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I have this question in my assignment.

-There are 70 students in this class.

Is this considered a proposition? And is this true or false? As this statement can only be answered if we know which class it is and it's subjective to the person.

PeterJ
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  • Yeah but in that case the proposition is subjective and there isn't one correct universal answer. The other classes will have different answer. – PeterJ Aug 14 '23 at 11:18
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    Let me change to another question. Very simple "Johnny goes to school". Is this a proposition? But we don't know Johnny. – PeterJ Aug 14 '23 at 12:47
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    Right - a proposition is always a complete, truth-evaluable declarative sentence. Did you see this post, and similar ones? – Dietrich Burde Aug 14 '23 at 13:06
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    Is "the square of every number is nonnegative" a proposition? It is true of $\mathbb R$ and false of imaginary numbers. Similarly, the truth of "Cambridge is in Massachusetts" differs depending on the context. – ryang Aug 14 '23 at 15:35
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    I'd suggest not dwelling on this. In practice, a proposition is a complete, declarative sentence in a precise language. Subjectivity, ambiguity, and missing context are problems that should be avoided but are hard to formally define (even if your assignment suggests otherwise). Sometimes when reading a sentence you'll have to infer some context; that doesn't necessarily make it a non-proposition. – Karl Aug 14 '23 at 17:41
  • it is definitely a proposition. it is a sentence with a definite truth value, that is, either true or false. – RyRy the Fly Guy Aug 14 '23 at 21:41

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Whether some statement is known to be true or false is probably not the best way to think about whether it expresses a proposition or not.

Take, for example, the expression ‘There is life on other planets’. I think you would agree that this is a proposition that is either true or false … but at the same time, we don’t know whether it is true or false. Also, there is the added concern as to how to define ‘life’, or even ‘planet’ (see Pluto). But does any of this mean that ‘There is life on other planets’ is not a proposition? No. It has the grammatical for of a proposition, where we predicate something about a subject.

As Karl says in the Comments, you should not overthink this in terms of knowability, ambiguity, subjectivity, but simply see if it sounds like something where you say something about something. The kinds of exercises that ask you whether some expression is a proposition typically just want you to be able to distinguish expressions like ‘My shirt is red’, ‘John likes Bob’, ‘God exists, and even ‘Firgles are snooby’ (all propositions) from expressions like ‘my shirt’, ‘Bob’, ‘Hey!’, ‘Can you pass me the salt, please?’, and ‘hgcd th hcdh’ (all not propositions).

Bram28
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