No, it's nothing like that. In the liars paradox, the statement is inherently uncomputable.
In this case the statement is either true or false, and the truth or false of the statement doesn't change anything. Your belief in whether the statement is true or false changes your belief in whether the statement is true or false - there's no basis for assuming that in the general case it would alter the actual truth of the statement (it could, in as much as e.g. you could have a simulation that keeps running as long as you believe you're in an isolated moment, and freezes you and discards the rest the moment you believe time is real).
Now, it is true that you can't trust your own state of mind to truthfully represents a physical reality. That this means you also can't trust your own logic is irrelevant, because irrespective of whether you believe this to be true or false, the absence of any external source of validation of your senses or state of mind or existence in time means the statement must inherently be true irrespective of your trust in your mind.
This claim gives a straightforward condition to falsify it: Find any single source of external validation that does not depend on your senses or observation of it. If you can, then the claim above is false.
Given you absolutely can't, the logical conclusion is that the claim is true.
In this case the statement is either true or false, and the truth or false of the statement doesn't change anything. Your belief in whether the statement is true or false changes your belief in whether the statement is true or false - there's no basis for assuming that in the general case it would alter the actual truth of the statement (it could, in as much as e.g. you could have a simulation that keeps running as long as you believe you're in an isolated moment, and freezes you and discards the rest the moment you believe time is real).
Now, it is true that you can't trust your own state of mind to truthfully represents a physical reality. That this means you also can't trust your own logic is irrelevant, because irrespective of whether you believe this to be true or false, the absence of any external source of validation of your senses or state of mind or existence in time means the statement must inherently be true irrespective of your trust in your mind.
This claim gives a straightforward condition to falsify it: Find any single source of external validation that does not depend on your senses or observation of it. If you can, then the claim above is false.
Given you absolutely can't, the logical conclusion is that the claim is true.