|Biconditional: notation ↔; a statement that is true if the two sides have the same truth value ("true" or "false"). The biconditional (also bisubjunction) is part of the object language. Contrary to that is equivalence (⇔) which belongs to meta language. A biconditional that is always true is an equivalence.|
|Geach, Peter T.
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Equivalence/Biconditional/GeachVsBlack: "is materially equivalent" is not synonymous with "if and only if" - "Three line" is often read as "materially equivalent" - equivalence only between sentences, not names of sentences - Problem: Tom loves Mary ↔ Mary loves Tom "only significant if "↔" (thee line) is read as "iff" rather than "materially equivalent".
Logic Matters Oxford 1972