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1 solution
I will take the definition of a proposition to be a declarative sentence which is either true or false, but not both true and false.
Now if what the given sentence states is true then it is in fact false, and if it is false then it is in fact true. As there is no way to associate a truth value to the given sentence, it cannot be considered to be a proposition.
This sentence is an example of the Liar Paradox . In short, it is a paradox only if we consider it to have meaning, so if we instead consider it meaningless, or "nonsense", then the apparent paradox is resolved. However, this can be seen as a circular argument, as our motive in considering it as meaningless is simply to resolve the paradox, which is something we refuse to tolerate. Rather, what is required is a systematic analysis of self-reference within a system of logic.