truth-value
lowformal, academic, technical
Definition
Meaning
In logic and philosophy, the property of a statement, proposition, or formula being either true or false.
The state or property of being true, false, or indeterminate (e.g., in multi-valued logics); by extension, used metaphorically to refer to the 'validity' or 'factual correctness' of any claim or piece of information.
Linguistics
Semantic Notes
The term is fundamentally a technical concept in formal logic, semantics, and analytic philosophy. It is often used in discussions about the meaning of sentences, propositional attitudes, and logical inference.
Dialectal Variation
British vs American Usage
Differences
No significant differences in meaning or usage. Spelling follows local conventions: hyphenated in both varieties, but occasionally written as one word (truthvalue) in American philosophical journals, though this is rare.
Connotations
Highly technical in both varieties. Neutral, precise, and academic.
Frequency
Equally low and confined to academic/technical contexts in both varieties.
Vocabulary
Collocations
Grammar
Valency Patterns
The truth-value of [noun phrase] is [adjective]To assign a truth-value to [noun phrase][Noun phrase] lacks a truth-valueVocabulary
Synonyms
Strong
Neutral
Weak
Vocabulary
Antonyms
Phrases
Idioms & Phrases
- “To be a matter of truth-value (rare, technical idiom)”
Usage
Context Usage
Business
Virtually never used.
Academic
Central term in philosophy of language, logic, formal semantics. Used to analyze arguments, meaning, and information.
Everyday
Not used in everyday conversation. Misunderstood if used.
Technical
Precise term in logic programming, computer science (especially in AI and knowledge representation), and mathematical logic.
Examples
By Part of Speech
verb
British English
- The logician will truth-value the atomic formulae before proceeding.
- We need to truth-value these claims systematically.
American English
- The philosopher wanted to truth-value each premise individually.
- AI systems can truth-value simple propositions.
adverb
British English
- He argued truth-value functionally, focusing solely on true/false outcomes.
- The statement is to be evaluated truth-value independently of context.
American English
- The system processes sentences truth-value neutrally at first.
- These operators combine truth-value sensitively.
adjective
British English
- We examined the truth-value assignments in the logic exercise.
- This is a complex truth-value analysis of vague predicates.
American English
- The truth-value functional connective is central to propositional logic.
- Their approach involves a truth-value conditional framework.
Examples
By CEFR Level
- True or false are the two main truth-values.
- The teacher asked if the sentence 'It is raining' had a clear truth-value.
- In classical logic, every proposition must have a truth-value of either true or false.
- Philosophers debate whether future contingent statements have a determinate truth-value now.
- The semantic theory was criticised for failing to provide a principled method for assigning a truth-value to paradoxical statements like 'This sentence is false'.
- Kripke's analysis of presupposition failure introduces the concept of a truth-value gap for non-referring definite descriptions.
Learning
Memory Aids
Mnemonic
Think of a TRUE/FALSE checkbox on a form. The 'value' you tick (true or false) is the TRUTH-VALUE of that statement.
Conceptual Metaphor
TRUTH IS A MEASURABLE QUANTITY (like a number on a scale); LOGICAL REASONING IS MATHEMATICS.
Watch out
Common Pitfalls
Translation Traps (for Russian speakers)
- Do not confuse with 'ценность истины' (the value or worth of truth), which is an ethical concept. 'Truth-value' is a technical, logical property, best translated as 'логическое значение', 'значение истинности'. Avoid 'правдивая ценность'.
Common Mistakes
- Using it as a fancy synonym for 'truth' in everyday contexts (e.g., 'I doubt the truth-value of his story').
- Spelling as 'true value', which refers to an accurate measurement.
- Treating it as a countable noun for multiple 'truths' instead of multiple truth-values (true/false).
Practice
Quiz
In which context is the term 'truth-value' MOST appropriately used?
FAQ
Frequently Asked Questions
No, in standard logic, only declarative statements (propositions) that assert something about the world can be true or false, and thus have a truth-value. Questions and commands are not truth-apt.
No. Truth-value is a binary or discrete classification (true, false, indeterminate). Probability is a continuous measure of likelihood between 0 and 1. However, in some fuzzy logic systems, truth-values can be expressed as degrees.
It is the foundation of formal logic and semantics. It allows us to define logical concepts like validity, entailment, and consistency, and is crucial for the analysis of meaning, reasoning, and the design of computing systems.
In classical two-valued logic, no. But in multi-valued or fuzzy logics, truth-values can extend beyond simple true/false to include values like 'unknown', 'possible', or a numerical degree (e.g., 0.7 true).