So you knew all the way that LP is an Antinomy?
Only you don't know you can also prove:

~(A <=> ~A)

Says the same basically. And if you have
dichotomy, B <=> ~A, you can also prove:

~(A <=> B)

If you don't have dichotomy, what do you
have then, when there are two propositional

variables A and B? Is it necessarely Trichotomy?

Dan Christensen schrieb am Sonntag, 30. September 2012 um 04:56:08 UTC+2:
> For RP using an "is a set predicate" Set:
>
> 1 Set(r) & ALL(a):[a e r <=> ~a e a]
> Premise
>
> 2 Set(r)
> Split, 1
>
> 3 ALL(a):[a e r <=> ~a e a]
> Split, 1
>
> 4 r e r <=> ~r e r
> U Spec, 3
>
> 5 ~EXIST(r):[Set(r) & ALL(a):[a e r <=> ~a e a]]
> Conclusion, 1
>
> LP using an "is a well-defined statement" predicate S, and an "is
> true" predicate T:
>
> 1 S(x) & [T(x) <=> ~T(x)]
> Premise
>
> 2 S(x)
> Split, 1
>
> 3 T(x) <=> ~T(x)
> Split, 1
>
> 4 ~EXIST(x):[S(x) & [T(x) <=> ~T(x)]]
> Conclusion, 1
> Dan
> Download my DC Proof 2.0 software at http://www.dcproof.com

Do I vagely remember even this thread from 2012, since it
spilled into comp.lang.prolog, and I objected the spamming?
Maybe you got carried away how Zuhair set the stage:

> T: There is sufficient evidence for acceptance
> F: There is sufficient evidence for rejection
> I : There is no sufficient evidence to accept or reject

Nope Zuhair isn't to blame, he is fully awake:

> 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!

Not like sleepy Biden Dan Christensen.

Mild Shock schrieb am Montag, 18. September 2023 um 21:21:24 UTC+2:
> So you knew all the way that LP is an Antinomy?
> Only you don't know you can also prove:
>
> ~(A <=> ~A)
>
> Says the same basically. And if you have
> dichotomy, B <=> ~A, you can also prove:
>
> ~(A <=> B)
>
> If you don't have dichotomy, what do you
> have then, when there are two propositional
>
> variables A and B? Is it necessarely Trichotomy?
> Dan Christensen schrieb am Sonntag, 30. September 2012 um 04:56:08 UTC+2:
> > For RP using an "is a set predicate" Set:
> >
> > 1 Set(r) & ALL(a):[a e r <=> ~a e a]
> > Premise
> >
> > 2 Set(r)
> > Split, 1
> >
> > 3 ALL(a):[a e r <=> ~a e a]
> > Split, 1
> >
> > 4 r e r <=> ~r e r
> > U Spec, 3
> >
> > 5 ~EXIST(r):[Set(r) & ALL(a):[a e r <=> ~a e a]]
> > Conclusion, 1
> >
> > LP using an "is a well-defined statement" predicate S, and an "is
> > true" predicate T:
> >
> > 1 S(x) & [T(x) <=> ~T(x)]
> > Premise
> >
> > 2 S(x)
> > Split, 1
> >
> > 3 T(x) <=> ~T(x)
> > Split, 1
> >
> > 4 ~EXIST(x):[S(x) & [T(x) <=> ~T(x)]]
> > Conclusion, 1
> > Dan
> > Download my DC Proof 2.0 software at http://www.dcproof.com