What about the sentence “This English sentence has six words?” It’s self-referential, but it’s certainly not meaningless, is it? And yet if you believe it, it doesn’t tell you anything except something about itself.
(EDIT: Maybe my claim is conflating the proposition TESHSW with the written representation of the proposition, which it describes and does tell you something about. Perhaps simply “This sentence is either true or false” is a better example—I don’t think that is meaningless at all, either, just trivial.)
Consider the statement “BLGRGHLKH is either true or false”, where BLGRGHLKH is a meaningless combination of letters I just made up.
I interpret the statement “BLGRGHLKH is true” as meaningless (in fact, by Tarski, this statement correlates with BLGRGHLKH, which we know is meaningless), but I am tempted to say the statement “BLGRGHLKH is either true or false” is true, maybe just as a reflex of declaring “X is either true or false” true for all values of X.
That calls into question the ability to move from “This sentence is either true or false” sounding meaningful to “This sentence is false” sounding meaningful.
I think quotation-referent distinction makes this sufficiently different from Liar. The referent of this sentence is the the quotation “This English sentence has six words”, which is not quite the same as the referent being the meaning of the sentence. It’s no more self-referential than “This sentence is written in black ink”.
I agree with you. That’s basically what I was getting at afterward in my edit. I’m just trying to dig up a statement which is unambiguously true, but yet isn’t at all useful. I think that “This sentence is either true or false” fits the bill.
Hmm. If you visualize meaning as a mapping between representation space and some subset of expectation space, “this English sentence has six words” forms a tight little loop disconnected from the rest of the universe. That seems to me like as good an indication as any that the statement has no useful consequences.
The distinction between “meaningless” and “trivial” seems pretty semantic to me.
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..
I will expect new things about where the zeros are. That means I can expect new things about my graphing calculator.
What about the sentence “This English sentence has six words?” It’s self-referential, but it’s certainly not meaningless, is it? And yet if you believe it, it doesn’t tell you anything except something about itself.
(EDIT: Maybe my claim is conflating the proposition TESHSW with the written representation of the proposition, which it describes and does tell you something about. Perhaps simply “This sentence is either true or false” is a better example—I don’t think that is meaningless at all, either, just trivial.)
Consider the statement “BLGRGHLKH is either true or false”, where BLGRGHLKH is a meaningless combination of letters I just made up.
I interpret the statement “BLGRGHLKH is true” as meaningless (in fact, by Tarski, this statement correlates with BLGRGHLKH, which we know is meaningless), but I am tempted to say the statement “BLGRGHLKH is either true or false” is true, maybe just as a reflex of declaring “X is either true or false” true for all values of X.
That calls into question the ability to move from “This sentence is either true or false” sounding meaningful to “This sentence is false” sounding meaningful.
I think quotation-referent distinction makes this sufficiently different from Liar. The referent of this sentence is the the quotation “This English sentence has six words”, which is not quite the same as the referent being the meaning of the sentence. It’s no more self-referential than “This sentence is written in black ink”.
I agree with you. That’s basically what I was getting at afterward in my edit. I’m just trying to dig up a statement which is unambiguously true, but yet isn’t at all useful. I think that “This sentence is either true or false” fits the bill.
Hmm. If you visualize meaning as a mapping between representation space and some subset of expectation space, “this English sentence has six words” forms a tight little loop disconnected from the rest of the universe. That seems to me like as good an indication as any that the statement has no useful consequences.
The distinction between “meaningless” and “trivial” seems pretty semantic to me.
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..