Ingo Schwarze wrote: > Eliah has beautifully demonstrated this for both Mathematics > and Physics. What is flabbergasting me about such questions > is that these are extremely old facts - essentially, known for > more than 70 years - and many people still believe that formal > science can be both complete and consistent.
For the record, I do not believe that there is necessarily no complete and entirely correct *physical* theory "out there" to be discovered. Such a theory, when formalized mathematically, would have to allow well-formed undecidable statements. But those statements would not necessarily be *about* physical reality, any more than an applied system that modestly extends Zermelo-Frankel set theory (with or without the Axiom of Choice) to contain axioms about voter demographics is incomplete with respect to classification of voters due to the undecidability of the Continuum Hypothesis. In other words, the "complete physics" would actually use only part of the mathematical framework used to formalize it. It's also possible that a complete and correct theory of physics will be discovered and be accepted, and still not be formalized mathematically. Quantum Electrodynamics is probably the most successful scientific theory ever (in terms of the number, consistency, and precision of its predictions), and yet as far as I know it has still not been formalized in the mathematical sense. -Eliah
