Editing Quasi-empiricism in mathematics (section)

===Operational aspects===
Several recent works pertain to this topic. [[Gregory Chaitin]]'s and [[Stephen Wolfram]]'s work, though their positions may be considered controversial, apply. Chaitin (1997/2003)<ref name="limits">[[Gregory Chaitin|Chaitin, Gregory J.]], 1997/2003, ''[https://books.google.com/books?id=kwBpDQAAQBAJ&pg=PA96 Limits of Mathematics]'' {{webarchive |url=https://web.archive.org/web/20060101134749/http://cs.umaine.edu/~chaitin/lm.html |date=January 1, 2006 }}, Springer-Verlag, New York, NY. {{ISBN|1-85233-668-4}}</ref> suggests an underlying randomness to mathematics and Wolfram (''[[A New Kind of Science]]'', 2002)<ref name="new">[[Stephen Wolfram|Wolfram, Stephen]], 2002, ''A New Kind of Science'' ([http://www.wolframscience.com/nksonline/notes-section-12.8 Undecidables]), Wolfram Media, Chicago, IL. {{ISBN|1-57955-008-8}}</ref> argues that undecidability may have practical relevance, that is, be more than an abstraction.

Another relevant addition would be the discussions concerning [[interactive computation]], especially those related to the meaning and use of [[Alan Turing|Turing]]'s model ([[Church-Turing thesis]], [[Turing machines]], etc.).

These works are heavily computational and raise another set of issues. To quote Chaitin (1997/2003): {{Quote|Now everything has gone topsy-turvy. It's gone topsy-turvy, not because of any philosophical argument, not because of [[Kurt Gödel|Gödel]]'s results or [[Alan Turing|Turing]]'s results or my own incompleteness results. It's gone topsy-turvy for a very simple reason—the computer!<ref name="limits"/>{{rp|96}}}}

The collection of "Undecidables" in Wolfram (''[[A New Kind of Science]]'', 2002)<ref name="new"/> is another example.

[[Peter Wegner (computer scientist)|Wegner's]] 2006 paper "Principles of Problem Solving"<ref>[http://www.cs.brown.edu/people/pw/home.html Peter Wegner], Dina Goldin, 2006, "[http://portal.acm.org/citation.cfm?doid=1139922.1139942 Principles of Problem Solving]". ''Communications of the ACM'' 49 (2006), pp. 27–29</ref> suggests that ''[[interactive computation]]'' can help mathematics form a more appropriate framework ([[empirical]]) than can be founded with [[rationalism]] alone. Related to this argument is that the [[Function (mathematics)|function]] (even recursively related ad infinitum) is too simple a construct to handle the reality of entities that resolve (via computation or some type of analog) n-dimensional (general sense of the word) systems.