- This statement is not true
2.This statement is true only if true and not true.
(1) and (2) are clearly different sentences, but do they express the same proposition?
If yes, then it becomes clear from (2) that the proposition is clearly contradictory, since if (2) is true and therefore the proposition that (2) expresses is the case then (2) should be true and not true.
therefore the proposition that (2) expresses is a contradiction. if it expresses the same proposition as (1) then the proposition that (1) expresses is a contradiction. but then (1) does also 'say' that it is true about itself or to put it sloppily 'not true=true' according to (1) but then the paradox that we seem to have by conventional analysis evaporates , since if we assign to (1) that it is not true , and therefore that it is not the case what it says namely that (1) is 'not true=true' , then it must be not 'not true=true' , which obviously does not result in (1) being true!
Also taking into consideration that e.g. the sentences :
a. It is not the case that it is true that it is raining
b. it is true that it is raining only if it is true and not true that it is raining.
(a) and (b) do clearly express the same proposition even tho they are different sentences.
So do they express the same proposition (according to conventional definition of a proposition)?