Logic, Symbolic and mathematical

We characterize Godel's philosophy of mathematics, as presented in his
published works, with possible clarification and support provided by his
posthumously published drafts, as being formulated by Godel as an optimistic
neo-Kantian epistemology superimposed on a Platonic metaphysics. We further
consider that Godel's more general philosophical worldview can also be
characterized as such. We provide a philosophical interpretation of Godel's
rotating universe solutions to Einstein's field equations that is contrary to Godel's
own philosophical interpretation. We compare Godel's worldview with our
materialistic worldview. Our materialistic worldview developed from interpreting
Godelian type results, but stands in contrast to Godel's worldview. Finally, our
materialistic worldview serves to further explicate, by contrast , Godel's Platonic
world view.

A methodology is presented to construct an approximate fuzzy-mapping algorithm that maps multiple inputs to single outputs given a finite training set of argument vectors functionally linked to corresponding scalar outputs. Its scope is limited to problems where the features are known in advance, or equivalently, where the expected functional representation is known to depend exclusively on the known selected variables. Programming and simulations to implement the methodology make use of Matlab Fuzzy and Neural toolboxes and a PC application of Prolog, and applications range from approximate representations of the direct kinematics of parallel manipulators to fuzzy controllers.