SUO: Re: Irreducible Try-It-And-See
Matthew West wrote:
>
> Dear Lee,
>
> I thought we had gotten beyond this.
> Indeed I thought we had got to the
> point where it was demonstrated
> (by Pat, but by me previously)
> that in representation terms
> anything can be reduced to
> dyadic relations.
>
> This caused a change in tack to saying that there are axioms that
> require more than 2 arguments (not a particular surprise to me).
> The question remaining is then whether there are any axioms that
> cannot be reduced to some set of independent axioms that involve
> only 3 elements.
>
> Regards
>
> Matthew
¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤
Matthew,
No, that is not an accurate summation
of the general state of understanding
on this topic, and no such result has
been demonstrated, not in those terms.
What we have demonstrated so far is limited to this:
1. No 3-adic relations are reducible to composites or products
of 2-adic relations, in the sense of relational composition.
2. Some 3-adic relations are reducible to, or reconstructible
from 2-adic relations, in the sense of projective reduction.
I do not understand the reasons behind
the persistence of this error, except
out of some dogma of reductionism or
just plain wishful thinking that the
world be less complex than it is.
Furthermore, any attempt by folks "way out here"
to canonize this account by methods other than
the ordinary methods of reasoned inquiry, say,
by enscouncing it in some liturgical doctrine
to "record this as an 'official' outcome of
the SUO group", no doubt soon to be joined
by the complementary "Index of Books" that
nobody but the duly-appointed Censors may
read, for fear of being contaminated with
alien doctrines that may weaken the Faith
of those too naive to think for themselves,
well, such a course would only bring ridicule
on the SUO Effort, and by those who mince their
words far less finely than I do. Please try to
understand, a statement like "anything can be
reduced to dyadic relations" is just bound to
sound to whole communities of folks who work
with this stuff every day like you just said
that rectangular matrices are not closed with
respect to matrix multiplication, and I am just
trying to prevent you and the SUO Group as a whole
from being subject to these embarrassments. People
have to seek out their own authorities, if that is
what it takes, but the "arguments" that have been
cited so far on behalf of this putative reduction
suffer from an "ignoratio elenchi" that is really
quite astounding, for all of its cleverness and
its diligence in racing down the wrong track.
Many Regards,
Jon Awbrey
¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤