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. 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. 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 ... :-) Godfrey -- PDML Pentax-Discuss Mail List [email protected] http://pdml.net/mailman/listinfo/pdml_pdml.net
