Is “I am a liar” a paradox?

If “I am a liar is true”, then “I am a liar is false.”

If “I am a liar is false” then “I am a liar is true.”

So of course it is not a paradox. It is simply a variable X which cannot be given a True or False value (they give contradictions).

For example “Air Force1 is flying” can’t be given a True or False value without further information.

Suppes gives a “modern day version:”

The only sentence on this board is false.

Since there is nothing else on the board, the only sentence being referred to has to be: “The only sentence on this board is false,” so that

The only (The only sentence on this board is false) on this board is false.

The only [The only (The only sentence on this board is false) on this board is false] on this board is false.

.

which is not a paradox, it is simply nonsense.

Wicki gives the version:

This statement is false: (A)

Call “This statement is false: (A)” X(A)

Then X(T) =F and X(F)=T, ie, X(A) = notA

If “statement” is “This statement is false: (A)” then you get the same nonsensical circular definition as above, which reminds one of “Russels Paradox,”

On this subject Suppes mentions Cantor’s paradox of the greatest Cardinal number, an “intuitive proof” of which he begins with “…the cardinal number n of the set S of all sets.” Also “….set of all Subsets of S and its cardinal p.” There is no such thing as the set of all sets or subsets.

I seem to recall seeing Logic has been reformed so as to avoid Russels Paradox. Which eliminates any rational discussion because it is impossible to follow. However, I recall statements such as xεx, which is still Russels paradox.