Built upon formal mathematical systems, physical models are subject to the limitations of those systems. Gödel’s Incompleteness theorems state these formal systems are incomplete, and therefore so are the physical models built upon them. Expanding the axioms of the formal mathematical system can resolve the incompleteness of the original system, even though the expanded system remains incomplete. Given these two levels, of physical models built upon mathematical tools, we should consider whether we have adequate mathematical tools to describe physical reality and whether we have an accurate model of reality. Can we find aspects of reality that expand our models and are there expanded mathematical tools for us to build new models upon?
Donald G Palmer