Jim Choate wrote: > > On Wed, 20 Nov 2002, Peter Fairbrother wrote: > >> Completeness has nothing to do with whether statements can or cannot be >> expressed within a system. >> >> A system is complete if every sentence that is valid within the system can >> be proved within that system. > > Introduction to Languages, Machines and Logic > A.P. Parks > ISBN 1-85233-464-9 > pp 240 and 241
A "non-mathematical" "easy to read" primer (quotes from Springer-Verlag). I don't have a copy. If Alan Parkes says Godelian completeness is other than the definition above then he is wrong - possible, he is a multimedia studies teacher, and afaik is not a mathematician - but I suspect you misread him. FYI, I just googled "completeness godel". First five results plus some quotes are at the bottom. Five minutes, which I could have spent better. RTFM. -- Peter Fairbrother ....................... Googling "completeness" and "Godel", first five results: http://www.math.uiuc.edu/~mileti/complete.html No simple definition of completeness. Nice intro to models though. www.chaos.org.uk/~eddy/math/Godel.html "Completeness is the desirable property of a logical system which says that it can prove, one way or the other, any statement that it knows how to address." www.uno.edu/~asoble/pages/1100gdl.htm "Completeness = If an argument is valid, then it is provable" http://www-cs-students.stanford.edu/~pdoyle/quail/questions/11_15_96.html "A complete theory is one contains, for every sentence in the language, either that sentence or its negation." http://www.wikipedia.org/wiki/Kurt_Godel -- link to http://www.wikipedia.org/wiki/Goedels_completeness_theorem "It states, in its most familiar form, that in first-order predicate calculus every universally valid formula can be proved."
