Logic / Logic 262 · Atom · ~20 seconds

Free vs. Bound Variables

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State

A variable is bound when a quantifier's scope covers it, free otherwise. Statements have no free variables.

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In (x)Fx ⊃ Gx, the second x is free — the quantifier's scope ended at Fx. Compare (x)(Fx ⊃ Gx).

Watch for

Parentheses set quantifier scope exactly as they set connective scope (129). Same discipline, higher stakes.