the return of the master : tommy1729
amy666
but for a good reason.
i made many conjectures on sci.math , but lately ive spent much time on improving my proof methods.
especially in number theory.
( once again related to factoring yes )
now i am in posession of the most amazing number theory proofs.
i have proof of the infinitude of prime twins for example.
also a certain erdos conjecture is proved.
most of my conjectures about number theory posted on sci.math are also proved now.
i am now stronger than ever.
therefore the title :
the return of the master : tommy1729
of course i wont give these results for free.
i apologize to denis feldmann - as i promised ; if i would ever make very strong claims - 'officially'.
most of you probably dont believe me , so let the flamewars begin ...
regards
tommy1729
David R Tribble
> i have been absent for a while.
> but for a good reason.
> now i am in posession of the most amazing number theory proofs.
> i have proof of the infinitude of prime twins for example.
> also a certain erdos conjecture is proved.
> of course i wont give these results for free.
Then why bother telling anyone here?
Test Toob
"amy666" <tomm...@hotmail.com> wrote in message
news:18978223.60229.1246484...@nitrogen.mathforum.org...
>i have been absent for a while.
Good news, you blithering mathforum.org imbecile.
> but for a good reason.
> i made many conjectures on sci.math , but lately ive spent much time on
> improving my proof methods.
No one cares, you blithering mathforum.org fuckwit.
> especially in number theory.
Crap snipped, you blithering mathforum.org douche-nozzle.
omega
>
> but for a good reason.
>
> i made many conjectures on sci.math , but lately ive
> spent much time on improving my proof methods.
>
> especially in number theory.
>
> ( once again related to factoring yes )
>
> now i am in posession of the most amazing number
> theory proofs.
Welcome back ! Long life King Tommy Lionheart! But be careful, Milord ! During your long
captivity, Duke Marty, the heretic Usurper with a triple "M" on his black flag (or berry),
claimed he's able to prove that P = NP, and many other wonderful things. Thus, I'm afraid
your throne is in great danger, Master...
David Belanger
> i have proof of the infinitude of prime twins for example.
> also a certain erdos conjecture is proved.
What, no Halting Problem?
Transfer Principle
> i have been absent for a while.
Welcome back, tommy1729!
> i have proof of the infinitude of prime twins for example.
> of course i wont give these results for free.
I must admit that this is one of the rare times that I
actually agree with Tribble. I mentioned several times
my disdain for spending money to read about math. Most
of the time, the standard theorists are the ones who
are suggesting that I spend money on books. This time,
it's tommy1729, often labeled a so-called "crank," who
is soliciting money for math.
I won't spend money for standard math, and so I won't
spend money on any other math, either.
So tommy1729 claims that he has a proof that there
exist infinitely many twin primes. Many other posters,
including JSH and more recently, Musatov (another
"crank" who had made hundreds of posts since tommy1729
temporarily left sci.math), have made similar claims
of solving long-standing conjectures in number theory,
and so I won't accept that tommy1729 has a proof, at
least not just yet.
We know that tommy1729 has come up with his own
mereological set theory, TST. And so I wonder whether
tommy1729's proof is in the theory TST rather than PA
or even ZFC. But we notice how some theorems of
classical analysis can be proved using nonstandard
analysis, or NSA. A quick Google search reveals proofs
of the Jordan Curve Theorem and the infinitude of the
primes (_all_ the primes, not just twin primes) that
are written in NSA. Yet these proofs do transfer over
to classical analysis.
And so, it might be possible that tommy1729 could have
a proof that there are aleph_0 twin primes, and the
proof is written in TST, yet the proof can transfer to
PA or ZFC as well. Of course, I'll never know, since
I'll never spend a dime to see the proof. If the proof
is genuine, this might convince the standard theorists
to accept TST as a respectable theory.
Also, I'm still waiting for a complete axiomatization
of the theory TST. Hopefully, I won't have to spend
money to see those axioms either.
Transfer Principle
wrote:
Of course not. The Halting Problem is provably unsolvable. On
the other hand, it is conceivable that someone might have a
proof of the Twin Prime or Erdos conjectures, since these,
unlike the Halting Problem, are not provably unsolvable.
Fishcake
MeAmI.org
What is a berry?
amy666
no.
and no P = NP.
ask musatov for his P = NP proof :p :p
regards
tommy1729
amy666
no set theory is needed to interpret my proofs.
in fact all is countable.
its an 18 th century kind a proof :)
regards
tommy1729
David C. Ullrich
<kiwis...@math.sunysb.edu> wrote:
>This is a joke right? Please someone tell me that this is a joke.
You evidently arrived here during the period when he's been
gone. Look up the history on google.
David C. Ullrich
"Understanding Godel isn't about following his formal proof.
That would make a mockery of everything Godel was up to."
(John Jones, "My talk about Godel to the post-grads."
in sci.logic.)
Jon Slaughter
"Fishcake" <kiwis...@math.sunysb.edu> wrote in message
news:12589421.61255.1246506...@nitrogen.mathforum.org...
> This is a joke right? Please someone tell me that this is a joke.
No, it's not a joke... he really is a genius!
Jon Slaughter
"amy666" <tomm...@hotmail.com> wrote in message
news:18978223.60229.1246484...@nitrogen.mathforum.org...
>
> but for a good reason.
>
> i made many conjectures on sci.math , but lately ive spent much time on
> improving my proof methods.
>
> especially in number theory.
>
> ( once again related to factoring yes )
>
> now i am in posession of the most amazing number theory proofs.
>
> i have proof of the infinitude of prime twins for example.
>
> also a certain erdos conjecture is proved.
>
> most of my conjectures about number theory posted on sci.math are also
> proved now.
>
> i am now stronger than ever.
>
> therefore the title :
>
> the return of the master : tommy1729
>
>
> of course i wont give these results for free.
>
Of course not! Why should you. A genius like yours should be rewarded with
great riches and many virgins! You will surely be a shining example of what
humans have evolved to when looked back upon. The human race owes you a
great debt! I suggest you kill yourself now so you can get all the fame and
glory you deserve! It's the only logical way and since your a genius I know
you understand that.
MoeBlee
> Most
> of the time, the standard theorists are the ones who
> are suggesting that I spend money on books.
Whatever "standard theorist" means, I don't suggest how you should
spend your money. I just say that you make it very difficult on
yourself to get a good systematic understanding of certain subjects
without reading any books on those subjects. How you get the books -
by purchase, by borrowing, or by stealing is another matter.
> We know that tommy1729 has come up with his own
> mereological set theory, TST.
Oh yes, the one that is inconsistent (unless he further qualifies it).
MoeBlee
MoeBlee
> I'll never spend a dime to see the proof.
You don't mean that literally do you? I mean, if for a dime you could
have a copy of a proof (say, an actually correct proof) of the twin
primes conjecture, you'd spend the dime, right?
MoeBlee
Eddie Parker
Another mathforum.org imbecile wasting valuable oxygen and bandwidth.
Kill yourself. Do it now. Do it publicly. Do it violently.
fernando revilla
> of course i wont give these results for free.
But we don't know which are your professional fees.
Marshall
Sure he means it literally. What do you think the "Transfer Principle"
is? It's that he won't Transfer any of his money for math, on
Principle.
Marshall
Transfer Principle
On Jul 2, 11:39 am, MoeBlee <jazzm...@hotmail.com> wrote:
> On Jul 1, 8:19 pm, Transfer Principle <lwal...@lausd.net> wrote:
> > Most of the time, the standard theorists are the ones who
> > are suggesting that I spend money on books.
> Whatever "standard theorist" means, I don't suggest how you should
> spend your money.
I was just pointing out how both the so-called "cranks" and
their opponents are trying to convince me to read their
respective materials. Since I won't read all the materials
that MoeBlee has recommended that I read merely because he
posts that it's a good idea, I won't read tommy1729's work
merely because he suggests it either.
And while I'm on this topic, let me quote MoeBlee from a
separate post of his:
> > I'll never spend a dime to see the proof.
> You don't mean that literally do you? I mean, if for a dime you could
> have a copy of a proof (say, an actually correct proof) of the twin
> primes conjecture, you'd spend the dime, right?
OK, I'll give this one to MoeBlee. Since I was willing to
spend more than a literal dime for the Dover books, I'd
be willing to spend a literal dime for an actually
correct proof of the Twin Primes Conjecture.
Of course, tommy1729 hasn't even stated exactly how much
he is charging for the proof. So I don't know how many
dimes (or should I say, _Euros_ since he is European) I
would have to spend to see his alleged proof, which he
claims is actually an elementary proof. Skepticism, of
course, is in order since one wonders how such an
_elementary_ proof has eluded previous mathematicians.
> > We know that tommy1729 has come up with his own
> > mereological set theory, TST.
> Oh yes, the one that is inconsistent (unless he further qualifies it).
Here we go again. I've already explained to MoeBlee why
his proof of the inconsistency of TST is invalid, and
yet he is still claiming that TST is inconsistent.
I've noticed that certain so-called "crank" theories
(not just TST) have a key property in common that ZFC
lacks, making them difficult to be accepted by stan --
actually, instead of "standard theorists," let me use
the phrase "adherents of ZFC" because here I want to
highlight the differences between ZFC and many of these
alternate theories. Let me explain the differences.
Consider a theory in the language of ZFC, and suppose
one of its axioms is:
AxAyAz (xez & zey -> xey)
Obviously, this axiom doesn't hold in ZFC. In ZFC, it
doesn't make sense to conclude that xey simply because
xez and zey. Indeed, if we let a, b, and c be any sets
such that aec and ceb, if ~aeb, then x=a, y=b, z=c is
already a counterexample, and if aeb, then it's still
easy to find a counterexample, x=a, y=b\{a}, z=c. For
if b is a set in ZFC, then so is b\{a} (easy proved
via Separation Schema). So in other words adherents of
ZFC expect xey to be _independent_ of xez and xey in
that the former can't be proved from the latter. Even
though in some cases we can prove _non-membership_
(so we can prove ~yex from xez and xey, via Foundation
or Regularity), we can never prove _membership_ xey
simply by knowing how x,y are related to a set z. Of
course, if we added some additional structure, say by
stating that x,y,z are _ordinals_, then one can prove
that xey after all.
But in TST,
AxAyAz (xez & zey -> xey)
is indeed an _axiom_. Adherents of ZFC might try to
prove TST inconsistent by attempting to construct the
example x=a, y=b\{a}, z=c from above -- but this
doesn't work in TST. Instead, an alleged proof that
TST is inconsistent is, in actuality, a proof that an
object corresponding to b\{a} doesn't exist in TST! So
this proof shows that "e" doesn't work in TST the way
the adherents of ZFC expect it to. Because of this,
galathaea has suggested that tommy1729 use somewhat
different notation, such as:
AxAyAz (xcz & zcy -> xcy)
so that "c" is the _parthood_ primitive, to emphasize
that "c" doesn't work the way "e" does in ZFC. In ZFC
xey is independent of xez and zey, but in TST, we see
that xcy is _provable_ from xcz and zcy. An alleged
proof that TST is inconsistent based on b\{a} just
shows how the prover is unaware of how "c" works and
makes the unwarranted assumption that it works just
as "e" does in ZFC.
Let's go back to MoeBlee's alleged proof that TST is
inconsistent now. One of tommy1729's axioms is:
Ax x=[x]
MoeBlee's alleged proof involves instantiating to the
case x=0, so that we have 0={0}. And obviously, the
empty set 0 can't equal the non-empty set {0}. Hence
a contradiction, therefore TST is inconsistent.
And once again, here's the error. First of all, by
"0", MoeBlee means an object x such that:
Ay ~ycx
But one of the axioms of TST is:
Ax xcx
And even MoeBlee should be able to see that from this
axiom, we should be able to prove:
Ax Ey ycx
Yet MoeBlee assumes the negation of this theorem,
namely that Ex Ay ~ycx -- indeed, that such an x exists
and is unique, so that we can let 0 be the unique x
such that Ay ~ycx. But Ex Ay ~ycx is an unwarranted
assumption that MoeBlee makes only because Ex Ay ~yex
is provable in _ZFC_. But as I said before, ZFC's "e"
and TST's "c" don't work the same way.
Of course, tommy1729 sometimes refers to an object [],
which MoeBlee assumes satisfies Ay ~yc[] -- yet we've
already proved that it doesn't. So what is []? To
find out, we need two more axioms:
Ax Ey xcy
AxAy (xcy & ycx -> x=y)
as well as an Extensionality-like Axiom. From these
axioms, we prove the existence of a unique object
whose only part is itself, and we call it [].
So we don't have Ay ~yc[], but we do have:
Ay (yc[] -> y=[])
A full definition of the bracket notation would
require us to define the concept of an "atom." This
post is already long enough, so I won't give the
definition here, but the definition was given in
previous TST threads.
The axiomatization of the theory TST isn't finished yet
(and tommy1729 has stopped considering TST in order to
work on other theories such as the infinitude of the
twin primes and other pursuits). Ideally, the theory
TST should be equiconsistent with Z+proper classes, with
V_(omega+omega+1) serving as a model for both. TST should
not map symbol "c" to the same set that Z+proper classes
maps the symbol "e" to. Instead, TST might map the symbol
"e" to the same set that Z+proper classes maps the
relation "is a _subset_ of" to.
TST should be able to do as much analysis and math for
the sciences that the theory Z+proper classes can.
MoeBlee
> I was just pointing out how both the so-called "cranks" and
> their opponents are trying to convince me to read their
> respective materials. Since I won't read all the materials
> that MoeBlee has recommended that I read merely because he
> posts that it's a good idea, I won't read tommy1729's work
> merely because he suggests it either.
I thought it was a matter of spending money, not a matter of reading
per se.
> > > We know that tommy1729 has come up with his own
> > > mereological set theory, TST.
> > Oh yes, the one that is inconsistent (unless he further qualifies it).
>
> Here we go again. I've already explained to MoeBlee why
> his proof of the inconsistency of TST is invalid, and
> yet he is still claiming that TST is inconsistent.
Your "explanation" is incorrect. Just as I said: his theory is
inconsistent unless he further qualifies it.
NOPE. I (and I think plenty of the people who know more than I do)
very well understand that one doesn't prove inconsistency of a theory
merely by showing that one (or even any number) of its axioms (thus
theorems too) contradict some other theory. I very well understand
that one doesn't prove inconsistency of a theory merely by showing
that some universal generalization that is an axiom of that theory
does not hold for some other theory.
You've wasted a lot of words just to set up a blatant strawman.
> Let's go back to MoeBlee's alleged proof that TST is
> inconsistent now. One of tommy1729's axioms is:
>
> Ax x=[x]
>
> MoeBlee's alleged proof involves instantiating to the
> case x=0, so that we have 0={0}.
Is that what I did? Please refer to the specific post so that I can
have the context.
I don't recall using the empty set in my argument (maybe I did; but I
don't recall it).
> And obviously, the
> empty set 0 can't equal the non-empty set {0}. Hence
> a contradiction, therefore TST is inconsistent.
I don't recall that that was my argument (maybe it was, but please
refer to the actual post so that I can see the context).
> And once again, here's the error. First of all, by
> "0", MoeBlee means an object x such that:
>
> Ay ~ycx
No, I don't. Not if "c" is primitive or defined with 'e' ALSO in the
theory.
Anyway, I made use of nothing that tommy himself didn't stipulate.
> But one of the axioms of TST is:
>
> Ax xcx
Please refer to the exact post in which tommy gave his axiomatization,
so that we can see exactly what he proposed, and all the axioms
together so that we can evaluate for inconsistency AMONG them.
> And even MoeBlee should be able to see that from this
> axiom, we should be able to prove:
>
> Ax Ey ycx
>
> Yet MoeBlee assumes the negation of this theorem,
> namely that Ex Ay ~ycx
Where did I do this? Where did I assume anything that tommy did not
himself include in his axioms?
> -- indeed, that such an x exists
> and is unique, so that we can let 0 be the unique x
> such that Ay ~ycx. But Ex Ay ~ycx is an unwarranted
> assumption that MoeBlee makes only because Ex Ay ~yex
> is provable in _ZFC_. But as I said before, ZFC's "e"
> and TST's "c" don't work the same way.
I used no axioms of ZFC other than those tommy said he includes in his
axiomatization.
> Of course, tommy1729 sometimes refers to an object [],
> which MoeBlee assumes satisfies Ay ~yc[] -- yet we've
> already proved that it doesn't. So what is []? To
> find out, we need two more axioms:
Again, please link or at least name the thread and post numbers so
that we can evaluate what was actually posted and not your re-
interpretation of what was posted.
> Ax Ey xcy
> AxAy (xcy & ycx -> x=y)
>
> as well as an Extensionality-like Axiom. From these
> axioms, we prove the existence of a unique object
> whose only part is itself, and we call it [].
>
> So we don't have Ay ~yc[], but we do have:
>
> Ay (yc[] -> y=[])
>
> A full definition of the bracket notation would
> require us to define the concept of an "atom."
tommy eventually said what he meant by bracket notation. It was not
different enough from "{ }" notation so that, GIVEN THE REST OF HIS
AXIOMS, he could avoid contradiction.
> This
> post is already long enough, so I won't give the
> definition here, but the definition was given in
> previous TST threads.
>
> The axiomatization of the theory TST isn't finished yet
> (and tommy1729 has stopped considering TST in order to
> work on other theories such as the infinitude of the
> twin primes and other pursuits). Ideally, the theory
> TST should be equiconsistent with Z+proper classes, with
> V_(omega+omega+1) serving as a model for both. TST should
> not map symbol "c" to the same set that Z+proper classes
> maps the symbol "e" to. Instead, TST might map the symbol
> "e" to the same set that Z+proper classes maps the
> relation "is a _subset_ of" to.
>
> TST should be able to do as much analysis and math for
> the sciences that the theory Z+proper classes can.
Of course, it proves all the theorems that can be stated in the
language. Inconsistent theories do that.
MoeBlee
Transfer Principle
> On Jul 3, 2:05 pm, Transfer Principle <lwal...@lausd.net> wrote:
> > Let's go back to MoeBlee's alleged proof that TST is
> > inconsistent now. One of tommy1729's axioms is:
> > Ax x=[x]
> > MoeBlee's alleged proof involves instantiating to the
> > case x=0, so that we have 0={0}.
> Is that what I did? Please refer to the specific post so that I can
> have the context.
> I don't recall using the empty set in my argument (maybe I did; but I
> don't recall it).
> that we can evaluate what was actually posted and not your re-
> interpretation of what was posted.
Post numbers? Maybe those newsreaders that I can't afford
have post numbers, but I have no access to them.
So let me instead give a date. The thread was titled at
least three different times (nothing anyone would want to
read (or: crank boxing (or: the death of the dance))),
and the post in which MoeBlee gave his proof was given on
December 19, 2008, at 2121 Greenwich Mean Time:
> 1 Ax x=[x] .... axiom
> 2 Ay(y in [x] <-> y=x) ... from tommy1729's own qualifying statement
> 3 Ax x in [x] ... from 2
> 4 Ex Ay y not-in x ... axiom
> 5 Ay y not-in x ... existential instantiation from 4
> 6 x = [x] .... from 1
> 7 Ay y not-in [x] ... from 5, 6
> 8 ~Ey y in [x] ... from 7
> 9 x in [x] ... from 2
> 10 Ey y in [x] ... from 9
> But 8 and 10 is a contradiction.
> You are welcome to say exactly what is not first order logic applied
> to his axioms.
> Or in simple English:
> There is an x such that for all y, y not in x (_empty set axiom_). So
[emphasis mine]
> let x be such that for all y, we have y not in x. But for all x, we
> have x=[x] and x in [x], so x in x. So x itself is a y such that y in
> x. Contradiction.
Already, we can see that MoeBlee's proof _does_ use the
empty "set" after all. Essentially, he claims that from
"x=[x]" we prove that every object is a "singleton," yet
the empty "set" is not a "singleton," hence what he
believes to be a contradiction.
Looking at MoeBlee's lines 1-10 again:
> 1 Ax x=[x] .... axiom
> 2 Ay(y in [x] <-> y=x) ... from tommy1729's own qualifying statement
> 3 Ax x in [x] ... from 2
> 4 Ex Ay y not-in x ... axiom
> 5 Ay y not-in x ... existential instantiation from 4
> 6 x = [x] .... from 1
> 7 Ay y not-in [x] ... from 5, 6
> 8 ~Ey y in [x] ... from 7
> 9 x in [x] ... from 2
> 10 Ey y in [x] ... from 9
the errors are in lines 2 and 4. MoeBlee believes that
these are accurate renderings of tommy1729's axioms from
English to symbolic language of the theory, but I don't
believe that these are accurate at all.
In December, MoeBlee pointed out that his line 2 is
derived from tommy1729's remark, as follows:
> "[x] = is the set that contains x ( only )
> however x may be a set itself."
To MoeBlee, or anyone accustomed to working in ZFC, this
would appear to define [x] as a singleton, a set whose
lone element is x. But in mereology, we _can't_ conclude
from this remark that [x] is a "singleton" in the sense
of line 2, that any y in [x] must be x itself.
Similarly, line 4 is based on a ZFC definition of empty
set, but we can't conclude in mereology that [] is a set
such that for any y, y not-in [].
Indeed, the use of the word "in" to represent the lone
two-place predicate of the theory is a bit awkward,
since it doesn't work the same way as "e" in ZFC. This
is why galathaea suggested that tommy1729 use the symbol
"c" to represent the lone two-place predicate, so that
someone like MoeBlee wouldn't have made the mistakes that
he ends up making.
So what are the correct interpretations of tommy1729's
remarks in English that MoeBlee should have used instead
of his lines 2 and 4. Let's compare MoeBlee's incorrect
ZFC-based Empty Set Axiom with the correct mereological
Empty Set Axiom:
ZFC Empty Set:
> 4 Ex Ay y not-in x ... axiom
Mereological Empty Set:
Ex Ay xcy
So this object x is a part (not an "element," but a
_part_) of every set. At first, this doesn't necessarily
sound like an empty set. But we can prove that this set
must be the smallest possible set.
Proof:
1 Ex Ay xcy ... Mereological Empty Set
2 Ay xcy ... Existential Instantiation
3 Ax Ay (xcy & ycx) -> x=y ... Antisymmetry Axiom
(mentioned in my last post)
4 Ay (xcy & ycx) -> x=y ... Universal Instantiation
5 Ay xcy -> (ycx -> x=y) ... equivalent to step 4
(since "(P&Q)->R" and "P->(Q->R)" are equivalent --
checking the truth tables, both evaluate to false when
P=Q=true, R=false and to true otherwise)
6 ycx -> x=y ... Modus Ponens (steps 5,2)
So we see that x (which has been instantiated to be an
empty set) has the property that if y is a part of x,
then y must be x itself. This object has only one part,
namely itself. And since x must be a part of every set,
x must be the smalllest possible set -- no smaller set
is possible since no set can avoid having x as a part.
Now we'd like to _define_ [], the empty set, to be
this particular set x. Of course, I already know that
MoeBlee doesn't accept definitions without a proof of
existence and uniqueness. We've already proved that an
empty set exists, so now we must prove it's unique. To
do so, we let y be an empty set as well, by rewriting
the Empty Set Axiom with a change of dummy variables so
that we can instantiate to another set y, in order to
prove that if x and y are both empty sets, then x=y.
7 Ey Ax ycx ... Mereological Empty Set, change variables
8 Ax ycx ... Existential Instantiation
9 ycx ... Universal Instantiation
10 x=y ... Modus Ponens (steps 6,9)
The proof is very similar to the proof that the identity
of a group must be unique. We've proved that any set y
that's a part of x must be x itself, but y, being an
empty set, must be a part of every set. And so y is a
part of x, and since the only part of x is x itself, y
must equal x. QED
Therefore the empty set is unique, and so we can
justifiably write the definition:
[] =def the unique x s.t. Ay xcy
What about a definition of [x]? We are reminded of the
definition of the notation {} in ZFC as given by Suppes,
who gives a separate definition for {x}, {x,y}, {x,y,z},
and {x,y,z,w}. Formally, we actually have four separate
function symbols, a one-place symbol {}, a two-place
symbol {,}, a three-place symbol {,,}, and finally, a
four-place symbol {,,,}.
So we can define a one-place function symbol for []. I
have been trying to figure out a good definition for
[x] that satisfies MoeBlee's eliminability requirement
for acceptable definitions. And the best definition so
far appears to be simply:
[x] =def x
Can't get more "eliminable" than that!
The first non-trivial definition for [], therefore,
would be a two-place function symbol [,]. But first, we
would need a definition for atomic, which is to be a
one-place predicate:
x atomic <->def Ey ~xcy & Ay (ycx <-> y=x v Az ycz)
or, using the previously defined symbol []:
x atomic <->def ~x=[] & Ay (ycx <-> y=x v y=[])
The "~x=[]" (or "Ey ~xcy") part is to prevent [] itself
from being an atom. We want to avoid [] being an atom
for the same reason that we avoid 1 being a prime.
Then we can define the two-place function symbol [x,y]:
[x,y] =def the z s.t. Aw (w atomic & wcz -> wcx v wcy)
Existence and uniqueness? Most mereological theories
have an axiom guaranteeing existence, so there's no
reason that TST can't have one. Such an axiom would be
the analog of ZFC's Pairing Axiom. Uniqueness is
guaranteed by the analog of ZFC's Extensionality Axiom,
which I mentioned in a previous post.
It also might be more elegant if we could avoid
mentioning "atomic" and write something like:
[x,y] =def the z s.t. Av zcv <-> xcv & ycv
Now this might require something like a Separation
Schema to prove existence and uniqueness. The former
might be more intuitive, while the latter would be a
little bit shorter. I'm not sure which one tommy1729
(or galathaea, the poster who had been helping him
with his theory) would prefer.
Once [x,y] has been defined, we actually could write a
different definition of [x]:
[x] =def [x,x]
(from analogy with the definition {x} =def {x,x} given
by Suppes for ZFC) and prove as a theorem, tommy1729's
infamous remark:
Ax x=[x].
But we can just take this as a definition until enough
axioms to prove it as a theorem have been agreed upon.
In any rate, these are the correct definitions for []
and [x] that are required for the proof to work. The
correct definitions don't satisfy MoeBlee's lines 2 or
4 of his proof, and so MoeBlee's proof does not show
that TST is inconsistent.
Brian Chandler
> Post numbers? Maybe those newsreaders that I can't afford
> have post numbers, but I have no access to them.
I'm fascinated. Can you actually name any (1) of these newsreaders you
can't afford?
Brian Chandler
MoeBlee
MoeBlee below:
> > 1 Ax x=[x] .... axiom
> > 2 Ay(y in [x] <-> y=x) ... from tommy1729's own qualifying statement
> > 3 Ax x in [x] ... from 2
> > 4 Ex Ay y not-in x ... axiom
> > 5 Ay y not-in x ... existential instantiation from 4
> > 6 x = [x] .... from 1
> > 7 Ay y not-in [x] ... from 5, 6
> > 8 ~Ey y in [x] ... from 7
> > 9 x in [x] ... from 2
> > 10 Ey y in [x] ... from 9
> > But 8 and 10 is a contradiction.
> > You are welcome to say exactly what is not first order logic applied
> > to his axioms.
> > Or in simple English:
> > There is an x such that for all y, y not in x (_empty set axiom_). So
> [emphasis mine]
> > let x be such that for all y, we have y not in x. But for all x, we
> > have x=[x] and x in [x], so x in x. So x itself is a y such that y in
> > x. Contradiction.
>
> Already, we can see that MoeBlee's proof _does_ use the
> empty "set" after all.
I said absolutely nothing about "set" in that proof.
> Essentially, he claims that from
> "x=[x]" we prove that every object is a "singleton," yet
> the empty "set" is not a "singleton," hence what he
> believes to be a contradiction.
Okay, in conversational terms. But the proof itself relies only on
formulas.
> the errors are in lines 2 and 4. MoeBlee believes that
> these are accurate renderings of tommy1729's axioms from
> English to symbolic language of the theory, but I don't
> believe that these are accurate at all.
Look at tommy's own statement about what he meant by '[]'. If my
symbolization is not a perfect rendering of what tommy himself said,
then let tommy say so, or show just what is not faithful in my
rendering.
> In December, MoeBlee pointed out that his line 2 is
> derived from tommy1729's remark, as follows:
>
> > "[x] = is the set that contains x ( only )
> > however x may be a set itself."
>
> To MoeBlee, or anyone accustomed to working in ZFC, this
> would appear to define [x] as a singleton, a set whose
> lone element is x. But in mereology, we _can't_ conclude
> from this remark that [x] is a "singleton" in the sense
> of line 2, that any y in [x] must be x itself.
Damn it! tommy didn't say "This is mereology and when I say "[x] = is
the set that contains x ( only )" I don't mean anything about sets but
I mean something about mereology which the poster Transfer Principle
will clarify at a later date." Moreover, I didn't borrow ANYTHING from
an understanding of ZFC. Rather, when Tommy says "[x] = is the set
that contains x ( only )" that simply is symbolized as
Ay(yex <-> y=x).
x is the object (whether set of WHATEVER) such that the only object
that bears the "e-relation" (WHATEVER that might be) to x is x itself,
and x does bear the e-relation to itself.
It's not complicated.
Coming around LATER to say, in effect, "Oh this is REALLY something
else, something about mereology that is not actually articulated by
tommy" is simply REVISING tommy. As I SAID, tommy's system is
inconsistent UNLESS he revises it. That you find ways to revise it
does not contradict that what he himself specified is inconsistent.
> Similarly, line 4 is based on a ZFC definition of empty
> set, but we can't conclude in mereology that [] is a set
> such that for any y, y not-in [].
Damn it! tommy HIMSELF said he was using the ZFC axiom!
And I said NOTHING about "SET". Rather, tommy said he adopts that ZFC
axiom (among others) and I simply wrote down the axiom as a line in
the argument! Sheesh! What is your TRIP, man?!
> Indeed, the use of the word "in" to represent the lone
> two-place predicate of the theory is a bit awkward,
> since it doesn't work the same way as "e" in ZFC.
But the word "in" by me makes use of no sense OTHER than just to stand
for the symbol 'e', just as that symbol occurs in the exact axioms
that tommy says he adopts. Use ANY symbol, such as "@" or whatever,
and we still get the contradiction.
> This
> is why galathaea suggested that tommy1729 use the symbol
> "c" to represent the lone two-place predicate, so that
> someone like MoeBlee wouldn't have made the mistakes that
> he ends up making.
Use "c" then! Replace every instance of "in" or "e" by "c". Fine, the
contradiction is still present, MERELY by the formulas that tommy
HIMSELF says he adopts as certain of his axioms, along with his OWN
statement of what "[]" stands for.
> So what are the correct interpretations of tommy1729's
> remarks in English that MoeBlee should have used instead
> of his lines 2 and 4. Let's compare MoeBlee's incorrect
> ZFC-based Empty Set Axiom with the correct mereological
> Empty Set Axiom:
>
> ZFC Empty Set:
>
> > 4 Ex Ay y not-in x ... axiom
>
> Mereological Empty Set:
> Ex Ay xcy
WHAT?! tommy specified no such axiom! He said he adopts the ZFC axiom.
So replace "in" by "c" (it matters not what SYMBOL we use):
ExAy ~ycx.
Then replace 'in' by 'c' in the rest of my proof. It makes no
difference!
> So this object x is a part (not an "element," but a
> _part_) of every set. At first, this doesn't necessarily
> sound like an empty set. But we can prove that this set
> must be the smallest possible set.
Why in the world are you trying to derive an argument about tommy's
system by referencing some VERY DIFFERENT system from what he HIMSELF
specified?
The question was whether TOMMY'S system is consistent, not whether
YOUR VERY DIFFERENT system is consistent. And this is not just a
matter of replacing "in" or "e" with "c" but rather that tommy said he
adopts the ZFC axiom (even if we use "c" instead of "in" or "e"), and
he did NOT specify that he ESCHEWS
ExAy ~ycx
and instead adopts
ExAy xcy.
And, again, whether you call it "c" or "e" or "in" or "part of", the
ZFC axiom (WHICH tommy adopts) is (now using "c"):
ExAy ~ycx
and NOT
ExAy xcy.
> Proof:
> 1 Ex Ay xcy ... Mereological Empty Set
NO, the axiom that TOMMY adopted is:
ExAy ~ycx.
(If we use "c" instead of "e" or "in".)
> 2 Ay xcy ... Existential Instantiation
> 3 Ax Ay (xcy & ycx) -> x=y ... Antisymmetry Axiom
> (mentioned in my last post)
WHAT?! tommy adopted no such axiom!
Though, actually, ADDING an axiom won't make an inconsistent system
consistent anyway.
Anyway, if I recall, tommy adopted extensionality:
Axy(Az(zcx <-> xcy) -> x=y).
(If we use "c" instead of "e" or "in".)
That's enough for today. I'll leave off the rest of your post.
PLEASE, get straight the difference between TOMMY'S axioms and
definitions as HE posted them and YOUR very different axiom(s)!
One more though:
> [x] =def x
But that is NOT what TOMMY said, is it? What is your problem that you
can't distinguish what OTHER people say from what YOU would revise it
to?
Please do me a favor: Just take a moment to reflect on the notion that
what OTHER people say is not necessarily what YOU think they should
have said.
Now, if YOU wish to propose some OTHER theory from tommy's or even to
substantially REVISE what tommy posted, then fine; you might devise
some consistent theory. But what I said stands: tommy's system is
inconsistent UNLESS he revises it. I.e., obviously, if we REVISE
tommy's system we might get a consistent one.
MoeBlee
Transfer Principle
I performed a Google search for the words newsreader+"per
month" in order to find newsreaders with monthly fees. Any
newsreader with a monthly fee, I can't afford.
The search results are:
www.forteinc.com/
www.newsreader.com/faq.htm
www.newsrover.com/service.htm
www.usenet-replayer.com/.../de.comm.software.newsreader.html
What I don't want is for this to turn into yet another
argument about newsreaders. The point is that MoeBlee
asked for a post number. Google doesn't give me access
to post numbers. It seems reasonable to deduce that if
I had a more competent newsreader, I would have access
to these post numbers after all.
Maybe the newsreaders which provide post numbers are
rather expensive. Maybe such newsreaders are free. The
point is that I don't have access to post numbers --
and I'm not going to download a newsreader, even if it
is free, for the sole purpose of finding one little
post number to give to MoeBlee.
The one thing that will drive me to go to another
newsreader -- even if it is free -- will be if enough
posters follow Phil Carmody's advice and start a
blanket killfile of Google. Only then will I search for
another newsreader, and hopefully it will be free.
Tonico
Ah, lwalke! Certainly your disguise was a rather poor one when you
decided to "defend" the stupidities that Tommy/Amy has posted in the
past, but that last parraph completely discovers you: so "you don't
believe" so and so, uh? And who gives half a damn what you "believe"
or not in this? Unless tommy, or whoever, doesn't make crystal clear
what he means with his nonsenses, and this is already way above
tommy's capabilities, we can understand from his ramblings what is
written in plain english and/or what is standard within mathematics.
Again, as usual, you insist in giving meaning, signification and
intention to OTHER people's messages, and I must say that you
miserably fail in this.
Anyway, welcome back: some may have missed you here.
Regards
Tonio
Jesse F. Hughes
> What I don't want is for this to turn into yet another
> argument about newsreaders. The point is that MoeBlee
> asked for a post number. Google doesn't give me access
> to post numbers. It seems reasonable to deduce that if
> I had a more competent newsreader, I would have access
> to these post numbers after all.
What Moe probably meant to request was the message-ID, which is
available if you hit the mis-named "Show original" link under "More
options" when reading a post from Google. (Of course, Google
*doesn't* show the original post. Instead, they obfuscate anything
that looks like an email address. Bah.)
But don't let that stop your whine about how you're so poor, you can't
afford free access to Usenet (except through Google).
And, the primary purpose of Moe's request was that you give verifiable
information regarding where he said what he said. All this nonsense
about "post numbers" (a nonsensical term that resulted because you
mistook a verb for a noun) is beside the point.
--
"No sane person actually believes that religion mumbo-jumbo[...] Of
course, very few people [...] would ever admit that they don't
actually believe any of it. Of course I can't prove this, so don't
ask. But you know it's true as well as I do." -- Mensanator
Transfer Principle
Oh, really? Let's repeat MoeBlee's line from last Christmas
once again:
> > > There is an x such that for all y, y not in x (_empty [...] axiom_).
> > [emphasis mine]
So what's the word from the original December post between
the words "empty" and "axiom"?
> > > "[x] = is the set that contains x ( only )
> > > however x may be a set itself."
> > To MoeBlee, or anyone accustomed to working in ZFC, this
> > would appear to define [x] as a singleton, a set whose
> > lone element is x. But in mereology, we _can't_ conclude
> > from this remark that [x] is a "singleton" in the sense
> > of line 2, that any y in [x] must be x itself.
> Damn it! tommy didn't say "This is mereology and when I say "[x] = is
> the set that contains x ( only )" I don't mean anything about sets but
> I mean something about mereology
Was tommy1729 discussing mereology? Let's go back to yet
another old post. This was originally posted over a year
ago, on May 10, 2008, at 1657 GMT (1857 Central European
Summer Time, the timezone from which tommy1729 posted),
in the thread titled, "Denis Feldmann proved the Riemann
Hypothese [sic]!!!!":
"1) Denis feldmann doesnt know what the hell _Mereology_ is.
[emphasis mine]
"8) Denis tries to rediculize x = [x] but only makes a fool
out of himself by implying set theory ( mereology actually )
does directly relate to RH and he knows nothing about RH NOR
Mereology. ( despite efforts of lwalke3 )
"9) Denis feldmann posted the most crankiest post on sci.math
ever , since he claimes short proof of RH. SURE he might argue
it is based on assuming the correctness of my ideas , but even
then, as said , the logic is flawed and things are unrelated ,
whereas its really based on NOT UNDERSTANDING MEREOLOGY as
lwalke tried to explain him.
"10) denis cant do proofs. denis cant do logic. denis cant do
mereology. denis didnt know the gudermannian. dennis supported
davids "integral" x dx = 2x (or something wrong like that) so
cant do calculus. denis avoids number theory subjects."
As we can see, after galathaea and I told tommy1729 that
what he was doing was mereology, he agreed, and so he
emphasizes to Feldmann in this post that what he was
doing was mereology, a subject about which Feldmann even
_admits_ later in the thread that he doesn't know well.
Back then Feldmann, just as MoeBlee does now, believed
that TST was inconsistent, and so TST would prove all
theorems, including the Riemann Hypothesis. Then
tommy1729 explained why it was not so.
So we see that even tommy1729 himself admits that his
theory is mereological.
> Rather, when Tommy says "[x] = is the set
> that contains x ( only )" that simply is symbolized as
> Ay(yex <-> y=x).
> x is the object (whether set of WHATEVER) such that the only object
> that bears the "e-relation" (WHATEVER that might be) to x is x itself,
> and x does bear the e-relation to itself.
> It's not complicated.
But in mereology, one can't even prove that there even
_exists_ an object such that the only object that bears
the "e-relation" (or "c-relation") to it is x itself. In
fact, galathaea has pointed out that in the flattened
mereology, any object that is c-related to x is also
related to all the objects that are c-related to x. In
other words, the c-relation is _transitive_.
Many times has tommy1729 expressed his desideratum that
elementhood and subsethood be collapsed into a single
concept, the c-relation of parthood. Many times,
galathaea has stated that the flattened mereology will
accomplish tommy1729's desideratum. And tommy1729 has
accepted her explanation.
> Coming around LATER to say, in effect, "Oh this is REALLY something
> else, something about mereology that is not actually articulated by
> tommy"
[...] but was articulated by _galathaea_, and tommy1729
has agreed with her.
In the flattened mereology, the parthood relation "c"
is reflexive, antisymmetric, and transitive. I wish
that tommy1729 could say something like: "Here are the
axioms of TST. The primitive 'c' is reflexive,
antisymmetric, and transitive," or something to that
effect -- but most likely, tommy1729 doesn't know how
to articulate his desiderata into rigorous, symbolic,
mereological axioms. That's why galathaea, who likely
knows more about mereology than everyone else in this
thread _combined_, helped him learn what the flattened
mereology is and how it satisfies his desiderata.
> > Similarly, line 4 is based on a ZFC definition of empty
> > set, but we can't conclude in mereology that [] is a set
> > such that for any y, y not-in [].
> Damn it! tommy HIMSELF said he was using the ZFC axiom!
Really? Most of the time, tommy1729 has said that he
is _not_ working in ZFC. Also, an object x such that
for any y, y not-in x, doesn't even _exist_ in the
flattened mereology, which tommy1729 has agreed with
galathaea that he is using. Of course, if one assumes
in a theory in which such an object doesn't exist that
such an object exists, of course one is going to
arrive at a contradiction!
> And I said NOTHING about "SET".
OK, replace "set" with "object" then. Sometimes
tommy1729 refers to his objects as "sets," and other
times he doesn't.
> > Mereological Empty Set:
> > Ex Ay xcy
> WHAT?! tommy specified no such axiom! He said he adopts the ZFC axiom.
He said he adopts galathaea's flattened mereology.
> > [x] =def x
> But that is NOT what TOMMY said, is it?
It is a definition satisfying eliminability, that
obviously satisfies tommy1729's desiderata. There might
be another possible definition for [x] that also
satisfies his desiderata, but such a definition would
rely on axioms that I'm not sure that even galathaea
herself has mentioned. MoeBlee's definition for [x], on
the other hand, doesn't satisfy tommy1729's desiderata.
Notice that MoeBlee suggests that we defer to the
inventor of the notation [x] in order to find out how
the notation is being used. OK -- except that tommy1729
isn't the inventor of the notation [x], and for that
matter, neither was galathaea. I've forgotten this
myself, until I discovered what I wrote on this a year
ago in that same thread:
> > So if [x] doesn't mean {x}, then what does it mean? As I
> > stated earlier, the first poster to use the notation [x] was not
> > tommy1729, but Zuhair (over at sci.logic). So we must
> > determine what Zuhair means by [x].
So _zuhair_, not tommy1729, invented the notation [x]! So
we must see whether MoeBlee's alleged inconsistency proof
is still valid if we use the definition of [x] that the
actual _inventor_ of the notation, _zuhair_, used. Maybe
I should search for the thread in which _zuhair_ defines
the notation [x].
> Please do me a favor: Just take a moment to reflect on the notion that
> what OTHER people say is not necessarily what YOU think they should
> have said.
Come to think of it, there's a reason this keeps happening,
namely that I keep arguing with MoeBlee and others about
what so-called "cranks" believe, but then the so-called
"crank" leaves the thread. I see that tommy1729 isn't
posting in this thread anymore. So once again, there's no
way to know what tommy1729 really believes.
So once again, I leave this thread until the OP tommy1729
posts again.
Brian Chandler
> On Jul 6, 4:04 pm, Brian Chandler <imaginator...@despammed.com> wrote:
> > A thinly-disguised LWalke wrote:
(Sorry, I think I missed the dots off the end of your name, Mr
Principle...)
> > > Post numbers? Maybe those newsreaders that I can't afford
> > > have post numbers, but I have no access to them.
> > I'm fascinated. Can you actually name any (1) of these newsreaders you
> > can't afford?
>
> I performed a Google search for the words newsreader+"per
> month" in order to find newsreaders with monthly fees. Any
> newsreader with a monthly fee, I can't afford.
>
> The search results are:
>
> www.forteinc.com/
Congratulations! The other three are a couple of news feed providers
and a 404, but this first one does indeed offer a newsreader which one
can buy for $29. Sadly I won't be able to try it, because it only
appears to work on an operating system whose vendor insists is the
cheapest (keyword: "TCO"), but I'm fortunate not to be so financially
constrained to use it, but I can afford to use Linux instead.
> www.newsreader.com/faq.htm
> www.newsrover.com/service.htm
> www.usenet-replayer.com/.../de.comm.software.newsreader.html
Oh, minor clarification: of course the dots after "Principle" are just
run-on dots. I'm not under the false impression that your new name
also ends in dots.
Anyway, carry on chanelling now.
Brian Chandler
amy666
>
> Come to think of it, there's a reason this keeps
> happening,
> namely that I keep arguing with MoeBlee and others
> about
> what so-called "cranks" believe, but then the
> so-called
> "crank" leaves the thread. I see that tommy1729 isn't
> posting in this thread anymore. So once again,
> there's no
> way to know what tommy1729 really believes.
>
> So once again, I leave this thread until the OP
> tommy1729
> posts again.
well , i posted already alot about my ideas.
and you have quite a good idea about what i believe.
i am far from " gone " in this thread.
i just
1) didnt want to interupt the conversation
2) despite still intrested in mereology and TST ( fixed point set theory ) i also regret that EVERY POST changes subject to set theory / ZFC / mereology.
3) i am communicating my proofs to others and have thus less time.
but thanks for defending me and showing the inconsistancy of others.
regards
tommy1729
MoeBlee
Yes, really. Where in that proof of mine you just quoted do you see
the word "set", or for that matter, anything other than first order
logic applied to tommy's axiom plus a symbolization of his definition
of "[]"?
> Let's repeat MoeBlee's line from last Christmas
> once again:
>
> > > > There is an x such that for all y, y not in x (_empty [...] axiom_).
> > > [emphasis mine]
>
> So what's the word from the original December post between
> the words "empty" and "axiom"?
OH PLEASE!!! You could call it the "empty schnozzola axiom" for that
matters! You are SO dense!
It was TOMMY who said he adopted those axioms. The NAME of the axiom
is "the empty set axiom", but the ONLY thing I USED is the FORMULA:
ExAy ~yex.
Sheesh!
So what?! He never (at least in the thread I made my proof, or in any
thread I happened to read) REstated his axioms or his definition of
'[ ]' in any other form than he originally gave them. Just the fact
that at some point he mumbles something about "mereology" or that '[]'
is to be regardes as "merelogoy" doesn't provide an alternative
formluation to the one HE GAVE.
> > Rather, when Tommy says "[x] = is the set
> > that contains x ( only )" that simply is symbolized as
> > Ay(yex <-> y=x).
> > x is the object (whether set of WHATEVER) such that the only object
> > that bears the "e-relation" (WHATEVER that might be) to x is x itself,
> > and x does bear the e-relation to itself.
> > It's not complicated.
>
> But in mereology,
WHAT mereology? I mean, WHAT SPECIFIC axioms or definitions that TOMMY
gave?
And it wouldn't MATTER even if he ADDED mereological axioms. He said
he adopted certain axioms (and he gave a certain definition of '[ ]').
All I did in my proof was use first order logic on those axioms and
that definition. Whether you call it 'mereology', 'tommyology' or
'stupidology', doesn't make an inconsistent set of axioms consistent!
> one can't even prove that there even
> _exists_ an object such that the only object that bears
> the "e-relation" (or "c-relation") to it is x itself.
Please, show what exact step in my proof is not first order logic
applied to tommy's axioms, whether written with 'e' or with 'c'. And I
mean tommy's axioms and definitions AS HE WROTE THEM.
> In
> fact, galathaea has pointed out that in the flattened
> mereology, any object that is c-related to x is also
> related to all the objects that are c-related to x. In
> other words, the c-relation is _transitive_.
You can point out all kinds of wonderful things about whatever
mereological theory you wish to discuss. That doesn't change the
inconsistency of tommy's system AS HE WROTE IT, and whatever he CALLS
it.
> Many times has tommy1729 expressed his desideratum that
> elementhood and subsethood be collapsed into a single
> concept, the c-relation of parthood. Many times,
> galathaea has stated that the flattened mereology will
> accomplish tommy1729's desideratum. And tommy1729 has
> accepted her explanation.
Desiderata are not axioms! If tommy desires something different, then
let him provide different axioms from the ones he actually GAVE.
What don't you understand about this?
> > Coming around LATER to say, in effect, "Oh this is REALLY something
> > else, something about mereology that is not actually articulated by
> > tommy"
>
> [...] but was articulated by _galathaea_, and tommy1729
> has agreed with her.
>
> In the flattened mereology, the parthood relation "c"
> is reflexive, antisymmetric, and transitive. I wish
> that tommy1729 could say something like: "Here are the
> axioms of TST. The primitive 'c' is reflexive,
> antisymmetric, and transitive," or something to that
> effect -- but most likely, tommy1729 doesn't know how
> to articulate his desiderata into rigorous, symbolic,
> mereological axioms.
Then my point is UPHELD. I said tommy's system is inconsistent unless
he revises it.
> That's why galathaea, who likely
> knows more about mereology than everyone else in this
> thread _combined_, helped him learn what the flattened
> mereology is and how it satisfies his desiderata.
Great, then that will be a DIFFERENT system from the one I proved
inconsistent. What don't you understand about this?
> > > Similarly, line 4 is based on a ZFC definition of empty
> > > set, but we can't conclude in mereology that [] is a set
> > > such that for any y, y not-in [].
> > Damn it! tommy HIMSELF said he was using the ZFC axiom!
>
> Really?
Yes, really. Look at the post in which tommy gave his axioms. He
listed some axioms, which he called either "set theory axioms" or
"ZFC axioms" (I don't recall which).
> Most of the time, tommy1729 has said that he
> is _not_ working in ZFC.
I didn't say he is working in ZFC. I said he adopted certain ZFC
axioms. In my proof I used only the ZFC axioms that HE said he
adopted.
> Also, an object x such that
> for any y, y not-in x, doesn't even _exist_ in the
> flattened mereology, which tommy1729 has agreed with
> galathaea that he is using. Of course, if one assumes
> in a theory in which such an object doesn't exist that
> such an object exists, of course one is going to
> arrive at a contradiction!
>
> > And I said NOTHING about "SET".
>
> OK, replace "set" with "object" then. Sometimes
> tommy1729 refers to his objects as "sets," and other
> times he doesn't.
>
> > > Mereological Empty Set:
> > > Ex Ay xcy
> > WHAT?! tommy specified no such axiom! He said he adopts the ZFC axiom.
>
> He said he adopts galathaea's flattened mereology.
In that thread, or in any other thread offshoot, where did tommy say
that he is throwing OUT the ZFC empty set axiom and using Ex Ay xcy
instead?
How ridiculous you are!
Someone says, "I also adopt the set theoretical empty set axiom" or "I
also adopt the ZFC empty set axiom" (which is virtually unanimously
understood as ExAy ~yex) but we are supposed to take that to mean he
actually adopts some COMPLETELY different principle!
> > > [x] =def x
> > But that is NOT what TOMMY said, is it?
>
> It is a definition satisfying eliminability, that
> obviously satisfies tommy1729's desiderata.
So what? It is NOT the definition he gave. The definition he gave is
the one I used.
> There might
> be another possible definition for [x] that also
> satisfies his desiderata, but such a definition would
> rely on axioms that I'm not sure that even galathaea
> herself has mentioned. MoeBlee's definition for [x], on
> the other hand, doesn't satisfy tommy1729's desiderata.
Then HE needs to restate his definition, because, AS HE GAVE IT, he
has an inconsistent system.
> Notice that MoeBlee suggests that we defer to the
> inventor of the notation [x] in order to find out how
> the notation is being used. OK -- except that tommy1729
> isn't the inventor of the notation [x], and for that
> matter, neither was galathaea. I've forgotten this
> myself, until I discovered what I wrote on this a year
> ago in that same thread:
I didn't state a GENERAL principle that we must use the definition
given by any inventor of a notation. Rather, I just said that MY proof
happens to be based on tommy's own definition.
> > > So if [x] doesn't mean {x}, then what does it mean? As I
> > > stated earlier, the first poster to use the notation [x] was not
> > > tommy1729, but Zuhair (over at sci.logic). So we must
> > > determine what Zuhair means by [x].
>
> So _zuhair_, not tommy1729, invented the notation [x]!
So what? My proof is not about inventions of notations!
> So
> we must see whether MoeBlee's alleged inconsistency proof
> is still valid if we use the definition of [x] that the
> actual _inventor_ of the notation, _zuhair_, used.
No we don't! That is insane! Notations are used by many people in many
ways with many different definitions. To evaluate TOMMY's system, I'm
going to refer to TOMMY's definition, not to some OTHER definition.
Man, you are really running this whole thing past even your ordinary
ridiculousness.
> Maybe
> I should search for the thread in which _zuhair_ defines
> the notation [x].
>
> > Please do me a favor: Just take a moment to reflect on the notion that
> > what OTHER people say is not necessarily what YOU think they should
> > have said.
>
> Come to think of it, there's a reason this keeps happening,
> namely that I keep arguing with MoeBlee and others about
> what so-called "cranks" believe,
WHATEVER tommy "believes" (if even the word 'believe' makes sense
regarding tommy), he posted his axioms and definitions. What he posted
is inconsistent, AS HE POSTED IT. That's all I've said.
> but then the so-called
> "crank" leaves the thread. I see that tommy1729 isn't
> posting in this thread anymore. So once again, there's no
> way to know what tommy1729 really believes.
He may BELIEVE all kinds of things. I went by what he POSTED.
> So once again, I leave this thread until the OP tommy1729
> posts again.
MoeBlee
MoeBlee
> but thanks for defending me and showing the inconsistancy of others.
WHAT inconsistency of others?
MoeBlee
Transfer Principle
> On Jul 7, 1:40 am, Transfer Principle <lwal...@lausd.net> wrote:
> > the errors are in lines 2 and 4. MoeBlee believes that
> > these are accurate renderings of tommy1729's axioms from
> > English to symbolic language of the theory, but I don't
> > believe that these are accurate at all.
> Ah, lwalke! Certainly your disguise was a rather poor one when you
> decided to "defend" the stupidities that Tommy/Amy has posted in the
> past, but that last parraph completely discovers you: so "you don't
> believe" so and so, uh? And who gives half a damn what you "believe"
> or not in this?
And who gives half a damn what Tonio believes or not
in this? Just because Tonio believes that the things
tommy1729 posts are "stupidities" doesn't mean that
everyone must agree with his opinion.
I'm giving the reasons why I don't consider what
tommy1729 posts to be stupid. Tonio is free to agree
or disagree with my opinion, and I don't give half a
damn that Tonio disagrees with my opinion.
> Unless tommy, or whoever, doesn't make crystal clear
> what he means with his nonsenses, and this is already way above
> tommy's capabilities
It's probably above Tonio's capabilities, too. And I
admit that it's above my capabilities too. What Tonio
calls "stupidity" is what others call "mereology," and
the real expert on mereology is galathaea. And so her
capabilities in mereology is way above those of anyone
else on this thread.
> Again, as usual, you insist in giving meaning, signification and
> intention to OTHER people's messages
I'd much rather give meaning to other people's messages
than simply dismiss them as "stupidities."
I.N.R.I. Logic
Well spoken and I applaud you for taking a stance in the name of
constructivity.
Thanks!
Transfer Principle
> On Jul 6, 9:13 pm, Transfer Principle <lwal...@lausd.net> wrote:
> > Oh, really?
> Yes, really. Where in that proof of mine you just quoted do you see
> the word "set", or for that matter, anything other than first order
> logic applied to tommy's axiom plus a symbolization of his definition
> of "[]"?
I concede that MoeBlee's proof consists of FOL= applied to
some axioms. I don't concede that axioms to which MoeBlee
applied FOL= are the axioms that tommy1729 had in mind.
> > But in mereology,
> And it wouldn't MATTER even if he ADDED mereological axioms. He said
> he adopted certain axioms (and he gave a certain definition of '[ ]').
> All I did in my proof was use first order logic on those axioms and
> that definition. Whether you call it 'mereology', 'tommyology' or
> 'stupidology', doesn't make an inconsistent set of axioms consistent!
In December, galathaea, who knows more about mereology than
anyone else in this thread, failed to convince MoeBlee that
his so-called inconsistency proof is invalid. If MoeBlee
won't be convinced by galathaea, and she knows more about
mereology than I do, why would I have any better luck than
she did in convincing him that he doesn't have a valid
proof that TST is inconsistent?
And so I will give up trying to convince MoeBlee, since I
can't find anything that will convince him that he doesn't
have an inconsistency proof.
But I do have one more comment to make here:
> > He said he adopts galathaea's flattened mereology.
> Someone says, "I also adopt the set theoretical empty set axiom" or "I
> also adopt the ZFC empty set axiom" (which is virtually unanimously
> understood as ExAy ~yex)
The Empty Set Axiom is virtually unanimously understood? How
ironic that MoeBlee would say this, because I've noticed
that in another thread, MoeBlee is in a debate with David
Ullrich and several other mathematicians over exactly what
the Empty Set Axiom is, and in particular, whether an Axiom
of Infinity is needed to prove that the empty set exists.
There appears to be three schools of thought here:
1. An explicit Empty Set Axiom is required to prove that
the set 0 exists in ZFC.
2. The existence of 0 is provable from the axioms of
Infinity and Separation Schema.
3. The existence of 0 is provable from the axioms of
FOL= and Separation Schema.
Ullrich argues (2). MoeBlee argues (3). So there is hardly
a consensus on the Empty Set Axiom, contrary to what MoeBlee
posts in this thread! Ironically, there's probably more of a
consensus among _mereologists_ about the smallest object
than there is among _set theorists_. The only debate is
whether the object [] should be called "the empty set," or
"bottom," or some other name.
I was tempted to post in the Ullrich empty set thread,
but have avoided doing so until now. But now that MoeBlee
has started talking about the "virtual unanimity" of the
Empty Set Axiom among set theorists, I will jump into the
Ullrich thread after all.
Transfer Principle
You're welcome! Posters like MoeBlee and Tonio often claim
that they are open-minded about set theories other than
ZFC, including mereology and constructivist set theory,
yet their behavior in threads like this prove otherwise.
Transfer Principle
> > So once again, I leave this thread until the OP
> > tommy1729 posts again.
> well , i posted already alot about my ideas.
> and you have quite a good idea about what i believe.
> i am far from " gone " in this thread.
> i just
> 1) didnt want to interupt the conversation
> 2) despite still intrested in mereology and TST ( fixed point set theory ) i also regret that EVERY POST changes subject to set theory / ZFC / mereology.
Sorry about that. I was the one who first mentioned TST,
I wanted to know whether tommy1729's proposed proof of
Twin Primes was written in the theory TST. As tommy1729
already mentioned, the proof requires only simple
arithmetic (presumably PA), and thus isn't set theoretic
at all, whether ZFC or TST.
But then MoeBlee insised that TST is inconsistent again,
and that lead to yet another debate about TST.
> 3) i am communicating my proofs to others and have thus less time.
> but thanks for defending me and showing the inconsistancy of others.
You're welcome!
Tonico
As usual, lwalke, when you get excited you lose the track. The problem
since long ago has been twofold: one, that tommy's ramblings are about
things he hardly knows anything about and are full of undefined or ill-
defined stuff, and two that YOU have decided to undertake the task of
explaining and clarifying what tommy writes, usually in a way that
assigns to other people intentions, sayings and claims that those
other peopel NEVER intented, said or claimed.
You deeply admire, or like, or sympathize with tommy, and you hardly
want to make some sense out of his nonsensical posts. Fine, that's
good (let's be nice), but then you get into discussion with other
people, and when that other people points that tommy's posts make no
sense here or there, you decide that tommy actually meant this and
that in that part of his post. how do you know? And if he did, why
didn't he explicitly do so when he wrote his posts?
This all in an old business, and the last time you dared to give
significations, intentions, definitions, etc. to tommy's AND other
partipants' posts here, people made it clear to you that what you were
doing was a stupid, and sometimes even annoying, thing.
Stop assigning things to others, stop inventing stuff about others,
and stop making up definitions, clarifications and etc. to tommy's
writings: that is HIS job. Can't you understand this?
Lastly, a new example in this reincarnation as transfer principle of
yours, lwalke: you wrote that "What Tonio calls "stupidity" is what
others call "mereology". Well, let's see you pointing the exact place
where I called mereology, or ANYTHING equivalent to it, a stupidity.
I did call tommy's post stupidities, and one again you're making up
stuff.
Too bad you changed only your nick
Regards
Tonio
Herbert Newman
> Too bad you changed only your nick
No other way! When he searched for his brain (for replacement), he didn't
find it.
Herb
Transfer Principle
> On Jul 8, 7:21 am, Transfer Principle <lwal...@lausd.net> wrote:
> > You're welcome! Posters like MoeBlee and Tonio often claim
> > that they are open-minded about set theories other than
> > ZFC, including mereology and constructivist set theory,
> > yet their behavior in threads like this prove otherwise.
> As usual, lwalke, when you get excited you lose the track. The problem
> since long ago has been twofold: one, that tommy's ramblings are about
> things he hardly knows anything about
...and that Tonio hardly knows anything about either. The
only real expert on this subject is galathaea.
> YOU have decided to undertake the task of
> explaining and clarifying what tommy writes, usually in a way that
> assigns to other people intentions, sayings and claims that those
> other peopel NEVER intented, said or claimed.
Let's see what tommy1729 wrote about my posts earlier:
"and you have quite a good idea about what i believe."
So according to tommy1729 _himself_, I have quite a
good idea about what tommy1729 believes, contrary to
Tonio's stating that I claim what tommy1729 never
intended at all. So I have a better idea than Tonio
about what tommy1729 believes.
> You deeply admire, or like, or sympathize with tommy, and you hardly
> want to make some sense out of his nonsensical posts. Fine, that's
> good (let's be nice), but then you get into discussion with other
> people, and when that other people points that tommy's posts make no
> sense here or there, you decide that tommy actually meant this and
> that in that part of his post. how do you know?
I know from reading the discussion between tommy1729 and
galathaea about the subject of mereology. Therefore, my
interpretation about what tommy1729 intends is based on
what galathaea wrote about it.
> And if he did, why
> didn't he explicitly do so when he wrote his posts?
It's because tommy1729 doesn't know much about mereology --
and is still trying to _learn_ more about mereology, which
is more than we can say about Tonio.
> This all in an old business, and the last time you dared to give
> significations, intentions, definitions, etc. to tommy's AND other
> partipants' posts here, people made it clear to you that what you were
> doing was a stupid, and sometimes even annoying, thing.
And dismissing tommy1729's posts as mere "stupidities" is
sometimes an even more annoying thing.
Tonio is right that tommy1729 doesn't know much about how
mereology works. When galathaea saw this, she took it upon
herself to _teach_ tommy1729 how mereology works, rather
than simply call him stupid, as Tonio has done.
> Lastly, a new example in this reincarnation as transfer principle of
> yours, lwalke: you wrote that "What Tonio calls "stupidity" is what
> others call "mereology". Well, let's see you pointing the exact place
> where I called mereology, or ANYTHING equivalent to it, a stupidity.
> I did call tommy's post stupidities
Right, and based on tommy1729's discussion with galathaea,
his post _is_ equivalent to the flattened mereology. Thus,
by calling tommy1729's post "stupidities," Tonio _is_
calling something equivalent to mereology a "stupidity."
> Too bad you changed only your nick [and not your brain,
> adds Newman.]
Yeah, Tonio and Newman would like that. They'd love it if
I would change to a brain that's "intelligent" enough to
know that Tonio and Newman are 100% right and tommy1729's
posts are 100% "stupidities." I'd much rather change to a
brain "intelligent" enough to finish helping tommy1729
write a complete axiomatization to TST that would make
the theory equiconsistent with Z+proper classes. It's too
bad I can't change to that brain.
Tonico
Who EVER talked, or even hinted, about being "right" or wrong"? Do you
see how you make stuff up, lwalke? When did I even hinted about me
being right and tommy being wrong in this or that? His nonsense many
times isn't even wrong to talk about: he uses symbols with a well
defined signification in maths, and when somebody points out that what
he wrote he says: "Oh, wait: that symbol wasn't meant to be understood
like that, but like this"....like using in a mathematical paper the
symbol 7, and then write that in the naturals we have that 7 + 1 = 10,
and when somebody notes the nonsense then we jump and say: wait! when
I used the symbol "7" I actually meant what others call "9".
You wrote bove that tommy's post (about mereology, I presume) is
equivalent to the flattened mereology. What is this? I don't know, and
I don't intend to play it like I do. In fact, googling "flattened
mereology" I found...nothing except YOUR own words in past threads
about this. Of course, this does not mean that thing is worthless, but
I can't see how you can know that what tommy wrote is equivalent to
that thing...unless you can tell me, please, what the heck "flattened
mereology" is.
And, of course, it could just be that this thing just doesn't exist in
the web or even that I just couldn't find stuff about it.
You have decided that galathea knows better than ALL THE REST about
mereology. Why? Who knows...perhaps because she wrote more about it
than anyone else?
You finally conceede that tommy knows little about mereology; too bad
you didn't continue on this track and deduced the logical deduction:
tommy's talks, and a lot!, about something he doesn't know much about.
And it is not like he asks, explores or stuff. No, he CLAIMS,
determines and consistently rambles about that stuff he barely knows
about.
Then you wrote this pearl of argumentation that I hope someoen will
treasure and chersih as it deserves:
" I know from reading the discussion between tommy1729 and galathaea
about the subject of mereology. Therefore, my interpretation about
what tommy1729 intends is based on
what galathaea wrote about it."
Hmmm, let's see if we can make some order in here: you know about
mereology from reading the thread(s) where tommy and galathea talked
about this (and this did NOT stopped you from discussing over and over
with people that know a lot about set theory and stuff)...and then you
interpreted tommy's intentions (another person's intentions) based on
what galathea (yet ANOTHER person) wrote about it....ok, let's see if
I got this straight: you interpreted tommy's post(s) in mereoloy (and
discussed, and assigned intentions, definitions, thoughts, meanings,
etc. to tommy's posts) based on what third party (galathea) wrote
about it!!!
So, you established hearsay from hearsay....in mathematics!
Again, let us remember that we are NOT talking here about
interpreting, studying or translating what a person wrote about some
well-known stuff, but about what a person INVENTED about something:
how in the hollie mollie name of the world can you, or even galathea,
know that, in particular when you wrote that she was trying to teach
tommy about it!?
No contest, lwakle: you're the king of the hearsay, of the "I read
this, I understand, interpret and convey it like that, and I discuss,
argue, quarrel about it like those".\\
A pity, really...
Tonio
Jesse F. Hughes
> I'm giving the reasons why I don't consider what
> tommy1729 posts to be stupid. Tonio is free to agree
> or disagree with my opinion, and I don't give half a
> damn that Tonio disagrees with my opinion.
Er, that's fine. And, similarly, many people don't give a damn about
your opinion. I'm just not sure what your point is.
--
Scientists have calculated that the chance of anything so patently
absurd actually existing are millions to one. But magicians have
calculated that million-to-one chances crop up nine times out of ten.
-- Terry Pratchett on Intelligent Design. Or something.
MoeBlee
> On Jul 7, 12:13 pm, MoeBlee <jazzm...@hotmail.com> wrote:
>
> > On Jul 6, 9:13 pm, Transfer Principle <lwal...@lausd.net> wrote:
> > > Oh, really?
> > Yes, really. Where in that proof of mine you just quoted do you see
> > the word "set", or for that matter, anything other than first order
> > logic applied to tommy's axiom plus a symbolization of his definition
> > of "[]"?
>
> I concede that MoeBlee's proof consists of FOL= applied to
> some axioms. I don't concede that axioms to which MoeBlee
> applied FOL= are the axioms that tommy1729 had in mind.
Who knows what he "had in mind"? I just went by what he POSTED.
> > Someone says, "I also adopt the set theoretical empty set axiom" or "I
> > also adopt the ZFC empty set axiom" (which is virtually unanimously
> > understood as ExAy ~yex)
>
> The Empty Set Axiom is virtually unanimously understood? How
> ironic that MoeBlee would say this, because I've noticed
> that in another thread, MoeBlee is in a debate with David
> Ullrich and several other mathematicians over exactly what
> the Empty Set Axiom is,
You are a LIAR. Ullrich and I have NOT disagreed about what the empty
set axiom is:
> and in particular, whether an Axiom
> of Infinity is needed to prove that the empty set exists.
(1) THAT wasn't the debate! (See my remarks there.)
(2) What is required to prove the existence of an empty set is a
DIFFERENT matter from what the empty set AXIOM is. Damn, you are
confused!
> There appears to be three schools of thought here:
> 1. An explicit Empty Set Axiom is required to prove that
> the set 0 exists in ZFC.
> 2. The existence of 0 is provable from the axioms of
> Infinity and Separation Schema.
> 3. The existence of 0 is provable from the axioms of
> FOL= and Separation Schema.
>
> Ullrich argues (2). MoeBlee argues (3). So there is hardly
> a consensus on the Empty Set Axiom,
(1) I addressed your ill-premised trichotomy in that other thread.
(2) The above is not even about the empty set AXIOM!
> contrary to what MoeBlee
> posts in this thread!
No, you are TERRIBLY confused not only about the set theory but about
the nature of my spat with Ullrich.
> Ironically, there's probably more of a
> consensus among _mereologists_ about the smallest object
> than there is among _set theorists_. The only debate is
> whether the object [] should be called "the empty set," or
> "bottom," or some other name.
WHAT debate about that? If you're referring to my proof of the
inconsistency of tommy's system, then there is NOTHING in my proof
that hinges on what "[ ]" should be CALLED.
> I was tempted to post in the Ullrich empty set thread,
> but have avoided doing so until now. But now that MoeBlee
> has started talking about the "virtual unanimity" of the
> Empty Set Axiom among set theorists, I will jump into the
> Ullrich thread after all.
It is virtually unanimous that the empty set axiom is (or equivalent,
per the given theory, to):
ExAy ~yex in context of Z set theories
or
where '0' is primitive
Ay ~ye0
or
Ex(x is a set Ay ~yex) in possible other theories.
Given an explicit context, when we refer to "the empty set axiom" it
is widely understood, virtually unanimous, that what that refers to -
and especially where the context is stated as ZFC or loosely "set
theory", unless qualified otherwise - is some equivalent of ExAy ~yex.
That one could pedantically quibble about this context or that or this
quirk in formulation or that is aside the point that the empty set
axiom in set theory is virtually unanimously understood to assert that
there is a class (moreover, a set, as the case may be) that has no
members and not some other undisclosed meaning that tommy carries in
his mind.
MoeBlee
MoeBlee
You're a LIAR. Show one post where I expressed any reluctance
whatsoever to allow such theories as mereology and constructive set
theory. I read about Lesniewski and about Myhill's JSL article on
constructive set theory and in the relevant parts of Van Dalen and
Troelstra's two volumes, before you even started POSTING in these
groups.
A clue: Stating that tommy gave certain axioms that he HIMSELF said
were the set theory (or ZFC, whatever he said) axioms and then a
definition but that then just saying "it's consistent because it's
mereology" is silliness is NOT being closed minded about mereology and
constructive set theory.
Stop LYING about me.
MoeBlee
P.S. Here's my "consistent" theory in classical first order logic
(with the sole primitive 'R'):
ExAy(Ryx <-> ~Ryy).
It's consistent because it's not set theory but rather it's
schnozzolaology theory.
Now don't dispute me on this, unless you want to stand guilty of being
closed minded about schnozzolaology theory!
MoeBlee
David R Tribble
>> Posters like MoeBlee and Tonio often claim
>> that they are open-minded about set theories other than
>> ZFC, including mereology and constructivist set theory,
>> yet their behavior in threads like this prove otherwise.
>
MoeBlee wrote:
> You're a LIAR. Show one post where I expressed any reluctance
> whatsoever to allow such theories as mereology and constructive set
> theory. I read about Lesniewski and about Myhill's JSL article on
> constructive set theory and in the relevant parts of Van Dalen and
> Troelstra's two volumes, before you even started POSTING in these
> groups.
Take comfort in the fact that most readers here (I would
think) are quite aware of Walker's, um, dissonance regarding
"standard" and "non-standard" set theorists.
I, for one, can't take anything he says seriously about what
"the standard theorists" say or believe. I've given up trying
to figure out what he hopes to accomplish by trying to interpret
the various crank postings here as the foundations of actually
meaningful math.
MoeBlee
By the way, Mr. Transfer Principle, you refer to "MoeBlee's criteria
for definitions", but you'd be much more informative if you referred
to them as "Lesniewski's criteria", which is the same Lesniewski who
is so important in the development of your much admired subject of
mereology. And, to emphasize and be clear, these are criteria you can
find in just about any textbook on mathematical logic, and even in the
two set theory books you have - the one by Suppes and the one by Levy.
Meanwhile, I have to confess that I am relishing you making a fool of
yourself by claiming that the following is NOT a correct application
of the rule of universal instantiation:
AxEbAy(yeb <-> (yex & (yey & ~yey))
EbAy(yeb <-> (yex & (yey & ~yey)) ... universal instantiation
I LOVE and ADMIRE your willingness to be the clown!
MoeBlee
Transfer Principle
> P.S. Here's my "consistent" theory in classical first order logic
> (with the sole primitive 'R'):
> ExAy(Ryx <-> ~Ryy).
> It's consistent because it's not set theory but rather it's
> schnozzolaology theory.
> Now don't dispute me on this, unless you want to stand guilty of being
> closed minded about schnozzolaology theory!
OK, here's the difference between mereology and schnozzolaology.
Obviously, what MoeBlee is trying to argue is that if one would
apply FOL= to his lone axiom:
> ExAy(Ryx <-> ~Ryy)
one would obtain a contradiction (Russell's paradox), and if one
would apply FOL= to the axioms:
> 1 Ax x=[x] .... axiom
> 2 Ay(y in [x] <-> y=x) ... axiom
> 4 Ex Ay y not-in x ... axiom
one would obtain a contraction, so that the former theory would
be inconsistent if and only if the latter theory is inconsistent
regardless of the labels "mereology" and "schnozzolaology."
The difference? MoeBlee stated his axiom symbolically, so that
one can apply FOL= to it to derive the contradiction. On the
order hand, tommy1729 _didn't_ state his axioms symbolically
(except for "Ax x=[x]" of course), but stated them in _English_,
so that one can't apply FOL= to them unless one can rewrite them
in symbols -- conversion from meta to object language.
My argument was _never_ that FOL= applied to Axioms 1,2,4 does
not lead to a contradiction, or that somehow the "mereology"
label could cover up the contradiction. My argument was that
Axioms 2,4 don't represent a faithful translation of tommy1729's
desiderata from English to object language. The purpose of the
label "mereology" is to figure out what tommy1729's desiderata
actually are, so that we'd know _how_ exactly to translate the
axioms from English to object language.
Here's a more apt analogy. Suppose we were to introduce a theory
called "schnozzolaology," and we state that in this theory there
is an axiom that provides for the existence of a "Russell set,"
which is a set that contains all and only the sets that don't
contain themselves. Now the question is, is:
> ExAy(Ryx <-> ~Ryy)
a faithful translation of this axiom from English to object? If
so -- and on the surface it does -- then of course one would be
likely to write the proof:
> ExAy(Ryx <-> ~Ryy) ... axiom
> Ex(Rxx <-> ~Rxx) ... universal instantiation
> Rxx <-> ~Rxx ... contradiction
and declare the theory inconsistent.
But what if the translation isn't faithful at all? For example,
it could be that in "schnozzolaology," there are two types of
objects, "schnozzes" and "schnoozes," which act similar to
sets and proper classes, respectively. And so, just as classes
can only contain sets as elements, we find out that only
schnozzes can be elements of other objects. Thus, the line:
> ExAy(Ryx <-> ~Ryy)
would _not_ be a faithful rendering of the axiom. Instead, it
would be more like:
> ExAy((y is a schnozz & Ryx) <-> ~Ryy)
And "schnozz" might be a primitive, or there might even be an
ingenious way to define "schnozz" so that the usual proof of
Russell's paradox doesn't occur (i.e., so that the proposed
Russell set would be a "schnooz" rather than a "schnozz").
The word "schnozzolaology" sounds like a word MoeBlee might
have made up -- but then again, Tonio thought that I had made
up the word "mereology" (and I'll address a separate post to
Tonio a little later). It could be the "schnozzolaology" is
already an established term in mathematical literature, and
if one already knew how "schnozzolaology" works, then one
would already be familiar with "schnozzes" and know that only
"schnozzes" can be elements. Therefore, the use of the word
"schnozzolaology" tells the reader _how_ to translate an
axiom from English to object language. The word doesn't cover
up the contradiction -- it tells how to translate the English
in order to avoid the contradiction.
And so the same is with "mereology." MoeBlee already admitted
in the other thread that "mereology" dates back to the time
of the mathematician Lesniewski. I don't know whether the
axioms supplied by galathaea are Lesniewski's or not -- but
assume for now that they are. Then, when tommy1729 uses the
axiom "an empty set exists," we should go back to galathaea
or Lesniewski to see how to translate this into English. And
to galathaea (and probably Lesniewski as well), if [] is the
empty set, then we can prove that:
[] in [] (or []c[])
which means that:
> 4 Ex Ay y not-in x ... axiom
is not a faithful rendering of "an empty set exists." The
word "mereology" isn't a way to cover up the contradiction,
instead it's a flag to indicate that one shouldn't use the
ZFC Empty Set axiom, but an axiom that makes sense with the
theories of galathaea and Lesniewski.
MoeBlee
> tommy1729 _didn't_ state his axioms symbolically
> (except for "Ax x=[x]" of course)
No, he stated them by NAMING them as the particular set theoretic (or
"ZFC", or whatever his exact wording) that he was adopting. So, if he
meant them to be other than the ordinary Z axioms, he would need to
SAY SO.
In particular, when he mentions that he adopts the empty set axiom it
would be LUDICROUS for him to expect anyone NOT to take that as "ExAy
~yex" but rather as "ExAy xey" (or use 'c' instead of 'e', it matters
not). And then later somewhere or another mumbling some assent to
somebody something about "mereology" does not constitute saying "Wait,
I take back the empty set axiom that I mentioned earlier and instead
I'm using "ExAy xey". IF he had said that, then, upon my noticing
that, or being notified of that, then OF COURSE, I would have to
recognize that the theory he is NOW stating is different from the one
he ORIGINALLY stated. And, moreover, just as you may find in my
original proof, certain disclaimers to the very effect that I am
taking tommy's adoption of "set theory" (or "ZFC" or whatver word he
used) axioms at face value (especially, as in retrospect, he made NO
mention at that time that he doesn't really mean the set theory axioms
but rather something about mereology that he is merely GESTURING
toward by mentioning the specific set theory axioms he mentioned.
So, unless he states some specific revision to the axioms and
definition he gave, the axioms along with his definition, AS HE GAVE
THEM, are inconsistent. And YOUR OWN revision is YOUR system, whatever
that might be in RELATION to tommy's system AS HE STATED it and as it
still stands uncorrected by him, since mumbling something about
mereology is not a correction of axioms, as a correction of axioms
requires saying "Okay, not that one, but THIS one (some particular
actual axiom, not just a mumble about 'mereology') (or perhaps some
unambiguous description of a set of axioms) instead".
You are exerting too much verbiage trying to rationalize this.
So, go ahead and present whatever axioms you like that you consider to
be INSPIRED by tommy's system. That is a DIFFERENT matter though.
Meanwhile, I'm finding it DELICIOUS that you are so willing to make a
fool of yourself by claiming that an my instance of
AxP
____
P
is not valid universal instantiation.
MoeBlee
MoeBlee
And recently you've been plain lying about me again. I am asking you
to stop doing it. I am asking you to stop reading into my posts, WAY
PAST what I actually posted, to twist into something I did not say and
is not implied by what I said. It wouldn't be so bad if it were an
occasional innocent misparaphrase or misunderstanding, but you've
resorted to just blatant lying.
MoeBlee
cartman18
> > 4 Ex Ay y not-in x ... axiom
I dont think that can be true in a flat mereology and i doubt if it was said or intended.
For instance if x is a set itself , that contains y and 'in' is considered to intend the union of the meanings : element of / subset of / element of subsets of / subsets of subsets of /
Then "2" does not follow.
And that does not violate the principle " elementhood = subset " that tommy/galathaea ( who ? ) came up with.
Transfer Principle
> On Jul 8, 10:00 pm, Transfer Principle <lwal...@lausd.net> wrote:
> > Yeah, Tonio and Newman would like that. They'd love it if
> > I would change to a brain that's "intelligent" enough to
> > know that Tonio and Newman are 100% right and tommy1729's
> > posts are 100% "stupidities." I'd much rather change to a
> > brain "intelligent" enough to finish helping tommy1729
> > write a complete axiomatization to TST that would make
> > the theory equiconsistent with Z+proper classes. It's too
> > bad I can't change to that brain.
> Who EVER talked, or even hinted, about being "right" or wrong"? Do you
> see how you make stuff up, lwalke? When did I even hinted about me
> being right and tommy being wrong in this or that? His nonsense many
I concede this point to Tonio. I admit that I forgot that
there are often three levels of correctness, namely
"right," "wrong," and "not even wrong." And sometimes,
tommy1729 is considered to be "not even wrong."
This is one reason I feel compelled to intercede, so that
I can rewrite tommy1729's "not even wrong" statements into
those that are at least "wrong." Often times, I rewrite
something that's "not even wrong" into a sensible statement
in order to _ask_ whether it's right or wrong.
But Tonio would just state that tommy1729's statements are
"not even wrong," rather than see whether the corrected
sensible statement is right or wrong, nor if wrong, how to
make it right.
> You wrote bove that tommy's post (about mereology, I presume) is
> equivalent to the flattened mereology. What is this? I don't know, and
> I don't intend to play it like I do. In fact, googling "flattened
> mereology" I found...nothing
Neither galathaea, tommy1729, nor I invented the word
"mereology" at all. Indeed, the first sci.math poster to
use the word "mereology" was zuhair. One established
mathematician who worked in mereology was Lesniewski,
mentioned by MoeBlee in this thread. A good website to
learn more about mereology is at Stanford:
http://plato.stanford.edu/entries/mereology/
Admittedly, the words "flat" or "flattened" don't appear
at Stanford. I know that galathaea used the term "flat"
to describe mereology. Actually, zuhair was the first to
use the term "flat sets."
The word "flatten" is often used by computer programmers,
especially LISP programmers, to describe taking a list
whose entries are themselves lists and combining them
into a list without lists as entries -- the word "flat"
suggests combining "levels" of lists within lists within
lists to a list with a single, flat "level."
Another way to think about what "flatten" means is to
consider the set theory ZFC+urelements. Then if x is a
set, then x flattened would be the set of all urelements
of the transitive closure of x.
> You have decided that galathea knows better than ALL THE REST about
> mereology. Why? Who knows...perhaps because she wrote more about it
> than anyone else?
She certainly knows more about mereology than Tonio, who
admits that he doesn't know what mereology is. If there
is a more expert mereologist on sci.math than galathaea,
then I wish that person would enter the thread and
straighten out tommy1729's mereology once and for all.
> Then you wrote this pearl of argumentation that I hope someoen will
> treasure and chersih as it deserves:
> " I know from reading the discussion between tommy1729 and galathaea
> about the subject of mereology. Therefore, my interpretation about
> what tommy1729 intends is based on what galathaea wrote about it."
> Hmmm, let's see if we can make some order in here: you know about
> mereology from reading the thread(s) where tommy and galathea talked
> about this (and this did NOT stopped you from discussing over and over
> with people that know a lot about set theory)
Exactly -- who know a lot about _set theory_. I don't deny
that Tonio knows more about _set theory_, especially ZFC,
than I do.
When someone wants to know more about set theory, then
Tonio is the right person to ask. When someone wants to know
more about mereology, then galathaea suits better. And right
now, I want to know more about mereology.
> So, you established hearsay from hearsay....in mathematics!
> A pity, really...
Yes, it's a pity that I have to establish "hearsay" in order
to extract a sensible statement out of something that Tonio
considers "not even wrong." But I'd rather search for the
sensible mereological theory then simply dismiss tommy1729's
post as being "not even wrong" and "stupidity." If only that
expert mereologist whom Tonio has alluded would post and fix
tommy1729's theory for good!
Transfer Principle
> MoeBlee wrote:
> > You're a LIAR. Show one post where I expressed any reluctance
> > whatsoever to allow such theories as mereology and constructive set
> > theory. I read about Lesniewski and about Myhill's JSL article on
> > constructive set theory and in the relevant parts of Van Dalen and
> > Troelstra's two volumes, before you even started POSTING in these
> > groups.
> "the standard theorists" say or believe. I've given up trying
> to figure out what he hopes to accomplish by trying to interpret
> the various crank postings here as the foundations of actually
> meaningful math.
What I hope to accomplish is to discuss theories other than
ZFC, in a forum such that proponents of the theory can give
its advantages, and opponents of the theory can give its
disadvantages, without words such as "crank" being thrown
around repeatedly. Reading an alternate theory in a book is
undesirable because of the money that has to be spent as
well as the lack of interaction with the inventor of the
proposed theory.
At any rate, I hope to accomplish more by doing what I'm
doing now than by simplying throwing away so-called "crank"
theories as being "rubbish" that's "not even wrong."
MoeBlee
> On Jul 8, 9:16 pm, David R Tribble <da...@tribble.com> wrote:
>
> > MoeBlee wrote:
> > > You're a LIAR. Show one post where I expressed any reluctance
> > > whatsoever to allow such theories as mereology and constructive set
> > > theory. I read about Lesniewski and about Myhill's JSL article on
> > > constructive set theory and in the relevant parts of Van Dalen and
> > > Troelstra's two volumes, before you even started POSTING in these
> > > groups.
> > I, for one, can't take anything he says seriously about what
> > "the standard theorists" say or believe. I've given up trying
> > to figure out what he hopes to accomplish by trying to interpret
> > the various crank postings here as the foundations of actually
> > meaningful math.
>
> What I hope to accomplish is to discuss theories other than
> ZFC, in a forum such that proponents of the theory can give
> its advantages, and opponents of the theory can give its
> disadvantages, without words such as "crank" being thrown
> around repeatedly.
For the thousandth time, people don't usually get called 'crank'
merely for proposing theories other than ZFC!
< Reading an alternate theory in a book is
> undesirable because of the money that has to be spent as
> well as the lack of interaction with the inventor of the
> proposed theory.
Penny-wise/brain-foolish.
> At any rate, I hope to accomplish more by doing what I'm
> doing now than by simplying throwing away so-called "crank"
> theories as being "rubbish" that's "not even wrong."
Wonderful. Meanwhile, please stop lying about me.
MoeBlee
Marshall
But that's his favorite technique! How would he wind
people up so effectively without it?
Marshall
Transfer Principle
> P.S. to Jul 8, 3:08 pm, MoeBlee <jazzm...@hotmail.com>:
> yourself by claiming
...or, to be more precise, repeating Ullrich's claim...
> that the following is NOT a correct application
> of the rule of universal instantiation:
> AxEbAy(yeb <-> (yex & (yey & ~yey))
> EbAy(yeb <-> (yex & (yey & ~yey)) ... universal instantiation
And I repeat Ullrich's response:
"You can't erase the initial "Ax" in the first line except
in a context where we're assuming that something exists."
So since MoeBlee considers my declaring his use of UI as
invalid to be "delicious," he might consider Ullrich's
declaring his use of UI as invalid to be "delicious," too.
> Meanwhile, I'm finding it DELICIOUS that you are so willing to make a
> fool of yourself by claiming that an my instance of
> AxP
> ____
> P
> is not valid universal instantiation.
In the other thread, MoeBlee mentions "domains of discourse,"
in that universal instantiation allows one to instantiate to
any object in the domain of discourse. But unless one can
prove that the object really is in the domain of discourse,
one can't validly instantiate to it -- especially not when
trying to prove that the object really _is_ in the domain of
discourse (which would obviously be circular). And if the
domain of discourse happens to be _empty_, then one can't
instantiate to any object at all.
And so I find it "delicious" that MoeBlee thinks that he can
instantiate to objects that aren't in the domain of discourse
(or at least not yet proved to be there).
Transfer Principle
Thanks for posting this, cartman18! I agree with this post 100%.
And so cartman18, who appears to be an expert in the flattened
mereology, states that line "2" doesn't follow. But where does
line "2" come from? It is the second line in MoeBlee's ten-step
so-called "proof" that tommy1729/galathaea's theory is an
inconsistent theory.
So MoeBlee's the one who posted a line that doesn't follow. So
once again, I am highly appreciative of this post.
Tonico
Who claimed you did?
Indeed, the first sci.math poster to
> use the word "mereology" was zuhair. One established
> mathematician who worked in mereology was Lesniewski,
> mentioned by MoeBlee in this thread.
I did know that before the very first thread on this.
A good website to
> learn more about mereology is at Stanford:
>
> http://plato.stanford.edu/entries/mereology/
Thank you very much: I'm not interested at all at the moment, but I
shall treasure the info for the unlikely case that I shall be
interested in that at some point int he future.
>
> Admittedly, the words "flat" or "flattened" don't appear
> at Stanford. I know that galathaea used the term "flat"
> to describe mereology. Actually, zuhair was the first to
> use the term "flat sets."
>
> The word "flatten" is often used by computer programmers,
> especially LISP programmers, to describe taking a list
> whose entries are themselves lists and combining them
> into a list without lists as entries -- the word "flat"
> suggests combining "levels" of lists within lists within
> lists to a list with a single, flat "level."
>
> Another way to think about what "flatten" means is to
> consider the set theory ZFC+urelements. Then if x is a
> set, then x flattened would be the set of all urelements
> of the transitive closure of x.
>
> > You have decided that galathea knows better than ALL THE REST about
> > mereology. Why? Who knows...perhaps because she wrote more about it
> > than anyone else?
>
> She certainly knows more about mereology than Tonio, who
> admits that he doesn't know what mereology is.
You again demonstrate to all that you are either deeply stupid, or
ashtonishingly dishonest and a huge liart, or a very poor reader: I
did NOT say and/or admit nothing of the like simply because that is
not true: I do know a little bit about mereology. What I wrote
(attention! read the the following v-e-r-y s-l-o-w-l-y!!) is
that...I...do...not...know...what...flattened...mereology...is.
Hmmm...did you get that?
Of course, it may very well be that galathea, and many others, know
much more about mereology than I do, among other things because that
is not a subject that specially appeals to me.
If there
> is a more expert mereologist on sci.math than galathaea,
> then I wish that person would enter the thread and
> straighten out tommy1729's mereology once and for all.
>
Well, it may be that not everybody is so desperately eager in
correcting brats with a nasty attitude when they write their
stupidities, just like you seem to be, for a reason that I just cannot
see.
> > Then you wrote this pearl of argumentation that I hope someoen will
> > treasure and chersih as it deserves:
> > " I know from reading the discussion between tommy1729 and galathaea
> > about the subject of mereology. Therefore, my interpretation about
> > what tommy1729 intends is based on what galathaea wrote about it."
> > Hmmm, let's see if we can make some order in here: you know about
> > mereology from reading the thread(s) where tommy and galathea talked
> > about this (and this did NOT stopped you from discussing over and over
> > with people that know a lot about set theory)
>
> Exactly -- who know a lot about _set theory_. I don't deny
> that Tonio knows more about _set theory_, especially ZFC,
> than I do.
>
Even that could be a wrong statement: how in the world can you
possibly know that, for the Great Pumpkin's sake?! As far as I know,
you could know way more that I do about ZFC and stuff. Please do stop
assuming unbased stuff about OTHERS.
> When someone wants to know more about set theory, then
> Tonio is the right person to ask.
Again the same nonsense as above...**sigh**
When someone wants to know
> more about mereology, then galathaea suits better. And right
> now, I want to know more about mereology.
>
Good for you
> > So, you established hearsay from hearsay....in mathematics!
> > A pity, really...
>
> Yes, it's a pity that I have to establish "hearsay" in order
> to extract a sensible statement out of something that Tonio
> considers "not even wrong." But I'd rather search for the
> sensible mereological theory then simply dismiss tommy1729's
> post as being "not even wrong" and "stupidity." If only that
> expert mereologist whom Tonio has alluded would post and fix
> tommy1729's theory for good!
What expert mereologist have I alluded at all? Dude, you must be on
meds...and pretty strong ones, indeed! Behold what happened to M.J.
and take care, please.
Tonio
Pd. Stop making up stuff.
Transfer Principle
> On Jul 9, 2:01 pm, Transfer Principle <lwal...@lausd.net> wrote:
> > tommy1729 _didn't_ state his axioms symbolically
> > (except for "Ax x=[x]" of course)
> No, he stated them by NAMING them as the particular set theoretic (or
> "ZFC", or whatever his exact wording) that he was adopting. So, if he
> meant them to be other than the ordinary Z axioms, he would need to
> SAY SO.
Let's look at the recent post of cartman18, who appears to
be an expert on mereology. I repeat cartman18's post for
emphasis here:
> 2 Ay(y in [x] <-> y=x) ... axiom
> 4 Ex Ay y not-in x ... axiom
cartman18:
"I dont think that can be true in a flat mereology and i doubt if it
was said or intended."
And so despite MoeBlee insisting that line 2 was either
said or intended by tommy1729, we see that cartman18,
the mereology expert, says it's doubtful. Line 2 was
definitely never _said_ by tommy1729, and cartman18
knows that someone working in mereology wouldn't
_intended_ to say it either.
"For instance if x is a set itself , that contains y and 'in' is
considered to intend the union of the meanings : element of / subset
of / element of subsets of / subsets of subsets of /
Then "2" does not follow."
This is the key point here. Since the symbol "in" (or
"e", or "c", or whatever the primitive is) is intended
to mean _both_ element _and_ subset, we see that:
> 2 Ay(y in [x] <-> y=x) ... axiom
isn't even possible because if y is a _subset_ of x,
y is a priori in x even though y isn't itself x. In
flat mereology, therefore, there usually is _no_ set
such that y is in the set iff y=x. And so, I repeat
cartman18's line once again for emphasis:
"Then "2" does not follow.
And that does not violate the principle " elementhood = subset " that
tommy/galathaea ( who ? ) came up with."
Line 2 of MoeBlee's proof doesn't follow from tommy1729's
explicitly expressed desiderata that the notions of
elementhood and subsethood be a single concept. Therefore,
MoeBlee, while having proved that lines 1,2,4 are
together inconsistent, hasn't proved that the theory TST
is in fact inconsistent.
> You are exerting too much verbiage trying to rationalize this.
Maybe I am. If galathaea can't convince MoeBlee that he
doesn't have a proof that TST is inconsistent, why would
I have any better chance at convincing him? But let's see
whether the words of cartman18 can convince MoeBlee that
Transfer Principle
> And recently you've been plain lying about me again.
I address some of these "lies" in the Ullrich thread, in
a post directed to Hughes. That post contains proposed
corrections to some of these "lies."
doug
Transfer Principle wrote:
Why in the world are you posting this to the physics group?
We have enough cranks here as it is.
Jesse F. Hughes
> And so cartman18, who appears to be an expert in the flattened
> mereology, states that line "2" doesn't follow.
Does "appears to be an expert" mean "says something I like"?
--
Jesse F. Hughes
"Most people don't even know what a rootkit is, so why should they
care about it."
-- Thomas Hesse, sony executive defends DRM-by-rootkit.
Jesse F. Hughes
> On Jul 9, 3:16 pm, cartman18 <cartmaneri...@hotmail.com> wrote:
>> > > 2 Ay(y in [x] <-> y=x) ... axiom
>> > > 4 Ex Ay y not-in x ... axiom
>> I dont think that can be true in a flat mereology and i doubt if it was said or intended.
>> For instance if x is a set itself , that contains y and 'in' is considered to intend the union of the meanings : element of / subset of / element of subsets of / subsets of subsets of /
>> Then "2" does not follow.
>> And that does not violate the principle " elementhood = subset " that tommy/galathaea ( who ? ) came up with.
>
> Thanks for posting this, cartman18! I agree with this post 100%.
>
> And so cartman18, who appears to be an expert in the flattened
> mereology, states that line "2" doesn't follow. But where does
> line "2" come from? It is the second line in MoeBlee's ten-step
> so-called "proof" that tommy1729/galathaea's theory is an
> inconsistent theory.
Let's review exactly what Tommy said his axioms are:
,----
|
| 1) axiom of extensionality
|
| 2) axiom of the empty set
|
| 3) axiom of pairing
|
| 4) axiom of union
|
| 5) non-standard elements within the set of real numbers always have
| properties that correspond to the properties of infinitesimal and
| unlimited elements.
|
| 6) this set theory is game theory in disguise , whatever holds in
| game theory can be restated in this set theory.
|
| this set theory is complete and consistant apart from solving
| equations.
|
| this set theory is the analogue of a computer with oo resourses (as
| should be since math is about computation)
|
| 7) axiom of logic : x = [x] ( also if x = empty )
`----
Now, we'll ignore the obviously nonsensical axioms (5) and (6). Axiom
2 refers to the axiom of the empty set. As Moe points out, there
really is only one axiom known as the empty set axiom:
(Ex)(Ay)NOT(y in x).
You can pretend that Tommy meant something else, but he didn't.
Axiom (7) is the one that is most opaque. I asked Tommy at the time
what the function symbol [...] meant. Here's what he replied:
> > You haven't defined what [x]
> > means, but if it is
> > supposed to mean the singleton containing x (usually
> > written "{x}"),
> > then the theory is provably inconsistent.
> [x] = is the set that contains x ( only )
> however x may be a set itself.
Now, it seems to me that if you say [x] is the set that contains x
*only*, then you're saying two things:
(1) [x] contains x.
(2) [x] does not contain any other thing.
In other words,
(Ay)(y in [x] <-> y = x).
The alternative that galathaea (who is, alongside cartman18,
apparently an expert in mereology) offers is that [...] by definition
just is the identity function, so that axiom (7) says nothing
interesting in the least. Rather, it introduces useless notation for
the identity function.
In this alternative, axiom (7) is really, utterly irrelevant to TST.
Rather than assert something interesting (namely, that an
independently defined and interesting function is in fact equal to the
identity function in TST), axiom (7) instead introduces superfluous
notation.
> So MoeBlee's the one who posted a line that doesn't follow. So once
> again, I am highly appreciative of this post.
No, cartman18 hasn't read Tommy's original post. It's hard to
imagine that Tommy meant anything besides the empty set axiom when he
mentioned the empty set axiom.
--
"You see, sometimes being delusional is the best way to get that good
idea. And if you're too afraid to test the limits of sanity, then you
can't be a highly creative person. That probably explains some of
you." -- James S. Harris explains himself, too
MoeBlee
> On Jul 9, 11:04 am, MoeBlee <jazzm...@hotmail.com> wrote:
>
> > P.S. to Jul 8, 3:08 pm, MoeBlee <jazzm...@hotmail.com>:
> > Meanwhile, I have to confess that I am relishing you making a fool of
> > yourself by claiming
>
> ...or, to be more precise, repeating Ullrich's claim...
NO, Ullrich did NOT claim that the step is not valid universal
instantiation!
You are totally confused.
> > that the following is NOT a correct application
> > of the rule of universal instantiation:
> > AxEbAy(yeb <-> (yex & (yey & ~yey))
> > EbAy(yeb <-> (yex & (yey & ~yey)) ... universal instantiation
>
> And I repeat Ullrich's response:
>
> "You can't erase the initial "Ax" in the first line except
> in a context where we're assuming that something exists."
So what? His point is NOT that the application of universal
instantiation there is INVALID!
> So since MoeBlee considers my declaring his use of UI as
> invalid to be "delicious," he might consider Ullrich's
> declaring his use of UI as invalid to be "delicious," too.
You're totally confused. The contention I had with Ullrich is NOT as
to the validity of my use of universal instantiation.
> > Meanwhile, I'm finding it DELICIOUS that you are so willing to make a
> > fool of yourself by claiming that an my instance of
> > AxP
> > ____
> > P
> > is not valid universal instantiation.
>
> In the other thread, MoeBlee mentions "domains of discourse,"
> in that universal instantiation allows one to instantiate to
> any object in the domain of discourse.
Did I ACTUALLY put it in that way? If I did, then it is not precise.
Universal instantiation allows one to instantiate to a TERM that is
free for the variable in the matrix. Universal instantiation is
SYNTACTICAL. However, of course, the semantical upshot is that if a
property holds for all objects in a domain of discourse then that
property holds for any particular object in that domain of discourse.
> But unless one can
> prove that the object really is in the domain of discourse,
> one can't validly instantiate to it
You're TOTALLY confused. Universal instantiation is a SYNTACTICAL rule
of inference. The instantiation is to a TERM.
(Technical notes: I've actually seen systems that have the rule of
universal instantiation written so that instantiation requires first
proving an existence clause (this works to get passed the problem of
definite descriptions that don't properly refer); but that is not what
is at stake here, as my use is in plain first order logic that doesn't
have that special formulation. Also, some systems require
instantiations not be to the same variable but rather to 'temporary
constants' or things like that. But again, my use is not in such
systems but rather in plain first order logic as found in dozens and
dozens of textbooks; and my instantiation to the same variable could
just as well be replaced in my proof to whatever temporary constant
and the proof still goes through.)
> -- especially not when
> trying to prove that the object really _is_ in the domain of
> discourse (which would obviously be circular). And if the
> domain of discourse happens to be _empty_, then one can't
> instantiate to any object at all.
YOU DON'T LISTEN. Plain first order logic has a semantics that
stipulates non-empty domain, and quantifier rules that match.
> And so I find it "delicious" that MoeBlee thinks that he can
> instantiate to objects that aren't in the domain of discourse
> (or at least not yet proved to be there).
You're making a first class clown and jerk of yourself.
ASK ANY LOGICIAN whether in plain first order logic (such as in
Enderton, Shoenfield, and probably most of the other most widely
referenced sources) both of the following are correct universal
instantiation:
AxP
____
P
and
AxFx
_____
AxF0
(where, in the second case, '0' is a 1-place function symbol of the
language).
/
Damn! I can't BELIEVE I'm in a discussion with someone who is claiming
that
AxFx to Fx
or
AxFx to F0 (where '0' is a 0-place function symbol of the language)
are not correct universal instantiation.
PLEASE, Mr. Transfer Principle, just look at a damn book on logic! Or
ASK ANY LOGICIAN.
MoeBlee
MoeBlee
> On Jul 9, 3:07 pm, MoeBlee <jazzm...@hotmail.com> wrote:
>
> > On Jul 9, 2:01 pm, Transfer Principle <lwal...@lausd.net> wrote:
> > > tommy1729 _didn't_ state his axioms symbolically
> > > (except for "Ax x=[x]" of course)
> > No, he stated them by NAMING them as the particular set theoretic (or
> > "ZFC", or whatever his exact wording) that he was adopting. So, if he
> > meant them to be other than the ordinary Z axioms, he would need to
> > SAY SO.
>
> Let's look at the recent post of cartman18, who appears to
> be an expert on mereology. I repeat cartman18's post for
> emphasis here:
>
> > 2 Ay(y in [x] <-> y=x) ... axiom
> > 4 Ex Ay y not-in x ... axiom
>
> cartman18:
> "I dont think that can be true in a flat mereology and i doubt if it
> was said or intended."
>
> And so despite MoeBlee insisting that line 2 was either
> said or intended by tommy1729, we see that cartman18,
> the mereology expert, says it's doubtful.
I can't believe you're STILL trying to spin and rationalize this!
I don't claim that (2) is a MEREOLOGICAL axiom. I don't claim that IF
tommy REVISES what he says to some other certain mereological axiom
then a consistent system might be had.
Rather, just look at what tommy SAID. I said THEN even that I am
merely basing on what he said and that if he means differently then he
is welcome to specify exactly what different thing it is he means. But
he has not done that (to my knowledge). Just mumbling some assent to
someone something about "mereology" is not a correction of a
definition or axiom.
> Line 2 was
> definitely never _said_ by tommy1729, and cartman18
> knows that someone working in mereology wouldn't
> _intended_ to say it either.
Other than mumbling something about "mereology" tommy didn't specify
any single particular mereological axiom or definition when he gave
his axioms or definitions to which I responded, not (to my knowledge)
has he given a specific correction to any of his axioms or definitions
since.
Why can't you get over the fact that YOUR own notion of how a
consistent theory might be formed is not in fact what tommy himself
posted?
MoeBlee
MoeBlee
You don't need scare quotes around 'lies' there. They are lies. And
your followups have even more lies in them.
MoeBlee
MoeBlee
Just for the record, I'm replying to whatever groups are listed
already from the post of the other poster(s). If anyone wishes to cut
his replies from certain groups, then my own replies will follow
suit.
MoeBlee
MoeBlee
> Let's review exactly what Tommy said his axioms are:
> ,----
> |
> | 1) axiom of extensionality
> |
> | 2) axiom of the empty set
> |
> | 3) axiom of pairing
> |
> | 4) axiom of union
> |
> | 5) non-standard elements within the set of real numbers always have
> | properties that correspond to the properties of infinitesimal and
> | unlimited elements.
> |
> | 6) this set theory is game theory in disguise , whatever holds in
> | game theory can be restated in this set theory.
My argument doesn't even depend on this, but, in context of Mr.
Transfer Principle harping about mereology, again we see tommy, TWICE
say "this SET theory" [all caps added].
> | this set theory
"this SET theory" [all caps added]
> is complete and consistant apart from solving
> | equations.
> |
> | this set theory
"this SET theory" [all caps added]
> is the analogue of a computer with oo resourses (as
> | should be since math is about computation)
> |
> | 7) axiom of logic : x = [x] ( also if x = empty )
And again, my proof (along with Hughes and Ullrich, if I recall; I'm
not claiming my proof is original, especially as it is a mere
TRIVIALITY) doesn't even depend on tommy having at least FOUR times
called it a "SET theory" [emphasis added]; but rather this just puts
in context Mr. Transfer Principle's harping on mereology, and even as
his argument about that fails in any case.
MoeBlee
MoeBlee
One correction to what I wrote. tommy didn't refer to these as "ZFC
axioms" or "set theoretical axioms" as I thought he had said one of
those two. Rather he named the thread:
tommy1729 set axioms
and then at least FOUR times, mentioned the theory as a "SET
theory" [emphasis added].
And my proof of inconsistency doesn't even depend on such facts other
than that when he mentions such things as "the empty set axiom", one
cannot be expected to think that he does not mean the ordinary empty
set axiom but rather some other very different thing.
And I am reminded how that thread ended. tommy asked me a question
that really was a silly exercise. I performed the exercise and asked
him what is the point of it. Of course, he never replied; never gave
even the courtesy of telling me why I should have done the exercise.
He's a child, whether chronologically or emotionally, and he's
virtually illiterate as to subjects such as logic and set theory (and
to think that he's competent enough in mereology (!) to state a
special mereological theory is pure fantasy).
MoeBlee
cartman18
>
> > On Jul 9, 3:16 pm, cartman18
> <cartmaneri...@hotmail.com> wrote:
> >> > > 2 Ay(y in [x] <-> y=x) ... axiom
> >> > > 4 Ex Ay y not-in x ... axiom
> and i doubt if it was said or intended.
> >> For instance if x is a set itself , that contains
> y and 'in' is considered to intend the union of the
> meanings : element of / subset of / element of
> subsets of / subsets of subsets of /
> >> Then "2" does not follow.
> >> And that does not violate the principle "
> elementhood = subset " that tommy/galathaea ( who ? )
> came up with.
> >
> > Thanks for posting this, cartman18! I agree with
> this post 100%.
> >
> > And so cartman18, who appears to be an expert in
> the flattened
> > mereology, states that line "2" doesn't follow. But
> where does
> > line "2" come from? It is the second line in
> MoeBlee's ten-step
> > so-called "proof" that tommy1729/galathaea's theory
> is an
> > inconsistent theory.
>
> Let's review exactly what Tommy said his axioms are:
> ,----
> |
> | 1) axiom of extensionality
He probably meant the inverse axiom of extensionality.
For all A and B if A = B then C Element of / subset of A <=> C Element of / subset of B
> |
> | 2) axiom of the empty set
It does not lead to "2" as commented before.
"4" is equivalent.
No problem.
Apart from the case of an empty set containing an empty set.
( follows from 7) )
For this anomaly , some models don't consider empty set as a set.
Basically if the axiom is for a flat mereology or related it is considered as the " existence " of the empty set axiom.
-> empty set exists.
this avoids A E and NOT , they depend on model choices.
> |
> | 3) axiom of pairing
In mereology this is : Given two sets, there is a set whose members are exactly the two given sets.
It might have another name to avoid confusion with the ZF one , which might be slightly different.
If you want some kind of Union to exist , you need a similar axiom.
I think much of the confusion occurs because of interpretations of "in" and similar are different in ZF and mereology.
So for example a proof or an equivalent axiom might be a proof or equivalent in some model but not another.
> |
> | 4) axiom of union
I'm not sure about this one.
But i don't see a problem either.
> |
> | 5) non-standard elements within the set of real
> numbers always have
> | properties that correspond to the properties of
> infinitesimal and
> | unlimited elements.
> |
> | 6) this set theory is game theory in disguise ,
> whatever holds in
> | game theory can be restated in this set theory.
> |
> | this set theory is complete and consistent apart
> from solving
> | equations.
> |
> | this set theory is the analogue of a computer with
> oo resources (as
> | should be since math is about computation)
> |
> | 7) axiom of logic : x = [x] ( also if x = empty )
> `----
>
> Now, we'll ignore the obviously nonsensical axioms
> (5) and (6). Axiom
> 2 refers to the axiom of the empty set. As Moe
> points out, there
> really is only one axiom known as the empty set
> axiom:
>
> (Ex)(Ay)NOT(y in x).
>
> You can pretend that Tommy meant something else, but
> he didn't.
As commented above ; it holds unless y is the empty set.
In fact , even this can be defended if y = [y] and 3-valued logic is allowed.
BEWARE of 3-valued logic.
I suggest adding - for clarity , not necc !! -
[[],x] = [x]
He should agree with that.
( in that case , ordinary 2-logic will do as well )
>
> Axiom (7) is the one that is most opaque. I asked
> Tommy at the time
> what the function symbol [...] meant. Here's what he
> replied:
>
> > > You haven't defined what [x]
> > > means, but if it is
> > > supposed to mean the singleton containing x
> (usually
> > > written "{x}"),
> > > then the theory is provably inconsistent.
That cannot be intended , at least not by the above axioms in a flattened mereology.
>
> > [x] = is the set that contains x ( only )
> > however x may be a set itself.
>
> Now, it seems to me that if you say [x] is the set
> that contains x
> *only*, then you're saying two things:
>
> (1) [x] contains x.
> (2) [x] does not contain any other thing.
He has to if he wants to talk about flattened mereology and [x] = x.
>
> In other words,
>
> (Ay)(y in [x] <-> y = x).
That is not " in other words " , but completely different.
Once again " in " is your confusion.
your " in " is the ZF version.
>
> The alternative that galathaea (who is, alongside
> cartman18,
> apparently an expert in mereology) offers is that
> [...] by definition
> just is the identity function, so that axiom (7) says
> nothing
> interesting in the least. Rather, it introduces
> useless notation for
> the identity function.
? So you CHANGED your opinion from wrong to nothing interesting ?
Surely you realize you cannot claim
1) its wrong
2) i understand it
3) its not wrong but its nothing interesting
You cannot have all 3 !
>
> In this alternative, axiom (7) is really, utterly
> irrelevant to TST.
YOU determine what axioms are irrelevant to somebody new proposed axiomatic system ???
Wow
> Rather than assert something interesting (namely,
> that an
> independently defined and interesting function is in
> fact equal to the
> identity function in TST), axiom (7) instead
> introduces superfluous
> notation.
Not at all.
Without axiom 7 , we wouldnt even be sure its a flat mereology.
>
> > So MoeBlee's the one who posted a line that doesn't
> follow. So once
> > again, I am highly appreciative of this post.
>
> No, cartman18 hasn't read Tommy's original post.
> It's hard to
> imagine that Tommy meant anything besides the empty
> set axiom when he
> mentioned the empty set axiom.
>
> --
> "You see, sometimes being delusional is the best way
> to get that good
> idea. And if you're too afraid to test the limits of
> sanity, then you
> can't be a highly creative person. That probably
> explains some of
> you." -- James S. Harris explains
> himself, too
James has a point. But I assume JSH = James Harris so he is better at philosophy then factoring.
Too many 'courses' are about peoples limitations , thus giving them those limitations.
Cheers
Cartman
cartman18
> For the thousandth time, people don't usually get
> called 'crank'
> merely for proposing theories other than ZFC!
But i guess it happens alot on sci.math.
Can you give 5 counter-examples ?
>
> < Reading an alternate theory in a book is
> > undesirable because of the money that has to be
> spent as
> > well as the lack of interaction with the inventor
> of the
> > proposed theory.
>
> Penny-wise/brain-foolish.
>
> MoeBlee
The problem with paying for books is - in my humble opinion - you only know if it was good AFTER you read it. And usually it wasnt good. Not because it was bad or wrong, but because it repeated alot of things already covered in your other books.
Cheers
Cartman
Tonico
> > For the thousandth time, people don't usually get
> > called 'crank'
> > merely for proposing theories other than ZFC!
>
> But i guess it happens alot on sci.math.
>
> Can you give 5 counter-examples ?
..
What do you want examples of? People not being called cranks when
proposing set theoreis different from ZFC? Don't you think this is a
"little" ridiculous?
Why not better you, or anyone else interested, give examples of people
being called a crank widely in the NG (this meaning: not being called
a crank by one or two people who can be personal foes of his, but by a
larger number) by the very fact of proposing alternative set theories?
I mean, why guess? Can you find examples?
..
> > < Reading an alternate theory in a book is
> > > undesirable because of the money that has to be
> > spent as
> > > well as the lack of interaction with the inventor
> > of the
> > > proposed theory.
>
> > Penny-wise/brain-foolish.
>
> > MoeBlee
>
> The problem with paying for books is - in my humble opinion - you only know if it was good AFTER you read it. And usually it wasnt good. Not because it was bad or wrong, but because it repeated alot of things already covered in your other books.
This hardly happens a lot with mathematics. First, because you can get
to know the book in some library of some mathematics school of some
college/university around, and second because you can always use the
web to read reviews, opinions and sometimes even excerpts of the books
in google books, yahoo books, springer, amazon, etc.
All this diminish the risk of expending money on a book and getting
disappointed at it afterwards...though it can happen, of course.
Tonio
>
> Cheers
>
> Cartman
MoeBlee
The quote indentation formatting I receive from the post is so mixed
up it is clouded as to who is supposed to have said what. In
particular it leaves out attribution to Jesse Hughes whose comments
are the main subject of the post. I'll just take it as it displays for
me:
He could have meant many things or he might have no meaning at all.
We're talking about a very confused person who spreads arbitrary
notation and assertions around like he's using peanut butter and jelly
as pizza topping. There's little basis to second guess what he might
mean. Meanwhile, we have what he posted, and when someone says "the
axiom of extensionality", it is common to take that to mean, indeed,
the axiom of extensionality.
> For all A and B if A = B then C Element of / subset of A <=> C Element of / subset of B
The above is just an instance of a theorem schema of identity theory
anyway.
Informally put, if A=B, then what holds for A holds for B. There's no
need for another axiom for that (unless '=' is taken as primitive, not
taken from identity theory; but in this case, he would need to finish
the axiomatization for '=', unless he had some sense of '=' that
doesn't include "x=x". Moreover, how would he propose to implement the
other axioms without extensionality? Maybe he could, but he sure
showed no indication what he would have in mind.)
Anyway, again, he said 'the axiom of extensionality', and as part of
his SET theory, so it would be beyond ordinary not to take that to
mean the axiom of extensionality.
> > | 2) axiom of the empty set
>
> It does not lead to "2" as commented before.
What "2"? Line 2 in my proof? That comes from tommy's explanation of
his "[ ]" notation. Line 2 in my proof was not claimed to come from
the empty set axiom
> "4" is equivalent.
>
> No problem.
>
> Apart from the case of an empty set containing an empty set.
There's no provision for this mentioned by tommy.
He said he adopts the empty set axiom. I simply wrote down the empty
set axiom:
ExAy ~yex.
> ( follows from 7) )
>
> For this anomaly , some models don't consider empty set as a set.
WHATEVER models do, I just gave a purely syntactical proof. I merely
took his axioms and definitions and applied first order logic with
identity. A contradiction results.
> Basically if the axiom is for a flat mereology or related it is considered as the " existence " of the empty set axiom.
>
> -> empty set exists.
>
> this avoids A E and NOT , they depend on model choices.
You mean the universal quantifier, existential quantifier and negation
symbol? I used no model theory "choices". I simply applied SYNTATICAL
proof in first order logic with identity.
> > | 3) axiom of pairing
>
> In mereology this is : Given two sets, there is a set whose members are exactly the two given sets.
I'm not disposed now to say what goes on with mereology. But I do wish
to point out that, as far as tommy's system is concerned and my proof
of its consistency (if that is what you're talking about), whatever
you may say about mereology, he plainly stated the names of certain
famous set theory axioms for what he called his "set theory", and I
just derived a contradiction from that and other axioms and
definitions that he gave also.
> It might have another name to avoid confusion with the ZF one , which might be slightly different.
>
> If you want some kind of Union to exist , you need a similar axiom.
>
> I think much of the confusion occurs because of interpretations of "in" and similar are different in ZF and mereology.
WHOSE confusion. tommy just said that he's giving a set theory and he
named some famous set theory axioms along with some other
verbalizations he calls "axioms". I merely applied his named set
theory axioms along some of the other material he presented.
There's no such provision mentioned by tommy.
> In fact , even this can be defended if y = [y] and 3-valued logic is allowed.
If tommy's system is in some special 3-value logic, then he should
have said so.
> BEWARE of 3-valued logic.
>
> I suggest adding - for clarity , not necc !! -
>
> [[],x] = [x]
>
> He should agree with that.
>
> ( in that case , ordinary 2-logic will do as well )
Whatever you now suggest is a different story from what tommy posted.
If your point is to show some hints toward reconstituting tommy's
theory, then fine; but if your point is to say that tommy's theory
itself is not inconsistent then you're arguing be means of revising
simply what he posted.
> > Axiom (7) is the one that is most opaque. I asked
> > Tommy at the time
> > what the function symbol [...] meant. Here's what he
> > replied:
>
> > > > You haven't defined what [x]
> > > > means, but if it is
> > > > supposed to mean the singleton containing x
> > (usually
> > > > written "{x}"),
> > > > then the theory is provably inconsistent.
>
> That cannot be intended , at least not by the above axioms in a flattened mereology.
Again, are you assuming that tommy is an actually RATIONAL person who
thinks and reasons rationally about logic, set theory, even mereology
and such.
> > > [x] = is the set that contains x ( only )
> > > however x may be a set itself.
>
> > Now, it seems to me that if you say [x] is the set
> > that contains x
> > *only*, then you're saying two things:
>
> > (1) [x] contains x.
> > (2) [x] does not contain any other thing.
>
> He has to if he wants to talk about flattened mereology and [x] = x.
Then let him introduce his flattened mereology axioms and drop the set
theory axioms he named that make his system inconsistent.
> > In other words,
>
> > (Ay)(y in [x] <-> y = x).
>
> That is not " in other words " , but completely different.
>
> Once again " in " is your confusion.
>
> your " in " is the ZF version.
NO, WRONG, ZF was not invoked by Jesse.
> > The alternative that galathaea (who is, alongside
> > cartman18,
> > apparently an expert in mereology) offers is that
> > [...] by definition
> > just is the identity function, so that axiom (7) says
> > nothing
> > interesting in the least. Rather, it introduces
> > useless notation for
> > the identity function.
>
> ? So you CHANGED your opinion from wrong to nothing interesting ?
No, he didn't. Obviously, you didn't follow the line of argument he's
giving. He's not saying that what tommy posted is not inconsistent.
Rather, he's saying that if one rationalizes tommy's system in a
certain way (that is not even present in what tommy wrote), then that
leaves an axiom that is otiose anyway, thus just one more doubt as to
the viability of even the EX POST FACTO rationalization of what tommy
wrote.
> Surely you realize you cannot claim
>
> 1) its wrong
> 2) i understand it
> 3) its not wrong but its nothing interesting
>
> You cannot have all 3 !
Surely, you'll realize that if you re-read Jesse's post you'll see why
the above is irrelevant to what he actually posted.
> > In this alternative, axiom (7) is really, utterly
> > irrelevant to TST.
>
> YOU determine what axioms are irrelevant to somebody new proposed axiomatic system ???
>
> Wow
He said "in this alternative". In the ALTERNATIVE explanation, the
axiom is irrelevant in the sense that it is purely logical.
> > Rather than assert something interesting (namely,
> > that an
> > independently defined and interesting function is in
> > fact equal to the
> > identity function in TST), axiom (7) instead
> > introduces superfluous
> > notation.
>
> Not at all.
>
> Without axiom 7 , we wouldnt even be sure its a flat mereology.
Why would you need to be sure its a flat mereology? That there may be
some OTHER theory of mereology that is consistent is not in dispute.
Meanwhile, the theory that tommy himself posted is inconsistent. And
proof of tha that doen't depend on invoking models or ZFC, but rather
on just putting down the axioms he mentioned along with the definition
he gave of "[ ]", just as the definition used in the proof used
NOTHING that tommy did not himself include in his explanation.
MoeBlee
MoeBlee
> > For the thousandth time, people don't usually get
> > called 'crank'
> > merely for proposing theories other than ZFC!
>
> But i guess it happens alot on sci.math.
What happens? That a person gets called a crank merely for proposing a
theory other than ZFC?
I'm not archives-omniscient, so I can't say it's never happened. But
if one claims that it does usually happen, then I'd welcome seeing
examples.
> Can you give 5 counter-examples ?
Five counter-examples to what?
You mean five examples of people being called a crank merely for
proposing a theory other than ZFC?
Or do you mean five examples of a person proposing a theory other than
ZFC but not being called a crank?
As to the former, why would I need to think of such examples?
As to the latter, sure, people talk about Z, ZF, NBG, NF, constructive
type theory, category theory, IST, PA, PRA, constructive set theory,
AFA, category theory, mereology, naive Cantor set theory, Frege's
system, PM, second order theories, etc. etc. etc. They might not talk
about all of those things often. But I haven't noticed one being
called a crank merely for proposing discussion of such theories. Also,
there's a poster who seems to come up with his "theory of the week".
But there are not many non-cranks who happen to propose original
theories in sci.math and sci.logic. Such discussions are usually found
at FOM, where all kinds of research is discussed, even as today one
poster mentioned a theory he devised without the axiom of
extensionality (or some alternative to it; I haven't had a chance yet
to look over his paper); and of course, the literature of the subject
- in journals and books - is brimming with research on alternatives to
ZFC.
> The problem with paying for books is
that it costs money.
> - in my humble opinion - you only know if it was good AFTER you read it.
One can take advice and opinions from other people, reference
bibliographies, read reviews, read portions online, read portions in a
bookstore or library. Of course, no book comes with a guarantee that
it will suit you.
> And usually it wasnt good. Not because it was bad or wrong, but because it repeated alot of things already covered in your other books.
Of course books that are introductions to a particular subject will
cover much common ground. But still there may be enough that is
different in one book to make it worthwhile, and even coverage of the
same material may be helpful toward understanding from the different
perspectives of individual authors or even toward solidifying one's
understanding through repetition or through hearing the same concept
expressed in two different ways. And of course, that books overlap in
material is no reason not to get at least ONE book on whatever
particular subject one needs information and understanding about.
MoeBlee
MoeBlee
Aside from the matter of tommy's system, would you please post a
specification of a theory of flattened mereology? That includes as
much of the following you would be generous enough to provide:
A specification of the language, its primitives, formation rules,
logical axioms/rules, definitions, and non-logical axioms.
And if it's a plain first order theory in classical logic, then all
that would be needed is to specify the primitives of the language,
definitions, and non-logical axioms.
Thanks,
MoeBlee
MoeBlee
P.S.
I know that mereology, incluing formalizations of it, has a role in
philosophy, but where can I find a deveolopment of mathematics, say
arithmetic then analysis, within mereology? What progress has been
made in that direction? Is there a satisfactory treatement of this in
some book or paper? And where can I find such a thing done within
flattened mereology in particular?
MoeBlee
MoeBlee
> On Jul 9, 3:07 pm, MoeBlee <jazzm...@hotmail.com> wrote:
> > 2 Ay(y in [x] <-> y=x) ... axiom
> > 4 Ex Ay y not-in x ... axiom
>
> cartman18:
> "I dont think that can be true in a flat mereology and i doubt if it
> was said or intended."
See my reply directly to cartman18.
> And so despite MoeBlee insisting that line 2 was either
> said or intended by tommy1729, we see that cartman18,
> the mereology expert, says it's doubtful. Line 2 was
> definitely never _said_ by tommy1729, and cartman18
> knows that someone working in mereology wouldn't
> _intended_ to say it either.
tommy said he adopts the empty set axiom. The empty set axiom is:
ExAy ~yex.
If tommy meant otherwise, he would need to say so. All of this
rationalization about mereology is quite aside the point.
> "For instance if x is a set itself , that contains y and 'in' is
> considered to intend the union of the meanings : element of / subset
> of / element of subsets of / subsets of subsets of /
> Then "2" does not follow."
Even IF some indication were later given that 'in' and 'subset of' are
fuzed in meaning, then tommy would have to explain that, re-formulate,
and replace his definition of '[ ]'. One can speculate how to
RECONSTITUTE tommy's statements to come up with something else, that
is not at issue. What is at issue is that what tommy posted, just as
he posted it, is inconsistent.
> This is the key point here. Since the symbol "in" (or
> "e", or "c", or whatever the primitive is) is intended
> to mean _both_ element _and_ subset, we see that:
Such a stipulation is not in tommy's formulation. And even if he did
later say something to such an effect, he never gave an actual axiom
to replace his saying he adopts "the empty set axiom". Nor is there
anything in his formluation to indicate how 'in' and 'subset of' are
to synonymous.
> > 2 Ay(y in [x] <-> y=x) ... axiom
>
> isn't even possible because if y is a _subset_ of x,
> y is a priori in x even though y isn't itself x.
No such post-stipulation appears in tommy's axioms.
> In
> flat mereology, therefore, there usually is _no_ set
> such that y is in the set iff y=x.
(1) tommy gave no flat mereology. He posted what he calls a "set
theory" and mentioned some famous set theory axioms as among his
axioms. Moreover, he said himself what is tantamount to "y in [x] iff
y=x".
(2) By the way, aside from tommy, where is this axiomatization of flat
mereology found from which you are inferring various things?
> And so, I repeat
> cartman18's line once again for emphasis:
>
> "Then "2" does not follow.
> And that does not violate the principle " elementhood = subset " that
> tommy/galathaea ( who ? ) came up with."
>
> Line 2 of MoeBlee's proof doesn't follow from tommy1729's
> explicitly expressed desiderata that the notions of
> elementhood and subsethood be a single concept.
IF tommy ever gave such an explicit desiderata, then he contradicted
himself in yet another sense. Jesse asked for the definition, and
tommy gave it. If that is not what tommy meant, then he needs to
withdraw his definition and replace it with something else. And his
part in his post-definition exchanges with Jesse about the matter
quickly descended into typical tommy-like incoherence.
> Therefore,
> MoeBlee, while having proved that lines 1,2,4 are
> together inconsistent, hasn't proved that the theory TST
> is in fact inconsistent.
TST, as it was STATED by tommy, is inconsistent, as I showed. That Mr.
Transfer Principle can suggest a way to reconstitute the theory to
something consistent is not disputed.
By the way perhaps Mr. Transfer Principle would be so kind as to
actually post here such a reconstituted theory (my apologies if I
overlooked it in another thread).
> > You are exerting too much verbiage trying to rationalize this.
>
> Maybe I am. If galathaea can't convince MoeBlee that he
> doesn't have a proof that TST is inconsistent, why would
> I have any better chance at convincing him?
It's not a matter of convincing me. It's a matter of recognizing for
yourself that how you might reconstitute tommy's theory is a different
matter from what the theory is at it was posted.
> But let's see
> whether the words of cartman18 can convince MoeBlee that
> he doesn't have an inconsistency proof.
So far, he's been pretty off base.
MoeBlee
Jesse F. Hughes
>>
>> Now, we'll ignore the obviously nonsensical axioms
>> (5) and (6). Axiom
>> 2 refers to the axiom of the empty set. As Moe
>> points out, there
>> really is only one axiom known as the empty set
>> axiom:
>>
>> (Ex)(Ay)NOT(y in x).
>>
>> You can pretend that Tommy meant something else, but
>> he didn't.
>
> As commented above ; it holds unless y is the empty set.
Tommy surely could have said so when asked what he meant by the empty
set axiom. Or he could have stated the axiom to begin with. He
didn't, yet you assume that he had a clear idea in mind and simply
failed to express it.
> In fact , even this can be defended if y = [y] and 3-valued logic is allowed.
>
> BEWARE of 3-valued logic.
Er, whatever. It seems fairly ridiculous to think that Tommy meant to
be working in 3-valued logic and didn't mention it.
Er, yes, that *is* the straightforward formalization of (1) and (2).
> Once again " in " is your confusion.
>
> your " in " is the ZF version.
No, "in" is just a two-place relation symbol. The formula above is
the straightforward translation of the plain English.
In any case, I won't continue this argument. At the time, I *asked*
Tommy what he meant. He was incapable of stating clearly whether what
I wrote was correct or not. The obvious conclusion is that he meant
nothing precise at all.
--
Jesse F. Hughes
"You may not realize it but THOUSANDS of people read my posts.
You are putting your stupidity on wide display."
-- James S. Harris knows about wide displays of stupidity.
Transfer Principle
> Re Jul 10, 2:36 pm, cartman18 <cartmaneri...@hotmail.com>:
> If tommy's system is in some special 3-value logic, then he should
> have said so.
From a post of tommy1729 dated September 16, 2008, at 2049
Greenwich time (2249 West European Summer Time):
"a typical sci.math discussion.
the answer ?
-> 3 valued logic !
since the question of the OP is similar to :
is 0 negative or positive ?
and the answer is neither ;
thus the question + or - for every real has 3 possible outcomes.
binary representations clearly " fail " but 3-valued logic works very
fine !!"
David Ullrich's response to tommy1729 dated September 17, 2008,
at 1002 Greenwich time:
"It's certainly true that 0 is neither positive nor negative.
The idea that this somehow leads to or requires 3-valued
logic is simply stupid."
tommy1729's response to Ullrich dated September 17, 2008, at
1639 Greenwich time (1839 West European Summer Time):
"first you admit , then you take that back to say im stupid ?
three possible values => positive , negative , neither.
thus three valued logic.
surely even you can understand that ?!?
if you agree that the question is A positive or negative has 3
potential answers for any real A , but only one correct for A = 0 ..."
Transfer Principle
> On Jul 10, 3:03 pm, cartman18 <cartmaneri...@hotmail.com> wrote:
> > But i guess it happens alot on sci.math.
> What happens? That a person gets called a crank merely for proposing a
> theory other than ZFC?
There's a strong correlation between opposition to ZFC
and being labeled a so-called "crank," whether MoeBlee
will admit it or not. I've already noticed this
correlation, and now so has cartman18.
> As to the latter, sure, people talk about Z, ZF, NBG, NF, constructive
> type theory, category theory, IST
IST, like Srinivasan? OK, then, is Srinivasan considered
to be a "crank," or not?
> PA, PRA, constructive set theory,
> AFA, category theory, mereology
Mereology? That's the whole point of this entire thread,
namely whether tommy1729 is trying to propose a mereology
theory and whether he should called "crank" for it!
> naive Cantor set theory
Naive Cantor set theory? Isn't that theory _inconsistent_
as proved by Russell (as in Russell's paradox)? If anyone
deserves to be called "crank," it's an adherent of naive
Cantor set theory. Notice that I don't consider TST to be
inconsistent in the same way that naive Cantor set theory
is inconsistent. Possibly MoeBlee believes otherwise.
> there's a poster who seems to come up with his "theory of the week".
Obviously MoeBlee is referring to zuhair. We all know
that zuhair used to be called "crank." Now he's a
sort of reformed ex-"crank."
> But there are not many non-cranks who happen to propose original
> theories in sci.math and sci.logic. Such discussions are usually found
> at FOM, where all kinds of research is discussed, even as today one
> poster mentioned a theory he devised without the axiom of
> extensionality (or some alternative to it)
Sounds interesting. I could've sworn that, back when
someone (other than MoeBlee) was trying to prove one
of zuhair's theories inconsistent, someone provided a
link to a theory in which somehow, Extensionality came
out as a _theorem_. This was well over a year ago, so
I don't recall the context.
Of course, we know how Virgil believes that all "sane"
theories satisfy Extensionality. So I wonder whether
Virgil would consider this theory that MoeBlee is
mentioning here to be "sane." Then again, I don't know
what the heck this "FOM" place is, or whether Virgil
or posters similar to him are regular posters there.
> > The problem with paying for books is
> > - in my humble opinion - you only know if it was good AFTER you read it.
> One can take advice and opinions from other people, reference
> bibliographies, read reviews, read portions online, read portions in a
> bookstore or library. Of course, no book comes with a guarantee that
> it will suit you.
Aha! I'm glad to see that cartman18 has also seen a
flaw in MoeBlee's repeated suggestions that the
"cranks" ought to read a book.
Also, I've already mentioned another flaw with this
advice that has nothing to do with money. Interactive
discussion with someone who's more familiar with the
new theory (including the inventor of the theory) is
much more feasible in an online forum than by reading
a book. Indeed, this is the 21st century. In this day
and age, with the amount of technology available, I
consider the advice that the best way to learn or
discuss something is to read it in a book to be -- to
put it bluntly -- _archaic_.
Transfer Principle
> On Jul 9, 9:31 pm, "Jesse F. Hughes" <je...@phiwumbda.org> wrote:
> > | 6) this set theory is game theory in disguise , whatever holds in
> > | game theory can be restated in this set theory.
> "this SET theory" [all caps added]
> > is complete and consistant apart from solving
> > | equations.
> > | this set theory
> "this SET theory" [all caps added]
At this point in the discussion, my argument was that
MoeBlee's translation from tommy1729's axiom (2) from
English ("axiom of the empty set") to object language
("ExAy ~yex") was wrong, because it doesn't follow in
a _mereology_ theory that such an object exists.
MoeBlee's counterargument here is that in tommy1729's
axiom (6), the phrase "set theory" appears, which
means that MoeBlee is justified in translating the
English axiom "axiom of the empty set" into the
object language as "ExAy ~yex", since this is the
set theoretical axiom of the empty set and axiom (6)
uses the phrase "set theory." At any rate, here our
arguments should result in a wash, since my use of
the word "mereology" to translate tommy1729's axiom
should be equally valid as MoeBlee's use of the phrase
"set theory" to translate the axiom.
Part of the problem here is that to galathaea, the
words "set theory" and "mereology" are not mutually
exclusive, in that the objects of a mereology theory
can still be called "sets." Indeed, later on she even
criticized me for making "set theory" and "mereology"
sound as if they are mutually exclusive, and argued
that every set theory, even ZFC, has a mereology (but
instead of the _flattened_ mereology, ZFC would have
the _standard_ mereology).
And so tommy1729, following galathaea, used the word
"set" to describe objects of his theory, and called
his theory TST, for "tommy1729's _set_ theory." But
my use of the phrase "standard mereology," following
galathaea, only led to confuse tommy1729's opponents,
who criticized me for suggesting that ZFC would have
something called "standard mereology."
Since no one other than galathaea claims that set
theory and mereology are not mutually exclusive (not
even others who work in mereology, including zuhair
and Stanford), and such a claim only led to confusion,
I no longer claim that every theory including ZFC has
a mereology. But suddenly, the definitions of "set
theory" and "mereology" have arisen again, since these
definitions are crucial for translating tommy1729's
axioms from English into object language.
With all of this in mind, though, I will declare that
our use of the phrases "set theory" and "mereology" to
translate tommy1729 from English to object language is
indeed a wash. So I can no longer claim that the word
"mereology" is alone sufficient to determine what
exactly tommy means by "axiom of the empty set."
So now what? We are left wondering what exactly
tommy1729 means by "axiom of the empty set." I believe
still that the mereological empty set is the intended
definition -- _because_ the set theoretical definition
of empty set leads to a contradiction. The former, not
the latter, satisfies tommy1729's desiderata.
No matter what one thinks tommy1729's desiderata to be,
one of them is obviously not that the theory should be
easily proved inconsistent!
I believe that if there are two possible definitions of
something (that is, two possible translations from
English to object language), and one of the definitions
leads to a contradiction, that _proves_ that the other
definition is the intended one. On the other hand, the
opponents of tommy1729 appear to me to believe that if a
translation from English to object language leads to a
contradiction, then the theory is gibberish, and "not
even wrong," and not worth considering.
So to me, MoeBlee's proof that the set theoretic
definition of "empty set" leads to a contradiction is
_proof_ that tommy1729 intends the other definition, the
mereological definition, of "empty set."
Of course, cartman18's mentioning of three-valued logic
throws a wrench into the mix. With three-valued logic,
it might be possible that MoeBlee's definition of empty
set can still be used, yet his proof is still not valid,
because the formula:
[]c[]
has the third truth value.
I'm not completely sure how three-valued logic works,
but I once read somewhere that three-valued logic can
be used to resolve Russell's paradox, because an
object x satisfying:
xex <-> ~xex
can still hold if:
xex
has the third truth value.
(And this can be tied back to MoeBlee's "schnozzolaology"
example from earlier. Perhaps "schnozzolaology" happens
to be a theory with three truth values. Then there can
exist a "schnozzola" that contains all "schnozzolas" that
don't contain themselves, and whether this "schnozzola"
contains itself has the third truth value.)
Transfer Principle
> ,----
> |
> | 1) axiom of extensionality
> |
> | 2) axiom of the empty set
> |
> | 3) axiom of pairing
> |
> | 4) axiom of union
> |
> | 5) non-standard elements within the set of real numbers always have
> | properties that correspond to the properties of infinitesimal and
> | unlimited elements.
> |
> | 6) this set theory is game theory in disguise , whatever holds in
> | game theory can be restated in this set theory.
> |
> | this set theory is complete and consistant apart from solving
> | equations.
> |
> | this set theory is the analogue of a computer with oo resourses (as
> | should be since math is about computation)
> |
> | 7) axiom of logic : x = [x] ( also if x = empty )
> `----
> Now, we'll ignore the obviously nonsensical axioms (5) and (6).
I disagree that axioms (5) and (6) are obviously nonsensical,
for both (5) and (6) sound like Conway's surreal numbers. We
already know that there exist infinitesimal and unlimited
surreal numbers, and they are used in game theory. So we
can interpret (5) and (6) as asserting that the surreals can
be constructed in this theory. But, like Hughes, I won't
attempt to rewrite (5) or (6) into object language.
And so let me try to write the other axioms into the object
language, using mereology, based on a hybrid of what I see
in tommy1729's, galathaea's, and cartman18's posts, as well
as the mereology page at Stanford.
Axiom 1) is the easiest. There's no mereological reason to
deviate from extensionality:
1) AxAy (x=y <-> Az (zcx <-> zcy))
For Axiom 2), I use the axiom called "Bottom" that's listed
on the Stanford page. It appears that galathaea is using
this definition of empty set:
2) ExAy xcy
I've already explained why such an object must be empty. In
particular, recall that "c" acts like "subset" (cartman18
has alluded to this fact several times), so the axiom
asserts that there exists an object that is a part of (i.e.
is a subset of) every other set. And the only set that
could possibly be a subset of every other set is empty. I
have already explained why this object must be unique, so
we can call it "[]".
For Axiom 3), I've mentioned several possibilities for
Pairing earlier in this thread, but the one that seems to
be the most elegant, and follows in the spirit of 2), is:
3) AaAbExAy (xcy <-> acy & bcy)
Once again, this might sound backwards, but we must think
of "c" as being like "subset". So this object [a,b] is a
part ("subset") of every set of which both a and b are
also both parts ("subsets").
Suppose we tried writing Pairing in a way that looks more
familiar to a user of ZFC:
3') AaAbExAy (ycx <-> y=a v y=b)
Suppose that we have:
a = [1,2]
b = [3,4]
(where 1,2,3,4 are all atomic). Then we ought to have:
x = [a,b] = [[1,2],[3,4]] = [1,2,3,4]
yet axiom 3') asserts that only a and b are parts of x, and
not 1,2,3,4 which ought to be part of x since this is a
_flattened_ mereology. The axiom:
3") AaAbExAy (ycx <-> yca v ycb)
is still flawed, because it doesn't assert that [2,3] is a
part of x, which it ought to be in a flattened mereology.
And so we use Axiom 3) instead of 3') or 3").
To me, Axiom 4) is a bit tricky. Earlier cartman18 wrote:
"> |
> | 4) axiom of union
I'm not sure about this one.
But i don't see a problem either.
If you want some kind of Union to exist , you need a similar axiom."
I think the confusion about the Union is that in ZFC, the
if x is a set, the U(x), the set whose existence is
guaranteed by the ZFC Union Axiom, is a set whose elements
are the elements of elements of x -- i.e., the elements of
x are the subsets of U(x). But if x is an object in the
flattened mereology, then all the parts of parts of x are
already parts of x, so U(x) would just be x itself. Indeed
the word "union" appears only one at Stanford, and it
wasn't in the context of a Union Axiom or U(x) (instead
Stanford used the word "Union" the same way that cartman18
did in saying that meaning "c" has the _union_ of the
meaning of "e" and "is a subset of").
And so I'll leave out 4) until either tommy1729, cartman18,
or another mereologist explains what exactly a "Union" is
in the context of mereology.
And that brings us to 7). Let's review what Hughes has to
say about Axiom 7):
> Axiom (7) is the one that is most opaque. I asked Tommy at the time
> what the function symbol [...] meant. Here's what he replied:
> > [x] = is the set that contains x ( only )
> > however x may be a set itself.
> In other words,
> (Ay)(y in [x] <-> y = x).
> The alternative that galathaea (who is, alongside cartman18,
> apparently an expert in mereology) offers is that [...] by definition
> just is the identity function, so that axiom (7) says nothing
> interesting in the least. Rather, it introduces useless notation for
> the identity function.
> In this alternative, axiom (7) is really, utterly irrelevant to TST.
> Rather than assert something interesting (namely, that an
> independently defined and interesting function is in fact equal to the
> identity function in TST), axiom (7) instead introduces superfluous
> notation.
Let's recall the defintion of {} in ZFC as given by Suppes. To
Suppes, {} actually represents four different functions -- a
1-place function {x}, a 2-place function {x,y}, a 3-place
function {x,y,z}, and a 4-place function {x,y,z,w}. I actually
can't see why {} can't be an n-place function symbol for
arbitrarily large (yet finite) n, but Suppes only defines {}
as an n-place function symbol for n=1,2,3,4.
So we can let [] be an n-place function symbol for arbitrarily
large (yet finite) n. Now, as Hughes notes, the 0-place and
1-place function symbols [] are utterly trivial:
[] =def the unique x such that Ay xcy
[a] =def a
We need to reach the 2-place symbol before we find a symbol
whose definition isn't trivial. We might as well let [a,b]
be the object given by the axiom of pairing:
[a,b] =def the unique x such that Ay (xcy <-> acy & bcy)
Once we do that, we can define the 3- and 4-place symbols:
[a,b,d] =def [[a,b],d]
[a,b,d,e] =def [[a,b,d],e]
Note that by definition, we have that [[a,b],d] = [a,b,d],
so that we're already "flattening" all of our sets as the
flattened mereology requires. All we need now are for sets
such as [a,[b,d]] to also flatten to [a,b,d]. And these
are the axioms with which I'd replace 7) -- the axioms
stating that "c" is reflexive, antisymmetric, and
transitive -- the cornerstones of flattened mereology.
7a) Ax xcx
7b) AxAy (xcy & ycx -> x=y)
7c) AxAyAz (xcy & ycz -> x=z)
There's one thing that I haven't incorporated into these
axioms, and that is three-valued logic, which cartman18
and tommy1729 have both mentioned in their posts. But I
need to learn more about three-valued logic before I can
incorporate this into the axioms.
Transfer Principle
> On Jul 9, 8:08 pm, Transfer Principle <lwal...@lausd.net> wrote:
> > MoeBlee, while having proved that lines 1,2,4 are
> > together inconsistent, hasn't proved that the theory TST
> > is in fact inconsistent.
> TST, as it was STATED by tommy, is inconsistent, as I showed. That Mr.
> Transfer Principle can suggest a way to reconstitute the theory to
> something consistent is not disputed.
> By the way perhaps Mr. Transfer Principle would be so kind as to
> actually post here such a reconstituted theory (my apologies if I
> overlooked it in another thread).
Well, I'm not sure whether MoeBlee would count this as a
"reconstituted" theory, but I did translate tommy1729's
axioms 1)-7) (or at least as many as I could) from
English to object language.
What I didn't incorporate into that theory was the
three-valued logic mentioned in cartman18's posts, as
well as from tommy1729's old post in September. Back in
September, tommy1729 suggested that if P is a 1-place
predicate symbol denoting "is positive", then we might
want to have:
"P1" is true.
"P(-1)" is false.
"P0" has the third truth value.
And presumably, if x is not a real number, then "Px"
would also have the third truth value. One thing that
is interesting about this is that we can define the
1-place predicate "is negative" as:
Nx <->def ~Px.
Unfortunately I don't know exactly how 3-valued logic
is supposed to work. Therefore, I don't know how to
incorporate it into the axioms I mentioned earlier.
One problem with trying to incorporate tommy1729's
desiderata into a rigorous theory is that there are
so many of them that differ from ZFC. We know that two
of his desiderata are:
1) There is a largest set U (with card(U)=aleph_aleph_0).
2) The theory is mereological in nature.
So sometimes I want to consider theories which satisfy
_some_ of his desiderata but not others -- and once I
found a theory in which the first desideratum is
satisfied, progressively add more desiderata until all
of them are satisfied.
So at first I tried to find a theory in which 1) is
satisfied, and so searched for theories such as
Z+proper classes in which, being a class theory, it
would prove the existence of the proper class of all
sets (often called U or V). But it was criticized for
not satisfying 2), so that the theory has nothing to do
with tommy1729's TST.
Thus, no one is going to let me satisfy the desiderata
one at a time, but all at once. In the end, it turns
out that this might be better, anyway. It might be
more elegant to have a theory which is mereological,
and the mereology _itself_ provides for a largest
possible set U. All we need is this axiom, which
Stanford calls Top:
ExAy ycx
And voila! We have a largest possible set, and we may
call this set U. This set U has a cardinality, which
_could_ be aleph_aleph_0. But we can build from here
and search for axioms which will guarantee that the set
U whose existence is derived from the Top Axiom will
have cardinality aleph_aleph_0.
But now tommy1729 gives us what appears to be a third
desideratum, which I will accept as such until I hear
someone say otherwise:
3) The theory is based on three-valued logic.
Since I'm not familiar with three-valued logic, I'd
like it if I could delay considering 3) until I become
more familiar with 3-valued logic, and try to work on
theories that satisfy 1) and 2). But then, just as
back when I ignored 2) in favor of 1), someone might
say that if I don't incorporate 3) into the theory
right away, it will have nothing to do with TST.
But notice that, even right now, there's a problem
with the axioms that I have stated so far -- and this
problem has nothing to do with inconsistency. Upon
further inspection of the axioms, I just realized that
none of the axioms that I stated in this, or any other
TST thread, ever prove that more than one object
actually exists! On the surface, it might appear that
the axioms Top and Bottom prove the existence of
objects U and [] -- but it's actually possible that
U=[], and that no set other than [] exists!
Other axioms that appear to prove that more than one
set exists actually don't. The axiom of pairing, which
in ZFC proves the existence of the separate sets 0 and
{0}, can't prove the existence of two sets in the
mereology theory, since [[]]=[]. We have to already
have distinct sets a and b in order to form the set
[a,b] (which still might equal a or b). In older
threads, I tried to include ordered pairs, another of
tommy1729's expressed desiderata, and state that:
AaAbAcAd ((a,b)=(c,d) <-> a=c & b=d)
but in order to prove that (a,b)=(c,d) are distinct,
we have to already have distinct sets a,c (or b,d) --
otherwise, it's possible that every ordered pair is
equal to []!
This problem occurred back in the Ullrich thread,
where Ullrich conceded that in a class theory, one
can prove from Class Comprehension alone that 0 exists
and is a class, but one needs other axioms to prove
that 0 is a set. Otherwise, it might be possible that
0 is a proper class -- and would equal the proper
class V of all sets, since no sets exist! We need to
provide for the existence of one set in order to
guarantee that ~V=0 and hence 0 is a set.
This problem also occured in some of zuhair's old
theories, where it was possible that only one set
exists (often either 0 or a Quine atom depending on
the particular theory). Notice that a theory which
can't prove the existence of more than one set isn't
necessarily inconsistent, since it has a model -- of
course, the universe (carrier set) of this model would
have a cardinality of one. (Also, note that in each of
these examples, as soon as we have two sets, then one
can prove that infinitely many sets exist.)
The solution in some of zuhair's theories was to add
some sort of ad hoc axiom, such as:
ExEy ~x=y
in order to guarantee that at least two objects exist,
and we can do something similar in mereology:
ExEy ~xcy
But it would be much more elegant if we could prove
that at least two objects exist by using desideratum
3) -- 3-valued logic -- that I've been avoiding using
until now! For we have:
"UcU" is true (since ycU for every object y), but
"[]c[]" has the third truth value (via cartman18).
And so if phi is the formula "xcx", then phi(U) and
phi([]) would have different truth values, so that
U and [] must necessarily be distinct -- and so at
least two objects exist. And as soon as we have two
objects, then we can make infinitely many more objects
using ordered pairs.
And so I see that it's generally a good idea to
consider all of the desiderata at once. By looking at
only 1) and ignoring 2), I couldn't see that U should
exist, and by considering 2) and ignoring 3), I
couldn't see that U isn't equal to [].
And so I'll try to come up with a reconstituted theory
as soon as I learn a little more about three-valued
logic (since I don't even know how to _write_ axioms
in 3-valued logic).
Tonico
> On Jul 9, 9:31 pm, "Jesse F. Hughes" <je...@phiwumbda.org> wrote:
>
>
>
>
>
> > Let's review exactly what Tommy said his axioms are:
> > ,----
> > |
> > | 1) axiom of extensionality
> > |
> > | 2) axiom of the empty set
> > |
> > | 3) axiom of pairing
> > |
> > | 4) axiom of union
> > |
> > | 5) non-standard elements within the set of real numbers always have
> > | properties that correspond to the properties of infinitesimal and
> > | unlimited elements.
> > |
> > | 6) this set theory is game theory in disguise , whatever holds in
> > | game theory can be restated in this set theory.
> > |
> > | this set theory is complete and consistant apart from solving
> > | equations.
> > |
> > | this set theory is the analogue of a computer with oo resourses (as
> > | should be since math is about computation)
> > |
> > | 7) axiom of logic : x = [x] ( also if x = empty )
> > `----
> > Now, we'll ignore the obviously nonsensical axioms (5) and (6).
>
> I disagree that axioms (5) and (6) are obviously nonsensical,
> for both (5) and (6) sound like Conway's surreal numbers.
I bet you love (or will love, if you didn't hear of this before), the
(in)famous faith dogma of the catholic church which says "God, our
Creator and Lord, can be known with certainty, by the natural light of
reason from created things. (De fide.)"
There! Obviating the rare pearl in axiom (5) that reads "non-standard
elements within the set of real numbers", the rest of (5) and (6) is
kindda faith dogma as the forementioned dogma of the catholic church:
in particular 6, because theories in disguise are so naughty in
mathematics....ah!
Tonio
Jesse F. Hughes
[blah, blah, blah, blah...]
You seem to be missing the point. I was talking about Tommy's set
theory. You're making up something else.
The only one who should be explaining what Tommy meant is Tommy (not
that his reports are necessarily trustworthy -- anyone can
misrepresent his past opinions of course). Moe and I were responding
to Tommy's suggestions and asking Tommy for clarification. Our proofs
of inconsistency have nothing to do with this different theory you're
discussing.
If Tommy meant what you say he meant, he could have cleared it up
months ago.
As it is, I've no idea why so much time is spent discussing a months
old post by Tommy and the subsequent proofs of inconsistency.
--
"By initially making it virtually impossible to maintain a heterogenous
environment of Word 95 and Word 97 systems, Microsoft offered its customers
that most eloquent of arguments for upgrading: the delicate sound of a
revolver being cocked somewhere just out of sight." --Dan Martinez
Aatu Koskensilta
> Also, some systems require instantiations not be to the same variable
> but rather to 'temporary constants' or things like that.
The more-or-less standard term is 'parameter'.
--
Aatu Koskensilta (aatu.kos...@uta.fi)
"Wovon mann nicht sprechen kann, dar�ber muss man schweigen"
- Ludwig Wittgenstein, Tractatus Logico-Philosophicus
MoeBlee
> MoeBlee <jazzm...@hotmail.com> writes:
> > Also, some systems require instantiations not be to the same variable
> > but rather to 'temporary constants' or things like that.
>
> The more-or-less standard term is 'parameter'.
Okay, though 'parameter' also takes on different senses by different
authors. In any case, if I recall, I have seen 'temporary constant'
used for the situation I mentioned.
MoeBlee
Herbert Newman
Another -imho preferable- term: "arbitrary names".
Herb
master1729
( i quickly comment , i might overlook some things , im in a hurry )
no , rather like cartman said , the reverse axiom of extensionality.
im sorry i stated it wrong.
7c is wrong.
xcy & ycz -> xcz not x=z
>
> There's one thing that I haven't incorporated into
> these
> axioms, and that is three-valued logic, which
> cartman18
> and tommy1729 have both mentioned in their posts. But
> I
> need to learn more about three-valued logic before I
> can
> incorporate this into the axioms.
is [] in [A] ?
yes and no : A = [A] = [[],A] = [[[]],A]
(in TST / fixed point set theory / tommy1729 set theory )
maybe this ' yes and no ' is the origin of 3 valued thinking.
notice how ' yes and no ' only makes sence with the empty set.
and once again the issue about x = [x] and the meaning of " in ".
btw ( you keep forgetting ) there are no " classes " in my set theory.
see thread " fixed point set theory ".
and they are not needed , because no paradoxes occur.
( all sets contain themselves (x = [x]) + no big ordinals )
regards
tommy1729
MoeBlee
> lwalke wrote :
> > 7a) Ax xcx
> > 7b) AxAy (xcy & ycx -> x=y)
> > 7c) AxAyAz (xcy & ycz -> x=z)
>
> 7c is wrong.
Mereology without transitivity? Perhaps someone might say if there is
a such a thing or whether such a thing ordinarily would be called a
'mereology'.
> is [] in [A] ?
>
> yes and no : A = [A] = [[],A] = [[[]],A]
>
> (in TST / fixed point set theory / tommy1729 set theory )
WHAT theory is that NOW?
> maybe this ' yes and no ' is the origin of 3 valued thinking.
Maybe you have no idea what you're doing.
> notice how ' yes and no ' only makes sence with the empty set.
No, I didn't notice that, nor do I even know what you mean by it.
> and once again the issue about x = [x] and the meaning of " in ".
What ABOUT it?
> btw ( you keep forgetting ) there are no " classes " in my set theory.
You mean no PROPER classes, perhaps?
And WHAT set theory?
If there's some 3-valued logic, or something else, then please specify
the language syntax and the logical axioms/rules. Please specify your
non-logical primitives and definitions (in proper definitional form),
and then give your non-logical axioms written in your language
extended by definitions.
Meanwhile, when you refer to your "set theory" or your "theory", it
has no definite reference.
> see thread " fixed point set theory ".
If I spend my time looking for that, will I find a coherently stated
theory?
> and they are not needed , because no paradoxes occur.
Perhaps no contradictions are KNOWN to occur.
> ( all sets contain themselves (x = [x]) + no big ordinals )
That would look great on the wall of graffiti next to the market in my
neighborhood.
MoeBlee
master1729
hmm
i dont know about this one.
for cardinality its fine , but you know i dont like ordinals.
further more , i " proved " U via the " fixed point " idea.
( wont go into details , no time )
>
> And voila! We have a largest possible set, and we may
> call this set U. This set U has a cardinality, which
> _could_ be aleph_aleph_0. But we can build from here
> and search for axioms which will guarantee that the
> set
> U whose existence is derived from the Top Axiom will
> have cardinality aleph_aleph_0.
>
> But now tommy1729 gives us what appears to be a third
> desideratum, which I will accept as such until I hear
> someone say otherwise:
>
> 3) The theory is based on three-valued logic.
hmm desideratum seems a heavy word.
i wasnt aiming at 3-valued , but the idea occured.
notice that russels paradox is resolved WITHOUT 3 valued logic ; all sets contain themselves x = [x] x c x x e x
( i would not have accepted a 3 valued logic solution to Russel btw )
>
> Since I'm not familiar with three-valued logic, I'd
> like it if I could delay considering 3) until I
> become
> more familiar with 3-valued logic, and try to work on
> theories that satisfy 1) and 2). But then, just as
> back when I ignored 2) in favor of 1), someone might
> say that if I don't incorporate 3) into the theory
> right away, it will have nothing to do with TST.
>
> But notice that, even right now, there's a problem
> with the axioms that I have stated so far -- and this
> problem has nothing to do with inconsistency. Upon
> further inspection of the axioms, I just realized
> that
> none of the axioms that I stated in this, or any
> other
> TST thread, ever prove that more than one object
> actually exists! On the surface, it might appear that
> the axioms Top and Bottom prove the existence of
> objects U and [] -- but it's actually possible that
> U=[], and that no set other than [] exists!
i could know more about proving existance.
this is intresting.
i disagree with the ZFC way , but i dont know all the other ways.
timothy golden and i have suggested just taking 0 , 1 and the successor function as axioms.
'seperating number theory and set theory' !?
but im open to alternatives.
congratulations :)
regards
tommy1729
MoeBlee
> lwalke wrote :
> > ExAy ycx
>
> hmm
>
> i dont know about this one.
>
> for cardinality its fine , but you know i dont like ordinals.
And ExAy ycx has WHAT to do with ordinals?
> further more , i " proved " U via the " fixed point " idea.
>
> ( wont go into details , no time )
Little doubt.
> notice that russels paradox is resolved WITHOUT 3 valued logic ; all sets contain themselves x = [x] x c
> x x e x
"x = [x] x c x x e x"
Whatever that means, only you could explain how it "resolves"
Russell's paradox.
You do understand that Russell's paradox does not require any notion
of set or elementhood, but rather, it applies to any 2-place
predicate, right?
> timothy golden and i have suggested just taking 0 , 1 and the successor function as axioms.
What does it mean to take 0 and 1 as axioms?
> 'seperating number theory and set theory' !?
Omigod, you'r such a genius! Separating number theory and set theory!
MoeBlee
Transfer Principle
> > reason to deviate from extensionality:
> > 1) AxAy (x=y <-> Az (zcx <-> zcy))
> no , rather like cartman said , the reverse axiom of extensionality.
> im sorry i stated it wrong.
OK, there's been several references lately to the
"reverse" (or converse) axiom of extensionality. In
fact, I mentioned it back in the WM threads, and
then cartman18 wrote it, then tommy1729 agreed with
cartman18's axiom.
Let's think about what a "reverse" axiom of
extensionality might be. Going back to ZFC, we can
write the following:
Forward Axiom of Extensionality:
AxAy (Az (zex <-> zey) -> x=y)
Reverse Axiom of Extensionality:
AxAy (x=y -> Az (zex <-> zey))
When I first mentioned reverse Extensionality in
the WM threads, it was then pointed out by WM's
opponents that this isn't really an axiom, but
actually a theorem of FOL= alone, because:
AxAy (x=y -> (phi(x) <-> phi(y))
is already valid for every formula phi. In the
WM thread, I was trying to claim that some of WM's
"shifting sets" are actually counterexamples to
(reverse) Extensionality, only to be told that this
is not the case.
And now cartman18 and tommy1729 are referring to a
sort of reverse Extensionality. Therefore, as of
now, I can't figure out what reverse Extensionality
is, but perhaps once I find out, I might be able to
apply it to TST and (its negation to) WM's theory.
> > For Axiom 2), I use the axiom called "Bottom" that's
> > on the Stanford page. It appears that galathaea is
> > using this definition of empty set:
> > 2) ExAy xcy
> is [] in [A] ?
> yes and no : A = [A] = [[],A] = [[[]],A]
> (in TST / fixed point set theory / tommy1729 set theory )
> maybe this ' yes and no ' is the origin of 3 valued thinking.
> notice how ' yes and no ' only makes sence with the empty set.
Both cartman18 and tommy1729 agree on this point. And so
we want []c[A] to have the third truth value for every
set A, and so we write:
2) ExAy (xcy has the third truth value)
But how do we write this? Notice that in logic, to
say that a proposition phi is true we just write "phi,"
and to say that a proposition phi is false we would
write "~phi," since if phi is false then ~phi is true.
So what if phi has the third truth value. Well, we know
that if phi has the third truth value, then so does
~phi, and so we would write this as:
2) ExAy (xcy <-> ~xcy)
Axiom 2) is obviously inconsistent if we are working in
two-valued logic, but in three-valued logic it's valid.
And so we would also have:
[] =def the unique x such that Ay (xcy <-> ~xcy)
> > 7a) Ax xcx
> > 7b) AxAy (xcy & ycx -> x=y)
> > 7c) AxAyAz (xcy & ycz -> x=z)
> 7c is wrong.
> xcy & ycz -> xcz not x=z
An obvious typo on my part. I stand corrected.
> btw ( you keep forgetting ) there are no " classes " in my set theory.
> see thread " fixed point set theory ".
Thanks. I'll definitely check it out.
Transfer Principle
> On Jul 13, 1:24 pm, master1729 <tommy1...@gmail.com> wrote:
> > lwalke wrote :
> > 7c is wrong.
> Mereology without transitivity?
Actually, I was the one who made the error, not tommy1729 --
notice that what I wrote as 7c) isn't transitivitiy. Indeed,
we see that tommy1729 then writes transitivity correctly, in
one of the lines that MoeBlee snipped:
> > xcy & ycz -> xcz not x=z
I wish that I hadn't made that typo, since it only led to
more confusion. But MoeBlee should not hold tommy1729
responsible for _my_ error.
So the answer to MoeBlee's question is _no_, this is not
mereology without transitivity -- rather it's mereology
without _my_ typo error.
> > (in TST / fixed point set theory / tommy1729 set theory )
> WHAT theory is that NOW?
It's all the same theory.
In the old thread "fixed point set theory" back from last
February and March, we discussed that "fixed point" is
supposed to be a schema of the form:
Fixed Point Schema:
If phi is a 1-place function symbol satisfying certain
properties (that have yet to be determined), then
Ex phi(x)=x
And these properties to be determined are chosen such
that the schema is as inclusive as possible without
leading to a contradiction. Notice that due to the
three-valued logic, even instances which appear to lead
to contradictions in two-valued logic don't necessarily
lead to contradictions in three-valued logic. So if we
have the following function (where 1 is atomic):
phi(x) = [], if 1cx
= 1 otherwise
and x happens to be the fixed point of this function,
then we would have that 1cx iff ~1cx. But this only
means that "1cx" has the third truth value.
As soon as one of us (tommy1729, cartman18, or myself)
can determine which instances of the schema avoid any
contradictions in three-valued logic, then we'll be
able to state the Fixed Point Schema.
Jesse F. Hughes
> On Jul 13, 1:24 pm, master1729 <tommy1...@gmail.com> wrote:
>> lwalke wrote :
>
>> > 7a) Ax xcx
>> > 7b) AxAy (xcy & ycx -> x=y)
>> > 7c) AxAyAz (xcy & ycz -> x=z)
>>
>> 7c is wrong.
>
> Mereology without transitivity? Perhaps someone might say if there is
> a such a thing or whether such a thing ordinarily would be called a
> 'mereology'.
No, (7c) is not transitivity as written, due to a typo.
--
I was driving down the interstate through Winslow, Arizona,
I had Seven Vices on my mind --
Sloth and Avarice, Fornication, Television,
Whiskey, Beer and Wine. -- Austin Lounge Lizards
Jesse F. Hughes
> Both cartman18 and tommy1729 agree on this point. And so
> we want []c[A] to have the third truth value for every
> set A, and so we write:
>
> 2) ExAy (xcy has the third truth value)
>
> But how do we write this? Notice that in logic, to
> say that a proposition phi is true we just write "phi,"
> and to say that a proposition phi is false we would
> write "~phi," since if phi is false then ~phi is true.
>
> So what if phi has the third truth value. Well, we know
> that if phi has the third truth value, then so does
> ~phi, and so we would write this as:
>
> 2) ExAy (xcy <-> ~xcy)
>
> Axiom 2) is obviously inconsistent if we are working in
> two-valued logic, but in three-valued logic it's valid.
This may be what you want, but you should clearly state what
three-valued logic you have in mind before stating that it's valid in
that logic, don't you think?
In, for example, Kleene's logic, the third value stands for unknown.
It seems strange to think that []c[A] is unknown, so this logic must
not be what Tommy has in mind (if he has anything at all in mind).
As usual, you seem to have things backwards (to a lesser extent than
Tommy, perhaps). You express desiderata as if they were settled
matters, when you should be starting out stating the calculus you wish
to use.
--
"This sucks," said a Pennsylvania State University student [...] " Why
can't the college let me do what I want to do with my computer? The
school computer security guys are being way more annoying than the
spyware was." -- A student pines for his disabled spyware
master1729
good quotes :)
thanks.
Lwalke3 is my biographer x)
regards
tommy1729
master1729
the issue with Russel is about sets containing themselves or not.
but x = [x] means all sets contain themselves.
>
> > timothy golden and i have suggested just taking 0 ,
> 1 and the successor function as axioms.
>
> What does it mean to take 0 and 1 as axioms?
>
> > 'seperating number theory and set theory' !?
>
> Omigod, you'r such a genius! Separating number theory
> and set theory!
Sure why not ?
Number theory is much older , its foundations dont need ZFC or any mereology or set theory ( only from the viewpoint of set theorists perhaps but not from the viewpoint of number theorists ( who were often critics of cantor btw ) ) and set theory has no applications to number theory anyways ( nor anything else ) apart from perhaps goodstein's sequence. ( hdb even disagrees on that btw )
>
> MoeBlee
>
regards
tommy1729
master1729
> On Jul 13, 1:24 pm, master1729 <tommy1...@gmail.com>
> wrote:
> > lwalke wrote :
>
> > > 7a) Ax xcx
> > > 7b) AxAy (xcy & ycx -> x=y)
> > > 7c) AxAyAz (xcy & ycz -> x=z)
> >
> > 7c is wrong.
>
> Mereology without transitivity? Perhaps someone might
> say if there is
> a such a thing or whether such a thing ordinarily
> would be called a
> 'mereology'.
Galathaea said my ideas were close to mereology.
It cannot be traditional mereology , since then it wouldnt be new.
>
> > is [] in [A] ?
> >
> > yes and no : A = [A] = [[],A] = [[[]],A]
> >
> > (in TST / fixed point set theory / tommy1729 set
> theory )
>
> WHAT theory is that NOW?
they are the same , i just referred to the 3 names under which they have been posted under here on sci.math.
>
> > maybe this ' yes and no ' is the origin of 3
> valued thinking.
>
> Maybe you have no idea what you're doing.
plz
>
> > notice how ' yes and no ' only makes sence with the
> empty set.
>
> No, I didn't notice that, nor do I even know what you
> mean by it.
>
> > and once again the issue about x = [x] and the
> meaning of " in ".
>
> What ABOUT it?
and we end in another circular reasoning.
after 500 posts by me , lwalke , galathaea and others you just keep asking the same things again.
cartman and galathaea have already pointed out what ' in ' means.
and so did lwalke and stanford enc.
and you have read it.
you just wish you hadnt.
>
> > btw ( you keep forgetting ) there are no " classes
> " in my set theory.
>
> You mean no PROPER classes, perhaps?
>
> And WHAT set theory?
once again , as galathaea and others pointed out , and you also read before , i am entitled to call it what i want.
calling something a set is not invalid , not even in mereology.
especially not for the inventors.
>
> If there's some 3-valued logic, or something else,
> then please specify
> the language syntax and the logical axioms/rules.
> Please specify your
> non-logical primitives and definitions (in proper
> definitional form),
> and then give your non-logical axioms written in your
> language
> extended by definitions.
>
> Meanwhile, when you refer to your "set theory" or
> your "theory", it
> has no definite reference.
of course it has no reference , its a totally new concept , yet close to mereology.
rather , many things have been explained , but not accepted.
>
> > see thread " fixed point set theory ".
>
> If I spend my time looking for that, will I find a
> coherently stated
> theory?
you might get a better idea about why i consider aleph_aleph_0 the largest cardinality.
basicly its because aleph_aleph_0 is both the fixed point and the limit of the repeated power function P(x) and thus no larger cardinality can be created by power functions or unions , thus aleph_aleph_0 is the largest cardinality.
aleph_aleph_1 is just imagination or syntax manipulation that is unjustified since there is no function going from aleph_aleph_0 -> aleph_aleph_1 ( power and union dont do that )
>
> > and they are not needed , because no paradoxes
> occur.
>
> Perhaps no contradictions are KNOWN to occur.
>
> > ( all sets contain themselves (x = [x]) + no big
> ordinals )
>
> That would look great on the wall of graffiti next to
> the market in my
> neighborhood.
thats a good idea.
have fun with that.
>
> MoeBlee
>
>
>
regards
tommy1729
master1729
ok till here.
i will snip the rest , since that has nothing to do with my viewpoints and i dont agree.
the fixed point occured because ... oh well read the reply i gave to moeblee here ...
regards
tommy1729
Jesse F. Hughes
> you might get a better idea about why i consider aleph_aleph_0 the
> largest cardinality.
>
> basicly its because aleph_aleph_0 is both the fixed point and the
> limit of the repeated power function P(x) and thus no larger
> cardinality can be created by power functions or unions , thus
> aleph_aleph_0 is the largest cardinality.
>
> aleph_aleph_1 is just imagination or syntax manipulation that is
> unjustified since there is no function going from aleph_aleph_0 ->
> aleph_aleph_1 ( power and union dont do that )
Er, what power function do you have in mind?
Usually, P(X) = { Y | Y c x }, but you claim that in TST, Y e X if and
only if Y c X. Thus, evidently,
P(X) = { Y | Y c X }
= { Y | Y e X }
= X.
The identity function doesn't usually allow the construction of larger
cardinalities.
--
"I told her that I loved her.
She said she loved me too.
Neither one was lying,
Yet it wasn't true." -- Del McCoury Band