Before Logical Positivism


3. History of Logical Positivism.a. Before Logical Positivism.What were the main philosophical and scientific outcomes that influenced the rise of logical positivism? First of all, the Theory of Relativity exerted a great influence the early development of logical positivism, not only because of its scientific importance, but also for the philosophical suggestions that Einstein’s work contains. The first published work on the Special Theory of Relativity (Einstein's 'Elektrodynamik bewegter Körper' in Annalen der Physik, 17, 1905) begins with a discussion on simultaneity and length which is one of the most rigorous applications of the Verifiability Principle, about twenty years before Schlick's formulation. Moreover, one of Carnap's first works was an essay about the theory of space published in 1922. Reichenbach attended Einstein's lectures on the Theory of Relativity at Berlin in 1917 and wrote during the 1920s four books on that theory, and in 1915 and 1917 Schlock wrote two essays on the Theory of Relativity. The development of formal logic exerted a great influence on logical positivism. Carnap attended three courses on logic under the direction of Gottlob Frege, the father of modern logic. From a philosophical point of view, Frege asserted that all arithmetic statements are analytic a priori, and thus he denied the existence of synthetic a priori statements in arithmetic (note that for Frege geometry is synthetic a priori, because it is not reducible to logic). Therefore, in Frege's opinion, analytic statements are those that are logically true. K. Gödel, the logician who proved the completeness of first order logic and the incompleteness of arithmetic, was a member of the Vienna Circle. Logical positivists had extensive contacts with the group of Polish logicians who developed several branches of contemporary logic. Polish philosophy was significantly influenced by Kazimierz Twardowski (18661938), who studied at Vienna and taught at Lwow. Twardowski is the founder of Polish analytic philosophy. He taught several Polish philosophers and logicians, among them were:
Lukasiewicz and Ajdukiewicz published several essays in Erkenntnis, the journal of logical positivism that was edited by Carnap and Reichenbach. Alfred Tarski (19021983), who developed the theory of semantics for a formal language, took part to the congresses on scientific philosophy organized by the Vienna Circle and the Berlin Circle. He greatly influenced Carnap's philosophy of language. The Italian mathematician Giuseppe Peano (18581932) indirectly influenced the logical research of the logical positivists. He developed a logical symbolism adopted by Russell, now widely used. He proposed five axioms as a definition of the set of natural numbers. Gödel proved the Incompleteness Theorem with respect to Peano's axiomatization. Bertrand Russell's (18721970) mathematical logic exerted a major influence on logical positivism. Russell asserted the analytic character of the whole of mathematics. He endeavored to prove this assumption in his works Principles of Mathematics, 1903, and Principia Mathematica, 191013 (the last written with A. N. Whitehead). Principia Mathematica is a skilful application of logic to mathematics which gives rise to endless philosophical and technical research. Ernst Mach (18381916) – the physicist and philosopher, who taught physics at the University of Prague and theory of inductive science at Vienna – is regarded as a great source of inspiration to logical positivism. The official name of the Vienna Circle was Verein Ernst Mach, that is, Ernst Mach Association. He was a radical empiricist. He criticized the absolute theory of space and time advocated by Newton and Kant; he published a philosophical and historical analysis of classical mechanics; and he formulated the principle of economy of thought, according to which scientific theories are useful tools to make predictions, but they do not reflect an objective and independent reality. Mach's influence on early logical positivism is unquestionable. However, there are many differences between Mach and logical positivism. For example, Mach never accepted the reality of physical atoms. This extreme antirealism was not congenial to logical positivism. Schlick, at least in the first stage of his philosophical development, was a realist. He believed that science can give us a true description of an external world. He professed his admiration for Mach, but also asserted that Machian antirealism was too extreme and did not correctly depict the real activity of scientists. It must be noted that Schlick, under the influence of Wittgestein's Tractatus, eventually asserted that only statements without quantifiers are meaningful and thus scientific laws are not statements, but they are rules of inference, prescriptions to make forecasts. Hence, Schlick partially rejected his realism and accepted an interpretation of scientific laws similar to Machian economy of thought. Wittgenstein's Tractatus LogicoPhilosophicus exerted a remarkable influence on the Vienna Circle. Many meetings were dedicated to a pointbypoint analysis of that work. Not all of the logical positivists’ reactions to the Tractatus were positive, however. According to Neurath, it was full of metaphysics. Carnap (in his autobiography published in The Philosophy of Rudolf Carnap) said that Wittgenstein's influence on the Vienna Circle was overestimated. Moreover, Wittgenstein did not take part in the Vienna Circle's discussions; there were separate meetings between him, Schlick, Carnap, and Waismann. Wittgenstein's influence is evident in the formulation of the Verifiability Principle (see for example proposition 4.024 of the Tractatus, where Wittgenstein asserts that we understand a proposition when we know what happens if it is true, and compare this with Schlick's assertion "The definition of the circumstances under which a statement is true is perfectly equivalent to the definition of its meaning"). Wittgenstein influenced also the interpretation of probability. He asserted that every statement is a truth function of its elementary statements (Note: Wittgenstein employed the term elementary statement [Elementarsatze], while the term atomic proposition was used by Russell in his introduction to Tractatus). For example, (AvB) is a statement whose truth depends on the truth of its components A and B, according to the following truthtable:
Now suppose we know (A v B) is true and we want to know whether A is true. In the first, second and third row of the truthtable (A v B) is true. In two of those rows A is true too. So there is a probability 2/3 that A is true. That is, the probability of A given (A v B) is 2/3. The probability is thus a logical relation between two statements. It is very simple to find the probability of a statement P with respect to another statement Q. First of all, we write the truthtable of Q and count the rows where Q is true, suppose they are m. Among them, we count the rows where P is true, say n. The probability of P with respect to Q is thus n/m. This theory was accepted and used by Waismann ("Logische Analyse des Wahrscheinlichkeitsbegriffs" in Erkenntnis, 1, 1930). Waismann's work gave rise to an intense discussion with the Berlin Circle, whose members, namely von Mises and Reichenbach, supported a frequency interpretation. Note also that this procedure is suitable only when the statements are not universal, that is to say, P and Q must be statements without quantifiers. In the Tractatus, Wittgenstein argued that only simple propositions without quantifiers are meaningful. This point influenced Schlick's analysis of scientific laws.
