Matheology § 116

[WM]

Matheology § 116

How can the assumption of the infinite be justified?
Could not just this seemingly so fruitful hypothsesis of the
infinite have introduced straigth contradictions into mathematics,
thereby destroying the basic nature of this science that is so proud
upon its consistency?
[On the hypothesis of the infinite, Ernst Zermelo's Warsaw notes W4
(p. 171), reported in H.-D. Ebbinghaus, V. Peckhaus: "Ernst Zermelo,
An Approach to His Life and Work", Springer (2007) p. 292.]
For German original texts see: Das Kalenderblatt 100322
http://www.hs-augsburg.de/~mueckenh/KB/KB%20201-400.pdf

Regards, WM

[Jesse F. Hughes]

Er, not to put so fine a point on it, but many decades after he posed
that question, the answer is "apparently not." Oh, we might be wrong
and if so, we will hopefully discover this fact.

But you sure as fuck ain't shown us anything that counts as a "straight
contradiction".

Of course, you are too stupid to know what that means, much less
discover one, so I don't anticipate continuing this conversation, you
incompetent and disingenuous fool.

Do the right thing. Vow never to teach set theoretic topics again,
because you are obviously incapable of basic reasoning. (I would
suggest teaching no mathematics at all, but somehow your own personal
incapacities seem to arise mostly around infinite sets, for reasons
which I do not understand.)

--
Jesse F. Hughes

"Failure is not just a word. It's a verb."
-- James S. Harris failures remedial English

[Michael Stemper]

In article <871uh33...@phiwumbda.org>, "Jesse F. Hughes" <je...@phiwumbda.org> writes:

>WM <muec...@rz.fh-augsburg.de> writes:

>> How can the assumption of the infinite be justified?
>> Could not just this seemingly so fruitful hypothsesis of the
>> infinite have introduced straigth contradictions into mathematics,
>> thereby destroying the basic nature of this science that is so proud
>> upon its consistency?
>> [On the hypothesis of the infinite, Ernst Zermelo's Warsaw notes W4
>> (p. 171), reported in H.-D. Ebbinghaus, V. Peckhaus: "Ernst Zermelo,
>> An Approach to His Life and Work", Springer (2007) p. 292.]
>> For German original texts see: Das Kalenderblatt 100322
>> http://www.hs-augsburg.de/~mueckenh/KB/KB%20201-400.pdf
>
>Er, not to put so fine a point on it, but many decades after he posed
>that question, the answer is "apparently not." Oh, we might be wrong
>and if so, we will hopefully discover this fact.

My impression of this little quote was that it sounded like a rhetorical
question, something intended to open up an examination of that possibility.

>But you sure as fuck ain't shown us anything that counts as a "straight
>contradiction".

I'm willing to bet that if this book exhibited a contradiction rather
than simply asking "could there be one?", he would have been trumpeting
it. In fact, if Zermelo had found a contradiction, it would have been
well-known decades back, and ZF theory would have either been fixed or
tossed into the dustbin of history.

--
Michael F. Stemper
#include <Standard_Disclaimer>
Life's too important to take seriously.

[LudovicoVan]

"Michael Stemper" <mste...@walkabout.empros.com> wrote in message
news:k59gup$qbq$1...@dont-email.me...

> I'm willing to bet that if this book exhibited a contradiction rather
> than simply asking "could there be one?", he would have been trumpeting
> it. In fact, if Zermelo had found a contradiction, it would have been
> well-known decades back, and ZF theory would have either been fixed or
> tossed into the dustbin of history.

Just basic fallacies: all over the place.

-LV

[Jesse F. Hughes]

mste...@walkabout.empros.com (Michael Stemper) writes:

> In article <871uh33...@phiwumbda.org>, "Jesse F. Hughes" <je...@phiwumbda.org> writes:
>>WM <muec...@rz.fh-augsburg.de> writes:
>
>>> How can the assumption of the infinite be justified?
>>> Could not just this seemingly so fruitful hypothsesis of the
>>> infinite have introduced straigth contradictions into mathematics,
>>> thereby destroying the basic nature of this science that is so proud
>>> upon its consistency?
>>> [On the hypothesis of the infinite, Ernst Zermelo's Warsaw notes W4
>>> (p. 171), reported in H.-D. Ebbinghaus, V. Peckhaus: "Ernst Zermelo,
>>> An Approach to His Life and Work", Springer (2007) p. 292.]
>>> For German original texts see: Das Kalenderblatt 100322
>>> http://www.hs-augsburg.de/~mueckenh/KB/KB%20201-400.pdf
>>
>>Er, not to put so fine a point on it, but many decades after he posed
>>that question, the answer is "apparently not." Oh, we might be wrong
>>and if so, we will hopefully discover this fact.
>
> My impression of this little quote was that it sounded like a rhetorical
> question, something intended to open up an examination of that
> possibility.

Ya think?

A brief google didn't yield an English translation of the quote in
context. Perhaps someone else can point us in the right direction.

>>But you sure as fuck ain't shown us anything that counts as a "straight
>>contradiction".
>
> I'm willing to bet that if this book exhibited a contradiction rather
> than simply asking "could there be one?", he would have been trumpeting
> it. In fact, if Zermelo had found a contradiction, it would have been
> well-known decades back, and ZF theory would have either been fixed or
> tossed into the dustbin of history.
--

Quincy (age 5): Baba, play some [computer games].
Mama: Quincy, if you want [Baba] to live, don't make those
suggestions.
Quincy: Make those suggestions. Got it.

[Jesse F. Hughes]

Well, then, prove him wrong, son. Prove him wrong.

Because what he wrote (which was merely expressed as a probability)
seems plausible to me. But, listen, he might be wrong. Maybe Zermelo
was aware that ZF was inconsistent. Surely, though, the onus here is on
showing this fact. So, have you any reason to believe that Zermelo
discovered a contradiction in ZF?

--
"Sure, maybe I have a tiresome task that is nearly impossible, but
part of who I am is an endless amount of energy as long as there is
hope. Without hope, I find that I start to lose focus, and feel, just,
well, hopeless." -- James S. Harris

[LudovicoVan]

"Jesse F. Hughes" <je...@phiwumbda.org> wrote in message
news:87pq4nz...@phiwumbda.org...

> "LudovicoVan" <ju...@diegidio.name> writes:
>> "Michael Stemper" <mste...@walkabout.empros.com> wrote in message
>> news:k59gup$qbq$1...@dont-email.me...
>>
>>> I'm willing to bet that if this book exhibited a contradiction rather
>>> than simply asking "could there be one?", he would have been trumpeting
>>> it. In fact, if Zermelo had found a contradiction, it would have been
>>> well-known decades back, and ZF theory would have either been fixed or
>>> tossed into the dustbin of history.
>>
>> Just basic fallacies: all over the place.
>
> Well, then, prove him wrong, son. Prove him wrong.

Hey, uncle, there is nothing to prove there: and you are the one who teaches
this stuff! Indeed, if you need help here, google up a list of fallacies
and come back with your best bets: on whether you picked up the right one.

> Because what he wrote (which was merely expressed as a probability)
> seems plausible to me.

A fallacy is a logical falsity: nothing to do with contingencies.

> But, listen, he might be wrong. Maybe Zermelo
> was aware that ZF was inconsistent. Surely, though, the onus here is on
> showing this fact. So, have you any reason to believe that Zermelo
> discovered a contradiction in ZF?

The mistake has nothing to do with what Zermelo was or was not aware of.

-LV

[Jesse F. Hughes]

"LudovicoVan" <ju...@diegidio.name> writes:

> "Jesse F. Hughes" <je...@phiwumbda.org> wrote in message
> news:87pq4nz...@phiwumbda.org...
>> "LudovicoVan" <ju...@diegidio.name> writes:
>>> "Michael Stemper" <mste...@walkabout.empros.com> wrote in message
>>> news:k59gup$qbq$1...@dont-email.me...
>>>
>>>> I'm willing to bet that if this book exhibited a contradiction rather
>>>> than simply asking "could there be one?", he would have been trumpeting
>>>> it. In fact, if Zermelo had found a contradiction, it would have been
>>>> well-known decades back, and ZF theory would have either been fixed or
>>>> tossed into the dustbin of history.
>>>
>>> Just basic fallacies: all over the place.
>>
>> Well, then, prove him wrong, son. Prove him wrong.
>
> Hey, uncle, there is nothing to prove there: and you are the one who
> teaches this stuff! Indeed, if you need help here, google up a list
> of fallacies and come back with your best bets: on whether you picked
> up the right one.

I don't see any particular fallacy. You may be thinking that it's an
argument from ignorance, but it isn't. He gave explicit reasons for
believing why, in this case, the absence of evidence is indeed evidence
of absence: if Zermelo had discovered a contradiction, then either he
would have made it public or it is likely that others would also have
discovered the same contradiction in the intervening decades and it
would have been made public then.

>> Because what he wrote (which was merely expressed as a probability)
>> seems plausible to me.
>
> A fallacy is a logical falsity: nothing to do with contingencies.

"A logical falsity"? The term has no apparent meaning to me, aside from
"falsehood" or "contradiction", which you surely did not mean.

>
>> But, listen, he might be wrong. Maybe Zermelo
>> was aware that ZF was inconsistent. Surely, though, the onus here is on
>> showing this fact. So, have you any reason to believe that Zermelo
>> discovered a contradiction in ZF?
>
> The mistake has nothing to do with what Zermelo was or was not aware
> of.

That's odd, because all that Michael was commenting on was the
likelihood that Zermelo himself was aware of a contradiction.

You *did* read what Michael wrote before announcing that it was
fallacious, right?

--
Jesse F. Hughes

"What you call reasonable is suspect since you've proven yourself to
be an enemy of mathematics." -- James S. Harris defends the cause.

[LudovicoVan]

"Jesse F. Hughes" <je...@phiwumbda.org> wrote in message

news:87hapzz...@phiwumbda.org...

> "LudovicoVan" <ju...@diegidio.name> writes:
>> "Jesse F. Hughes" <je...@phiwumbda.org> wrote in message
>> news:87pq4nz...@phiwumbda.org...
>>> "LudovicoVan" <ju...@diegidio.name> writes:
>>>> "Michael Stemper" <mste...@walkabout.empros.com> wrote in message
>>>> news:k59gup$qbq$1...@dont-email.me...
>>>>
>>>>> I'm willing to bet that if this book exhibited a contradiction rather
>>>>> than simply asking "could there be one?", he would have been
>>>>> trumpeting
>>>>> it. In fact, if Zermelo had found a contradiction, it would have been
>>>>> well-known decades back, and ZF theory would have either been fixed or
>>>>> tossed into the dustbin of history.
>>>>
>>>> Just basic fallacies: all over the place.
>>>
>>> Well, then, prove him wrong, son. Prove him wrong.
>>
>> Hey, uncle, there is nothing to prove there: and you are the one who
>> teaches this stuff! Indeed, if you need help here, google up a list
>> of fallacies and come back with your best bets: on whether you picked
>> up the right one.
>
> I don't see any particular fallacy.

Look better.

> You may be thinking that it's an argument from ignorance, but it isn't.

No, that is just opposite of what I have just said.

I won't snip the rest of your lies, to the benefit of young students.

> He gave explicit reasons for
> believing why, in this case, the absence of evidence is indeed evidence
> of absence: if Zermelo had discovered a contradiction, then either he
> would have made it public or it is likely that others would also have
> discovered the same contradiction in the intervening decades and it
> would have been made public then.
>
>>> Because what he wrote (which was merely expressed as a probability)
>>> seems plausible to me.
>>
>> A fallacy is a logical falsity: nothing to do with contingencies.
>
> "A logical falsity"? The term has no apparent meaning to me, aside from
> "falsehood" or "contradiction", which you surely did not mean.
>
>>
>>> But, listen, he might be wrong. Maybe Zermelo
>>> was aware that ZF was inconsistent. Surely, though, the onus here is on
>>> showing this fact. So, have you any reason to believe that Zermelo
>>> discovered a contradiction in ZF?
>>
>> The mistake has nothing to do with what Zermelo was or was not aware
>> of.
>
> That's odd, because all that Michael was commenting on was the
> likelihood that Zermelo himself was aware of a contradiction.
>
> You *did* read what Michael wrote before announcing that it was
> fallacious, right?

-LV

[FredJeffries]

The simplest assumption
that we can make and that suffices for the foundation of arithmetic
(as
well as for that of classical mathematics in its entirety) is
precisely this idea
of the "infinite domains". This idea almost inevitably obtrudes itself
on us as
we engage in logico-mathematical thinking, and, in fact, our entire
science
has been built upon it throughout its historical development.

Ernst Zermelo - Collected Works/Gesammelte Werke, Lecture topics for
Warsaw 1929
"W5. Continuation: Can the consistency of arithmetic be 'proved'?"
page 385

http://www.springerlink.com/content/k7g57u1243086946/
if your library has a subscription

[Jesse F. Hughes]

Right. Very convincing. "Tell me how I am right, and if you can't,
then you're stupid."

Hey, I have a better idea. You tell me how you were right, you silly,
little prig.

>> He gave explicit reasons for
>> believing why, in this case, the absence of evidence is indeed evidence
>> of absence: if Zermelo had discovered a contradiction, then either he
>> would have made it public or it is likely that others would also have
>> discovered the same contradiction in the intervening decades and it
>> would have been made public then.
>>
>>>> Because what he wrote (which was merely expressed as a probability)
>>>> seems plausible to me.
>>>
>>> A fallacy is a logical falsity: nothing to do with contingencies.
>>
>> "A logical falsity"? The term has no apparent meaning to me, aside from
>> "falsehood" or "contradiction", which you surely did not mean.
>>
>>>
>>>> But, listen, he might be wrong. Maybe Zermelo
>>>> was aware that ZF was inconsistent. Surely, though, the onus here is on
>>>> showing this fact. So, have you any reason to believe that Zermelo
>>>> discovered a contradiction in ZF?
>>>
>>> The mistake has nothing to do with what Zermelo was or was not aware
>>> of.
>>
>> That's odd, because all that Michael was commenting on was the
>> likelihood that Zermelo himself was aware of a contradiction.
>>
>> You *did* read what Michael wrote before announcing that it was
>> fallacious, right?
>
> -LV
>
>
>

--
"Am I am [sic] misanthrope? I would say no, for honestly I never heard
of this word until about 1994 or thereabouts on the Internet reading a
post from someone who called someone a misanthrope."
-- Archimedes Plutonium

[FredJeffries]

On Oct 12, 7:31 am, WM <mueck...@rz.fh-augsburg.de> wrote:

The entirety of W4:

W4. How can the assumption of the infinite be justified?

Arithmetic—like basically any other mathematical discipline—consists,
generally
speaking, of propositions comprising infinite multitudes of particular
assertions. Its axioms are concerned with domains of things that can
be
mapped one-to-one (or one-to-many) onto proper partial domains and
hence
are really "actually infinite". To assume such infinite domains (which
do not
always have to be "sets" in the set-theoretic sense of the word!) is
therefore
to make the basic assumption underlying all mathematics, which, as
such,
certainly requires some justification as well (in accordance with the
principle
of sufficient reason!). A "proof", in the proper sense of the word, is
of course
not possible where an axiomatic assumption is concerned, as is the
case here.
But equally impossible is the realization by means of an explicitly
specified
and ready-made model since the infinite as such defies, after all, all
attempts
at making it manifest. Such an assumption is capable of justification
solely
by its success, by the fact that it (and it alone!) has made possible
the creation
and development of all extant arithmetic, which is, in essence, simply
a science of the infinite. But is the existence of this science
justified? Could
it not be the case that this seemingly so fruitful hypothesis of the
infinite
carries contradictions into mathematics, thereby utterly destroying
the real
essence of this science, which prides itself so much on the
correctness of its
inferences? As paradoxical as it may seem in the case of a science
that has
achieved the greatest successes in the two thousand years of its
development,
we cannot immediately dismiss without closer consideration the
possibility
that our mathematics rests on contradictions. But, now, can the
consistency
of ("infinitistic") arithmetic itself be proved by logico-mathematical
means?
To provide a "consistency proof" by means of realization in a model
capable
of exhibition or by embedding the "infinitistic" arithmetic in a
"finitistic"
one is, according to what was said above, out of the question. What
therefore
remains is the possibility of showing that contradictions detectable
by
formal-logical means are not derivable from the arithmetical axioms.
Such
a demonstration, if it were possible, would have to rest on a thorough
and
complete formalization of all the logic relevant to mathematics. Any
"incompleteness"
of the underlying "proof theory" such as a neglected possible
inference would jeopardize the entire proof. But, now, since such
"completeness"
can obviously never be guaranteed, it is,is, in my opinion, not
possible to
furnish a formal proof of the consistency.

From Ernst Zermelo - Collected Works/Gesammelte Werke, pp 383-385

[LudovicoVan]

"Jesse F. Hughes" <je...@phiwumbda.org> wrote in message

news:874nlzz...@phiwumbda.org...

> "LudovicoVan" <ju...@diegidio.name> writes:
>> "Jesse F. Hughes" <je...@phiwumbda.org> wrote in message
>> news:87hapzz...@phiwumbda.org...
>>> "LudovicoVan" <ju...@diegidio.name> writes:
>>>> "Jesse F. Hughes" <je...@phiwumbda.org> wrote in message
>>>> news:87pq4nz...@phiwumbda.org...
>>>>> "LudovicoVan" <ju...@diegidio.name> writes:

<snip>

>>>>>> Just basic fallacies: all over the place.
>>>>>
>>>>> Well, then, prove him wrong, son. Prove him wrong.
>>>>
>>>> Hey, uncle, there is nothing to prove there: and you are the one who
>>>> teaches this stuff! Indeed, if you need help here, google up a list
>>>> of fallacies and come back with your best bets: on whether you picked
>>>> up the right one.
>>>
>>> I don't see any particular fallacy.
>>
>> Look better.
>>
>>> You may be thinking that it's an argument from ignorance, but it isn't.
>>
>> No, that is just opposite of what I have just said.
>>
>> I won't snip the rest of your lies, to the benefit of young students.
>
> Right. Very convincing. "Tell me how I am right, and if you can't,
> then you're stupid."

Do your own home work.

> Hey, I have a better idea. You tell me how you were right, you silly,
> little prig.

A hint is: that was synthesis, not analysis.

Another is that I have snipped what is irrelevant to the point I have
raised.

-LV

[FredJeffries]

W5. Continuation: Can the consistency of arithmetic be "proved"?

Another argument against attempts at proving the consistency would run
as follows: Any formal "proof theory", which would have to underly
such
an attempt, assumes the form of a logico-mathematical theory that is
concerned
with a domain of propositions (or assertions) which are connected by
means of (logical) fundamental relations and which are subject to
certain "axioms",
namely the logical principles. These axioms essentially demand, among
other things, the unlimited possibility of connecting the propositions
under
consideration (in any finite number of combinations). In other words,
they
themselves again presuppose an infinite domain, thereby defining in
turn an
"infinitistic" system in precisely the same sense as that of
arithmetic, whose
very legitimacy is being called into question. Hence, any such "proof"
really
already presupposes what is to be proved. Now, to this line of
reasoning we
could of course raise an objection by which the alleged "circle" can
be avoided,
or so it would appear. The axiom system underlying our "proof theory"
could
be so designed that actually infinite domains would still be permitted
but not
(explicitly) demanded, such as it may certainly happen with non-
categorical
systems, as was explained above. Then, any derivation nominally made
for
unlimited chains of inference (in order to show the consistency) would
hold
all the more for those which are limited: if we cannot derive a
contradiction
from a given assumption by using chains of inference of arbitrary
length, then
we certainly cannot do so by using chains of limited length either!
But, then,
is such a rendition of the logical axioms really feasible? Would we
not rather
have to assume the unlimited validity of the logical principles if
anything at
all is to be "proved" concerning this question of consistency? And it
is precisely
these basic laws that inevitably postulate "infinite" domains, that
is,
domains that can be mapped onto proper parts. But if this is the case,
then
the existence of the infinite as a logical postulate, which must form
the basis
of any "proof theory", is already guaranteed a priori and does not
stand in
need of a proof at all. Generally speaking, propping up the formalism
on the
formalism itself again simply won’t do; at some point, there has to be
real
thought, something has to be posited or assumed. And the simplest

assumption
that we can make and that suffices for the foundation of arithmetic
(as
well as for that of classical mathematics in its entirety) is
precisely this idea
of the "infinite domains". This idea almost inevitably obtrudes itself
on us as
we engage in logico-mathematical thinking, and, in fact, our entire
science
has been built upon it throughout its historical development.

From Ernst Zermelo - Collected Works/Gesammelte Werke, pp 385-387

[Jesse F. Hughes]

Very convincing!

>
>> Hey, I have a better idea. You tell me how you were right, you silly,
>> little prig.

> A hint is: that was synthesis, not analysis.
>
> Another is that I have snipped what is irrelevant to the point I have
> raised.

I don't do homework assigned by silly, little prigs.

Seems to me that you're simply farting. If you have a fucking point,
come right out and make it. If not, release your gas elsewhere.

From where I stand, you had no point at all and you don't want to admit
it, so you'd like for me to make your point for you. This is a
startlingly common strategy on Usenet, and as far as I can recall, it
has *never* worked.

But, keep trying. It's bound to work some day.

>
> -LV
>
>>>> He gave explicit reasons for
>>>> believing why, in this case, the absence of evidence is indeed evidence
>>>> of absence: if Zermelo had discovered a contradiction, then either he
>>>> would have made it public or it is likely that others would also have
>>>> discovered the same contradiction in the intervening decades and it
>>>> would have been made public then.
>>>>
>>>>>> Because what he wrote (which was merely expressed as a probability)
>>>>>> seems plausible to me.
>>>>>
>>>>> A fallacy is a logical falsity: nothing to do with contingencies.
>>>>
>>>> "A logical falsity"? The term has no apparent meaning to me, aside from
>>>> "falsehood" or "contradiction", which you surely did not mean.
>>>>
>>>>>
>>>>>> But, listen, he might be wrong. Maybe Zermelo
>>>>>> was aware that ZF was inconsistent. Surely, though, the onus here is
>>>>>> on
>>>>>> showing this fact. So, have you any reason to believe that Zermelo
>>>>>> discovered a contradiction in ZF?
>>>>>
>>>>> The mistake has nothing to do with what Zermelo was or was not aware
>>>>> of.
>>>>
>>>> That's odd, because all that Michael was commenting on was the
>>>> likelihood that Zermelo himself was aware of a contradiction.
>>>>
>>>> You *did* read what Michael wrote before announcing that it was
>>>> fallacious, right?
>
>
>

--
Jesse F. Hughes
"Imagine an angry mob in a post-apocalyptic world out for blood
against anyone who even LOOKS like a mathematician--whatever that
vaguely means to them." -- James S. Harris has odd dreams

[LudovicoVan]

"Jesse F. Hughes" <je...@phiwumbda.org> wrote in message

news:87zk3ry...@phiwumbda.org...
<snipped>

> From where I stand, you had no point at all and you don't want to admit
> it, so you'd like for me to make your point for you. This is a
> startlingly common strategy on Usenet, and as far as I can recall, it
> has *never* worked.

I just won't spoil it. -- But, there is no understanding with the liar,
only waste.

-LV

[Jesse F. Hughes]

Oh, dear! Now I'll never know how you were correct and insightful!

My life is a hollow shell.

Fuckin' transparent moron.

--
"Do you know some logic? Please apply it.
If all a in A also are b in B, then it is not excluded that also a c
in C that is not in A nevertheless is a b in B."
-- Wolfgang Meuckenheim, an actual professor

[LudovicoVan]

"Jesse F. Hughes" <je...@phiwumbda.org> wrote in message

news:87vcefx...@phiwumbda.org...

> "LudovicoVan" <ju...@diegidio.name> writes:
>> "Jesse F. Hughes" <je...@phiwumbda.org> wrote in message
>> news:87zk3ry...@phiwumbda.org...
>> <snipped>
>>
>>> From where I stand, you had no point at all and you don't want to admit
>>> it, so you'd like for me to make your point for you. This is a
>>> startlingly common strategy on Usenet, and as far as I can recall, it
>>> has *never* worked.
>>
>> I just won't spoil it. -- But, there is no understanding with the liar,
>> only waste.
>
> Oh, dear! Now I'll never know how you were correct and insightful!
>
> My life is a hollow shell.
>
> Fuckin' transparent moron.

Just re-read my first reply to you, fuckin' stupid liar.

-LV

[LudovicoVan]

"LudovicoVan" <ju...@diegidio.name> wrote in message
news:k59r2k$2gp$1...@dont-email.me...

In fact, I rather wonder how so many people seem to think that their going
round in circles may work indeed but with the morons. Morons hypnotizing
other morons, that's our social ladder.

-LV

[Jesse F. Hughes]

FredJeffries <fredje...@gmail.com> writes:

> On Oct 12, 7:31 am, WM <mueck...@rz.fh-augsburg.de> wrote:
>> Matheology § 116
>>
>> How can the assumption of the infinite be justified?
>>    Could not just this seemingly so fruitful hypothsesis of the
>> infinite have introduced straigth contradictions into mathematics,
>> thereby destroying the basic nature of this science that is so proud
>> upon its consistency?
>> [On the hypothesis of the infinite, Ernst Zermelo's Warsaw notes W4
>> (p. 171), reported in H.-D. Ebbinghaus, V. Peckhaus: "Ernst Zermelo,
>> An Approach to His Life and Work", Springer (2007) p. 292.]
>> For German original texts see: Das Kalenderblatt 100322http://www.hs-augsburg.de/~mueckenh/KB/KB%20201-400.pdf
>
> The entirety of W4:
>
> W4. How can the assumption of the infinite be justified?
>

> Arithmetic--like basically any other mathematical discipline--consists,

Thanks, Fred!

--
Jesse F. Hughes
"If anything is true in general about Usenet, it's that people can go
on and on about just about anything." -- James Harris speaks the
truth.

[Jesse F. Hughes]

"LudovicoVan" <ju...@diegidio.name> writes:

> "Jesse F. Hughes" <je...@phiwumbda.org> wrote in message
> news:87vcefx...@phiwumbda.org...
>> "LudovicoVan" <ju...@diegidio.name> writes:
>>> "Jesse F. Hughes" <je...@phiwumbda.org> wrote in message
>>> news:87zk3ry...@phiwumbda.org...
>>> <snipped>
>>>
>>>> From where I stand, you had no point at all and you don't want to admit
>>>> it, so you'd like for me to make your point for you. This is a
>>>> startlingly common strategy on Usenet, and as far as I can recall, it
>>>> has *never* worked.
>>>
>>> I just won't spoil it. -- But, there is no understanding with the liar,
>>> only waste.
>>
>> Oh, dear! Now I'll never know how you were correct and insightful!
>>
>> My life is a hollow shell.
>>
>> Fuckin' transparent moron.
>
> Just re-read my first reply to you, fuckin' stupid liar.

Done. I still don't get it.

So, spell it out. Tell me what Michael's fallacy was and show me how he
committed that fallacy.

--
"He isn't capable of actually defining his terms, or axiomatizing
them, or deriving consequences from them. The kindest course of action
is to humor him[...]Just pat him on the head and say 'Tony, aren't you
the cutest little mathematician!'" -- Daryl McCullough on Tony Orlow.