With your concurrence, we would like to add your web site URL – http://humanfuture.info/en/home/ – to the list of links on the Links Page of the http://www.dialectics.org web site:

http://www.dialectics.org/dialectics/Links.html .

Your view of modern mathematics as a whole as embodying a “symbolic dialectics”, though with a mystical “philosophy” [actually an “ideology” in Marx’s sense] about what this mathematics really is, reminds us of Marx’s comment to the effect that “reason always exists, but not always in a rational form”. We might adapt this quote, for your application, to something like: “dialectical reason has always existed in mathematics, but not always in an explicitly dialectical rational form”.

Nevertheless, for our part, we find that, just as Marx’s immanent critique of the mystification-permeated science of classical political economy led to a new, improved science of Marxian ‘psychohistorical socio-politico-economics’, as set forth in the volumes of Marx’s Das Kapital, so too an immanent critique of the mystification-enfettered ‘ideo-science’ of modern mathematics tends to yield new, improved mathematics.

To begin with, this new, improved mathematics includes, in our experiences, through the immanent critique of the standard Peano/Dedekind “Natural” numbers system of arithmetic, a Lakatosian “counter-example” axioms-system of arithmetic, which is one of the “predicted” non-standard models of the “Natural” numbers arithmetic, whose algebra is also a ‘contra-Boolean algebra’, modeling a categorial-dialectical logic: an algebra in which a strong contrary to Boole’s “fundamental law of thought” [asserting an “inescapability” of LINEAR algebraic logic] is a theorem that arises deductively from the axioms of this “non-standard” arithmetic.

]]>Regards,

Miguel

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