Consider following two sentences.
- $x^2 = 1.$
- Today is Thursday.
The first statement can't be a proposition. because the truth of (1) depends on the value of $x$. For some values of $x$ it is true (for $-1$ and $1$) and false for others.
We can apply the same reasoning for (2) (can we?) and conclude that it is not a valid proposition either as the truth of (2) depends on what day is $\text{Today}$.
A student pointed out that (2) could be a valid proposition if the intention was to state it for just one day i.e. today.
I argued that if it were the case, then the proposition should have been more precise (by including the date may be ?)
My question is that , in the form (2) is currently written can it be considered a valid proposition ?
And if it is not valid, can it be written in a form without removing the word "Today" so that it becomes a valid proposition?
Best Answer
Actually, they all can be proposition. The issue lie in what you count any of these as variable.
Look at this:Interpretation
If you let "today" and "x" be constant, then yes both of them are indeed proposition. The fact that they can varies is because of interpretation.
If you don't let them be constant, then they are not proposition.
In other word, whether they are or not depends on what are constant and what are not, which is up to you.