To give you an example (a few more are cited in that paper of Weaver) those who hold it as unimportant generally do not write in usual academic venues about it, but it goes something like:
As the logician Arnon Avron puts it
Surely a meaningless sentence cannot say anything about anything, in
particular not about itself (or anything else). So relying on what ‘it
says of itself’ depends on taking for granted that it is meaningful . . . I
do wonder now if I am missing something here, and if so - what can it
Needless to say, for me the ‘liar sentences’ of all types are indeed completely meaningless, which is why I was never bothered by them . . .
In fact if you follow the FOM discussion referenced, Avron goes on to say:
On Sun, Jul 19, 2015 at 05:07:10PM -0500, Nik Weaver wrote:
So you would agree that the liar sentence is not true?
My immediate answer is: No, I do not agree, because a bunch of words
should be a meaningful sentence before it deserves the honor of
asking whether it is true or not.
However, you might have intended to use the above words in order to ask
a question which is different from that which I have just answered.
(Thus intuitionists use the word "not", but the meaning they attach
to it - whatever it is - is not the meaning that ordinary people attach to it.)
So in order to find out what is the real intended meaning of your question, and
then answer it accordingly, please tell me your answers to the following questions:
- Would you agree that Eiffel tower is not true?
- Would you agree that the number 7 is not yellow?
- Would you agree that the liar sentence is not yellow?
- Would you agree that "This sentence is true" is not true?
- Would you agree that 1/0 is not less than 7, and also not greater than 7?
- Would you agree that the liar sentence is not less than 7, and also not greater than 7?
In a later post Avron mentions that:
the liar is known
for two thousands years or so, and (as far as I know)
mathematicians never really care about it. The story was completely
different when they faced Russel's paradox (or the other
"logical paradoxes") - and for good reasons.
So that's generally the gist of the "opposition" to it.