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Essay On 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 (1866-1938), 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:

  • Jan Lukasiewicz (1878-1956), who developed both the algebra of logic and a many-valued propositional calculus, which influenced Carnap's inductive logic and Reichenbach's interpretation of quantum physics, in which Reichenbach employed a three-valued propositional calculus.
  • Stanislaw Lesniewski (1886-1939), who was interested in the logical antinomies.
  • Kazimierz Ajdukiewicz (1890-1963), who taught philosophy of language, epistemology and logic.
  • Tadeusz Kotarbinski (1886-1981), who asserted that many alleged philosophical problems in fact are scientific problems; that is, they are the object of empirical science and not of philosophy, which deals with logical and ethical problems only.

Lukasiewicz and Ajdukiewicz published several essays in Erkenntnis, the journal of logical positivism that was edited by Carnap and Reichenbach.

Alfred Tarski (1902-1983), 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 (1858-1932) 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 (1872-1970) 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, 1910-13 (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 (1838-1916) – 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 anti-realism 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 anti-realism 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 Logico-Philosophicus exerted a remarkable influence on the Vienna Circle. Many meetings were dedicated to a point-by-point 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 truth-table:


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 truth-table (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 truth-table 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.

Logical Positivism

Shortly after the end of the first World War, a group of mathematicians, scientists, and philosophers began meeting in Vienna to discuss the implications of recent developments in logic, including Wittgenstein's Tractatus. Under the leadership of Moritz Schlick, this informal gathering (the "Vienna Circle") campaigned for a systematic reduction of human knowledge to logical and scientific foundations. Because the resulting logical positivism (or "logical empiricism") allowed only for the use of logical tautologies and first-person observations from experience, it dismissed as nonsense the metaphysical and normative pretensions of the philosophical tradition. Although participants sometimes found it difficult to defend the strict principles on which their programme depended, this movement offered a powerful vision of the possibilities for modern knowledge.

During the thirties, many of the younger positivists left Europe for England and the United States, where their influence over succeeding generations was enormous. Herbert Feigl and Otto Neurath concentrated on the philosophy of science, developing and refining systematic principles for study of the natural world. Mathematician Kurt Gödel used sophisticated reasoning to explore the limits of the logicist programme. Others became interested in the philosophy of language: Gustav Bergmann continued efforts to achieve a perspicuous representation of reality through an ideal logical language, while Friedrich Waismann began to examine the analysis of ordinary language.

Verifiability and Meaning

British philosopher A. J. Ayer presented many of the central doctrines of the positivist movement in his 1936 book, Language, Truth, and Logic. Ayer's polemical writing tried to show how the principle of verification could be used as a tool for the elimination of nonsense of every sort. In Ayer's formulation, the principle itself is a simple test:

We say that a sentence is factually significant to any given person, if and only if, [she or] he knows how to verify the proposition which it purports to express—that is, if [she or] he knows what observations would lead [her or] him, under certain conditions, to accept the proposition as being true, or reject it as being false.
Like the pragmatic theory put forward by Peirce, verificationism proposes that assertions are meaningful only when their content meets a (minimal) condition about the ways in which we would go about determining their truth. Moreover, like Hume's distinction between matters of fact and relations of ideas, the principle leaves no room for anything other than verifiable empirical observations of the natural world and the meaningless but useful tautologies of logic and mathematics.

Thus, much of Ayer's book was negative, emphasizing the consequences of a strict application of the positivist program to human pretensions at transcendental knowledge. Traditional metaphysics, with its abstract speculation about the supposed nature of reality, cannot be grounded on scientific observation, and is therefore devoid of significance. For the same reason, traditional religious claims are meaningless since it is impossible to state any observable circumstances under which we could be sure—one way or the other—about their truth. Even much of traditional epistemology is likely to fail the test; only the psychological study of observable human behavior regarding beliefs will remain. Mathematics and natural science are secure, but little else remains.

Although Ayer, Hempel, and other positivists spent a great deal of energy on technical refinements of the principle of verification, its basic content continued to guide the direction of the positivist movement. The major point is that much of what we try to say is meaningless blather.

The Logical Construction of the World

On a more positive note, the positivists supposed that what remains—consistent logical and mathematical reasoning, together with cautious observation of nature—comprises a great deal of worthwhile human knowledge. Rudolf Carnap's Der logische Aufbau der Welt (The Logical Structure of the World) (1929) outlined the world-view that is likely to result from a thorough application of the positivist program. The logical rigor of articles like "Testability and Meaning" (1936-37) illustrates both the power and the limitations of this procedure.

Carnap begins with an account of the methods and procedures by means of which we employ sensory observations to verify (or at least to confirm) the truth of scientific hypotheses about the operation of the physical universe. Using the formal methods of mathematical logic, then, the goal is to construct a strictly scientific language that perspicuously represents the structure of the world as a whole. The details are highly technical, of course, but it is only with the detailed treatment that the difficulties of the procedure become evident. The fundamental problem is that empirical generalizations are themselves incapable of direct support within such a system.

This was a crucial part of the insight of Karl Popper, another Viennese philosopher of science. Popper proposed abandonment of the quest for verification, noting that the key feature of scientific hypotheses is precisely their falsifiability rather than their confirmation. We best know what we mean when we carefully state the conditions under which we would be forced to give up what we have supposed.

Ethical Emotivism

The central tenets of logical positivism clearly have serious consequences when applied to moral philosophy. Attributions of value are not easily verifiable, so moral judgments may be neither true nor false, but as meaningless as those of metaphysics. Among the original members of the Vienna Circle, only Moritz Schlick devoted any attention to ethics at all, and he regarded it as the descriptive task of cataloging the ways in which members of a society express their feelings about human behavior of various sorts.

It was the American philosopher C.L. Stevenson who worked out the full implications of postivistic theories for expressions of moral praise or blame. The most vital issue to be considered is the meta-ethical question of what moral terms mean. Although Moore had correctly noted that good cannot be defined simply in terms of the approval of human beings, Stevenson made the even more radical suggestion that moral judgments have no factual content at all. Analysis of moral language should focus instead on its unique function as a guide to human behavior, what Stevenson called the "magnetism" of moral terms.

In "The Emotive Meaning of Ethical Terms" (1937) Stevenson argued that we must distinguish clearly between the descriptive or cognitive content of a term and its non-descriptive or emotive meaning. At a purely literal descriptive level, statements about moral value are indeed unverifiable and therefore meaningless, but considered as appeals to human emotions, they may have powerful dynamic effects. Saying "Murder is wrong," may have no factual significance, but it does succinctly convey a host of expressive suggestions, including (at least) "I don't like murder," "You shouldn't like murder," and "We should disapprove of murderers." Stevenson's ethical emotivism, further developed in Ethics and Language (1944), quickly became an influential twentieth-century noncognitivist theory about the meaning of moral language.

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