Hans Reichenbach, born on September 26th 1891 in Hamburg, Germany, was a leading philosopher of science, a founder of the Berlin circle, and a proponent of logical positivism (also known as neopositivism or logical empiricism). He studied physics, mathematics and philosophy at Berlin, Erlangen, Gottingen and Munich in 1910s. Among his teachers were the neo-Kantian philosopher Ernst Cassirer, the mathematician David Hilbert, and the physicists Max Planck, Max Born and Albert Einstein. Reichenbach received his degree in philosophy from the University at Erlangen in 1915; his dissertation on the theory of probability was published in 1916. He attended Einstein's lectures on the theory of relativity at Berlin in 1917-20; at that time Reichenbach chose the theory of relativity as the first subject for his own philosophical research. He became a professor at Polytechnic at Stuttgart in 1920.

__The Philosophy of Space and Time and the Philosophical Meaning of the Theory of Relativity__

In Reichenbach opinion, it must be realized that there are two different kinds of geometry, namely mathematical geometry and physical geometry. Mathematical geometry, a branch of mathematics, is a purely formal system and it does not deal with the truth of axioms, but with the proof of theorems, ie it only search for the consequences of axioms. Physical geometry is concerned with the real geometry, ie the geometry which is true in our physical world: it searches for the truth (or falsity) of axioms, using the methods of empirical science: experiments, measurements, etc; it is a branch of physics. How can physicists discover the geometry of the real world? Look at the following example, which Reichenbach analyses in Riemann's method is based on physical measurements. Reichenbach carefully examines the epistemological implications of measuring geometrical entities. The empirical measurement of geometrical entities depends on physical objects or physical processes corresponding to geometrical concepts. The process of establishing such correlation is called a What is the philosophical meaning of a co-ordinative definition? Reichenbach proposes the following problem, discussed in At a first glance, the principle of relativity of geometry proves it is not possible to discover the real geometry of our world. This is true if we limit ourselves to metric relationships. Metric relationships are geometric properties of bodies depending on distances, angles, areas, etc; examples of metric relationships are "the ratio of circumference to diameter equals pi" and "the volume of A is greater than the volume of B". But we can study not only distances, angles, areas but also the order of space, the Reichenbach examines the following example ( Reichenbach says the second possibility entails an anomaly in the law of causality. If we assume normal causality, topology become an empirical theory and we can discover the geometry of the real world. This example is another falsification of Kantian theory of synthetic a priori. Kant believed both the Euclidean geometry and the law of causality were a priori. But if Euclidean geometry were an a priori truth, normal causality might be false; if normal causality were an a priori truth, Euclidean geometry might be false. We arbitrarily can choose the geometry or we arbitrarily can choose the causality; but we cannot choose both. Thus the most important implication of the philosophical analysis of topology is that
Q], substitute 'multiply by F[Q]' to 'F[Q]'.Q by C' to 'P', where C=h/(2*pi*i), h is the Planck constant, pi equals 3.14…, i is the square root of -1.Q by C^2' to 'P', where C=h/(2*pi*i), h is the Planck constant, pi equals 3.14…, i is the square root of -1.
negation: cyclic (-) diametrical (?) complete (^))
Thus we cannot assert E2 and there is not any causal anomaly.
1921 'Bericht uber eine Axiomatik der Einsteinschen Raum-Zeit-Lehre' in 1929 'Stetige Wahrscheinlichkeits folgen' in 1933 'Kant und die Naturwissenschaft', 1947 1948 1951 1954 1956 1977 1977 1979 1983 1989 1979 |