In "Shadows of the Mind," Roger Penrose discusses the implications of Godel and Rosser's findings regarding formal systems. They demonstrated that a sufficiently complex formal system cannot prove its own consistency using its own rules and axioms. This limitation reveals a fundamental aspect of mathematics and logic, illustrating that there are truths that transcend the capabilities of formal frameworks.

This insight suggests that while formal systems can be powerful tools for understanding mathematical truths, they inherently possess boundaries. The inability to establish their own consistency leads to questions about the nature of consciousness and the limitations of human understanding, implying that some aspects of reality may be beyond formalization.