Let us return to Incompleteness Theorem: In order to immunize physical theories on the metatheoretical level and make them immune against the possible reproaches from the direction of Goedel
's Incompleteness theorem.
The second error of holists may lie in their overextension of Heisenberg's Principle of Uncertainty and/or Goedel
's Theorem which some of them use to imply that the physical and natural sciences can make no predictions about nature, and never could.
to have at least an amateur's grasp of the contributions of Newton, Maxwell, Darwin, Einstein, Heisenberg, Cantor, Goedel
, and Turing ...
If nothing else teaches us that, we should at least learn it from Goedel
's Incompleteness Theorem.
It should be noted that although the author uses the word "mathematics" throughout, and indeed makes brief--sometimes tangential--references to mathematical giants, Euclid, Cantor, Einstein, Goedel
, etc., nothing more than ordinary arithmetic and, possibly, a little elementary algebra in the second section is required to understand the material.
Beal is the kind of person whose light reading includes "The Tao of Physics" and "Goedel
, Escher, Bach," a hefty tome examining the connections among the works of the famous mathematician, artist and composer.
Several decades earlier in another field, the great mathematician Kurt Goedel
developed a theorem that demonstrated the impossibility that any mathematical system is both complete and consistent.
Thus, in an emerging system, one of the primary functions of the founders should be to explore what acceptable justification systems should be; for example, intuition, logic, causality, or does it "feel right." In doing this, however, it is helpful to remember the lessons learned from Kurt Goedel
(Cyphert, 1998) and to recognize that each choice of systems--even if only made on a temporary basis--will have significant impacts on which true items may be proven and which false items may be disapproved.
He presents an interesting discussion of certain mathematical riddles, as well as an examination of the folk-mathematical riddle "squaring the circle." Besides offering numerous insights into neck riddles, the transgression of levels that can be found in riddles, etc., this article adds observations from the likes of Quine, Goedel
, and Russell, which throw new and interesting light on the whole genre.
Badewitz is especially excited about Peter Goedel
's "Tangier - Legend of a City", a semi-docu featuring Armin Mueller-Stahl as a man searching for his lost love in the city of writers and artists.
The general romanticization is evident from the fact that even ordinary people are aware of the liar paradox and from popularizations of self-reference such as Douglas Hofstadter's inspiring Goedel
, Escher, Bach.