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

On Dec 22, 11:43 pm, lwal...@xxxxxxxxx wrote:

The line that I wish to challenge is line 4:

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

That's the empty set axiom. tommy1729 says he adopts the empty set
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)

tommy1729 said he adopts the "EMPTY SET AXIOM" [emphasis added]. That
there is SOME OTHER axiom that tommy1729 really meant or that better
goes with his notions is not at issue. I addressed the system that
tommy1729 gave, as he gave it. Why don't you understand this simple
thing? Once more: tommy 1729 stated that he adopts the empty set
axiom. The empty set axiom is:

ExAy y not-in x.

Using that axiom and the rest of what tommy1729 said about his system,
we derive a contradiction. It's that simple.

Again (and I don't understand why you don't understand this point): I
proved that tommy1729's system is inconsistent as he stated that
system. I didn't claim that one cannot come up with DIFFERENT axioms
that may or may not better capture something else that might or might
not be in his mind or might or might not be something better suited to
his purposes.

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)

But I DON'T prefer that in the case of tommy1729's system, since he
stated it as an axiom (I don't recall whether he even stated an axiom
schema of separation or replacement).

using only the subset relation and without mentioning
the primitive e. Then of course one would write:

4' Ex Ay x subset y

That's not the empty set axiom. It is implied by the empty set axiom,
but I don't know offhand what other axioms would be needed for (4') to
imply the empty set axiom.

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.

SO WHAT?

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.

Why can't you understand such a simple thing? tommy1729 stated the
empty set axiom as an axiom of his system. We know what the empty set
axiom is. And from it, with other things he says about his system, we
derive a contradiction. It's not a matter of what would happen if
tommy1729 adopted SOME OTHER axiom instead of the empty set; of course
that's a whole other ballgame, but it's not the ballgame we're in when
tommy1729 says he adopts the EMPTY SET AXIOM.

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.

Whatever the merits of that, it doesn't refute that tommy1729's system
is inconsistent when he says (along with other things) that he has the
empty set axiom.

MoeBlee

.

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