Re: kung fu mereotopology

Tonicopm@xxxxxxxxx wrote:
On Dec 24, 11:15 pm, lwal...@xxxxxxxxx wrote:
On Dec 24, 1:29 am, Tonic...@xxxxxxxxx wrote:

On Dec 24, 9:32 am, lwal...@xxxxxxxxx wrote:
First of all, I wonder precisely what word tommy1729 failed
to define, or redefined, in a way that would inspire Tonio
to compare it to redefining 1 as 2 in "1+1 = 3."
The 1 + 1 = 3 and etc. thing was NOT comparing to any definition, or
non-definition, Tommy did in his TST, but was used as a way to show
GALATHAEA's arguments' weakness...nothing to do with Tommy or his TST
at all!
But what was galathaea discussing? TST, and MoeBlee's proposed
proof of its inconsistency.

**Sigh**...read the whole damn thing again
OK. And you (Tonio), in that post, wrote:

In particular, the accusation of being focusing on the word "set"...in
a thread where someone explicitly tried to put forward a set theory of
his own...so ridiculous!! Like me talking of
politicians in a thread about politics: how could one dare??
So now we're in agreement that the person who made a
redefinition akin to 1+1 = 3 is galathaea, and the
word that she redefined that way is "set."


== No, we are not in agreement. In short, and to stop all this
wondering and wandering of yours along all kinds of interpretations of
what I wrote: Galathaea was defending Tommy's tries to define a set
theory and she told Moeblee, in her rather peculiar way, that what
Tommy wrote may be interpreted in ways different from the normal,
"standard" one that most "standard" mathematicans use, and that
Moeblee was using the narrow definitions and notions that were given
to him by "authorities" and etc., all this, imo, with lots of
condescending, patronizing and, again imo, belittling phrases and
descriptions.

Among OTHER things, Galathaea mentioned the word "set". In fact, these
are her exact words:

"and what you see as a set theory
is not what all people see as a set theory "

And from here my reaction. It's not G. defining the word set, is she
saying that the above, so she thinks, Tommy meant with his TST.

So there is no definition at all belonging to anybody "akin" to
1+1 = 3, so stop with this now. That is neither what I wrote nor what
I even meant to insinuate ...can you NOW understand this?


But first of all, what is the _real_ definition of
the word "set," the definition that galathaea changed
to suit her own purpose, anyway? The last time I
checked, in ZFC, set is a undefined _primitive_. (Of
course, in class theories such as NBG, "class" is the
undefined primitive object, and a set is a class that
is an element of another class.)

So if tommy1729 has decided that the basic objects of
his theory are sets, then no one, neither galathaea
nor MoeBlee, can give a definition to the primitive
concept of a "set."


== Great! Thanx for clearifying my point: Tommy decided what to call
sets to (disclaimer: I don't know whether this is actually true: I'm
just assuming it is to go along with you in this), and then nobody can
*** into his defining this, right? Unless, of course, someone points
out, just as Moeblee did, that that definition, along with other
stuff, leads us to a contradiction.


Since you (Tonio) directed me to reread galathaea's
post as well, let me do so:

"but your current tactic
moeblee
of focusing down on the word "set"
well
it's just showing off more of what you do not know
because
from the polish logicians to modern computer science
lesniewski to scott and beyond
mereologies have been used as foundations of set theories
the use is very common"

What's going on here? Clearly galathaea and MoeBlee
disagree on what a "set" is.


== Apparently so


Since we can't define the primitive "set," let me take
something which can be defined, "empty set" -- especially
since MoeBlee used an empty set in his proposed proof that
TST is inconsistent.

To MoeBlee, an "empty set" cannot have any element, not
even itself. This is, of course, how empty sets work in
standard set theories such as ZFC. In MoeBlee's proof, he
shows that tommy1729's "x = [x]" implies that the empty set
does contain itself, [] = [[]], hence a contradiction.

Then galathaea argued that in tommy1729's proposed theory,
that's not how [] works in the flattened mereology. So
MoeBlee countered that tommy1729 insisted that his was a
"set" theory, which allegedly precludes it from having the
flattened mereology.


== Ok, this is going just fine: I agree so far!


Then galathaea disagreed. So MoeBlee then accused her of
redefining "set" to satisfy her own argument, and then Tonio
compared her redefinition of set to 1+1 = 3.


== Too bad, we were advancing to nice! Read my first remark above, and
please do pay attention to the fact that I do NOT mess at all with
Galathaea's definitions, if any at all, but rather with her insistence
in telling Moeblee that when he (Moeblee) reads the word "set" in TST,
he's not to understand "set" as usual, but rather in a misterious,
mistifying, foggy and, UNDEFINED (apparently) as far as I can see up
to this moment, and unknown way.

And then comes my " 1 + 1 = 3 " thing, meaning: if A writes this
equation and then B says it is nonsense, then A retorting that for him
a first "1" on the left of an equation is to be understood as a "2"
because that's the way he likes is not a very intelligent and
intellectually honest thing to do, since if for some reason he wants
ALL the "1's" in the first place of some equation to be read as "2's",
then why the heck he did not define EXATLY that from the very
beginning?! That is my point in this, and perhaps it was also
Moeblee's, though I can't say for sure.


To galathaea, every set theory has a mereology -- even ZFC,
but ZFC's mereology is not the flattened one. To MoeBlee,
Tonio, and others, set theory and mereology are distinct
concepts, and being a set theory precluding a theory from
having mereology, and vice versa.


== This is not true. As I alreadys stated before, I know mostly
bananas about mereology, and my knowledge in set theory is a basic
one. I just can't tell either way since I don't know enough. Period.
This is also the reason I didn't mess in all the theoretical debate
and consequent brawl, but ONLY in the way of explaining and
understanding things: I think that if someone mentions set, we ALL are
free to understand that she/he meant the overwhelmingly usual and
standard thing, and NOT a new, undefined or ill-defined thing.


To galathaea and tommy1729, the objects of a theory having
flattened mereology may be called "sets." To MoeBlee, Tonio,
and others, the objects may be called something else, like
"fusions" or "heaps," but not "sets" -- and calling them
"sets" is an arbitrary redefinition akin to 1+1 = 3.


Again: no, and read prior remarks in this post


My point of view is that to convey, illustrate, introduce, etc. a new
"set" or "collection" theory, it would take several pages.
Or, at the minimum, the more explanations, the better for the
reader of sci.math .

This would not be true if the theory is so simple as to be
of no use to do analysis or algebra.

(BTW.: I wish to add that when I reply in a thread
with disagreements, I'm not necessarily disagreeing
with what the person to whom I reply is writing.)

David Bernier



To galathaea and tommy1729, an empty object can contain
itself (as a part). To MoeBlee, Tonio, and others, the empty
set cannot contain itself (as an element), and anyone saying
otherwise is an arbitratry redefinition akin to 1+1 = 3.


No. Read above


I can go on and on. The Stanford Encyclopedia of Philosophy,
which MoeBlee has suggested that I read earlier, does use
different symbols and terms for the flattened mereology,
such as "fusion" for "set," "part" for "element," "bottom"
for "empty set," "top" for "universal set," and so on.

To galathaea, these changes are merely cosmetic, and one can
call them "sets," "elements," and "empty set" if one chooses
to do so. To MoeBlee, Tonio, and others, these changes are
necessarily to distinguish set theory from mereology.


If Galathaea REALLY means the above, then I really wouldn't care to go
along with this, though I think it may be rather confusing. Anyway, I
think things must be crystal clear stated from the beginning to avoid
misunderstandings

Regards
Tonio
.

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