This is what Zuhair posted 2012, eleven years ago:

> So the statement "This statement is not true"
> is SOLVED intuitionistically.

Now he is jumping to conclusions a little bit, if he
would justify it with 3 valued logic or somesuch.
But anyway, this is also a result, that one might

obtain. Not 100% sure. We would need to show
that in intutionistic logic A <-> ~A can be satisfied.
Are 3-valued models also intuitionistic models?

Zuhair schrieb am Freitag, 28. September 2012 um 09:12:17 UTC+2:
> What is the truth value of the following statement?
>
> "This statement is False"
>
> Clearly this statement is not a proposition of two valued logic, since
> it neither can be true nor can it be false. So it is a proposition of
> multi-valued logic. Now there is another statement that is closely
> related to this one, that is the following:
>
> "This statement is True"
>
> Now this "can" be a proposition of two valued logic, but the problem
> is that we don't have sufficient information from it to say that it is
> true or false, so it is of an indeterminate truth "status".
>
> So the case with the first statement is that it: Cannot be true nor
> can it be false.
> While the case with the second is that it: Might be true or might be
> false
>
> The problem is that being true means Matching reality, while being
> false means not matching reality. A statement either Matches reality
> or not, there is no room for an in-between condition or a neither
> condition. This is the preferable setting of our senses of course, it
> might be the case that we can have really multiple values of truth,
> i.e. of matching reality.
>
> Now instead of thinking of truth 'values' which seems to be an ideal
> notion, we'd better think of the 'truth' status, and what I mean by
> this is OUR position from truth, i.e. what can we say about its truth
> value, so instead of saying this statement is true in this kind of
> absolute affirmative genre, it is more reasonable to say that we have
> enough information sufficient to accept this statement as being true.
> Also to say that a statement is false is to say that we have
> sufficient information to deem that statement as not matching reality,
> now a third truth status happens when we don't have sufficient
> information in either direction, however this later third truth status
> can be divided into two truth 'situations' where we can have different
> scenarios that causes this insufficient information, it might be the
> case the we have no information at all about its truth value, or it
> might be the case that we have some evidence, albeit insufficient,
> pointing of one direction and some evidence pointing to the other
> direction, in both situations we'd be not having sufficient
> information to make a decision on it truth, so we cannot accept it or
> reject it. So we can give an alternative explanation of Truth and
> False that are indeed practical and not ideal as the customary
> classical logic pertains, that alternative explanation is:
>
> T: There is sufficient evidence for acceptance
> F: There is sufficient evidence for rejection
> I : There is no sufficient evidence to accept or reject
>
> Now I is divided into two situations
>
> I_1: There is (insufficient) evidence in favor of each direction (i.e.
> Confusing)
> I_2: There is no evidence in any direction (Oblivious)
>
> Now lets analyze the sentences
>
> "This statement is True"
> "This statement is False"
>
> Clearly the first is Confusing (I_1), while the second is Oblivious
> (I_2). Both of course as I said above leads to inability to reject or
> accept the statement, the first because of conflicting evidence about
> the possibility of its truth value, the second because of absence of
> evidence pointing to its possible truth value.
>
> So in nutshell we have only Two truth values, T, F, this is at
> absolute level, and we have Three truth statuses, these are about
> knowledge of the truth values, and we have FOUR truth situations,
> these are about aetiology of truth statuses.
>
> Classical logic (Aristotle) is about the absolute level, i.e. about
> truth values!
> Three valued logic (Kleene's) is about truth statuses!
> Four valued logic (Belnap's) is about truth situations!
>
> Both the triple valued logic and the quadruple valued logic give
> answers to the truth value of the statement of the Liar Paradox,
> albeit the last with more detail.
>
> Let's see that:
>
> Assume truth value of "This statement is False" to be T.
> Then we'd be having sufficient evidence to accept it and sufficient
> evidence to reject it, which cannot be.
>
> Assume truth value of "This statement is False" to be F.
> Then there will be sufficient evidence to reject saying "This
> statement has sufficient evidence for it to be rejected", this will
> end up in saying
> We don't have sufficient evidence for rejecting it. Which is truth
> situation I and not F, which is also contradictory.
>
> Assume truth value of "This statement is False" to be I.
> This is:
> We don't have sufficient evidence to accept or reject (this statement
> has sufficient evidence for it to be rejected).
>
> This doesn't go further into any opposing situation. So it is the
> answer!
>
> However if we assume I_1, then it leads to a conflict since we don't
> have even insufficient evidence in favor of any truth value.
>
> So we are at situation I_2.
>
> This only shows that English can be understood in different ways.
>
> So the answer to whether the liar paradox statement is English (or any
> known spoken language that is stated equivalently in) or not, is to
> the positive.
>
> It is English!
>
> There is another closely related statement to the Liar paradox, that
> is:
>
> "This statement is not True"
>
> Now this can be solved!
>
> If we understand True as a status (the first one above), then the
> negation of this status is not the False status, here we'll be
> matching Intuitionism claims.
>
> When we say ~S to mean: We don't have sufficient evidence that S
> Matches reality. Now this doesn't mean that S is not true, it might be
> the case that S has the truth "value" T but we don't have sufficient
> evidence to arrive at that, so the situation of ~T do not lead to F,
> and this is enough to solve the above paradox, as follows:
>
> This statement is not true <-> This statement has no sufficient
> evidence for us to accept it.
>
> -> There is no sufficient evidence for us to accept "This statement
> has no sufficient evidence for us to accept it"
>
> This doesn't necessarily go further, it is NOT paradoxical.
>
> So the statement "This statement is not true" is SOLVED
> intuitionistically.
>
> Zuhair