Questions: Propositions and Semantic Content

Question 1

You say 'I am hungry' and your friend also says 'I am hungry.' Which of the following is true?

• A. You both uttered the same sentence and expressed the same proposition
• B. You uttered different sentences but expressed the same proposition
• C. You uttered the same sentence type but expressed different propositions
• D. You expressed different propositions because you used different words

Answer: (C)

This is the canonical case of indexicality. 'I am hungry' is the same sentence type — the same string of words — but 'I' refers to different people depending on who utters it. Once the referent of 'I' is fixed by context, the resulting propositions differ: one is about you being hungry, the other is about your friend being hungry. These are distinct propositions with potentially different truth values. The same sentence type, different propositions — showing that the sentence-proposition distinction is not a theoretical nicety but required to handle ordinary indexical language.

Question 2

Why can't sentences alone serve as the primary bearers of truth value, without introducing propositions?

• A. Sentences are too long to evaluate for truth — propositions are more compact
• B. Indexical sentences like 'I am here now' have no stable truth value independent of context; we need the context-fixed content (proposition) to assign truth
• C. Sentences are written or spoken, and truth is a property only of abstract objects
• D. Propositions are needed because different languages have different numbers of sentences

Answer: (B)

The problem with assigning truth directly to sentences is that indexical sentences like 'I am here now' are always trivially true when uttered but would be false if you moved — the sentence type itself has no fixed truth value. We need the proposition — the content with all context-sensitive expressions filled in — to get a stable truth-bearer. 'I am hungry' said by you right now expresses a proposition with a definite truth condition (you, hungry, now), which can be true or false. The sentence type has no such stability.

Question 3

The English sentence 'Snow is white' and the French sentence 'La neige est blanche' express the same proposition.

• T. True
• F. False

Answer: True

This is one of the core motivations for positing propositions as abstract entities distinct from sentences. If truth were a property of sentences (linguistic objects), 'snow is white' would be true in English but the French sentence would be a different thing with different truth conditions. Instead, both sentences express the same abstract content — the proposition that snow is white — which is true independently of which language or sentence is used to express it. This is why propositions are said to be language-independent.

Question 4

A single sentence type typically expresses exactly one proposition, regardless of context or speaker.

• T. True
• F. False

Answer: False

Indexical expressions — 'I,' 'you,' 'here,' 'now,' 'this,' 'today' — mean that the same sentence type can express different propositions in different contexts. 'I am in Paris' expresses a different proposition when Napoleon utters it versus when you utter it. 'Today is Tuesday' expresses a different proposition on different days. The sentence type is fixed; the proposition varies with context. This is precisely why propositions are theoretically necessary: they are the context-determined semantic contents that result once all context-sensitive expressions are resolved.

Question 5

What theoretical work do propositions do that sentences cannot do on their own?

Model answer: Propositions provide stable, context-independent truth-bearers. Sentences — especially those with indexical expressions like 'I,' 'here,' and 'now' — can express different things in different contexts, so they don't have fixed truth values. Propositions are the content that results after all context-sensitive elements are fixed; they are true or false simpliciter. They also explain cross-linguistic synonymy (different sentences, same meaning) and serve as the inputs to logical operators like negation and conjunction.

The proposition is the unit of logical evaluation: 'not P' negates the proposition P, not the sentence 'P'. For logical operators to work, they need inputs that have determinate truth values — sentences with indexicals don't provide this. Propositions also explain why translation preserves meaning: what is preserved across linguistic expression is the proposition, the abstract content. Without propositions (or something playing their theoretical role), semantic theory lacks a stable foundation for truth, logic, and cross-linguistic meaning.