jena, Carnap was a student of Gottlob Frege and through his lectures he was first introduced to modern logic (11). 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 (12).
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 (11).
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 (3).
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 (13). 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).
Carnap’s first major philosophical work- “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 (3).
In 1929, Carnap officially joined the Vienna Circle and became a leading member (3). 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 (4). They wished to define scientific rationality that against metaphysical speculation. For members of the circle (more importantly for Neurath(link), then 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) (16)
|Major Contributions====Analytic/Synthetic Distinction===
In the Aufbau, Carnap builds a hierarchical system where primary sensory information, called ‘elementary experience’, is the basis of empirical knowledge. From there, experience or observational statements are unified to statements of science, which describe the quantitative relation between the elements of experience. These rules of science are synthetic a posteriori, but are structured and organized to have formal properties resulting from constructional definitions and logical laws, which are analytic a priori (3). Building on Kant’s distinction of analytic/synthetic propositions, and a priori/a posteriori knowledge explained in Historical Context, Carnap modifies Kant’s analyticity criteria of containment by using a logic criteria, meaning that if a statement is purely logical it is analytic, while all other statements are synthetic. Carnap replaces Kant’s justification using a priori forms to justification in the form of modern logical relations between the observational synthetic statements and the infallible a priori logical laws that structure them (14).
In “The Logical Syntax of Language” (1934, English Tran. 1937)(link), Carnap formulates the distinction between analytic and synthetic statements in a boarder context of linguistic frameworks. For Carnap, a linguistic framework of science is comprised of two kinds of rules (5):
1) L-Rules – laws of logic and mathematics, these are analytical statements.
2) P-Rules – physical and empirical laws based on sensory experience that have factual content, these are synthetic statements.
By defining the rules of the framework, Carnap is able to give a syntactic formulation of logical consequence, where L-rules are logically determined and are independent of experience and defined as analytic a priori. Statements that are not logically determined are defined as synthetic statements (6). This formulation builds on the analytic/synthetic distinction made in the Aufbau, using a different taxonomy.
In Logical Syntax, Carnap posit the idea of linguistic frameworks to allow for changes in the appraisal or value of a scientific theory. He employs this idea of frameworks to explain changes in mathematical and logic laws in the foundation of science, as this has occurred with the replacement of Newtonian to Einsteinian worldview. Carnap argues for a Principle of Tolerance, which declares that there are no absolute rules of logic, meaning changes in L- rules will yield different frameworks with different appraisal methodologies and their choice is conventional. For Carnap, both L- and P- rules are subject to change within a framework to accommodate new scientific evidence (5).
Later in 1952 “Meaning Postulates” (link), Carnap clarifies his criteria of analyticity in the form of meaning postulates, logically true by meaning of words, or put more simply by language definition (14).
Demarcation Between Science and Pseudoscience – Scientific Significance
In the Aufbau, and later and more directly in “testability and Meaning”(link) Carnap develops criteria for distinguishing scientific statements from non-scientific or pseudoscientific ones. Scientific statements must comply with the Verification Principle, that is, they must be verifiable through experience (7).
This view can be understood from Carnap’s works in two different ways:
1) Strict Verification – a scientific proposition should be completely and directly testable through elementary experience.
2) Verifiable in Principle – a softer approach, stating that a scientific proposition is required to be conceptually testable, and is scientific even if no verifying or negating experience have been observed.
Different segments in the Aufbau can be understood either as strict or principally verifiable. Challenges with strict verification caused Carnap to drop this view later, as uncorroborated theories were considered unscientific.
Carnap’s choice in the Verification Principle, is also influenced by its consequences to metaphysics. It creates a barrier that differentiates scientific physical statements from speculative metaphysics statements. Verification is regarded as meaning criteria, where verifiable scientific propositions are considered meaningful, while metaphysical propositions are meaningless since they are not funded in experience. This view is also called Carnap’s Physicalism and is proposed for the value of directing science away from metaphysics, which according to Carnap, impede science from conducting in a fruitful way (7).
===Theory Choice – Probability and Inductive Logic===
Throughout his career Carnap has attempted in different formulations to employ the tools of probability and induction to the question of theory choice. Carnap’s motivation is to use these tools to produce a quantitative assessment to a degree of confirmation of a scientific theory (8). Carnap’s inductive logic attempts to formulate a logical relationship between a scientific statement or theory and a single observational evidence supporting that statement. If successful, this will solve Hume’s problem of induction by shifting from absolute certainty to different degrees of confirmations that will allow to rationally choose between two competing scientific theories (6). This has been the focus of Carnap’s work from 1940s until he died (4), and although he tried numerous mathematical tools and logical formulations, he did not succeed in constructing a satisfactory theory of inductive logic.
|Criticism====Quine – Against Analytic/Synthetic Distinction and Verification Principle===
The most fatal criticism against Carnap and the logical positivism movement was argued by Quine(link) in the famous 1951 paper “Two Dogmas of Empiricism” (link). In Two Dogmas, Quine attacks Carnap’s distinction between analytic and synthetic statements, by claiming a holistic view of science as an interconnected system of beliefs, in which there cannot be a clear distinction between analytic and synthetic propositions, as both equally face the ‘tribunal of experience’. In addition to rejecting analytic/synthetic distinction, Quine also argued against logical positivists Verification Principle and its reductionism of sensory experience. Quine claims that as it follows from the first dogma (against analyticity), even most simple sensory statements are interconnected, and cannot be claimed to be verifying or refuting in isolation (4)(5).
===Popper – Against Verification Principle and Inductive Logic===
Karl Popper first criticism against Carnap was directed at Carnap’s and the logical positivists’ Verification Principle and the demarcation between science and metaphysics. Influenced by his own views on the problem of demarcation, Popper argued that Carnap’s claims to ascribe meaning only to scientific statements is unjustified. Popper stated that metaphysics should not be meaningless only by virtue of not being scientific. At large, Popper viewed the Principle of Verification as resulting in both a too wide and a too narrow criterion of demarcation, as it fails to exclude a part of metaphysics called ‘rational theology’ as meaningless, while excluding virtually all laws of nature from meaning, as, according to Popper, laws of science cannot be reducible to observational reports, any more than metaphysical statements (9).
More interestingly, the infamous Popper-Carnap controversy, refers to Popper’s continued criticism on Carnap’s inductive logic. The critique was first presented in Popper’s 1954 paper “Degree of Confirmation” where he argued that combining a scientific theory’s degree of confirmation with quantitative probability will result in fatal error since following Carnap’s ‘Calculus of Probability’ had mathematical contradictions. A few months following the paper’s publication Bar Hillel, Carnap’s student, replied to Popper claiming that there is no serious error, but a verbal issue of misunderstanding between Popper and Carnap. In response to Bar-Hillel’s reply, Popper wrote another reply further scrutinizing Carnap’s views (10).
Popper’s criticism had two arguments against Carnap’s inductive logical (10):
1) It could not serve as criterion of demarcation, as it can act on *** - to this Carnap himself agreed.
2) it was self-contradictory in the treatment of unrestricted universal where the degree of confirmation approaches zero w
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