Propositional logic is not complete with respect to logical truth.

the verdict

REFUTED

the evidence says no

Recorded sources

0 sources for · 2 against

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AS REPORTEDno primary record reached; this is what the reporting says

Is it true that propositional logic is not complete with respect to logical truth?

No. Standard propositional logic is indeed complete with respect to classical logical truth and truth-functional interpretations, directly refuting the claim.

Verdict: REFUTED · 0 sources for, 2 against · Last checked 4 Aug 2026

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Evidence against · 2

Wikipedia: Propositional logic

Reference article covering this claim directly

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Wikipedia: Propositional logic. (n.d.). Wikipedia. https://en.wikipedia.org/wiki/Propositional_logic

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More against · 1

Stanford Encyclopedia of Philosophy: Propositional Logic

Notes that standard propositional calculus (pk) is complete with respect to the classical truth-functional interpretation.

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Stanford Encyclopedia of Philosophy: Propositional Logic. (n.d.). Stanford Encyclopedia of Philosophy. https://plato.stanford.edu/entries/logic-propositional/

Related receipts

Is it true that propositional logic is both sound and complete? SUPPORTED related question, same topic
Is it true that first-order logic is complete? SUPPORTED related question, same topic
Is it true that true and false are the only two truth values in classical logic? SUPPORTED related question, same topic

Receipt History

first checked04 Aug 2026

judged → REFUTED · 1004 Aug 2026

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