REICHENBACH, HANS
(1891–1953)

Hans Reichenbach was a leading philosopher of science and a proponent of logical positivism. He made important contributions to the theory of probability and to the philosophical interpretation of the theory of relativity, quantum mechanics, and thermodynamics.

Life

Reichenbach studied civil engineering, physics, mathematics, and philosophy at Berlin, Göttingen, and Munich in the 1910s. Among his teachers were neo-Kantian philosopher Ernst Cassirer, mathematician David Hilbert, and physicists Max Planck, Max Born, and Arnold Sommerfeld. Reichenbach received his degree in philosophy from the Friedrich-Alexander University of Erlangen-Nürnberg in 1915 with a dissertation on the theory of probability titled Der Begriff der Wahrscheinlichkeit für die mathematische Darstellung der Wirklichkeit (The Concept of Probability for the mathematical Representation of Reality), published in 1916. Between 1917 and 1920, while he was working as a physicist and engineer, Reichenbach attended Albert Einstein's lectures on the theory of relativity at Berlin. He was fascinated by the theory of relativity and in a few years published four books about this subject: The Theory of Relativity and A Priori Knowledge (1920), Axiomatization of the Theory of Relativity (1924), From Copernicus to Einstein (1927), and The Philosophy of Space and Time (1928). In 1920 he began teaching at the Technische Hochschule at Stuttgart as private docent.

With the help of Einstein, Planck, and Max von Laue, in 1926 Reichenbach became assistant professor in the physics department of Berlin University. In 1930 he undertook the editorship of the journal Erkenntnis (Knowledge) with Rudolf Carnap. In 1933, soon after Adolf Hitler became chancellor of Germany, Reichenbach was dismissed from Berlin University because his family had Jewish origin. He emigrated to Turkey, where he was appointed chief of the philosophy department of Istanbul University with a five-year contract. During his stay in Turkey he published The Theory of Probability (1935). In 1938 he moved to the United States, where he became professor at the University of California at Los Angeles. In the following years Reichenbach published Experience and Prediction (1938); Philosophic Foundations of Quantum Mechanics (1944); Elements of Symbolic Logic (1947); "The Philosophical Significance of the Theory of Relativity" in Albert Einstein: Philosopher-Scientist (1949), edited by Paul Arthur Schilpp; and The Rise of Scientific Philosophy (1951). Reichenbach died in 1953 while he was working on the nature of scientific laws and on the philosophy of time. The two books that came from this work, Nomological Statements and Admissible Operations (1954) and The Direction of Time (1956), were published posthumously.

Coordinative Definitions

An important tool introduced by Reichenbach for the philosophical analysis of scientific theories is that of coordinative definitions. According to Reichenbach, a mathematical theory differs from a physical theory because the latter uses a specific type of definition, named coordinative definition, which coordinates (that is associates) some concepts of the theory with physical objects or processes. An example of a coordinative definition is the definition of the standard unit of length in the metric system, which connects the meter with a rod housed in the International Bureau of Weights and Measures in Sèvres, or with a well-defined multiple of the wavelength of a determined chemical element. Another example is the definition of the straight line as the path of a ray of light in vacuum. A scientific theory acquires a physical interpretation only by means of coordinative definitions. Without such type of definitions a theory lacks of a physical interpretation and it is not verifiable, but it is an abstract formal system, whose only requirement is axioms' consistency.

Geometry well illustrates the role of coordinative definitions. In Reichenbach's opinion, there are two different kinds of theories concerning geometry, namely mathematical geometry and physical geometry. Mathematical geometry is a formal system that does not deal with the truth of axioms, but with the proof of theorems—that is, it only searches for the consequences of axioms. Physical geometry is concerned with the real geometry in the physical world; it searches for the truth or falsity of axioms using the methods of the empirical science. The physical geometry derives from the mathematical geometry when appropriate coordinative definitions are added. For example, if the concept of a straight line is coordinated with the path of a ray of light in a vacuum, the theory of relativity shows that the real geometry is a non-Euclidean geometry. Without coordinative definitions, Euclidean and non-Euclidean geometry are nothing but formal systems; with coordinative definitions, they are empirically testable. Coordinative definitions are conventions, because it is admissible to choose a different definition for a concept of a theory. In the case of geometry, with a different definition for the straight line, Euclidean geometry is true. In a sense, choosing between Euclidean and non-Euclidean geometry is not a matter of facts, but a matter of convention.

Relativity of Geometry

Reichenbach insists on the importance of the coordinative definitions in his philosophical analysis of the theory of relativity, especially in connection with the problem of determining the geometry of this world. In principle, scientists can discriminate between different geometry by means of measurements. For example, on the surface of a sphere, the ratio of the circumference of a circle to its diameter is less than π, whereas on the surface of a plane this ratio is equal to π. With a simple measurement of a circumference and of its diameter, we can discover we live on a sphere (the surface of Earth) and not on a plane. In the same way, using more subtle measurements, scientists can discover we live in a non-Euclidean space. However, there is a fundamental question: is measuring a matter of facts or does it depend on definitions? Reichenbach proposes the following problem, discussed in The Philosophy of Space and Time : is the length of a rod altered when the rod is moved from one point of space, say A, to another point, say B? We know many circumstances in which the length is altered. For example, the temperature in A can differ from the temperature in B. However, the temperature acts in a different way on different substances. If the temperature is different in A and in B, then two rods of different material, such as wood and steel, which have the same length in A, will have a different length in B. So we can recognize a difference in temperature and use suitable procedures to eliminate variations in measurement due to variations in temperature. In general, this is also possible for every differential force—that is, for every force that acts in a different way on different substances. But there is also another type of forces, called universal forces, which produce the same effect on all types of matter.

The best-known universal force is gravity, whose effect is the same on all bodies. What happens if a universal force alters the length of all rods, in the same way, when they are moved from A to B? By the very definition of universal forces, there are no observable effects. If we do not exclude universal forces, we cannot know whether the length of two measuring rods, which are equal when they are in the same point of space, is the same when the two rods are in two different points of space. Excluding universal forces is nothing but a coordinative definition. We can also adopt a different definition, in which the length of a rod depends on the point of space in which the rod stays. So the result of a measurement depends on the coordinative definition we choose. As a consequence, the geometrical form of a body, which depends on the result of measurements, is a matter of definition. The most important philosophical consequence of this analysis concerns the relativity of geometry. If a set of measurements supports a geometry G, we can arbitrarily choose a different geometry G′ and adopt a different set of coordinative definitions so that the same set of measurements supports G′, too. This is the principle of relativity of geometry, which states that all geometrical systems are equivalent. According to Reichenbach, it falsifies the alleged a priori character of Euclidean geometry and thus falsifies the Kantian philosophy of space.

Causal Anomalies

The principle of relativity of geometry is true for metric relationships—that is, for geometric properties of bodies depending on the measurement of distances, angles, and areas. The situation seems different when we are concerned about topology, which deals with the order of space—that is, the way in which the points of space are placed in relation to one another. A typical topological relationship is "point A is between points B and C." The surface of a sphere and the surface of a plane are equivalent with respect to metrics, provided an appropriate choice of the coordinative definitions, but they differ from a topological point of view.

Consider the following example presented by Reichenbach in The Philosophy of Space and Time. Intelligent beings living on the surface of a sphere can adopt coordinative definitions that, from a metric point of view, transform the surface of the sphere into the surface of a plane. However, there is an additional difficulty: Because the surface of a sphere is finite, it is possible to do a round-the-world tour, walking along a straight line from a point A and eventually returning to the point A itself. Of course this is impossible on a plane, and thus it would seem that these intelligent beings have to abandon their original idea that they are living on a plane and instead must recognize they are on a sphere. But this is not true, because another explanation is possible: They can assert that they had walked in a straight line to point B, which is different from point A but, in all other respects, is identical to A. They can also fabricate a fictitious theory of pre-established harmony—according to which everything that occurs in A immediately occurs in B—in order to explain the similarity between A and B. This last possibility entails an anomaly in the law of causality. We can reject causal anomalies, but only by means of an arbitrary definition. Thus topology depends on coordinative definitions, and the principle of relativity of geometry also holds for topology. According to Reichenbach, this example is another falsification of Kantian theory of synthetic a priori. In Kantian philosophy, the Euclidean geometry and the law of causality are both a priori, but if Euclidean geometry is an a priori truth, normal causality can be false; if normal causality is an a priori truth, Euclidean geometry can be false. We arbitrarily can choose the geometry, or we arbitrarily can choose the causality, but we cannot choose both.

Quantum Mechanics

Quantum mechanics differs from the other scientific theories because in this theory there is no possibility to introduce normal causality. No set of coordinative definitions can give an exhaustive interpretation of quantum mechanics free from causal anomalies.

It is important to explain some concepts used by Reichenbach in Philosophical Foundations of Quantum Mechanics, his main work about quantum mechanics. Using a wider sense of the word "observable," some events occurring in quantum mechanics are observable; they are events consisting in coincidences between particles or between particles and macroscopic material, like the collision of an electron on a screen, signaled by a flash of light. Events between such types of coincidences are unobservable; an example is the path of an electron between the source and the screen on which it collides.

Quantum observable events are called, by Reichenbach, phenomena, whereas unobservable ones are called interphenomena. Reichenbach explains that there are three main interpretations concerning interphenomena: wave interpretation, according to which matter consists of waves; corpuscular interpretation, according to which matter consists of particles; and Bohr-Heisenberg interpretation, according to which statements about interphenomena are meaningless. The first two interpretations are called exhaustive interpretations, because they include a complete description of interphenomena. The last is a restricted interpretation, because it prohibits assertions about interphenomena. A normal system is an interpretation in which the laws of nature are the same for phenomena and interphenomena. This definition of a normal system is modeled on a basic property of classical physics: the laws of nature are the same whether or not the object is observed.

With these definitions, it is possible to formulate Reichenbach's principle of anomaly in quantum mechanics: there is no normal system. Thus causal anomalies cannot be removed from quantum mechanics. However, there is another peculiarity in quantum mechanics: for every experiment there exists an exhaustive interpretation—which is a wave or a corpuscular interpretation—that provides a normal system, although limited to this experiment. In other words, there does not exist an interpretation free from all causal anomalies, but for every causal anomaly there does exist an interpretation that ruled out this anomaly. For example, if we adopt the corpuscular interpretation, we have to face causal anomalies raising from some experiments, such as the two-slits experiment. In this experiment a beam of electrons is directed toward a diaphragm with two open slits and an interference pattern is produced on a screen behind the diaphragm; the probability that an electron, passing through an open slit, will reach the screen at a given point is depending on whether the other slit is open or closed—with the electron behaving as if it is informed about the state of the other slit.

This causal anomaly is eliminated if we adopt the wave interpretation, according to which the interference patterns are produced by waves in conformity with Huygens's principle. The wave interpretation is in turn affected by other anomalies raising from the so-called reduction of the wave packet: The wave originating from an open slit occupies a hemisphere centered on the slit, but when the wave hits the screen, a flash is produced in a point only and the wave disappears in all other points. Apparently all physical properties transported by the wave, such as momentum and energy, suddenly materialized in a single point, even if they were distant from this point. This situation is explained without anomalies by the corpuscular interpretation. According to Reichenbach, in every experiment about quantum mechanics we can adopt an interpretation free from causal anomalies, but we have to use a different interpretation in a different experiment. Only two interpretations are required: the wave and the corpuscular interpretation. This is the real meaning of the duality of wave and corpuscle in quantum physics. The possibility of eliminating causal anomalies from every quantum experiment is called, by Reichenbach, the principle of eliminability of causal anomalies.

The Bohr-Heisenberg restricted interpretation of interphenomena named after Danish physicist Niels Bohr and German physicist Werner Karl Heisenberg, states that speaking about values of unmeasured physical quantities is meaningless. Reichenbach criticizes the Bohr-Heisenberg interpretation on two points. First, Heisenberg's indeterminacy principle becomes a meta-statement about the semantics of the language of physics; second, this interpretation implies the presence of meaningless statements in the language of physics.

Using a three-valued logic, in which admissible truth values are truth, falsehood, and indeterminacy, Reichenbach constructs another restrictive interpretation in which a statement about an unmeasured physical quantity can be neither true nor false, but indeterminate.

Interpretations of Reichenbach's Philosophy

An open question regards the relation between Reichenbach and conventionalism. His insistence on the major role played by the coordinative definitions, the relativity of geometry, the equivalence between wave and corpuscular interpretation of quantum mechanics has suggested that his philosophy can be ascribed to conventionalism. In Reichenbach's works there are some points corroborating this view. For example, he asserts that the philosophical meaning of the theory of relativity is that this theory proves the necessity of coordinative definitions, which are arbitrary, in situations in which empirical relations had been previously assumed. But there are also some elements against the conventionalist reading of Reichenbach's philosophy, as seen in the last paragraph of The Philosophy of Space and Time, in which Reichenbach affirms that the reality of space and time is an irrefutable consequence of his epistemological analysis; it is an assertion apparently incompatible with conventionalism. As an example of the debate about Reichenbach's attitude toward conventionalism, it is possible to mention the conventionalist interpretation of Reichenbach's philosophy developed by Adolf Grünbaum in Philosophical Problems of Space and Time (1973) and Hilary Putnam's counterarguments offered in "The Refutation of Conventionalism" (1975).

A different explication of Reichenbach's philosophy, based on an analysis of the role of the coordinative definitions in the light of Kantian philosophy, is advanced by Michael Friedman and exposed in Reconsidering Logical Positivism (1999). According to Friedman's interpretation, Reichenbach, in his first published work on the theory of relativity (Theory of Relativity and A Priori Knowledge ), distinguishes two different meanings of synthetic a priori, which are united in Kantian philosophy. In the first meaning, a synthetic a priori judgment is necessary and thus not modifiable; in the second meaning, a synthetic a priori statement is constitutive of the object. The coordinative definitions are not necessary judgments, because we can make use of a different definition. Moreover, all coordinative definitions are subjected to changes with the evolution of knowledge, so they are modifiable. Thus they are not a priori in the first meaning present in Kantian philosophy. But the coordinative definitions are required to give an empirical interpretation to a theory and so they are constitutive of the object of knowledge. Thus they are synthetic a priori in the second meaning present in Kantian philosophy. Friedman calls this type of a priori judgment "constitutive, relativized a priori" (1999, p. 62), because they are a priori in the constitutive sense, relative to a given theory.

Surely Kantian philosophy exerts a great influence on Reichenbach. He professes admiration for Kant in his first works. In the article "Kant und die Naturwissenschaft" (1933, p. 626) he says, "There is no doubt that he [Kant] was one of the few thinkers whose work showed the way on which the contemporary philosophy of natural science continues to proceed." According to Reichenbach, Kantian philosophy of nature is a meaningful theory, although it is superseded by the outcomes of contemporary physics. Later, Reichenbach accentuates his departure from Kant, stressing his criticism of synthetic a priori and developing many arguments against Kantian philosophy.

See also Causation: Philosophy of Science; Philosophy of Statistical Mechanics; Time.

Bibliography

Barone, Francesco. Il neopositivismo logico. Bari, Italy: Laterza, 1986.

Friedman, Michael. Dynamics of Reason. Stanford, CA: Center for the Study of Language and Information, 2001.

Friedman, Michael. Reconsidering Logical Positivism. New York: Cambridge University Press, 1999.

Grünbaum, Adolf. Philosophical Problems of Space and Time. Dordrecht, Netherlands: Reidel, 1973.

Putnam, Hilary. "The Logic of Quantum Mechanics." In Mathematics, Matter and Method. Philosophical Papers. Vol. 1. Cambridge, U.K.: Cambridge University Press, 1975.

Putnam, Hilary. "The Refutation of Conventionalism." In Mind, Language and Reality. Philosophical Papers. Vol. 2. Cambridge, U.K.: Cambridge University Press, 1975.

Salmon, C. Wesley, and Gereon Wolters, eds. Logic, Language, and the Structure of Scientific Theories: Proceedings of the Carnap-Reichenbach Centennial, University of Konstanz, 21–24 May 1991. Pittsburgh: University of Pittsburgh Press, 1994.

Schilpp, Paul Arthur, ed. Albert Einstein: Philosopher-Scientist. Evanston, IL: Library of Living Philosophers, 1949.

Spohn, Wolfgang, ed. Erkenntnis Orientated: A Centennial Volume for Rudolf Carnap and Hans Reichenbach. Boston: Kluwer Academic Publishers, 1991.

reichenbach's works

"Kant und die Naturwissenschaft." Die Naturwissenschaften 21 (1933): 601–606, 624–626.

From Copernicus to Einstein. New York: Alliance Book Corp., 1942.

Philosophic Foundations of Quantum Mechanics. Berkeley: University of California Press, 1944.

Elements of Symbolic Logic. New York: Macmillan, 1947.

The Theory of Probability: An Inquiry into the Logical and Mathematical Foundations of the Calculus of Probability. Translated by Ernest H. Hutten and Maria Reichenbach. Berkeley: University of California Press, 1949.

The Rise of Scientific Philosophy. Berkeley: University of California Press, 1951.

The Direction of Time. Edited by Maria Reichenbach. Berkeley: University of California Press, 1956.

The Philosophy of Space and Time. Translated by Maria Reichenbach and John Freund. New York: Dover Publications, 1957.

Axiomatization of the Theory of Relativity. Translated and edited by Maria Reichenbach. Berkeley: University of California Press, 1969.

Laws, Modalities, and Counterfactuals. Berkeley: University of California Press, 1976.

Mauro Murzi (2005)

REICHENBACH, HANS

(b. Hamburg, Germany, 26 September 1891; d. Los Angeles, California, 9 April 1953)

philosophy of science, logic.

Reichenbach was one of five children of Bruno Reichenbach, a prosperous wholesale merchant, and the former Selma Menzel. Both parents were members of the Reformed Church; his paternal grandparents were Jewish. The family was cultured, with a lively interest in music, chess, books, and the theater.

From 1910 to 1911 Reichenbach studied engineering in Stuttgart but, dissatisfied, turned to mathematics, physics, and philosophy, attending the universities of Berlin, Munich, and Gottingen. Among his teachers were Planck, Sommerfeld, Hilbert, Born, and Cassirer. He took his doctorate in philosophy at the University of Erlangen in 1915, and another degree by state examination in mathematics and physics at Göttingen in 1916. His doctoral dissertation was on the validity of the laws of probability for physical reality. He wrote it without academic guidance, for he could find no professor interested in the topic. The completed dissertation consisted of an epistemological treatise and a mathematical calculus. After traveling in vain to several universities in search of a sponsor willing and able to read both parts, Reichenbach found at Erlangen a philosopher and a mathematician, each willing to sponsor the part within his competence and together willing to accept the dissertation as a whole. Decades later he would chuckle when he cited their decision as a fallacy of composition, adding: “But I did not point that out to the good professors at that time!”

Reichenbach served for two and a half years in the Signal Corps of the German army, contracting a severe illness at the Russian front. Throughout his life he regarded war as catastrophe and considered it a duty of intellectuals to combat the attitudes from which wars arise. From 1917 to 1920 he worked in the radio industry, continuing his studies in the evening. He was one of the five to attend Einstein’s first seminar in relativity theory at the University of Berlin. From 1920 to 1926 he taught surveying, radio techniques, the theory of relativity, philosophy of science, and history of philosophy at the Technische Hochschule in Stuttgart.

In 1926 Reichenbach obtained a professorial appointment at the University of Berlin. Opposition to his appointment, due in part to his social activism during his student days and in part to his outspoken disrespect for many traditional metaphysical systems, was overcome by Einstein’s persistent and witty pleading. In 1930 Reichenbach and Rudolf Carnap founded and edited the journal Erkenntnis, which for many years was the major organ of the Vienna Circle of logical positivists, of the Berlin Gřoup for Empirical Philosophy, and of the International Committee for the Unity of Science. He also broadcast over the German state radio the lectures published in 1930 as Atom und Kosmos.

Within a few days of Hitler’s election to power in 1933, Reichenbach was dismissed from the University of Berlin and from the state radio. Anticipating this action, he was on his way to Turkey before the dismissal notices were delivered. From 1933 to 1938 he taught philosophy at the University of Istanbul, where he was charged with reorganizing instruction in that subject. He was delighted to find that among his students there were many excellent young teachers, who had been given paid leave of absence by Ataturk’s government so that they might profit from the presence in Turkey of German refugee professors.

In 1938 Reichenbach received his immigration permit to enter the United States, and from then until his death in 1953 was professor of philosophy at the University of California at Los Angeles, frequently lecturing at other universities and at congresses in the United States and Europe. Shortly before his death a volume was planned for the Library of Living Philosophers (edited by P. A. Schilpp) to include both Carnap and Reichenbach, but his death prevented fulfillment of the project.

As a teacher Reichenbach was extraordinarily effective. Carl Hempel, who studied under him at Berlin, stated: “His impact on his students was that of a blast of fresh, invigorating air; he did all he could to bridge the wide gap of inaccessibility and superiority that typically separated the German professor from his students.” His pedagogical technique consisted of deliberately oversimplifying each difficult topic, after warning students that the simple preliminary account would be inaccurate and would later be corrected. Students who pursued advanced work with him found him kindly, witty, morally courageous, and loyal. Those whose interests or convictions differed from his sometimes found him arrogant and intolerant.

Reichenbach never substantially altered his episte-mological stance, which can be briefly characterized as anti-Kantian, antiphenomenalistic empiricism. In his first book, Relativitätstheorie und Erkenntnis apriori (1920), he began his attack upon the Kantian doctrine of synthetic a priori knowledge, although at that time he still regarded the “concept of an object” as a priori. He declared, however, that this concept is a priori only in the sense of being a conceptual construction contributed by the mind to sense data, and not also, as Kant had believed, a priori in the sense of necessarily true for all minds. By 1930 Reichenbach had replaced this view with the thesis that the concept of a physical object results from a projective inductive inference. From that time on, he maintained that there is no synthetic a priori knowledge, defending this thesis by showing that every knowledge claim held by Kant to be a synthetic a priori truth could be classified as analytic a priori, synthetic a posteriori, or decisional. In accord with Helmholtz, Frege, and Russell, Reichenbach regarded the axioms and theorems of arithmetic as analytic a priori. He classified the parallel postulate and the theorems of Euclidean geometry as synthetic a posteriori if, in combination with congruence conventions, they are taken as descriptive of physical spatial relations. The Kantian principle of universal causality was also classified as synthetic a posteriori. In his later work, after reformulating the principle of causality in terms of inductive inference, Reichenbach denied that it applies to the subatomic realm of quantum theory. As for the Kantian moral synthetic a prioris, he regarded them as volitional decisions, neither true nor false.

By 1924 Reichenbach had developed his theory of “equivalent descriptions,” a central tenet of his theory of knowledge. It is formulated in his Axiomatik der relativistischen Raum-Zeit-Lehre (1924), in Philosophie der Raum-Zeit-Lehre (1928), in Atom und Kosmos (1930), in Experience and Prediction (1938), and in the less technical Rise of Scientific Philosophy (1951); and it is developed with new applications in his works on quantum mechanics and time. This theory attributes an indispensable role in physical theory to conventions but rejects the extreme conventionalism of Poincaré and his school. Reichenbach insisted that a completely stated description or physical theory must include conventional elements, in particular such “coordinating definitions” as equal lengths and simultaneous times. These definitions are not bits of knowledge, for such questions as whether or not two rods distant from each other have the same length are not empirically answerable. Hence such coordinations must be regarded as conventions, as definitions, as neither true nor false.

Physical theory contains much more than these conventional elements, however. The truth of a theory, the complete statement of which must include a set of coordinating definitions, is not a matter of convention but of empirical confirmation. Furthermore, one theory using one set of congruence conventions may be empirically equivalent to another theory using another set of conventions. For example, Riemannian geometry combined with the usual coordinating definitions of equal times, equal lengths, and straight lines yields a description of physical space equivalent to Euclidean geometry combined with coordinating definitions which attribute systematic changes to lengths of rigid rods.

This equivalence Reichenbach explicated as follows: When all possible observations confirm to the same degree two descriptions, one of which uses one set of congruence conventions and the other another set, the two descriptions are equivalent, that is, have the same knowledge content or cognitive meaning.

Theories of meaning had long been a focal concern of logical positivists, to whose work Reichenbach acknowledged indebtedness, offering his own theory of meaning as a development and correction of the positivists’ verifiability theory. He disagreed with the positivists on two crucial points. First, their theory made complete verifiability (as true or false) a condition of cognitive meaningfulness. This, Reichenbach pointed out, denies that statements confirmed with probability have cognitive meaning,and hence consigns to the category “meaningless” all generalizations and all predictions of science. The strictness of their limitation on cognitive meaning had forced the positivists into a phenomenalism which equated the conclusions of physical science with statements about sensory data. Reichenbach proposed to give the neglected but all-important concept of probability the central role in theory of meaning which it actually plays in scientific method. He regarded the relation between observational data and physical theory as a probability inference, not a logical equivalence. This permits a “realistic” (as opposed to the positivists’ phenomenalistic) view of the objects of scientific knowledge.

Reichenbach’s second disagreement with the positivists’ theory of knowledge involved the logical status of any criterion of cognitive meaningfulness. The positivists assumed that their theory was itself an item of knowledge, a description of the class of meaningful statements. Reichenbach declared that any definition of “knowledge” or of “cognitive meaning” is a volitional decision without truth character (see Experience and Prediction, ch. 1, esp. pp. 41, 62). He continued to use the label “theory of meaning” because each decision concerning what is to be accepted as cognitively meaningful is connected with two cognitive questions: whether the decision accords with the actual practice of scientists, and what subordinate decisions are logically entailed by the definition of meaning.

Reichenbach formulated his own decision concerning cognitive meaning in two principles: a proposition has meaning if it is possible to determine a degree of probability for it; and two sentences have the same meaning if they obtain the same degree of probability through every possible observation (for complete formulation, see Experience and Prediction, p. 54). The second of these principles he regarded as a modern version of Ockham’s razor, core of the anti-metaphysical attitude of every consistent empiricism. As examples of its application he cited Mach’s criticism of the concept of force and Einstein’s principle of the equivalence of gravitation and acceleration.

Throughout his life Reichenbach maintained that the mathematical or frequency concept of probability suffices and needs no supplementation by a priori equal probabilities or by such concepts as “degree of credibility.” For prediction of individual events the probability was the “best wager,” determined by the frequency of the narrowest class for which there were reliable statistics. He applied the frequency concept of probability to general hypotheses by regarding them as members of classes of hypotheses having known success ratios. These views were opposed by Russell in Human Knowledge, Its Scope and Limits, and were supported by Wesley Salmon in Foundations of Scientific Inference.

Reichenbach’s work on induction was closely connected with his theory of probability, for it introduced the distinction between appraised and unappraised (or “blind”) posits. The former have frequency probabilities attached to them; the latter admit of no probability estimate. One blind posit is involved in every inductive inference: the posit that frequencies of series of events converge toward limits. (Causal or one-to-one regularities are simply one case of statistical regularities.) With this thesis Reichenbach reopened the old question of the justification of induction. He accepted Hume’s argument that inductive inferences admit of neither deductive (demonstrative) justification nor inductive justification (at pain of circularity). Thus there can be no proof of any sort that inductive inferences will ever succeed in the future, let alone succeed more often than they fail.

Nevertheless, Reichenbach offered the following “pragmatic justification” of our use of inductive inferences. He showed that if the world becomes such that inductive inferences usually fail, as would happen if no past regularities were to continue into the future, then no principles of predictive inference could succeed. Hence inductive procedures offer us our only chance of making successful predictions, although we cannot know whether they will succeed or not. If there are series of events with frequencies which converge toward limits, inductive methods will lead to increasingly successful predictions as observed frequencies approach those limits; if this condition does not obtain, no method whatsoever of making predictions will succeed. Since we cannot know that this necessary condition of successful prediction will not obtain, it would be unreasonable to renounce the method which will yield success if it does obtain. The choice is between certain cognitive failure and our only chance of success. Hence, Reichenbach concluded, it is reasonable to make inductive inferences—that is, to adopt and act on the blind posit that frequencies of series of events will converge toward limits (see Experience and Prediction, secs. 38–40).

In “Philosophy: Speculation or Science?” (1947) and in The Rise of Scientific Philosophy (1951) Reichenbach drew the corollaries for ethics of his theory of knowledge. His definition of cognitive meaning precluded any extrascientific kinds of knowledge. Hence moral principles and ethical aims are volitional decisions, not items of knowledge. He condemned traditional Philosophical systems for conflating flating cognition and volition in the mistaken hope of establishing knowledge of ultimate values, and he also rejected John Dewey’s attempt to test moral judgments by scientific methods. “There is no such thing as “the good’ in the sense of an object of knowledge” (“Philosophy: Speculation or Science?” p. 21). In his brief writings on the nature of moral judgments, his style and tone are as dogmatic as the style and tone of other ethical noncognitivists of the era. He does not mention that his classification of moral judgments as volitional decisions is a classification dependent upon his own decisional definition of cognitive meaning.

The Direction of Time, nearly completed before Reichenbach’s death and published posthumously, is the culmination of his epistemological investigations of relativity physics and quantum theory. In it he applied his analyses of conventions, equivalent descriptions, probability inferences, and three-valued logic to subjective (experienced) time, to the time concepts of macrophysics, and to the possibility of establishing time order and time direction among subatomic events. He found that among the equivalent descriptions of the “interphenomena” of quantum theory, every possible description contains causal anomalies, reversals of time direction, or both. He concluded that both time order and time direction are statistical macrocosmic properties which cannot be traced to microcosmic events. To the question “Why is the flow of psychological time identical with the direction of increasing entropy?” his answer was “Man is a part of nature, and his memory is a registering instrument subject to the laws of information theory” (The Direction of Time, p. 269).

BIBLIOGRAPHY

I. Original Works. A complete bibliography is in Modem Philosophy of Science (below). Reichenbach’s earlier writings include Der Begriff der Wahrscheinlichkeit für die mathematische Darstelhmg der Wirklichkeit (Leipzig, 1915), his inaugural dissertation, also in Zeitschrift fur Philosophie and philosophische Kritik, 161 (1916), 210–239, and 162 (1917), 98–112, 223–253, and summarized in “Der Begriff der Wahrscheinlichkeit für die mathematische Darstellung der Wirklichkeit,” in Natunwissenschaften, 7 , no. 27 (1919), 482–483: Relativitätstheorie und Erkenntnis apriori (Berlin, 1920), trans. with an intro. by Maria Reichenbach as The Theory of Relativity and A Priori Knowledge (Berkeley-Los Angeles, 1965); Axiomatik der relativistischen Raum-Zeit-Lehre, no. 72 in the series Die Wissenschaft (Brunswick, 1924; repr. Brunswick, 1965), trans. by Maria Reichenbach with an intro. by W. C. Salmon as Axiomatization of the Theory of Relativity (Berkeley-Los Angeles, 1969); Von Kopernikus bis Einstein (Berlin, 1927), trans, by R. B. Winn as From Copernicus to Einstein (New York, 1942; paperback ed., 1957); Philosophie der Raum-Zeit-Lehre (Berlin Lei–pzig, 1928), trans. by Maria Reichenbach and John Freund, with intro. by Rudolf Carnap, as The Philosophy of Space and Time (New York, 1958); Atom und Kosmos. Das physikalische Weltbild der Gegenwart (Berlin, 1930), trans, by E. S. Allen, rev. and updated by Reichenbach, as Atom and Cosmos. The World of Modern Physics (London, 1932; New York, 1933; repr. New York, 1957); and Experience and Prediction. An Analysis of the Foundations and the Structure of Knowledge (Chicago, 1938).

Later works include “On the Justification of Induction,” in Journal of Philosophy, 37 , no. 4 (1940), 97–103, repr. in Herbert Feigl and Wilfried Sellars, eds., Readings in Philosophical Analysis (New York, 1949), 324–329; Philosophic Foundations of Quantum Mechanics (Berkeley-Los Angeles, 1944); “Bertrand Russell’s Logic,” in P. A. Schilpp, ed., The Philosophy of Bertrand Russell, vol. 5 in Library of Living Philosophers (Evanston, III., 1944), 23–54; Elements of Symbolic Logic (New York, 1947); “Philosophy: Speculation or Science?” in The Nation, 164 , no. 1 (4 Jan. 1947), 19–22, repr. as “The Nature of a Question,” in I. J. Lee, ed., The Language of Wisdom and Folly (New York, 1949), 111–113; The Theory of Probability …., trans, by Maria Reichenbach and E. H. Hutten, 2nd ed. (Berkeley-Los Angeles, 1949); “The Philosophical Significance of the Theory of Relativity,” in P. A. Schilpp, ed., Albert Einstein: Philosopher-Scientist, vol. 7 in Library of Living Philosophers (Evanston, Ill., 1949), 287–311, repr. in Herbert Feigl and May Brodbeck, eds., Readings in the Philosophy of Science (New York, 1953), 195–211, and in P. P. Wiener, Readings in Philosophy of Science (New York, 1953), 59–76; “Philosophical Foundations of Probability,” in Proceedings of the Berkeley Symposium on Mathematical Statistics and Probability (Berkeley-Los Angeles, 1949), 1–20; The Rise of Scientific Philosophy (Berkeley-Los Angeles, 1951; 1954; paperback ed., 1956); Nomological Statements and Admissible Operations, in Studies in Logic and the Foundations of Mathematics (Amsterdam, 1954); The Direction of Time, Maria Reichenbach, ed. (Berkeley-Los Angeles, 1956); and Modern Philosophy of Science: Selected Essays, Maria Reichenbach, ed. and trans. (London, 1959).

II. Secondary Literature. See A. Grünbaum, Philosophical Problems of Space and Time (New York, 1963),ch.3; A. Grünbaum, W. C. Salmon, et al., “A Panel Discussion of Simultaneity by Slow Clock Transport in the Special and General Theories of Relativity” in Philosophy of Science, 36 , no. 1 (Mar. 1969), 1–81; Ernest Nagel, “Review of Philosophical Foundations of Quantum Mechanics,” in Journal of Philosophy, 42 (1945), 437–444; and “Probability and the Theory of Knowledge,” in his Sovereign Reason (Glencoe, I11., 1954); Probability in Philosophy and Phenomenological Research, V–VI (1945), which contains papers by Reichenbach, D. C. Williams, Ernest Nagel, Rudolf Carnap, Henry Margenau, and others; Hilary Putnam, review of The Direction of Time, in Journal of Philosophy, 59 (1962), 213–216; W. V. Quine, review of Elements of Symbolic Logic ibid., 45 (1948), 161–166; Bertrand Russell, Human Knowledge,Its Scope and Limits (New York, 1948), passim; W. C. Salmon, “Should We Attempt to Justify Induction?” in Philosophical Studies, 8 (1957), 33–48; and Foundations of Scientific Inference (Pittsburgh, 1966), 1–15 and passim.

Cynthia A. Schuster