I'm speaking more about how we assess the relevance of a logical system to the real world. Even if a system is internally self-consistent, its utility depends on whether its premises and conclusions align with what we observe empirically. And because empirical observation is inherently statistical due to sampling and measurement limitations, the very act of verifying a logical system's applicability to reality introduces a statistical element. We just typically ignore this element because some of these systems seem to hold up consistently enough that we can take them for granted.