[lojban] Re: A Proposed Explanation of {gunma}

[John E Clifford <lojban-out@lojban.org>]

--- Jorge Llambías <jjllambias@gmail.com> wrote:

> On 12/15/05, John E Clifford
> <clifford-j@sbcglobal.net> wrote:
> > Looking over that chapter again, I note that
> > McKay is doing a very different thing there. 
> He
> > is arguing that plural
> quantification/reference
> > cannot be reduced to any singularist version
> and
> > that it does not require a singularist
> > underpinning of any sort.  All of which I
> agree
> > with; I am only saying that there are
> singularist
> > systems that are formally indistinguishable
> from
> > plural reference/quantification.
> 
> Isn't that contradictory? If plural reference
> cannot be reduced
> to any singularist version, how can it be
> equivalent to some
> singularist system?

They could have the same formal theorems without
one being definable in the other.  That is the
situation I am contemplating.  What is odd here
is that the two (or more) isomorphic theories are
also theories that apply to the same phenomena,
but even this is not unprecedented (though I
can't at the moment remember the classic
examples).

>  After all,
> > bunch theory does not *say* there is a bunch
> that
> > so and so, it just says that something is so
> and
> > so, leaving it open what that something
> is/are:
> > aF & bF & cF => [Ed]d-F regardless. Put
> another
> > way, McKay uses "plurality" and "plurals" in
> ways
> > that are to the naked eye not different from
> the
> > way a singularist uses "set" or "fusion" and
> this
> > is even more true in the formalism.

I have admit though that my remarks about the
fusion principle (the fusion of any two things
exists) was a bit of singularist thinking.  Even
if there such a plurality exists in some sense,
that does not mean that it is assigned to some
variable or term and thus [Ax][Ay][Ez](x in z & y
in z) is not true in every assignment and so not
a theorem (the special case where all assignments
are singular and individual shows that).  Now the
question is "What would be lost from bunches if
that principle did not occur?"  So far nothing
else that I'm sure I want seems to be affected,
but I haven't checked all that carefully.  In
particular, the break-down parts -- which seem to
me more important that the build-up parts -- seem
to work.  But I am open to correction on even that.


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