|
|
Confutus wrote:
> galathaea wrote:
[...]
> > > Post's "cyclical" system which is just a bit later
> > > than that of Lukasiewicz isn't nearly as useful for reasoning.
> >
> > i would disagree with this
>
> I haven't seen what it's useful for. My thought was something that
> reduces to classical logic if you eliminate the 3rd value, and Post's
> cyclical negation doesn't do that.
>
> > his system
> > provides a layered refinement
> > of the logics between the boolean and the heyting
> > and the structural distinctions
> > all have natural functional interpretations in decision theory
>
> I'm not familiar at all with decision theory, so I can't comment on
> that.
i must sincerely apologise
but i was confused in thie response
and had been internally speaking of stone algebras
this is not the first time i have mentally confused
stone and post logics
and a handicap i must be more careful about
this time was most certainly aided by hubris
see
i had seen your mention of cyclic negation
and i _knew_ negation in stone algebras was not cyclic
because of (~x) \/ (~~x) = 1
in fact
i have been looking for a cyclic negation lately
for some scribblings i have about embedding logics
in hypergeometric relations
and i _knew_ that it was something i'd seen before
but i have found no trace in my notebooks
and scanning through books had not been helpful
google and its scholar have been less than helpful here
at least with terms like "cyclic negation"
so i thought you had mispoke about the property
but of course
as you know
post algebras do have cyclic negation
and they are functionally complete
and (x) /\ (~x) /\ (~~x) /\ ... /\ ((~)^(n-1) (x)) = 0
and all of the other properties i have found
in my hypergeometric logics
and they are exactly the logics i have been looking for
i am deeply grateful to you for bringing this (back) to my knowledge
and i hope you will not mind it if i credit you for this
in the paper i am writing on these logics
i do not think i can express how much
this ties fragmentary pieces together
and i would have learned all this days earlier
if i had not assumed you mispoke
and lay blinded by ignorance and conceit...
[...]
> > if you were to take a separateness axiom of truth values
> > (any reasonably justifiable one
> > like the tendency you comment on)
> > and were led to a countable infinity of uncertain values
> >
> > what would be the down-side
> > philosophically?
>
> I don't know about philosophically. I do think it's easier and more
> practical to deal with one uncertain value than a countible infinity of
> them.
a very chrysippian compromise...
-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
galathaea: prankster, fablist, magician, liar
|
|