(This question was originally asked here, but I've decided to ask it in philosophy since it might be a better fit.)
I kind of feel like this is a silly question, but does taking the logical conjunction of two statements make any sense when one of the statements doesn't make sense?
For example, suppose we have the following two statements:
- Statement X: "47 is an even number."
- Statement Y: "The color of the number 5 smells like cinnamon."
The first statement is obviously false, but the second statement doesn't make much sense because 5 doesn't seem to have an inherent color (and colors don't seem to have inherent smells), so I'm not sure if it has a truth value. Is it possible that the second statement has no truth value, or do we force ourselves to assign a truth value to it?
If the second statement has no truth value, then consider statement Z: "The color of the number 5 smells like cinnamon and 47 is an even number." Since X is false, does that mean Z is false, or does Z have no truth value because Y has no truth value?
I'm asking because I'm not sure if it is considered valid to take the logical conjunction of two statements if one of the statements has no truth value. I think the only thing we can be certain of is that Z is not true.
Sorry, not well-versed in logic! Any guidance would be great!