Re: nothing anyone would want to read (or: crank boxing (or: the death of the dance))

On Dec 19, 12:29 pm, MoeBlee <jazzm...@xxxxxxxxxxx> wrote:
On Dec 18, 11:21 pm, lwal...@xxxxxxxxx wrote:
Thus MoeBlee _did_
assume something tommy1729 didn't post -- namely that
being a set theory and having a flattened mereology
are mutually exclusive (as did I, before galathaea
taught me otherwise).
I made NO SUCH ASSUMPTION. Please, refer EXACTLY to what I wrote. And
you can also refer to the symbolic 1-10 argument I just gave too.

OK, but before my argument, let me respond to a comment
MoeBlee (and also Aatu) made in another post:

You won't visit the FREE online site 'Stanford Encyclopedia Of
Philosophy'?

I _have_ visited that site before -- and read the page there
on mereology several times!

To prove that I've read it, let me use terminology from that
Stanford site in my argument.

The line that I wish to challenge is line 4:

4 Ex Ay y not-in x ... axiom

According to galathaea, an empty object [] exists.

According to Stanford, some merologies have an object often
called "Bottom." The axiom given by Stanford for Bottom is
that Bottom is a part of every object.

I admit that both galathaea's and Stanford's description
of [] or Bottom are a bit confusing to me. Apparently,
[] and Bottom are objects that have _no_ atomic parts, yet
aren't themselves atoms.

Keeping this in mind, I believe that the new line 4 below
captures the spirit intended by tommy1729, better than
MoeBlee's line 4:

4' Ex Ay xey. (axiom)

Notice that galathaea uses c for the primitive later on,
while Stanford uses P for "is a part of." Thus Stanford
writes the axiom as:

P.11 Ez Ax Pzx.

Recall that the primitive of the flattened mereology of
tommy1729 is analogous to the subset relation. Thus we
can see that MoeBlee's 4. is analogous to

4 Ex Ay y not-subset x.

(Notice I wrote not-subset -- I said nothing about "not
a proper subset"!)

Meanwhile my 4' (Stanford's P.11) is analogous to

4' Ex Ay x subset y.

Suppose someone wanted us to write the Empty Set
"Axiom" of ZFC (and I put "Axiom" in quotes because I
know how MoeBlee prefers to derive it from Separation)
using only the subset relation and without mentioning
the primitive e. Then of course one would write:

4' Ex Ay x subset y

and not

4 Ex Ay y not-subset x

Suppose someone attempted to prove ZFC inconsistent by
claiming that "Ex Ay y not-subset x" is equivalent to
its Empty Set "Axiom." Then of course MoeBlee would
reject the proof, because they're not equivalent in ZFC.

To me, MoeBlee using "Ex Ay y not-in x" to prove TST
inconsistent is exactly analogous to someone using
"Ex Ay y not-subset x" to prove ZFC inconsistent. Just
as MoeBlee would reject the latter, I (and galathaea)
reject the former.

This is a good way to think about the axioms of the
flattened mereology. Suppose one had to write the
axioms and theorems of ZFC, but using only the subset
relation and not the primitive e. Then this is how one
must write axioms in the flattened mereology.
.

Quantcast