Is "yesterday it was sunny" a proposition?

Question

I'm studying logical proposition. And I know that $P$ is a proposition if it's either true (T) or false (F), there are no other possibilities than being (T) or (F) and it can't be true and false. I know for exemple that "tomorrow it will be sunny" is not a proposition, because we can't know if it's true or false.

1. What about "yesterday it was sunny" ? I guess that we could check on the newspaper and say at the moment where we say it if it's true or false. So in somehow, I would say that it is a proposition, but in the other hand, the fact that the truth can change everyday, maybe it's not. What do you think ?

2. Since "tomorrow it will be sunny" is not a proposition, can I consider the proposition : "if tomorrow it will be sunny, then I'll go to the swimming pool" ? The question maybe strange, but I know that to consider the implication $\implies $, we consider the implication of two propositions. Since "tomorrow it will be sunny" is not a proposition, can I say that "if tomorrow it will be sunny, then I'll go to the swimming pool" is not a proposition ?

Answer 1

I know for exemple that "tomorrow it will be sunny" is not a proposition, because we can't know if it's true or false.

Actually, a proposition is by definition true or false, whether we know or don't know which it is. Of some propositions we can even prove that we cannot indeed know, and those we call (provably) undecidable. (Provability is relative to a specific formal system, but I won't get here into any more technical details.)

That said, IMO, "tomorrow it will be sunny" is a proposition: for the simplest formalization, just take "(to be) tomorrow" as an atomic proposition, denote it by $T$, then denote "(to be) sunny" by $S$, and you have the proposition $T \to S$ (which reads "to be tomorrow implies to be sunny": to express that "when it is tomorrow, then it will be sunny", i.e., in common English, that "tomorrow it will be sunny").

Now, assuming that we cannot in fact, here and now, know whether that proposition is or is not true, we should indeed conclude that the proposition is undecidable (we'd have to formalize what I have just said to technically conclude such a thing, but I hope it is easy to see that it would follow).

But notice that the assumption is not really a little assumption: we'd have to assume that predicting the future is impossible, and, while this is in most cases reasonable, it is something that not even contemporary physics would say for certain...

On the other hand, for a more "mundane" approach, and maybe more useful in this case, a fuzzy propositional logic could be used: where we could attach a level of confidence to the truth value of that proposition, as e.g. supported by a weather forecast.

Answer 2

As far as mathematical logic is concerned, a proposition is simply whatever you can assign a truth value to. But it doesn’t matter how you do it, what the sentence means and whether your assignment of truth values would be convincing to anyone or possible to justify in the real world. Propositional logic defines certain rules how to construct propositions from other propositions, and how to draw conclusions from propositions once you know their structure, but it doesn’t dictate what basic propositions you start with, and whether they can involve the past or the future.

You can simply consider “yesterday it was sunny” or “tomorrow it will be sunny” as atomic propositions that cannot be broken up any further. Logic doesn’t care how you interpret such propositions or evaluate their truth values. Maybe you remember yesterday’s weather, maybe you were only told what it was; maybe you have a perfect forecasting ability that allows you to see tomorrow’s weather, maybe you don’t. You might as well declare either true or false by fiat. Logic doesn’t care: it is only concerned with what conclusions you can draw once the basic facts are established.

For an example, imagine you have a machine that you can ask yes-no questions about tomorrow’s weather and it will answer with perfect accuracy. Propositional logic tells you that if you get YES answers for questions “will tomorrow be sunny or rainy?” (S ∨ R) and “will tomorrow not be rainy?” (¬R), you don’t need to additionally ask if tomorrow will be sunny (S), because you can draw that conclusion yourself from the answers you got already. And if you do and the machine replies NO (¬S), then you know must be broken, because it described an inconsistent state of affairs. But whether such a machine can actually exist falls outside the remit of logic.