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Actually now I am a little interested in that paradox.

The answer must be that A or A` must really be:

"The sentence is not either true or false" Lets set that up:

"This sentence is false"

We analyze it thus:

G: The sentence is not either true or false.

H: The sentence is not true

I: It must be not false

Hmm? Not sure I did that right? Does "not either true or false" = "not true or not false" IF not then  have to write it:

G: The sentence is not either true or false

H The sentence is not true

I: It is something other than true or false

What would that be?