Pure and applied geometries from a synthetic-axiomatic approach to theories. [Spanish]
Keywords:
Pure geometry, applied geometry, logical positivism, relativity and theory,Abstract
In this paper I draw a clear and precise distinction between pure or mathematical geometry and applied or physical geometry. I make this distinction inside two contexts: one, the re?ections about foundations of geometry due to the source of non-Euclidean geometry and, other one, the discussions by the logical positivists on general structure of empirical theories. In particular, such and like propose the logical positivists, I defend that pure geometry is a formal system that doesn’t tell us anything about physical reality, whereas applied geometry is a theory about physical space that comes of to interpret a mathematical geometry. I support this thesis in some Einstein’s ideas about the general theory of relativity. Finally, even though this picture of structure of physical geometry is relatively appropriate, I insist on the thesis of that main mistake of logical empiricist philosophy would be in making of this picture the dominant character of structure of scienti?c theories in general.
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