3 Truth and Inference

3.1 Truth as a Guide to Sentence Meaning

  • Understanding meaning involves knowledge about the truth value of sentences relative to situations.
  • Example Sentence: (1) "King Henry VIII snores."
    • The truth value of this sentence is context-dependent; it cannot be classified as genuinely true or false without reference to the state of the world.
    • At present (early 21st century), the sentence is false, as King Henry VIII died in 1547 AD.
    • Conversely, it may have been true in 1525 AD, highlighting that total knowledge of all situations is unattainable for most speakers.
  • Knowing a sentence's meaning implies an understanding of the situations wherein the proposition would be true:
    • Definition (2): “To know the meaning of a [declarative] sentence is to know what the world would have to be like for the sentence to be true.” (Dowty et al. 1981)
  • Concept of Proposition:
    • A proposition is a claim about the world, potentially true or false in various situations.
  • Some scholars argue that grammatical entities (sentences) do not hold truth values; only propositions do.
    • A speaker makes a true statement when the meaning of their sentence aligns with the state of affairs.
    • Using sentences as true or false is considered an imprecise way of speaking since the truth belongs to the propositions they express.

3.2 Analytic Sentences, Synthetic Sentences, and Contradictions

  • Understanding sentence meaning enables us to determine truth conditions.
  • Analytic Sentences (Tautologies):
    • These sentences are true under all circumstances, meaning they hold no informative power regarding the world.
    • Examples (3):
    • (3a) "Today is the first day of the rest of your life."
    • (3b) "Que será será."
    • (3c) A statement by Sen. Olympia Snowe regarding a health care reform vote highlights the tautological nature of some expressions.
  • Despite being non-informative, tautologies are used in speech for their communicative value, stemming from the pragmatic inferences they generate.
  • Contradictions:
    • Propositions that can never be true. Example (4): “And a woman who held a babe against her bosom said, 'Speak to us of children…'”
  • Synthetic Propositions:
    • Can be true or false depending on context; these form the majority of declarative sentences.
    • An effective semantic analysis should explain why certain sentences are analytic or contradictory.

3.3 Meaning Relations Between Propositions

  • Consider the pair of sentences (5):
    • (5a) "Edward VIII has abdicated the throne in order to marry Wallis Simpson."
    • (5b) "Edward VIII is no longer the King."
  • Entailment:
    • The truth of (5a) logically necessitates the truth of (5b).
    • Properties of entailment:
    1. Whenever proposition p is true, q must be true.
    2. If q is false, then p must also be false.
    3. These relations derive from the meanings of p and q, independent of context.
  • Example (6):
    • (6a) "I broke your Ming dynasty jar."
    • (6b) "Your Ming dynasty jar broke."
    • The relationship confirms that (6a) entails (6b).
  • Mutual Entailment:
    • Sentences that mutually entail each other are synonymous (7).
    • (7a) "Hong Kong is warmer than Beijing (in December)."
    • (7b) "Beijing is cooler than Hong Kong (in December)."
  • Inconsistency and Compatibility:
    • Incompatible propositions cannot both be true. Contradictions always hold opposing truth values.
    • Example (8):
      • (8a) "Ringo Starr is my grandfather."
      • (8b) "Ringo Starr is not my grandfather."
    • Contrary propositions may both be false in certain contexts but can’t co-exist as true (9).
  • Independent propositions:
    • Neither entail nor contradict each other, having an independent truth value.

3.4 Presupposition

  • Definition of Presupposition:
    • A statement that implies the truth of another statement or conveys information assumed to be shared in conversation.
  • Common Ground:
    • Refers to shared knowledge between speaker and hearer, including general world knowledge or information mentioned previously in conversation.
  • Trigger for Presupposition:
    • Certain words or grammatical constructions trigger presuppositions.
  • Example (10):
    • In the interaction between the March Hare and Alice, the use of “more” presupposes Alice had tea previously.
    • Presupposition Failure:
    • If the presupposition is incorrect (Alice had no tea), it leads to confusion or offense.
  • Identifying Presuppositions:
    • Unlike entailments, presupposed information remains unaffected by whether the speaker asserts, questions, or denies the truth of the presupposing statement.
    • For example, all variations of (11) imply the vice president falsified his dental records, highlighted by the presence of "regret."
  • Family of Sentences Test:
    • This test shows that presuppositions persist under negations and questions, unlike entailments, which do not.
    • Example (12a) presupposes that Susan has been dating an Albanian monk, with the presence of "stop."
  • Testing Presupposition Failure:
    • If a presupposition fails, the hearer may challenge it by expressing confusion about the claim (13).
  • Common Presupposition Triggers:
    • Definite Descriptions:
    • E.g., "the King of France" presupposes a unique entity exists.
    • Factive Predicates:
    • E.g., "regret, aware, realize" necessitate their complements be true.
    • Implicative Predicates:
    • E.g., "manage to presupposes try" underlines an underlying condition.
    • Aspectual Predicates:
    • E.g., stop presupposes duration of the event discussed.
    • Temporal and Relative Clauses:
    • The truth of subordinate clauses must hold true as part of the presupposition.
    • Comparisons:
    • E.g., comparative sentences bring in assumptions of known qualities.