To me at least the paradox arises from definitively a stated assertion of an entity's falseness using a channel, declarative written out sentence in this case, which implicitly asserts its truth. Some see this as a never ending circular and mutually exclusive and exhaustive loop of true and false, but the problem in the statement itself is not circular but exist at the same time, in the same space.
Are you suggesting there may be in error in assuming that something's truth value is persistent (through "time")?
In the Liar's paradox, does the proposition alternate between between true
in succession as it is evaluated (having no persistent truth value)?
Or are you saying that there is an error in assuming simultaneity?
If we reject simultaneity, I think that their are going to be too few logical operations left to derive anything meaningful. We can no longer use any transitive operations. I can no longer assert that if "A" is true and "B" is true, then "A and B" are true, because I have no right to presume that they are true simultaneously. All propositions then become logically isolated.
Or are you saying that the Liar's Paradox is simply an artifact of language not necessarily reflected in pure logic?
Pure logic (in the form of number theory) has an analogous paradox as proven by Gödel.
And Kurt Gödel's Incompleteness Theorem reminds of a riddle I know. See if you can find the solution to the riddle.
This riddle have clearly stated facts: Three pal's register to a hotel and the desk clerk bills them $60 for the room, payable in advance. So, each man pays the clerk $20 and go to their room. Some minutes later, the clerk becomes aware of his blunder of overcharging the group by$5. So he tells one of the hotel attendant to return $5 to the 3 friends who checked in a moment ago. Seeing an opportunity to make $2, he keeps the $2 to himself thinking that the three friends would have some trouble evenly dividing $5 between themselves, and then decides to tell them that the clerk made an error of overcharging $3, giving a dollar back to each of the the three men. And the attendant goes home for the day, with the extra $2 stolen from the exchange. Now, each of the three friends gets a dollar back, thus they each paid $19 for the room which is a total of $57 for the night. We know the attendant pocketed $2 and adding that to the $57 leaves you at $59, and not $60 which was originally spent. Where did the one dollar disappear to?
The error is in representing the $57 paid as a positive number while also representing the $2 stolen as a positive number (the assertion to "We know the attendant pocketed $2 and adding that to the $57 leaves you at $59").
Here is a table representing the situation:
Guests Desk Clerk
Starting | 60 0 0 |
Paid for Room | 0 60 0 |
Rebate to clerk | 0 55 5 |
Guests shorted | 3 55 2 |
Net Change -57 +55 +2
What is finally being asked of us is to know is an accounting of where all the money is. The "Guests Shorted" row shows this information.
The attempt is to mislead us into using the "Net Change" information to derive this accounting, which is possible only so long is care is taken to pay attention to the (+/-) signs of this information.
[-57 + 2 = -55] (net change for guest and clerk combined)
[+55] (net change for desk)
[-57 + 2 + 55 = 0] (net change for guest and clerk and desk combined)