The problem of self-application: Can the rules of logic be used to justify logic itself without circularity? Logic is the assumed foundation for all rational discourse and proof. But any attempt to prove that logic is valid (e.g., that the Law of Non-Contradiction holds) must use logical inference, thereby assuming what it sets out to prove. This leaves logic resting on an article of faith—that our cognitive machinery for reasoning is reliable. Furthermore, formal logical systems (like arithmetic) are inherently incomplete (Gödel), meaning there are true statements they cannot prove. The ultimate tool for certainty contains unavoidable uncertainties.
*Example: You say, "Logic is valid because it's self-evident." I ask, "Is that statement logically derived?" If yes, it's circular. If no, then you've used something other than logic (intuition) to justify logic, undermining its foundational status. The hard problem: We are trapped in a system of thought we cannot step outside of to validate. It's like trying to use a ruler to check if the ruler itself is 12 inches long. You have to assume the ruler is accurate to begin with. Logic is the ruler we use to measure all truth, but we can never truly calibrate it.* Hard Problem of Logic.
by Enkigal January 24, 2026
Get the Hard Problem of Logic mug.