By Hermann von Helmholtz (auth.)
 Hermann von Helmholtz within the heritage of clinical process In 1921, the centenary of Helmholtz' delivery, Paul Hertz, a physicist, and Moritz Schlick, a thinker, released a variety of his papers and lectures at the philosophical foundations of the sciences, lower than the identify Schriften zur Erkenntnistheorie. Combining characteristics of admire and feedback that Helmholtz might have demanded, Hertz and Schlick scrupulously annotated the texts. Their variation of Helmholtz was once of ancient effect, such as the impact between modern mathematicians and philosophers of Hermann Weyl's annotated version in 1919 of Riemann's nice dissertation of 1854 at the foundations of geometry. For numerous purposes, we're happy for you to deliver this Schlick/ Hertz variation to the English-reading global: first, and first, to honor the reminiscence of Hermann von Helmholtz; moment, as writings of ancient worth, to deepen the knowledge of arithmetic and the usual sciences, in addition to of psychology and philosophy, within the nineteenth centur- for Helmholtz needs to be comprehended inside no less than that huge a spread; 3rd, with Schlick, to appreciate the constructing empiricist philosophy of technological know-how within the early twentieth century; and fourth, to convey the contributions of Schlick, Hertz, and Helmholtz to methodological debate in our personal time, a part century later, lengthy after the increase and consolidation of logical empiricism, the explosion of physics considering that Planck and Einstein, and the improvement of psychology when you consider that Freud and Pavlov.
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Extra info for Epistemological Writings: The Paul Hertz/Moritz Schlick Centenary Edition of 1921 with Notes and Commentary by the Editors
But the other and greater arc of the same great circle is also a geodetic or straightest line, meaning that each of its smaller parts is a shortest line between its two endpoints. Because of this circumstance, we cannot simply identify the concept of a geodetic or straightest line with that of a shortest ON THE AXIOMS OF GEOMETRY 7 line. If moreover the two given points are endpoints of the same diameter of the sphere, then any plane through this diameter intersects the surface of the sphere in semicircles, all of which are shortest lines between the two endpoints.
The straight line is defined as the shortest between two points - in this one is specifying a magnitude. The axiom of parallels declares that if two straight lines in the same plane do not intersect (are parallel), the corresponding angles, or the alternate angles, made by a third line intersecting them are pairwise equal t. Or it is postulated, in place of this, that the sum of the angles any triangle is equal to two right angles. These too are cases of specifying magnitudes. ] 12 CHAPTERI magnitudes with respect to some spatial structure which is regarded as fixed (coordinate system).
One indeed can instance a certain behaviour 42 of the bodies that appear fixed to us, such that measurements in Euclidean space would turn out as if they had been performed in pseudo spherical or spherical space. To see this 43, I will point out first that if the whole of the linear dimensions of the bodies surrounding us, and with them those of our own body, were all decreased in the same proportion - say by half, or say they were all increased to double their size - we would be quite unable to notice such a change with our means of spatial intuition.
Epistemological Writings: The Paul Hertz/Moritz Schlick Centenary Edition of 1921 with Notes and Commentary by the Editors by Hermann von Helmholtz (auth.)