Epistemologia 38 (1):133-151 (2015)

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Abstract
A new hypothesis on the basic features characterising the Foundations of Mathematics is suggested. By means of them the entire historical development of Mathematics before the 20th Century is summarised through a table. Also the several programs, launched around the year 1900, on the Foundations of Mathematics are characterised by a corresponding table. The major difficulty that these programs met was to recognize an alternative to the basic feature of the deductive organization of a theory - more precisely, to Hilbert’s main tenet. Ironically, already half a century before the births of these programs the alternative organization has been substantially represented by Lobachevsky's theory on parallel lines. Moreover, although each program’s founder recognised the basic features in a partial way only, all together these programs represented just the four possible foundational approaches.
Keywords Two dichotmies  Oragnization  Infinity  History of Mathematics  Foundations programs
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DOI 10.3280/EPIS2015-001009
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References found in this work BETA

Subsystems of Second-Order Arithmetic.Stephen G. Simpson - 2004 - Studia Logica 77 (1):129-129.
Mathematical Thought From Ancient to Modern Times.M. Kline - 1978 - British Journal for the Philosophy of Science 29 (1):68-87.
In the Light of Logic.Solomon Feferman - 1998 - New York and Oxford: Oxford University Press.

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Foundations as Truths Which Organize Mathematics.Colin Mclarty - 2013 - Review of Symbolic Logic 6 (1):76-86.

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