Is "the dog is Batman" a proposition?

Question

I am starting my self-study in Discrete Math, and I want to understand what propositions are. I thought of a few statements, and want to know if they are propositions or not (I do not care if they are true or not yet):

I am Batman

I think this IS a proposition because here I am unambiguously stating that I am Batman.

You are Batman

I think this is NOT a proposition because here we don't know who "you" are.

The dog is Batman

I think this is NOT a proposition because here we don't know who "the dog" is.

Rocky the Boxer Dog is Batman

I think this IS a proposition because here we are clearly being told who the dog is.

Answer 1

may I ask why my Batman examples are propositions?

That your examples don’t have definite truth values is not because they aren’t propositions, but because you have not fixed the context.

For example, in our current reality and “you” and “the dog” as specified constants, all four statements are false. In a different universe, exactly two of them might be true.

So, the criteria “is either true or false” that you are working with is more accurately revised to “can be either true or false”.

P.S. The other posted answer says

"The first female US President was blonde" we have not had a female president yet so this statement doesn't make sense and therefore is not a proposition.

I disagree that the above example isn’t a proposition just because it is not meaningful or well-defined in the current context; consider the proposition ∀x x>0; by the above reasoning, it is not a proposition because in the universe of complex numbers it makes no sense.

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Addendum

Thank you for all your help ryang, coffeemath, Accelerator and DougSpoonwood. Yes I made these Batman sentences up. But from what I am gathering from the undergraduate Discrete Math books on this, it looks like what Doug said is the answer I am looking for. Since we don't have context yet, we can't call some of my sentences a proposition (in particular the "You" and "The Dog" ones) YET. But there likely is a context for me to have said those sentences, so we COULD say they're propositions. But if we are ONLY given these sentences ("You" and "The Dog" ones) and nothing else, they aren't propositions.

You want to believe that

• "My mother is Wonder Woman" and "Julia Roberts acted in The Price is Right", being clearly false to you, are propositions,

and that

• "You are Batman", having no clear truth value to you, is not a proposition.

After reading the replies on this page, you now also believe that lacking context is the problem with the latter, while the first sentence has a clear context.

However, this is fruitless cherry-picking. Once I point out that there is another Julia Roberts for which "Julia Roberts acted in The Price is Right" is true, is "Julia Roberts acted in The Price is Right" suddenly no longer a proposition (due to your realisation of insufficiency of context and that "Julia Roberts acted in The Price is Right" has no definite truth value)?

"My mother is Wonder Woman" appears to have a clear context only because you are reading it self-centrically; however, in the story that I am spinning, it is actually a true, not false, statement.

Do you not consider "The square of every nonzero number is positive" a proposition until I inform you that the discourse universe is $\mathbb R$ (then True) or that the discourse universe is the set of purely imaginary numbers (then False)?

My point is that:

1. the classification system that you want is not useful. Notice that I keep clunkily quoting that Julia Roberts string in its entirety, because I am having to refrain from calling it a 'sentence/proposition' since you think that whether it is a proposition or not depends on context. Isn't more useful to simply be able to just call it a proposition then analyse its truth value (or well-definedness) as the interpretation varies? Isn't this the goal of the formal-logic chapters of your Discrete Mathematics course?

2. actually, when discussing the truth of non-tautological non-contradiction propositions, the context/interpretation, even if not explicit, is always at least tacitly in the background.