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A New Foundation of Physical TheoriesSpecies of Structures and Axiomatic Basis of a PT

A New Foundation of Physical Theories: Species of Structures and Axiomatic Basis of a PT Species of Structures and Axiomatic Basis of a PT In the preceding chapter we described the general form of a mathematical theory in the context of a physical theory. The main task was to clarify the connection between physical realities and the abstract mathematical theory. Nevertheless, this explanation was not sufficient to apprehend the structure of the mathematical theory itself; it was especially not sufficient to see how MT gives the physically decisive conditions to MT . This problem was hidden behind the selection of the picture terms Q and s in MT ; for example, as i ν picture terms Q =IR × IR for the idealized marked spots, and as relation s 2 2 d(α ,α ; β ,β )= (α − β ) +(α − β ) 1 2 1 2 1 1 2 2 for the idealized distance. In this case we know that the terms Q, d describe a two-dimensional Euclidean geometry, but we only know this since we have learned that the terms Q, d constitute the analytic form of this geometry. This example also shows that the particular values (α ,α ) for an idealized 1 2 marked spot have no influence http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

A New Foundation of Physical TheoriesSpecies of Structures and Axiomatic Basis of a PT

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Publisher
Springer Berlin Heidelberg
Copyright
© Springer-Verlag Berlin Heidelberg 2006
ISBN
978-3-540-30832-4
Pages
63 –104
DOI
10.1007/3-540-30833-4_4
Publisher site
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Abstract

Species of Structures and Axiomatic Basis of a PT In the preceding chapter we described the general form of a mathematical theory in the context of a physical theory. The main task was to clarify the connection between physical realities and the abstract mathematical theory. Nevertheless, this explanation was not sufficient to apprehend the structure of the mathematical theory itself; it was especially not sufficient to see how MT gives the physically decisive conditions to MT . This problem was hidden behind the selection of the picture terms Q and s in MT ; for example, as i ν picture terms Q =IR × IR for the idealized marked spots, and as relation s 2 2 d(α ,α ; β ,β )= (α − β ) +(α − β ) 1 2 1 2 1 1 2 2 for the idealized distance. In this case we know that the terms Q, d describe a two-dimensional Euclidean geometry, but we only know this since we have learned that the terms Q, d constitute the analytic form of this geometry. This example also shows that the particular values (α ,α ) for an idealized 1 2 marked spot have no influence

Published: Jan 1, 2006

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