Re: Set Theory: Should You Believe



John Jones wrote:

The fact that mathematicians are unable and unwilling to translate
their tasks into common discourse leads one to believe either that the
foundations of mathematics are suspect, or that 'foundations' in
mathematics are not originary, simple and conceivable acts and
properties but fix-its enmeshed in the body of the mathematical
integrated text.

Even non-mathematicians can glean enough from the cracks between the
extensive symbology of mathematics to recognise conceptual
inconsistency. Set theory is rich with inconsistency which the
mathematician, high up in the branches, fails to see. It is doubtful
whether the mathematician has the skills to deal with mathematics at
the very deepest foundational levels, such skills generally being the
province of the philosopher.

But the problem is not confined to mathematics: The integral texts of
mathematics (the vast integrated, linked structure built from
formalism, author and argument in which mathematics is stored as a body
of knowledge) can, when the discipline is in crisis, be mandated upon
argument and theory, stifling authentic debate and creating divides and
allegiances. The phenomena occurs in any scholastic text.

quote source if used


Infinity is a tough nut to crack.

--
hz
.

Relevant Pages

  • Re: Set Theory: Should You Believe
    ... foundations of mathematics called "Set Theory: ... Excellent paper, Rupert. ... modern mathematics takes on many of the ... It has its essential creed---namely Set Theory, ...
    (sci.logic)
  • Re: Godels proof, truth, reality, self-awareness, and all that jazz
    ... If you think the basic notions and principles of set theory, ... alternative foundations for it, or the parts of it you consider worth ... producing interesting mathematics, alternative notions, striking break- ...
    (sci.math)
  • Re: set-theoretic foundation of categories
    ... > A Formal Background to Mathematics by R E Edwards? ... axiomatic set theory is in the appendix in:Kelly,John General Topology ... it does provide insights into foundations and is first ... rate.Regards,Stuart M Newberger. ...
    (sci.math)
  • Re: A quiet query from a visitor
    ... we do not have a universal language of mathematics ... we have never had a universal language of mathematics ... set-theoretic foundations and those who don't. ... presented from the start in terms of set theory (and in some ...
    (sci.math)
  • Re: Das Kalenderblatt 090628
    ... Whereas "Einleitung in die ... Mengenlehre" contained an exposition of classical set theory as well ... theory will be discussed in another book under the title "Foundations ... mathematics, e.g. arithmetic. ...
    (de.sci.mathematik)
Quantcast