huphuphup123 wrote: ↑Tue Sep 23, 2025 4:18 am
Eodnhoj7 wrote: ↑Sun Sep 21, 2025 6:34 pm
huphuphup123 wrote: ↑Sun Sep 21, 2025 4:09 pm
https://upload.wikimedia.org/wikipedia/ ... ox.svg.png
A - The statement to the right is true nature B - the statement to the left is false
if A is true B is true, but if A is false then B if false, if B is false then A is true, if A is true then B is true
What is the solution or meaning of this?
There are two answers that occur immediately to me.
The first:
In one condition the person is a liar, in another the person is not a liar. In the magnitude of all possible conditions this person is both a liar and not a liar. Each condition that occurs reveals the potentiality of said person's inmate qualities thus these qualities exist simultaneously until a specific condition occurs. The solution, and I have had discussions with AI over this that back up my stance, is that paradoxes are superpositioned logical states.
Second:
Another answer is everything the person says is a half truth, necessitating a lie, and a half lie, necessitating a truth. All assertions have gradient truth values where truth and falsity are less of a binary assertion and more of a gradient way of viewing things. The person being both a liar and truth teller points to a gradient viewpoint.
So there are two answers, both legitimate:
Paradoxes are superpositioned assertions.
Paradoxes are gradient assertions.
So you are saying that both "true and false" together is between true and false, it is a gradient between those two. But how can you have true and false together without it cancelling each other out?
Yes a gradient approach can occur.
The statement of "I am a liar" observes that the person in question both tells the truth and lies. So how does that occur?
Within a given framework of identity, lets say the time and space of a week or several years, that identity has multiple expressions within the given space. Sometimes it is a liar. Sometimes it is a truthteller.
Within the given framework these things occur simultaneously and in grades, sometimes more truth than lies are told or vice versa. These can be observes at meta-identities, identities within identities. So where an identity in the time and space of a week may be "x and y", within the meta identity "x" may only occur in one time and space and "y" within another, all of which are part of the larger time and space of a week.
So identity as grades can be akin to a meta-identity, and identity within an identity.
Now on the other hand all dualisms result in gradation by degree of the dualism itself. Take for example the following dualistic symbolic chain (if you want this in normal language just ask):
1. T
2. F
3. (T,F)
4. T(T,F)
5. F(T,F)
6. (T,F)(T,F)
7. T((T,F)(T,F))
8. F((T,F)(T,F))
9. (T,F)((T,F)(T,F))
10. Unto infinity.
Any dualism, and paradox requires a dualism by degree of differing but isomorphic expressions, results in infinite gradation of said dualism.
So the liars paradox results in different grades of true and false. This can be evidenced by true may be more than false on one set of days, vice versa, or all truths are partial truths and all lies are partial lies.
There is also another complementary way of viewing paradox:
Two opposing or various states existing at once in quantum mechanics is called superpositioning. These states existing at once are effectively indistinct potentiality. When the superposition states are observed one of the potential states is localized according to the state of the observer.
Now a paradox is similar. It is multiple values at once. The paradox is indistinct in its present state. Now when the paradox is observed one or more of the following things happens:
1. The observer chooses one of the several potential values and makes distinctions from there. You will see this in everyday life where a paradox of "this is that" is observed and people naturally takes sides. The paradox becomes a mirror of the observer in this scenario.
2. The observer adds context to the paradox. Now in a general paradox there is no context but the paradox itself and this leads to multiple states coexisting at once. Now if a paradox is given further context, by the observer(s), then a distinct value occurs.
For example the paradox of "I am a liar" had multiple values coexisting that results in the indistinct state of the paradox itself.
Now if the context of "on wednesdays" so we have "I am a liar on wednesdays" then the paradox ceases and we have a clearer and more defined assertion.
3. If opposites cancel eachother out then the paradox becomes pure logical potentiality, a logical space by which values can be projected or assigned. In these respects the paradox is empty of meaning and yet this emptiness becomes of mirror to the observer. As such it is a point by which the observers attention is transformed. You will find this method quite frequently in zen Buddhism where two opposing points, under the paradox, are observed and the cancelation causes a space of potentiality by which the observer is looking into a metaphorical mirror.
The key to all of this is context.
Context determines how the paradox unfolds to the observer.
Under one context the paradox can lead to gradation, another superpositioned logical states subject to context application, another a mirror to the observer by nature of being empty....so on and so forth.