truth-value gap
Very LowTechnical/Formal
Definition
Meaning
A situation in which a declarative statement is considered neither true nor false due to a failure of reference, presupposition, or semantic anomaly.
In linguistics and philosophy of language, a property of a sentence that lacks a definite truth value (true/false) under certain conditions, often because it contains a term without a referent, involves a category mistake, or violates a presupposition, leading to a lack of truth-conditional content.
Linguistics
Semantic Notes
A theoretical term from logic, semantics, and analytic philosophy. It applies to sentences that are not simply false but are semantically defective or undefined. Common causes include non-referring definite descriptions (e.g., 'The present King of France is bald'), category errors, or presupposition failures (e.g., 'John stopped smoking' when John never smoked).
Dialectal Variation
British vs American Usage
Differences
No significant regional differences in meaning or usage, as it is a formal academic term used identically in British and American philosophical and linguistic literature.
Connotations
Neutral, technical. Connotes analysis in formal semantics and logic.
Frequency
Exclusively used in technical academic contexts (philosophy, linguistics, computer science). No notable frequency difference between regions.
Vocabulary
Collocations
Grammar
Valency Patterns
[Sentence/Proposition] + falls into/has/creates/exhibits + a truth-value gap.The truth-value gap + arises from/stems from/is caused by + [semantic failure].Vocabulary
Synonyms
Strong
Neutral
Weak
Vocabulary
Antonyms
Phrases
Idioms & Phrases
- “[No common idioms. This is a technical compound noun.]”
Usage
Context Usage
Business
Never used.
Academic
Primary context. Used in philosophy of language, formal semantics, and logic to discuss the limits of bivalence and the analysis of problematic sentences.
Everyday
Never used.
Technical
Used in linguistics, analytic philosophy, and some areas of computer science (e.g., formal logic, knowledge representation).
Examples
By Part of Speech
verb
British English
- The sentence fails to be truth-evaluable.
- That proposition gaps under such an interpretation.
American English
- The claim cannot be assigned a truth value.
- The statement resists standard truth valuation.
adverb
British English
- [No standard adverbial use.]
American English
- [No standard adverbial use.]
adjective
British English
- It's a truth-value-gap case.
- They proposed a gappy semantics.
American English
- A truth-value-gap analysis was offered.
- Gappy propositions were discussed.
Examples
By CEFR Level
- [Not applicable for A2 level.]
- [Not applicable for B1 level. The term is highly specialised.]
- Philosophers say sentences like 'The round square is blue' have a truth-value gap because they talk about impossible things.
- Strawson's theory of presupposition holds that 'The King of France is wise' suffers from a truth-value gap due to the failure of existential presupposition, rather than being simply false as Russell argued.
Learning
Memory Aids
Mnemonic
Imagine a TRUE/FALSE test question that is so confusing or meaningless you can't tick either box; the space between the boxes is the GAP where its TRUTH VALUE should be.
Conceptual Metaphor
TRUTH IS A BINARY SWITCH (ON/OFF, TRUE/FALSE). A GAP is a failure for the switch to be in either position.
Watch out
Common Pitfalls
Translation Traps (for Russian speakers)
- Avoid a direct word-for-word translation like 'разрыв истинностного значения' without proper contextual explanation, as the concept is highly theoretical. The term is not part of general Russian vocabulary and would only be understood in specific academic circles, likely using the English term or a calque like 'лакуна истинностного значения'.
Common Mistakes
- Using it to describe a simple falsehood. A false statement has a truth value: false. A truth-value gap means having NO standard truth value.
- Confusing it with 'vagueness'. Vagueness concerns borderline cases (e.g., 'bald'), which may still be true or false; a gap involves a more fundamental semantic failure.
- Capitalising it as a proper noun; it is a common noun.
Practice
Quiz
Which of the following best describes a 'truth-value gap'?
FAQ
Frequently Asked Questions
The informal phrase 'not even wrong' captures a similar intuition—that a statement is so flawed it cannot be meaningfully evaluated as true or false. However, 'truth-value gap' is a precise technical term within formal semantics.
No. Truth values (true/false) apply only to declarative statements (propositions). Questions and commands are not truth-apt, so the concept of a 'gap' between true and false does not apply to them.
P.F. Strawson (presupposition failure), Bertrand Russell (who argued against gaps with his theory of descriptions), and more recently, proponents of multi-valued or partial logics like supervaluationism.
They are closely related. A category mistake (e.g., 'The number two is blue') often leads to a truth-value gap, as the predicate cannot be meaningfully applied to the subject. The category mistake is the cause; the gap is the resulting lack of a truth value.