Part of it is the rigor of set theory, and math in general. Ergo,
transfinite arithmetic
is useful in this sense. It also has some applications, in the sense that
we can
know the limits of the organon/tool/ideas.
Books to consult on this include:
Georg Cantor's _Contributions to the Founding of the Theory of Transfinite
Numbers_ (OK, but his symbol set is a bit archaic/provincial)
Morris Kline's _Mathematics: The Loss of Certainty_ (just about anything by
Kline is good:)
Rudy Rucker's _Infinity and the Mind_ (great lay intro plus some more technical
matters in appendices; he outlines issues well)
Daniel Ust
http://www.mcs.net/~tshell/ust/homepage.htm
http://www.geocities.com/Athens/Acropolis/8422/ust1.htm
http://freeradical.co.nz/
http://www.teleport.com/~jaheriot/posthum.htm