In my mind, I have the category “meaningless” as statements which can’t be assigned a truth value without breaking the consistency of our system, and “trivial” as statements which can be assigned a truth value, but don’t pay any rent at all.
Try this way: Working in boolean logic, “This sentence is either true or false” can be true, and it can’t be false, right? If we can make these definite remarks about its properties within our system, can we still call it meaningless? Even though it doesn’t have useful consequences. (A formal way of saying it doesn’t have useful consequences, I guess, is to say that for our useless statement B and for all A, P(A) = P(A|B) -- it isn’t any evidence for anything at all.)
Given your definitions, that makes sense. One of the points I was trying to make, though, is that “meaningless” is one of those words with several related but slightly different interpretations, and that a lot of the trouble in this thread seems to have come from conflicts between those interpretations. In particular, a lot of the people here seem to be using it to mean “lacks evidential value” without making a distinction between the cases you do.
As to which definition to use: I’d say it depends on what we’re looking at. If we’re trying to figure out the internal properties of the logical system we’re working with, it’s quite important to make a distinction between cata!trivial and cata!meaningless statements; the latter give us information about the system that the former don’t. If we’re looking at the external consequences of the system, though, the two seem pretty much equivalent to me—in both cases we can’t productively take truth or falsity into account..
In my mind, I have the category “meaningless” as statements which can’t be assigned a truth value without breaking the consistency of our system, and “trivial” as statements which can be assigned a truth value, but don’t pay any rent at all.
Try this way: Working in boolean logic, “This sentence is either true or false” can be true, and it can’t be false, right? If we can make these definite remarks about its properties within our system, can we still call it meaningless? Even though it doesn’t have useful consequences. (A formal way of saying it doesn’t have useful consequences, I guess, is to say that for our useless statement B and for all A, P(A) = P(A|B) -- it isn’t any evidence for anything at all.)
Given your definitions, that makes sense. One of the points I was trying to make, though, is that “meaningless” is one of those words with several related but slightly different interpretations, and that a lot of the trouble in this thread seems to have come from conflicts between those interpretations. In particular, a lot of the people here seem to be using it to mean “lacks evidential value” without making a distinction between the cases you do.
As to which definition to use: I’d say it depends on what we’re looking at. If we’re trying to figure out the internal properties of the logical system we’re working with, it’s quite important to make a distinction between cata!trivial and cata!meaningless statements; the latter give us information about the system that the former don’t. If we’re looking at the external consequences of the system, though, the two seem pretty much equivalent to me—in both cases we can’t productively take truth or falsity into account..