Questions: Presupposition and Assertion

Question 1

Consider the sentence: 'My brother stopped lying.' Which of the following demonstrates that 'My brother used to lie' is a *presupposition* rather than an ordinary entailment?

• A. It follows logically from the meaning of 'stopped'
• B. It is strongly implied in ordinary conversation
• C. It survives under negation: 'My brother didn't stop lying' still implies he used to lie
• D. It can be cancelled without contradiction by adding context

Answer: (C)

The diagnostic test for presupposition is projection — survival under embedding operators like negation, questions, and conditionals. An ordinary entailment is cancelled by negation: if P entails Q, then not-P does not entail Q. But presuppositions survive: 'My brother stopped lying' and 'My brother didn't stop lying' both carry the background assumption that he used to lie. The negation targets the assertion ('stopped') while leaving the presupposition ('used to lie') intact. This projection behavior is what distinguishes presuppositions from entailments and from implicatures (which can be cancelled without contradiction).

Question 2

Russell's example: 'The present king of France is bald.' Assuming France is a republic with no king, what is the semantic status of this sentence?

• A. False — there is no king, so a bald king of France does not exist, making the sentence false
• B. True — the sentence makes a vacuous claim about a non-existent entity, which is trivially satisfied
• C. Neither true nor false — the existence presupposition fails, and the sentence cannot be assigned a truth value
• D. Indeterminate only because we lack empirical information about whether the king is bald

Answer: (C)

This is the classic case of presupposition failure. The sentence 'The present king of France is bald' presupposes (via the definite description 'the present king of France') that there is a unique current king of France. If this presupposition fails, the sentence does not get to enter the true/false game — there is nothing to predicate baldness of. It is not merely false (as Russell originally argued in his theory of descriptions); it is semantically defective. This is the key contrast with ordinary false assertions: 'France is a monarchy' is simply false if France is a republic, but 'The king of France is bald' fails differently — it suffers presupposition failure.

Question 3

If 'John knows it is raining' presupposes that it is raining, then 'John does not know it is raining' also presupposes that it is raining.

• T. True
• F. False

Answer: True

This illustrates the projection property that defines presuppositions. 'Know' is a factive verb — it presupposes the truth of its complement. When you negate the sentence, the assertion changes (now claiming John lacks knowledge), but the presupposition (that it is in fact raining) is preserved. The same holds for questions ('Does John know it's raining?' still presupposes rain) and conditionals ('If John knows it's raining, he'll bring an umbrella' still presupposes rain). Projection through negation and other operators is the defining signature of presupposition, distinguishing it from both entailment and implicature.

Question 4

Presuppositions and conversational implicatures are both types of content that go beyond the literal semantic content of a sentence, so they behave similarly — both survive negation and are difficult to cancel.

• T. True
• F. False

Answer: False

Presuppositions and implicatures differ in a crucial way: implicatures are *defeasible* — they can be cancelled without contradiction. If I say 'Some students passed' and you ask if all did, I can add 'In fact, all of them did' without contradiction, cancelling the implicature that not all passed. But presuppositions resist cancellation: you cannot say 'John stopped smoking, but he never smoked' without contradiction (or at least radical pragmatic incoherence). This defeasibility test cleanly separates implicatures (pragmatic, cancellable) from presuppositions (semantic background, not cancellable).

Question 5

What is 'presupposition projection,' and why does it serve as the key diagnostic test distinguishing presuppositions from ordinary entailments?

Model answer: Presupposition projection is the phenomenon whereby a presupposition introduced in an embedded clause survives and becomes a presupposition of the entire sentence, even when the sentence is negated, questioned, or placed in a conditional. For example, if S presupposes P, then 'not S,' 'Is S?,' and 'If S, then Q' all also presuppose P. This behavior contrasts sharply with ordinary entailments: if S entails Q, then 'not S' does not entail Q (negation cancels entailments). Because negation cancels assertions but not presuppositions, negation provides the clearest diagnostic: embed the sentence under negation and ask whether the background assumption survives. If it does, the content is a presupposition; if it is cancelled, it is an entailment.

The name 'projection' describes how the presupposition 'projects out' of an embedded environment to become a presupposition of the whole. Understanding projection is essential for formal semantics because it shows that truth-conditional content and presuppositional content respond differently to logical operators — requiring either a three-valued semantics or a dynamic framework where utterances update context states rather than simply being evaluated against a static world.