[EMAIL PROTECTED] wrote: > On Oct 27, 2006, at 8:34 AM, Gonz wrote: > > >>>Whoa laddie! Mathematics is not a code, and it is not based on >>>observation. Observations of the world might inspire a Mathematical >>>concept which wonts for proof, but do not factor into the proof >>>itself. >>> >>>Mathematics is the study of provable truth using logic, which >>>provides a structure for science (the aggregation of predictive >>>knowledge through hypothesis and observation) to work with, not the >>>reverse. Mathematics also provides a structure for the development of >>>codes. >>> >> >>And yet, Godel tells us that you can only create logical systems that >>cannot be both complete and provable at the same time. > > > A mathematical proof is absolute and not based on observation, it is > based on logic. The question of completeness is orthogonal to the > question of provability, logical process is still a viable mechanism > for proof. > They are orthogonal, but linked together by Godels incompleteness theorem. The relationship to science/faith is an extrapolation. I.e. there will always be true facts that are not provable in the axioms that encompass the scientific structure that is based on them.
> Godel's proof about the completeness and provability of complex > systems does not dispute the usefulness of logic as a structural > basis for acquiring knowledge through science. It defines the limits > of the system, which if anything adds to the credibility of science > by establishing clear theoretical boundaries for the system of > interrogation. > Of course, its still useful (logic). But it (science/math) can never be complete, and the incompleteness theorem never defines the limits, it just says for any axiomatic system, there is true stuff about it that cannot be proven, hence it is a fact outside the axiomatic system. I.e. if God is a true fact outside our axiomatic system, then science can never prove nor disprove God. As the presumed designer of the system, we have essentially defined God to be outside of the system. It seems to me this was intentional on God's part, i.e. faith would not be necessary if you could prove God's existance or if He was here among us. The real mystery is then why would God make faith a necessary precondition? Genuine relationships are based on faith and trust. > Science does not allege to encompass completeness or proof in a > mathematical sense. It's function is to gain knowledge with > predictive value through test and observation. A scientific > hypothesis' criteria of proof is that observations of a test > demonstrate the behavior posed in the hypothesis. Further > observations can easily disprove a scientific hypothesis and add to > the knowledge base from which to formulate hypotheses, this is > embedded in the system. > > ===== > > Hmm. Maybe it's time to post a few photographs and return to > something remotely related to Pentax ... :-) Of course. :) I'm overdue for some PESOs. > > Godfrey > -- PDML Pentax-Discuss Mail List [email protected] http://pdml.net/mailman/listinfo/pdml_pdml.net
