Definition
Meta-reasoning is reasoning about reasoning rather than reasoning within a fixed system. The MU-puzzle's proof of unreachability is meta-reasoning: it doesn't use MIU rules; it uses arithmetic to reason about what MIU rules can produce. Gödel's theorem is mathematical meta-reasoning at full scale. Carroll's regress illustrates the irreducibility: rule-following itself cannot be reduced to a further rule.
Why it matters
How it works
To engage meta-reasoning, step out of the current rule system and consider its rules as objects of analysis. Ask: what does this system make possible? What does it make impossible? Are there invariants no rule can disturb? Is the question I'm asking expressible inside this system or only outside? Recognizing when to make this move is itself a meta-skill that is hard to teach but essential to high-level thinking.