| Topic: |
Religions > Atheism |
| User: |
"" |
| Date: |
12 Aug 2007 04:09:41 PM |
| Object: |
(mathematical) proof that there is no God |
* Definition: "God" means a being which is omniscient and omnipotent.
I intend to prove no such being can possibly exist.
(If you want to claim that there's a supernatural being which isn't
omniscient, or which isn't omnipotent, I have no proof against
that claim. I'm only disproving the usual claim.)
* Assume there is such a "God".
Because it's omniscient, it knows all the mathematical sets that
are even possible, not just the ones humans may eventually envision
or construct or prove to exist, but all the rest of the sets too.
Because it's omnipotent, it can construct the set of all sets.
Because it's omniscient, it knows for each set whether that set
contains itself as an element or not. (For example, the set of all
sets *does* contain itself as an element.)
Because it's omnipotent, it can construct the subset of the set of
all sets such that the set doesn't contain itself, i.e. the Russell
set. Unfortunately we now have a contradiction at this point, the
set contains itself iff it does not contain itself.
<http://en.wikipedia.org/wiki/Russell's_paradox>
<http://plato.stanford.edu/entries/russell-paradox/>
Hence one of our assumptions must have been false.
But we had only one assumption, namely that such a "God" exists.
Q.E.D.
<http://www.jimloy.com/logic/russell.htm>
"The story is a lie."
(That quote refers specifically to the story of "the Barber of Seville",
but the stories of "God" are all lies too,
the JHVH/Allah story, the "Great Spirit" story,
the Vedic stories, and all the others too.)
That brings up the question: Is lying for Jesus a sin?
That last Web page, though delightful in the way it deals with the
story of the Barber of Seville, has a flaw:
A set can contain sets. The set {{A, B, C}, {x, y}} contains two sets
{A, B, C} and {x, y}. It also contains the empty set, by the way.
No, it does not *contain* the empty set.
The empty set is a subset, but not an element.
Switching the definition of "contain" mid-paragraph is a no-no!!
Thou shalt not do that!!
Later in the same Web page:
... Kurt Godel proved that Number Theory (and by identical arguments,
every branch of mathematics) is inconsistent.
No, he proved it can't be simultaneously consistent and complete.
It's either inconsistent or incomplete.
(We hope it's incomplete, not inconsistent!)
.
|
|
| User: "Greywolf" |
|
| Title: Re: (mathematical) proof that there is no God |
12 Aug 2007 04:39:59 PM |
|
|
<SmarterThanTheAverageTroll@math.info.invalid> wrote in message
news:13butoli64qbv5c@corp.supernews.com...
* Definition: "God" means a being which is omniscient and omnipotent.
I intend to prove no such being can possibly exist.
'God' planned for his angels and mankind to be blissfully happy creatures
and reflect that blissful happiness right back onto him ... or 'them'. So
with the help of his son, 'God', 'God' designed, then created 'perfect'
angels, and man and woman -- *knowing* perfectly well *beforehand* that
things would not turn out the way they divinely planned. And why not?
Because the pair chose to create evil and muck up everything.
Well, they didn't plan for angels and mankind to be blissfully happy
creatures in the first place then!!
What's that old saying? 'Do the math'?
(Pssst. There's NO way, and I mean NOOOO way, a loving 'God' would *ever*
produce a universe like the one we're living in. And it doesn't take a math
genius to figure it out either.)
That said. Go get em' tiger! Math that Omni-nothing, Good-for-Nothing,
make-believe 'God' right out of existence!
Greywolf
.
|
|
|
| User: "Aatu Koskensilta" |
|
| Title: Re: (mathematical) proof that there is no God |
12 Aug 2007 05:00:09 PM |
|
|
"Greywolf" <greywolf@cybrzn.com> writes:
(Pssst. There's NO way, and I mean NOOOO way, a loving 'God' would *ever*
produce a universe like the one we're living in. And it doesn't take a math
genius to figure it out either.)
In the theological literature on theodicy you'll find oodles of
explanations for the apparent contradiction between God's goodness and
the evils of this world. A particularly disgusting illustration of one
approaches is found in Collin's _The Language of God_. Collin tells
his daughter was raped, and informs us this might have been allowed to
pass by God to teach him he can't forever shield his daughter from the
perils of the world. One wonders whether the rape was also a gentle
hint from a loving God to the poor girl that the world isn't always
flowers and sunshine. Less repulsive alternatives have been offered,
of course.
That said. Go get em' tiger! Math that Omni-nothing, Good-for-Nothing,
make-believe 'God' right out of existence!
There is no mathematical proof of God's non-existence. The troll's
"proof" was a typical example of the sort of inane "logical" waffling
some atheists seem to have a peculiar fondness of, which perhaps was
the point.
--
Aatu Koskensilta (aatu.koskensilta@xortec.fi)
"Wovon man nicht sprechen kann, daruber muss man schweigen"
- Ludwig Wittgenstein, Tractatus Logico-Philosophicus
.
|
|
|
| User: "Greywolf" |
|
| Title: Re: (mathematical) proof that there is no God |
12 Aug 2007 07:40:54 PM |
|
|
"Aatu Koskensilta" <aatu.koskensilta@xortec.fi> wrote in message
news:87tzr476s6.fsf@huxley.huxley.fi...
"Greywolf" <greywolf@cybrzn.com> writes:
(Pssst. There's NO way, and I mean NOOOO way, a loving 'God' would *ever*
produce a universe like the one we're living in. And it doesn't take a
math
genius to figure it out either.)
In the theological literature on theodicy you'll find oodles of
explanations for the apparent contradiction between God's goodness and
the evils of this world. A particularly disgusting illustration of one
approaches is found in Collin's _The Language of God_. Collin tells
his daughter was raped, and informs us this might have been allowed to
pass by God to teach him he can't forever shield his daughter from the
perils of the world. One wonders whether the rape was also a gentle
hint from a loving God to the poor girl that the world isn't always
flowers and sunshine. Less repulsive alternatives have been offered,
of course.
Yep. And they all point to the fact that 'God's people' aren't *really*
looking for truth. They *want* to belive. And come Hell or high water that's
*exactly* what they're going to do. But they'll wish you ill-will -- even
your *death* in some instances -- for not 'sharing' their irrational
beliefs.
That said. Go get em' tiger! Math that Omni-nothing, Good-for-Nothing,
make-believe 'God' right out of existence!
There is no mathematical proof of God's non-existence.
Yeah. <sheepishly admitted> I was guilty of what I often criticize
Christians for not doing: Not pointing out self-evident errors. But it would
be best for an atheist firmly grounded in mathmetics, in this particular
instance, to point to the error this atheist innocently made.
Greywolf
The troll's
"proof" was a typical example of the sort of inane "logical" waffling
some atheists seem to have a peculiar fondness of, which perhaps was
the point.
--
Aatu Koskensilta (aatu.koskensilta@xortec.fi)
"Wovon man nicht sprechen kann, daruber muss man schweigen"
- Ludwig Wittgenstein, Tractatus Logico-Philosophicus
.
|
|
|
| User: "Aatu Koskensilta" |
|
| Title: Re: (mathematical) proof that there is no God |
13 Aug 2007 04:06:55 AM |
|
|
"Greywolf" <greywolf@cybrzn.com> writes:
Yep. And they all point to the fact that 'God's people' aren't *really*
looking for truth. They *want* to belive. And come Hell or high water that's
*exactly* what they're going to do. But they'll wish you ill-will -- even
your *death* in some instances -- for not 'sharing' their irrational
beliefs.
Some do and some don't.
But it would be best for an atheist firmly grounded in mathmetics,
in this particular instance, to point to the error this atheist
innocently made.
Why? There is no need for any atheist insight in noting the proof is
pure waffle. The problem with this "proof", as with many others of
similar ilk, is that it relies on a number of utterly implausible
implicit assumptions, both mathematical and conceptual (or
theological, if you wish), and on outright mathematical
misconceptions.
--
Aatu Koskensilta (aatu.koskensilta@xortec.fi)
"Wovon man nicht sprechen kann, daruber muss man schweigen"
- Ludwig Wittgenstein, Tractatus Logico-Philosophicus
.
|
|
|
|
|
|
|
| User: "Arindam Banerjee" |
|
| Title: Re: (mathematical) proof that there is no God |
18 Aug 2007 03:41:28 AM |
|
|
<SmarterThanTheAverageTroll@math.info.invalid> wrote in message
news:13butoli64qbv5c@corp.supernews.com...
* Definition: "God" means a being which is omniscient and omnipotent.
Then such a being is sleeping, if not dead, if the being has any sense of
truth, goodness or beauty.
(Which is what I,as the Ruler of Hell, found out when I went to Heaven, to
complain to my grandfather God about conditions: Hell is currently
overpopulated with villains, and they have broken my hip bone in an
encounter and abducted my beautful twelfth wife. ObPlay: Norok Gulzar, or
Hell in Turmoil)
It is more useful to change one's perspectives about the Divine, rather than
give the Divine silly traits and then expect the Divine to live up to them.
But, western - and westernised - idiot-intellectuals have been doing just
that, and there is no sign they are changing for the better. Well, more
work for me then...
:)
.
|
|
|
|
| User: "L" |
|
| Title: Re: (mathematical) proof that there is no God [& Proof of God'sExistence] |
15 Aug 2007 01:35:51 PM |
|
|
Ciao Smarter!
: - )
Thank you for your proof:
SmarterThanTheAverageTroll@math.info.invalid wrote:
* Definition: "God" means a being which is omniscient and omnipotent.
I intend to prove no such being can possibly exist.
(If you want to claim that there's a supernatural being which isn't
omniscient, or which isn't omnipotent, I have no proof against
that claim. I'm only disproving the usual claim.)
* Assume there is such a "God".
Because it's omniscient, it knows all the mathematical sets that
are even possible, not just the ones humans may eventually envision
or construct or prove to exist, but all the rest of the sets too.
Because it's omnipotent, it can construct the set of all sets.
Because it's omniscient, it knows for each set whether that set
contains itself as an element or not. (For example, the set of all
sets *does* contain itself as an element.)
Because it's omnipotent, it can construct the subset of the set of
all sets such that the set doesn't contain itself, i.e. the Russell
set. Unfortunately we now have a contradiction at this point, the
set contains itself iff it does not contain itself.
<http://en.wikipedia.org/wiki/Russell's_paradox>
<http://plato.stanford.edu/entries/russell-paradox/>
Hence one of our assumptions must have been false.
But we had only one assumption, namely that such a "God" exists.
Q.E.D.
<http://www.jimloy.com/logic/russell.htm>
"The story is a lie."
(That quote refers specifically to the story of "the Barber of Seville",
but the stories of "God" are all lies too,
the JHVH/Allah story, the "Great Spirit" story,
the Vedic stories, and all the others too.)
That brings up the question: Is lying for Jesus a sin?
That last Web page, though delightful in the way it deals with the
story of the Barber of Seville, has a flaw:
A set can contain sets. The set {{A, B, C}, {x, y}} contains two sets
{A, B, C} and {x, y}. It also contains the empty set, by the way.
No, it does not *contain* the empty set.
The empty set is a subset, but not an element.
Switching the definition of "contain" mid-paragraph is a no-no!!
Thou shalt not do that!!
Later in the same Web page:
... Kurt Godel proved that Number Theory (and by identical arguments,
every branch of mathematics) is inconsistent.
No, he proved it can't be simultaneously consistent and complete.
It's either inconsistent or incomplete.
(We hope it's incomplete, not inconsistent!)
Translation (Italy):
++
cit on-1
++
*Definizione: "Dio" significa un ente che è omnisciente e omnipotente.
Io intendo provare che non esiste alcun ente di tale tipo.
(Se volete protestare che non c'è un ente che non è omnisciente, o che
non è omnipotente, non ho prova contro ciò. Sto solo confutando la
usuale conclamazione).
Assumiamo che c'è un tale "Dio".
Poiché è omnisciente, "it"(Dio) conosce tutte le posizioni matematiche
che siano mai possibili, non appena qualcuno (umano) eventualmente può
immaginare o costruire o provare per l'esistenza, ma anche tutte le
altre posizioni.
Poiché è omnipotente, "it"(Dio) può costruire un subset di tale set di
tutti set tale che il set non contenga se stesso, tale è detto il
Russell set (il paradosso della pietra pesante ndr.)
Sfortunamtamente ora noi abbiamo una contraddizione, il set contiene se
stesso se non contiene se stesso.
<http://en.wikipedia.org/wiki/Russell's_paradox>
<http://plato.stanford.edu/entries/russell-paradox/>
Da cui una delle due assunzioni deve essere falsa.
Ma noi avevamo solo una assunzione, nominalmente che tale "Dio" esiste.
QED.
++
cit off-1
++
Ti lascio lo sfizio di tradurre in inglese, caro Smarter:
++
cit on-2
++
Subject:
Re: E se dio non esistesse?[more info: teoria degli
insiemi]
Date:
Thu, 02 Aug 2007 19:29:42 GMT
From:
L <parmenide_2002@yahoo.it>
Organization:
[Infostrada]
Newsgroups:
it.cultura.ateismo, it.cultura.filosofia,
it.cultura.religioni
References:
1 , 2 , 3
Grazie del tuo intervento, Paggio.
Vado a leggere ..
Paggio wrote:
On 31 Lug, 20:08, L <parmenide_2...@yahoo.it> wrote:
Gigio wrote:
Teo 1:
===========================
Il dio che è Dio è uno solo.
===========================
Dim:
E' uno solo perché se ve ne fossero più di uno perderebbero la
caratteristica di poter essere Dio.
Qual'è la caratteristica per cui un dio è Dio?
L'omnipotenza.
Se non è omnipotente, un ente cessa di essere Dio, magari sarà qualche
altra cosa, ma non certo Dio.
Tu assumi come assioma che Dio sia onnipotente, cosa che potrebbe non
essere, ma accettando pure questo la tua dimostrazione non e' cmq
valida. Se dio e' onnipotente, puo' creare un'altra creatura a sua
immagine e somglianza onnipotente, di coseguenza dopo tale gesto non
e' piu' unico.
La tua obiezione è equivalente a il famoso "paradosso della pietra
pesante".
(Se non ti risultasse l'equivalenza magari ritorniamo anche su questo).
E' un paradosso apparentemente legittimo.
Però può essere smontato.
Ora ti mostro come:
=========================
Teorema (unicità di Dio):
=========================
IP: ci sia Dio
Tesi: è necessariamente unico.
Dimostrazione:
Supponiamo -ip.2: per assurdo- che vi siano 2 entità onnipotenti
(attributo base di Dio).
Tesi Alogos1 (assurda):
In tal caso una (indifferentemente) delle due entità (dio) sarebbe
onnipotente, ma non racchiuderebbe in sè ogni potenza, visto che -per
ipotesi (ip.2)- vi sarebbe un'altra entità (dio) che gli è disgiunta.
La tesi Alogos1 è però autocontraddittoria, visto che dice "del potere
ogni potenza del singolo dio", ma -contemporaneamente- afferma che vi è
più almeno un altro dio disgiunto da sè, quindi su cui non ha il
completo controllo (o potenza).
cvd.
=========================
Ed inoltre (qui si fa la storia dei NGs! notare la data 17 gennaio
2002):
Newsgroup: it.cultura.religioni
Da: Parmenide <Parmen...@libero.it>
Data: Thu, 17 Jan 2002 19:52:50 GMT
Locale: Gio 17 Gen 2002 20:52
Oggetto: Re: DIO ... [FAQ]: paradosso della pietra pesante
Rispondi all'autore | Inoltra | Stampa | Messaggio singolo | Mostra
originale | Segnala questo messaggio | Trova messaggi di questo autore
oid wrote:
"bip" <b...@sticazz.it> ha scritto nel messaggio
news:N8m18.1861$7m1.69480@twister1.libero.it...
ma dio esiste???
per dio intendi un essere onnipotente?
Allora no!
Come potrebbe, infatti,
creare una pietra pesante,
talmente pesante
che nessuno, neanche lui,
possa mai sollevare.
FAQ
paradosso della pietra pesante:
---
*Può Dio creare (grazie all'Onnipotenza) una pietra, P, talmente
pesante
da non poter essere sollevata da Lui?
#Risposta: se è Onnipotente ... sì la può creare
-> *ma allora non è Onnipotente, visto che c'è una cosa che non può
fare: sollevare P.
*Da cui discende che non può esistere un Dio Onnipotente.
---
teorema sul paradosso della pietra pesante:
in ipotesi che Dio non sia un ente, ma <Colui che è>,
tesi: il paradosso della pietra pesante è errato.
---
dimostrazione:
---
*Può Dio compiere un qualunque atto che lo ponga nella condizione di
essere non Onnipotente?
§No.
§Quindi può creare una Pietra, P, che non possa essere sollevata da
chiunque, tranne che da Lui!
*Gli manca l'azione di mettersi nella condizione di non Onnipotenza?
§No.
§Perché la mancanza di un'azione impossibile è fuori dall'esistenza,
cioè da Dio, essendo <Colui che è>.
c.v.d.
---
Nota1:
I simboli: *,#,§, sono di interlocuzione, per facilitare la lettura.
---
Nota2:
Il paradosso della pietra pesante è quindi causato da un errore sulla
definizione di Dio:
-Nel paradosso Dio è un ente definibile
(quindi con caratteristiche finite di appartenenza, essendo la classe
di
equivalenza chiusa)
-Nella realtà a <Colui che è> nulla prescinde -> è l'Inconcepibile!
(quindi con caratteristiche non finite di appartenenza, essendo la
classe di equivalenza aperta)
---
P.
Con questa osservazione smentisco pure la tua ipotesi successiva,
poiche' ti basi su cio' che ti ho appena smentito.
Con cio' non voglio dire che non credo in Dio, ma ritengo che sia
molto improbabile riuscire a dimostrarne l'esistenza, di conseguenza
credo che sia improbabile l'esistenza di Dio.
Paggio
Sul concetto di definizione applicato a Dio:
Teorema dell'esistenza di "X"
ipotesi A:
Sia "X" = "la collezione di tutte le collezioni" (costruibile,
collezionando gli enti, in bottom up).
ipotesi B:
Sia detta tale collezione "X" = L'ESSERE, nel senso specificato
dall'ipotesi A.
ipotesi C:
Sia "Omega" = "proiezione di X" (costruibile, con la misura di X, in
bottom up).
ipotesi D:
Sia detta tale "Omega" = ESISTERE, nel senso specificato dall'ipotesi C.
Tesi:
1) Si può dimostrare che "Omega è un sottoinsieme di X"
2) Si può dimostrare che "X esiste (grazie ad Omega)"
dimostrazione:
su "Omega = sottoinsieme di X":
Omega è certamente un insieme interno ad X (sottoinsieme proprio di X),
poiché non vi sono insiemi esterni a X, grazie alla ipotesi A.
su "X esistente":
Poiché certissimamente è costruibile la collezione di tutte le
collezioni (in bottom up), ossia X, sarà allora costruibile anche un suo
(di X) sottoinsieme, detto Omega, per misura di X.
Ma -per le ipotesi del teorema- ciò è equivalente a dire che "X esiste".
Infatti solo dall'esserci dell'ente, o dalla collezione di enti, è
possibile il relativo manifestarsi, esistere, mentre "la collezione di
tutte le manifestazioni" non fornisce informazioni (complete) su "tutto
ciò che è" e magari -singolarmente- tale X non si manifesta.
Il teorema quindi afferma un fatto non banale: trovato un metodo per
indicare (bottom up) il "tutto", non si è a conoscenza -specifica- di
tale tutto (si è a conoscenza solo per costruzione induttiva), ma
essendo che il "tutto" -a prescindere dalla relativa dimensione- è pur
maggiore dell'insieme vuoto, allora esiste, cioé afferisce alla sfera
dell'apparire -quando si manifesta- ed il relativo manifestarsi è un
sottoinsieme della completezza della "collezione di tutte le
collezioni", che gode senz'altro della proprietà di esistere, visto che
non è un insieme vuoto.
Ora per le sue caratteristiche, non vi è una collezioni di enti maggiori
di X.
Quindi equivalentemente si può dire che X = "Colui di cui non vi è il
maggiore".
Nella tradizione tale caratteristica è detta di Dio.
cvd.
++
cit off-2
++
Ciao SmarterThanTheAverageTroll,
Lino
.
|
|
|
|
| User: "L" |
|
| Title: Re: (mathematical) proof that there is no God [& Proof of God'sExistence] |
15 Aug 2007 03:01:18 PM |
|
|
Ciao Smarter!
: - )
Thank you for your proof:
SmarterThanTheAverageTroll@math.info.invalid wrote:
* Definition: "God" means a being which is omniscient and omnipotent.
I intend to prove no such being can possibly exist.
(If you want to claim that there's a supernatural being which isn't
omniscient, or which isn't omnipotent, I have no proof against
that claim. I'm only disproving the usual claim.)
* Assume there is such a "God".
Because it's omniscient, it knows all the mathematical sets that
are even possible, not just the ones humans may eventually envision
or construct or prove to exist, but all the rest of the sets too.
Because it's omnipotent, it can construct the set of all sets.
Because it's omniscient, it knows for each set whether that set
contains itself as an element or not. (For example, the set of all
sets *does* contain itself as an element.)
Because it's omnipotent, it can construct the subset of the set of
all sets such that the set doesn't contain itself, i.e. the Russell
set. Unfortunately we now have a contradiction at this point, the
set contains itself iff it does not contain itself.
<http://en.wikipedia.org/wiki/Russell's_paradox>
<http://plato.stanford.edu/entries/russell-paradox/>
Hence one of our assumptions must have been false.
But we had only one assumption, namely that such a "God" exists.
Q.E.D.
<http://www.jimloy.com/logic/russell.htm>
"The story is a lie."
(That quote refers specifically to the story of "the Barber of Seville",
but the stories of "God" are all lies too,
the JHVH/Allah story, the "Great Spirit" story,
the Vedic stories, and all the others too.)
That brings up the question: Is lying for Jesus a sin?
That last Web page, though delightful in the way it deals with the
story of the Barber of Seville, has a flaw:
A set can contain sets. The set {{A, B, C}, {x, y}} contains two sets
{A, B, C} and {x, y}. It also contains the empty set, by the way.
No, it does not *contain* the empty set.
The empty set is a subset, but not an element.
Switching the definition of "contain" mid-paragraph is a no-no!!
Thou shalt not do that!!
Later in the same Web page:
... Kurt Godel proved that Number Theory (and by identical arguments,
every branch of mathematics) is inconsistent.
No, he proved it can't be simultaneously consistent and complete.
It's either inconsistent or incomplete.
(We hope it's incomplete, not inconsistent!)
Translation (Italy):
++
cit on-1
++
*Definizione: "Dio" significa un ente che è omnisciente e omnipotente.
Io intendo provare che non esiste alcun ente di tale tipo.
(Se volete protestare che non c'è un ente che non è omnisciente, o che
non è omnipotente, non ho prova contro ciò. Sto solo confutando la
usuale conclamazione).
Assumiamo che c'è un tale "Dio".
Poiché è omnisciente, "it"(Dio) conosce tutte le posizioni matematiche
che siano mai possibili, non appena qualcuno (umano) eventualmente può
immaginare o costruire o provare per l'esistenza, ma anche tutte le
altre posizioni.
Poiché è omnipotente, "it"(Dio) può costruire un subset di tale set di
tutti set tale che il set non contenga se stesso, tale è detto il
Russell set (il paradosso della pietra pesante ndr.)
Sfortunamtamente ora noi abbiamo una contraddizione, il set contiene se
stesso se non contiene se stesso.
<http://en.wikipedia.org/wiki/Russell's_paradox>
<http://plato.stanford.edu/entries/russell-paradox/>
Da cui una delle due assunzioni deve essere falsa.
Ma noi avevamo solo una assunzione, nominalmente che tale "Dio" esiste.
QED.
++
cit off-1
++
Ti lascio lo sfizio di tradurre in inglese, caro Smarter:
++
cit on-2
++
Subject:
Re: E se dio non esistesse?[more info: teoria degli
insiemi]
Date:
Thu, 02 Aug 2007 19:29:42 GMT
From:
L <parmenide_2002@yahoo.it>
Organization:
[Infostrada]
Newsgroups:
it.cultura.ateismo, it.cultura.filosofia,
it.cultura.religioni
References:
1 , 2 , 3
Grazie del tuo intervento, Paggio.
Vado a leggere ..
Paggio wrote:
On 31 Lug, 20:08, L <parmenide_2...@yahoo.it> wrote:
Gigio wrote:
Teo 1:
===========================
Il dio che è Dio è uno solo.
===========================
Dim:
E' uno solo perché se ve ne fossero più di uno perderebbero la
caratteristica di poter essere Dio.
Qual'è la caratteristica per cui un dio è Dio?
L'omnipotenza.
Se non è omnipotente, un ente cessa di essere Dio, magari sarà qualche
altra cosa, ma non certo Dio.
Tu assumi come assioma che Dio sia onnipotente, cosa che potrebbe non
essere, ma accettando pure questo la tua dimostrazione non e' cmq
valida. Se dio e' onnipotente, puo' creare un'altra creatura a sua
immagine e somglianza onnipotente, di coseguenza dopo tale gesto non
e' piu' unico.
La tua obiezione è equivalente a il famoso "paradosso della pietra
pesante".
(Se non ti risultasse l'equivalenza magari ritorniamo anche su questo).
E' un paradosso apparentemente legittimo.
Però può essere smontato.
Ora ti mostro come:
=========================
Teorema (unicità di Dio):
=========================
IP: ci sia Dio
Tesi: è necessariamente unico.
Dimostrazione:
Supponiamo -ip.2: per assurdo- che vi siano 2 entità onnipotenti
(attributo base di Dio).
Tesi Alogos1 (assurda):
In tal caso una (indifferentemente) delle due entità (dio) sarebbe
onnipotente, ma non racchiuderebbe in sè ogni potenza, visto che -per
ipotesi (ip.2)- vi sarebbe un'altra entità (dio) che gli è disgiunta.
La tesi Alogos1 è però autocontraddittoria, visto che dice "del potere
ogni potenza del singolo dio", ma -contemporaneamente- afferma che vi è
più almeno un altro dio disgiunto da sè, quindi su cui non ha il
completo controllo (o potenza).
cvd.
=========================
Ed inoltre (qui si fa la storia dei NGs! notare la data 17 gennaio
2002):
Newsgroup: it.cultura.religioni
Da: Parmenide <Parmen...@libero.it>
Data: Thu, 17 Jan 2002 19:52:50 GMT
Locale: Gio 17 Gen 2002 20:52
Oggetto: Re: DIO ... [FAQ]: paradosso della pietra pesante
Rispondi all'autore | Inoltra | Stampa | Messaggio singolo | Mostra
originale | Segnala questo messaggio | Trova messaggi di questo autore
oid wrote:
"bip" <b...@sticazz.it> ha scritto nel messaggio
news:N8m18.1861$7m1.69480@twister1.libero.it...
ma dio esiste???
per dio intendi un essere onnipotente?
Allora no!
Come potrebbe, infatti,
creare una pietra pesante,
talmente pesante
che nessuno, neanche lui,
possa mai sollevare.
FAQ
paradosso della pietra pesante:
---
*Può Dio creare (grazie all'Onnipotenza) una pietra, P, talmente
pesante
da non poter essere sollevata da Lui?
#Risposta: se è Onnipotente ... sì la può creare
-> *ma allora non è Onnipotente, visto che c'è una cosa che non può
fare: sollevare P.
*Da cui discende che non può esistere un Dio Onnipotente.
---
teorema sul paradosso della pietra pesante:
in ipotesi che Dio non sia un ente, ma <Colui che è>,
tesi: il paradosso della pietra pesante è errato.
---
dimostrazione:
---
*Può Dio compiere un qualunque atto che lo ponga nella condizione di
essere non Onnipotente?
§No.
§Quindi può creare una Pietra, P, che non possa essere sollevata da
chiunque, tranne che da Lui!
*Gli manca l'azione di mettersi nella condizione di non Onnipotenza?
§No.
§Perché la mancanza di un'azione impossibile è fuori dall'esistenza,
cioè da Dio, essendo <Colui che è>.
c.v.d.
---
Nota1:
I simboli: *,#,§, sono di interlocuzione, per facilitare la lettura.
---
Nota2:
Il paradosso della pietra pesante è quindi causato da un errore sulla
definizione di Dio:
-Nel paradosso Dio è un ente definibile
(quindi con caratteristiche finite di appartenenza, essendo la classe
di
equivalenza chiusa)
-Nella realtà a <Colui che è> nulla prescinde -> è l'Inconcepibile!
(quindi con caratteristiche non finite di appartenenza, essendo la
classe di equivalenza aperta)
---
P.
Con questa osservazione smentisco pure la tua ipotesi successiva,
poiche' ti basi su cio' che ti ho appena smentito.
Con cio' non voglio dire che non credo in Dio, ma ritengo che sia
molto improbabile riuscire a dimostrarne l'esistenza, di conseguenza
credo che sia improbabile l'esistenza di Dio.
Paggio
Sul concetto di definizione applicato a Dio:
Teorema dell'esistenza di "X"
ipotesi A:
Sia "X" = "la collezione di tutte le collezioni" (costruibile,
collezionando gli enti, in bottom up).
ipotesi B:
Sia detta tale collezione "X" = L'ESSERE, nel senso specificato
dall'ipotesi A.
ipotesi C:
Sia "Omega" = "proiezione di X" (costruibile, con la misura di X, in
bottom up).
ipotesi D:
Sia detta tale "Omega" = ESISTERE, nel senso specificato dall'ipotesi C.
Tesi:
1) Si può dimostrare che "Omega è un sottoinsieme di X"
2) Si può dimostrare che "X esiste (grazie ad Omega)"
dimostrazione:
su "Omega = sottoinsieme di X":
Omega è certamente un insieme interno ad X (sottoinsieme proprio di X),
poiché non vi sono insiemi esterni a X, grazie alla ipotesi A.
su "X esistente":
Poiché certissimamente è costruibile la collezione di tutte le
collezioni (in bottom up), ossia X, sarà allora costruibile anche un suo
(di X) sottoinsieme, detto Omega, per misura di X.
Ma -per le ipotesi del teorema- ciò è equivalente a dire che "X esiste".
Infatti solo dall'esserci dell'ente, o dalla collezione di enti, è
possibile il relativo manifestarsi, esistere, mentre "la collezione di
tutte le manifestazioni" non fornisce informazioni (complete) su "tutto
ciò che è" e magari -singolarmente- tale X non si manifesta.
Il teorema quindi afferma un fatto non banale: trovato un metodo per
indicare (bottom up) il "tutto", non si è a conoscenza -specifica- di
tale tutto (si è a conoscenza solo per costruzione induttiva), ma
essendo che il "tutto" -a prescindere dalla relativa dimensione- è pur
maggiore dell'insieme vuoto, allora esiste, cioé afferisce alla sfera
dell'apparire -quando si manifesta- ed il relativo manifestarsi è un
sottoinsieme della completezza della "collezione di tutte le
collezioni", che gode senz'altro della proprietà di esistere, visto che
non è un insieme vuoto.
Ora per le sue caratteristiche, non vi è una collezioni di enti maggiori
di X.
Quindi equivalentemente si può dire che X = "Colui di cui non vi è il
maggiore".
Nella tradizione tale caratteristica è detta di Dio.
cvd.
++
cit off-2
++
Ciao SmarterThanTheAverageTroll,
Lino
.
|
|
|
| User: "Siddharta" |
|
| Title: Re: (mathematical) proof that there is no God [& Proof of God's Existence] |
17 Aug 2007 11:53:25 AM |
|
|
"L" <parmenide_2002@yahoo.it> ha scritto nel messaggio
news:46C35B8C.590464BE@yahoo.it...
Ciao Smarter!
: - )
Thank you for your proof:
SmarterThanTheAverageTroll@math.info.invalid wrote:
* Definition: "God" means a being which is omniscient and omnipotent.
I intend to prove no such being can possibly exist.
(If you want to claim that there's a supernatural being which isn't
omniscient, or which isn't omnipotent, I have no proof against
that claim. I'm only disproving the usual claim.)
* Assume there is such a "God".
Because it's omniscient, it knows all the mathematical sets that
are even possible, not just the ones humans may eventually envision
or construct or prove to exist, but all the rest of the sets too.
Because it's omnipotent, it can construct the set of all sets.
Because it's omniscient, it knows for each set whether that set
contains itself as an element or not. (For example, the set of all
sets *does* contain itself as an element.)
Because it's omnipotent, it can construct the subset of the set of
all sets such that the set doesn't contain itself, i.e. the Russell
set. Unfortunately we now have a contradiction at this point, the
set contains itself iff it does not contain itself.
<http://en.wikipedia.org/wiki/Russell's_paradox>
<http://plato.stanford.edu/entries/russell-paradox/>
Hence one of our assumptions must have been false.
But we had only one assumption, namely that such a "God" exists.
Q.E.D.
<http://www.jimloy.com/logic/russell.htm>
"The story is a lie."
(That quote refers specifically to the story of "the Barber of Seville",
but the stories of "God" are all lies too,
the JHVH/Allah story, the "Great Spirit" story,
the Vedic stories, and all the others too.)
That brings up the question: Is lying for Jesus a sin?
That last Web page, though delightful in the way it deals with the
story of the Barber of Seville, has a flaw:
A set can contain sets. The set {{A, B, C}, {x, y}} contains two sets
{A, B, C} and {x, y}. It also contains the empty set, by the way.
No, it does not *contain* the empty set.
The empty set is a subset, but not an element.
Switching the definition of "contain" mid-paragraph is a no-no!!
Thou shalt not do that!!
Later in the same Web page:
... Kurt Godel proved that Number Theory (and by identical arguments,
every branch of mathematics) is inconsistent.
No, he proved it can't be simultaneously consistent and complete.
It's either inconsistent or incomplete.
(We hope it's incomplete, not inconsistent!)
Translation (Italy):
++
cit on-1
++
*Definizione: "Dio" significa un ente che è omnisciente e omnipotente.
Poiché è omnipotente, "it"(Dio) può costruire un subset di tale set di
tutti set tale che il set non contenga se stesso, tale è detto il
Russell set (il paradosso della pietra pesante ndr.)
Certo che devi essere un mostro in matematica: set e subset si traducono con
insieme e sottoinsieme, e i lemmi inglesi non si usno *mai* in italiano
(quindi prevengo eventuali obiezioni) :-)
Per finire...poi dio illuminò Ernst Zermelo... e tutto andò a posto :-)
.
|
|
|
| User: "L" |
|
| Title: Re: (mathematical) proof that there is no God [& Proof of God'sExistence('rif.1')] |
18 Aug 2007 12:41:38 AM |
|
|
Spero che oltre che esperto di "mostri in matematica", tu sia abbastanza
*esperto di matematica* per dirmi:
1) cosa ci sarebbe di errato nel tradurre set = set ? (non vale più il
principio di identità?)
2) cosa hai da dire (oltre questioni di traduzione) sulla comparazione
delle due dimostrazioni?
Riassumo:
a) quella scritta in inglese proverebbe la inesistenza di un ente con
gli attributi di omniscienza/omnipotenza
b) quella scritta in italiano proverebbe la _esistenza_ nella
apparentemente stessa situazione, specificando -però- che "vi è una
asimmetria tra l'ipotetico e il reificato" per garantire il fatto che le
*esperienze esperimentabili* non sono tutte le ipotesi possibili, ma
solo alcune, e ciò -tra l'altro- risolve il paradosso di Russell che
generava l'aporia [perché NON distingueva lo spazio dell'ipotesi da
quello della misura, per suoi -di Russell- problemi relazionali che
-volendo- si potrebbero trattare da cosa fossero causati].
Vedasi -invece- la dimostrazione assurdità della "Tesi Alogos1" (nella
trattazione di rif.x tale asimmetria: 'rif.1').
Ma anche su ciò si può indagare in dettaglio, sempre per coloro che
apprezzino il tema.
Siddharta wrote:
Certo che devi essere un mostro in matematica: set e subset si traducono con
insieme e sottoinsieme, e i lemmi inglesi non si usno *mai* in italiano
(quindi prevengo eventuali obiezioni) :-)
Per finire...poi dio illuminò Ernst Zermelo... e tutto andò a posto :-)
Grazie dell'avere (spero) letto il tema in discussione.
Non sembrava che né in Italy, né altrove, vi fosse -finora- chi avesse
argomenti per cimentarvicisi, ma ciò era solo prima del tuo intervento,
si intende ..
L
.
|
|
|
| User: "Siddharta" |
|
| Title: Re: (mathematical) proof that there is no God [& Proof of God's Existence('rif.1')] |
18 Aug 2007 11:00:03 AM |
|
|
"L" <parmenide_2002@yahoo.it> ha scritto nel messaggio
news:46C6868F.6D0C3C60@yahoo.it...
Spero che oltre che esperto di "mostri in matematica", tu sia abbastanza
*esperto di matematica* per dirmi:
1) cosa ci sarebbe di errato nel tradurre set = set ? (non vale più il
principio di identità?)
E'una questione di convenzione: se lo scrivi in un articolo (in italiano) te
lo traducono nella nostra lingua :-) Punto e a capo.
2) cosa hai da dire (oltre questioni di traduzione) sulla comparazione
delle due dimostrazioni?
L'anitnomia di Russel è superata: se non definisci assiomaticamente una
teoria, è molto probabile che di imbatti in paradossi.
Che dio esista o no, è un problema che sta al di fuori della logica. Io per
esempio non ci credo, ma non ho bisogno di teoremi logici, che necessitano
di una metalogica, che necessità di una metalogica, che necessita....., per
farmene una ragione.
.
|
|
|
|
|
|
|
| User: "Rudolf Drabek" |
|
| Title: Re: (mathematical) proof that there is no God |
13 Aug 2007 01:23:58 PM |
|
|
On 12 Aug., 23:09, SmarterThanTheAverageTr...@math.info.invalid wrote:
* Definition: "God" means a being which is omniscient and omnipotent.
I intend to prove no such being can possibly exist.
(If you want to claim that there's a supernatural being which isn't
omniscient, or which isn't omnipotent, I have no proof against
that claim. I'm only disproving the usual claim.)
* Assume there is such a "God".
Because it's omniscient, it knows all the mathematical sets that
are even possible, not just the ones humans may eventually envision
or construct or prove to exist, but all the rest of the sets too.
Because it's omnipotent, it can construct the set of all sets.
Because it's omniscient, it knows for each set whether that set
contains itself as an element or not. (For example, the set of all
sets *does* contain itself as an element.)
Because it's omnipotent, it can construct the subset of the set of
all sets such that the set doesn't contain itself, i.e. the Russell
set. Unfortunately we now have a contradiction at this point, the
set contains itself iff it does not contain itself.
<http://en.wikipedia.org/wiki/Russell's_paradox>
<http://plato.stanford.edu/entries/russell-paradox/>
Hence one of our assumptions must have been false.
But we had only one assumption, namely that such a "God" exists.
Q.E.D.
<http://www.jimloy.com/logic/russell.htm>
"The story is a lie."
(That quote refers specifically to the story of "the Barber of Seville",
but the stories of "God" are all lies too,
the JHVH/Allah story, the "Great Spirit" story,
the Vedic stories, and all the others too.)
That brings up the question: Is lying for Jesus a sin?
That last Web page, though delightful in the way it deals with the
story of the Barber of Seville, has a flaw:
A set can contain sets. The set {{A, B, C}, {x, y}} contains two sets
{A, B, C} and {x, y}. It also contains the empty set, by the way.
No, it does not *contain* the empty set.
The empty set is a subset, but not an element.
Switching the definition of "contain" mid-paragraph is a no-no!!
Thou shalt not do that!!
Later in the same Web page:
... Kurt Godel proved that Number Theory (and by identical arguments,
every branch of mathematics) is inconsistent.
No, he proved it can't be simultaneously consistent and complete.
It's either inconsistent or incomplete.
(We hope it's incomplete, not inconsistent!)
My own truth is: because we have free will for certain possible
reasons, it is clear that God has let something open for our disposal,
thus he waived for a small piece of his omnipotence, but individually
he may interfere, if he likes.
Rudi
.
|
|
|
|
| User: "Shubee" |
|
| Title: Re: (mathematical) proof that there is no God |
12 Aug 2007 07:53:39 PM |
|
|
On Aug 12, 2:09 pm, SmarterThanTheAverageTr...@math.info.invalid
wrote:
* Definition: "God" means a being which is omniscient and omnipotent.
I intend to prove no such being can possibly exist.
(If you want to claim that there's a supernatural being which isn't
omniscient, or which isn't omnipotent, I have no proof against
that claim. I'm only disproving the usual claim.)
* Assume there is such a "God".
Because it's omniscient, it knows all the mathematical sets that
are even possible, not just the ones humans may eventually envision
or construct or prove to exist, ...
Your proof is obviously flawed, as all child mathematicians can see,
because there is a problem with the set of all sets even without
postulating the existence of God.
Shubee
http://www.everythingimportant.org/relativity/special.pdf
.
|
|
|
| User: "Paul Ilechko" |
|
| Title: Re: (mathematical) proof that there is no God |
12 Aug 2007 08:02:12 PM |
|
|
Shubee wrote:
On Aug 12, 2:09 pm, SmarterThanTheAverageTr...@math.info.invalid
wrote:
* Definition: "God" means a being which is omniscient and omnipotent.
I intend to prove no such being can possibly exist.
(If you want to claim that there's a supernatural being which isn't
omniscient, or which isn't omnipotent, I have no proof against
that claim. I'm only disproving the usual claim.)
* Assume there is such a "God".
Because it's omniscient, it knows all the mathematical sets that
are even possible, not just the ones humans may eventually envision
or construct or prove to exist, ...
Your proof is obviously flawed, as all child mathematicians can see,
because there is a problem with the set of all sets even without
postulating the existence of God.
That is neither true nor logical. If you really are a mathematician you
can do better than that.
The real problem is that you can't go ahead and claim that a magical
being can do something impossible, and then extrapolate that because
it's impossible, then the magical being can't exist. You either allow
magic into your system or you don't. I'd prefer not to, unless it's Penn
and Teller, but YMMV.
.
|
|
|
|
| User: "Stratum" |
|
| Title: Re: (mathematical) proof that there is no God |
12 Aug 2007 08:39:59 PM |
|
|
Shubee wrote:
Your proof is obviously flawed, as all child mathematicians can see,
because there is a problem with the set of all sets even without
postulating the existence of God.
If you have a problem with "the set of all sets," do you maintain
that such a set cannot exist?
.
|
|
|
| User: "Shubee" |
|
| Title: Re: (mathematical) proof that there is no God |
12 Aug 2007 09:19:05 PM |
|
|
On Aug 12, 6:39 pm, Stratum <stratum...@comcast.net> wrote:
Shubee wrote:
Your proof is obviously flawed, as all child mathematicians can see,
because there is a problem with the set of all sets even without
postulating the existence of God.
If you have a problem with "the set of all sets," do you maintain
that such a set cannot exist?
It is well known by all mathematicians that the set of all sets is an
object so incomprehensible that all the rules of logic break down:
http://en.wikipedia.org/wiki/Set_of_all_sets
http://www-history.mcs.st-and.ac.uk/HistTopics/Beginnings_of_set_theory.html
http://www.math.utah.edu/~pa/math/sets.html
I conclude that if such a childishly simple riddle in mathematics
defies all human comprehension, perhaps understanding the existence of
The Supreme Being is equally problematic.
http://www.everythingimportant.org/Godhead/
http://www.everythingimportant.org/viewtopic.php?t=741
Shubee
.
|
|
|
| User: "Aatu Koskensilta" |
|
| Title: Re: (mathematical) proof that there is no God |
12 Aug 2007 09:25:59 PM |
|
|
Shubee <e.Shubee@gmail.com> writes:
It is well known by all mathematicians that the set of all sets is an
object so incomprehensible that all the rules of logic break down:
The rules of logic in no way break down with the set of all sets. It
simply happens that as usually conceived in mathematics there provably
is no set containing every set. The explanation for this non-existence
is provided in the notion of a set as a collection in the so-called
cumulative hierarchy, as first articulated by Ernst Zermelo (of
Zermelo-Fraenkel set theory fame) in 1930.
I conclude that if such a childishly simple riddle in mathematics
defies all human comprehension, perhaps understanding the existence of
The Supreme Being is equally problematic.
The set of all sets or other similar notions do not defy "all human
comprehension". They also have nothing to do with Gods or any
theological conundrums.
--
Aatu Koskensilta (aatu.koskensilta@xortec.fi)
"Wovon man nicht sprechen kann, daruber muss man schweigen"
- Ludwig Wittgenstein, Tractatus Logico-Philosophicus
.
|
|
|
| User: "Shubee" |
|
| Title: Re: (mathematical) proof that there is no God |
12 Aug 2007 11:55:12 PM |
|
|
On Aug 12, 7:25 pm, Aatu Koskensilta <aatu.koskensi...@xortec.fi>
wrote:
Shubee <e.Shu...@gmail.com> writes:
It is well known by all mathematicians that the set of all sets is an
object so incomprehensible that all the rules of logic break down:
The rules of logic in no way break down with the set of all sets.
Only in the sense that a riddle has appeared where the intuition and
insight of mathematicians comes to an abrupt end. Sure, the most
trivial response is to deny the existence of a profound riddle and to
be satisfied with an arbitrary axiom set having the property that no
paradoxes are known to exist within it and which gives no insight
whatsoever.
It simply happens that as usually conceived in mathematics there
provably is no set containing every set.
You are overlooking the possibility of other axiom sets for set theory
where perhaps the set of all sets exists but the set of all sets not
members of themselves does not exist.
To illustrate, consider a parallel to the childish riddle: "God is
omnipotent. Can God make a rock so heavy that He can't lift it?" It
could very well be that God exists and is all-powerful but that the
requirement for the Supreme Being to make Himself powerless and also
to enumerate all the different ways for the Supreme Being to make
Himself powerless, is non-existent and nonsensical.
Shubee
The explanation for this non-existence
is provided in the notion of a set as a collection in the so-called
cumulative hierarchy, as first articulated by Ernst Zermelo (of
Zermelo-Fraenkel set theory fame) in 1930.
I conclude that if such a childishly simple riddle in mathematics
defies all human comprehension, perhaps understanding the existence of
The Supreme Being is equally problematic.
The set of all sets or other similar notions do not defy "all human
comprehension". They also have nothing to do with Gods or any
theological conundrums.
--
Aatu Koskensilta (aatu.koskensi...@xortec.fi)
"Wovon man nicht sprechen kann, daruber muss man schweigen"
- Ludwig Wittgenstein, Tractatus Logico-Philosophicus
.
|
|
|
| User: "Aatu Koskensilta" |
|
| Title: Re: (mathematical) proof that there is no God |
13 Aug 2007 04:11:40 AM |
|
|
Shubee <e.Shubee@gmail.com> writes:
Sure, the most trivial response is to deny the existence of a
profound riddle and to be satisfied with an arbitrary axiom set
having the property that no paradoxes are known to exist within it
and which gives no insight whatsoever.
There is nothing arbitrary in the standard axioms for set theory. As
said they are evident truths about the cumulative hierarchy, as
explained in any number of set theory textbook, e.g. Michael Potter's
_Set Theory and its Philosophy_. That there is no set of all sets in
the cumulative hierarchy is also one of the evident truths, and indeed
follows from the other evident principles adopted as axioms.
You are overlooking the possibility of other axiom sets for set theory
where perhaps the set of all sets exists but the set of all sets not
members of themselves does not exist.
There are theories of sets in which a set of all sets exist, most
famously Quine's New Foundations. However, these theories do not
codify any notion of set to be found in our actual mathematical
practice and thinking. Unlike theories such as ZFC, NF has no
motivating picture on which its axioms could be seen to be true, it's
a purely formal device of technical interest only.
--
Aatu Koskensilta (aatu.koskensilta@xortec.fi)
"Wovon man nicht sprechen kann, daruber muss man schweigen"
- Ludwig Wittgenstein, Tractatus Logico-Philosophicus
.
|
|
|
| User: "Shubee" |
|
| Title: Re: (mathematical) proof that there is no God |
13 Aug 2007 07:59:39 AM |
|
|
On Aug 13, 2:11 am, Aatu Koskensilta <aatu.koskensi...@xortec.fi>
wrote:
Shubee <e.Shu...@gmail.com> writes:
Sure, the most trivial response is to deny the existence of a
profound riddle and to be satisfied with an arbitrary axiom set
having the property that no paradoxes are known to exist within it
and which gives no insight whatsoever.
There is nothing arbitrary in the standard axioms for set theory. As
said they are evident truths about the cumulative hierarchy, as
explained in any number of set theory textbook, e.g. Michael Potter's
_Set Theory and its Philosophy_. That there is no set of all sets in
the cumulative hierarchy is also one of the evident truths, and indeed
follows from the other evident principles adopted as axioms.
I was fortunate enough to have Errett Bishop as one of my professors
at UCSD. He taught that set theory is "God's mathematics, which we
should leave for God to do."
http://en.wikipedia.org/wiki/Set_theory
I think it's very reasonable to believe that it's far too presumptuous
to claim that ZFC is ultimately the right definition of set theory.
Mathematical fantasies do exist.
Shubee
You are overlooking the possibility of other axiom sets for set theory
where perhaps the set of all sets exists but the set of all sets not
members of themselves does not exist.
There are theories of sets in which a set of all sets exist, most
famously Quine's New Foundations. However, these theories do not
codify any notion of set to be found in our actual mathematical
practice and thinking. Unlike theories such as ZFC, NF has no
motivating picture on which its axioms could be seen to be true, it's
a purely formal device of technical interest only.
--
Aatu Koskensilta (aatu.koskensi...@xortec.fi)
"Wovon man nicht sprechen kann, daruber muss man schweigen"
- Ludwig Wittgenstein, Tractatus Logico-Philosophicus
.
|
|
|
| User: "Aatu Koskensilta" |
|
| Title: Re: (mathematical) proof that there is no God |
13 Aug 2007 08:06:53 AM |
|
|
Shubee <e.Shubee@gmail.com> writes:
I was fortunate enough to have Errett Bishop as one of my professors
at UCSD. He taught that set theory is "God's mathematics, which we
should leave for God to do."
A famous quip indeed. As a counter one might offer the observation
that while Bishop style constructive mathematics might not be the
mathematics of God, it is the mathematics of a minor deity, a small
god capable of such impressive feats, beyond our mortal powers, as
determining of an arbitrarily large natural whether it's a prime or
not. In the end it's just a matter of which abstractions one finds
congenial and which not, however one might choose to express one's
dislike of this or that abstract mathematical picture or conception.
I think it's very reasonable to believe that it's far too presumptuous
to claim that ZFC is ultimately the right definition of set theory.
Mathematical fantasies do exist.
I didn't claim anything about whether ZFC is "ultimately the right
definition of set theory" whatever that means, only that it is not at
all arbitrary, and on the contrary has a very compelling and clear
motivation in the picture of the world of sets provided by the
cumulative hierarchy. Whether or not one considers this world of sets
a fantasy is nothing to the point.
--
Aatu Koskensilta (aatu.koskensilta@xortec.fi)
"Wovon man nicht sprechen kann, daruber muss man schweigen"
- Ludwig Wittgenstein, Tractatus Logico-Philosophicus
.
|
|
|
| User: "Shubee" |
|
| Title: Re: (mathematical) proof that there is no God |
13 Aug 2007 09:55:42 AM |
|
|
On Aug 13, 6:06 am, Aatu Koskensilta <aatu.koskensi...@xortec.fi>
wrote:
Shubee <e.Shu...@gmail.com> writes:
I was fortunate enough to have Errett Bishop as one of my professors
at UCSD. He taught that set theory is "God's mathematics, which we
should leave for God to do."
A famous quip indeed. As a counter one might offer the observation
that while Bishop style constructive mathematics might not be the
mathematics of God, it is the mathematics of a minor deity,
Constructive mathematics is the mathematics of cautious and very
doubting mathematicians who don't want to presume what the foundation
of God's Set Theory really is.
a small
god capable of such impressive feats, beyond our mortal powers, as
determining of an arbitrarily large natural whether it's a prime or
not. In the end it's just a matter of which abstractions one finds
congenial and which not, however one might choose to express one's
dislike of this or that abstract mathematical picture or conception.
I think it's very reasonable to believe that it's far too presumptuous
to claim that ZFC is ultimately the right definition of set theory.
Mathematical fantasies do exist.
I didn't claim anything about whether ZFC is "ultimately the right
definition of set theory" whatever that means, only that it is not at
all arbitrary, and on the contrary has a very compelling and clear
motivation
Naive set theory is also very compelling, intuitive, clearly motivated
and not at all arbitrary. It's just incorrect. And a proof that ZFC is
consistent wouldn't make it true.
in the picture of the world of sets provided by the
cumulative hierarchy. Whether or not one considers this world of sets
a fantasy is nothing to the point.
--
Aatu Koskensilta (aatu.koskensi...@xortec.fi)
"Wovon man nicht sprechen kann, daruber muss man schweigen"
- Ludwig Wittgenstein, Tractatus Logico-Philosophicus
.
|
|
|
|
|
|
|
|
|
|
| User: "Denis Feldmann" |
|
| Title: Re: (mathematical) proof that there is no God |
12 Aug 2007 09:32:51 PM |
|
|
Stratum a écrit :
Shubee wrote:
Your proof is obviously flawed, as all child mathematicians can see,
because there is a problem with the set of all sets even without
postulating the existence of God.
If you have a problem with "the set of all sets," do you maintain
that such a set cannot exist?
Yes ; this was the only sensible answer ever given to Russel's paradox
.
|
|
|
|
|
|
| User: "David Schwartz" |
|
| Title: Re: (mathematical) proof that there is no God |
28 Aug 2007 11:36:42 PM |
|
|
On Aug 12, 2:09 pm, SmarterThanTheAverageTr...@math.info.invalid
wrote:
Because it's omnipotent, it can construct the set of all sets.
What does "construct" mean in this context?
Your proof contains several other assumptions that might be false. For
example, one assumption is that the notion of a "set of all sets" it
meaningful to use in this way. It may be meaningful to talk about the
"set of all sets" as a rule of inclusion or exclusion (if it's a set,
yes, if not, no) but not meaningful to talk about it as a completed
object.
Another assumption is that the notion of whether or not a set contains
itself as an element is a meaningful notion for all types of infinite
sets. It may be that this is only meaningful for sets that can be
specified in particular ways and not meaningful for other types of
sets.
For example, consider the set of all sets for which a random-number
generator that randomly picks an integer between 1 and 10 picks an odd
integer. Is it meaningful to ask if this set includes itself as a
member or not? Is this a well-defined set? Your "set of all sets that
do not include themselves as a member" may be equally ill-defined.
DS
.
|
|
|
|
| User: "" |
|
| Title: Re: (mathematical) proof that there is no God |
13 Aug 2007 03:55:01 AM |
|
|
On Aug 12, 5:09 pm, SmarterThanTheAverageTr...@math.info.invalid
wrote:
* Definition: "God" means a being which is omniscient and omnipotent.
I intend to prove no such being can possibly exist.
(If you want to claim that there's a supernatural being which isn't
omniscient, or which isn't omnipotent, I have no proof against
that claim. I'm only disproving the usual claim.)
* Assume there is such a "God".
Because it's omniscient, it knows all the mathematical sets that
are even possible, not just the ones humans may eventually envision
or construct or prove to exist, but all the rest of the sets too.
Because it's omnipotent, it can construct the set of all sets.
Because it's omniscient, it knows for each set whether that set
contains itself as an element or not. (For example, the set of all
sets *does* contain itself as an element.)
Because it's omnipotent, it can construct the subset of the set of
all sets such that the set doesn't contain itself, i.e. the Russell
set. Unfortunately we now have a contradiction at this point, the
set contains itself iff it does not contain itself.
This is where your error is.
.
|
|
|
| User: "TruthCheck" |
|
| Title: Re: (mathematical) proof that there is no God |
13 Aug 2007 12:24:11 PM |
|
|
A statistical analysis of this should resolve the problem.
http://www.outersecrets.com/real/biblecode2.htm
.
|
|
|
|
| User: "Goro" |
|
| Title: Re: (mathematical) proof that there is no God |
13 Aug 2007 01:07:38 PM |
|
|
On Aug 13, 1:55 am, wrote:
On Aug 12, 5:09 pm, SmarterThanTheAverageTr...@math.info.invalid
wrote:
* Definition: "God" means a being which is omniscient and omnipotent.
I intend to prove no such being can possibly exist.
(If you want to claim that there's a supernatural being which isn't
omniscient, or which isn't omnipotent, I have no proof against
that claim. I'm only disproving the usual claim.)
* Assume there is such a "God".
Because it's omniscient, it knows all the mathematical sets that
are even possible, not just the ones humans may eventually envision
or construct or prove to exist, but all the rest of the sets too.
Because it's omnipotent, it can construct the set of all sets.
Because it's omniscient, it knows for each set whether that set
contains itself as an element or not. (For example, the set of all
sets *does* contain itself as an element.)
Because it's omnipotent, it can construct the subset of the set of
all sets such that the set doesn't contain itself, i.e. the Russell
set. Unfortunately we now have a contradiction at this point, the
set contains itself iff it does not contain itself.
This is where your error is.
I think if God created the presumed Set, that the Cat would jump out
and be found to be half-alive and half-dead, a Zombie Cat!
-goro-
.
|
|
|
|
|
| User: "Rupert" |
|
| Title: Re: (mathematical) proof that there is no God |
14 Aug 2007 12:45:18 AM |
|
|
On Aug 13, 7:09 am, SmarterThanTheAverageTr...@math.info.invalid
wrote:
* Definition: "God" means a being which is omniscient and omnipotent.
I intend to prove no such being can possibly exist.
(If you want to claim that there's a supernatural being which isn't
omniscient, or which isn't omnipotent, I have no proof against
that claim. I'm only disproving the usual claim.)
* Assume there is such a "God".
Because it's omniscient, it knows all the mathematical sets that
are even possible, not just the ones humans may eventually envision
or construct or prove to exist, but all the rest of the sets too.
I'm not clear on what it is to "know a set". To me, omniscience
entails knowing all the propositions expressible in language which it
is logically possible to know. I'm not clear that it entails knowing
all logically possible sets, whatever exactly that might mean.
.
|
|
|
| User: "TruthCheck" |
|
| Title: Re: (mathematical) proof that there is no God |
14 Aug 2007 02:50:09 AM |
|
|
Oh I forgot to mention, truth is presently being rejected, and the
owner of the truth, GOD, is presently losing the battle because of
this.
If this continues, I suggest you prepare yourself for your eventual
exposure to absolute Evil, which is the consequence of the destruction
of truths.
However, a statistical analysis of this should resolve the problem.
http://www.outersecrets.com/real/biblecode2.htm
.
|
|
|
| User: "Christopher A.Lee" |
|
| Title: Re: (mathematical) proof that there is no God |
14 Aug 2007 05:23:50 AM |
|
|
On Tue, 14 Aug 2007 00:50:09 -0700, TruthCheck <floppy01@idirect.com>
wrote:
Oh I forgot to mention, truth is presently being rejected, and the
owner of the truth, GOD, is presently losing the battle because of
this.
If this continues, I suggest you prepare yourself for your eventual
exposure to absolute Evil, which is the consequence of the destruction
of truths.
However, a statistical analysis of this should resolve the problem.
http://www.outersecrets.com/real/biblecode2.htm
Idiot.
.
|
|
|
| User: "TruthCheck" |
|
| Title: Re: (mathematical) proof that there is no God |
14 Aug 2007 12:13:07 PM |
|
|
On Aug 14, 6:23 am, Christopher A.Lee <ca...@optonline.net> wrote:
On Tue, 14 Aug 2007 00:50:09 -0700, TruthCheck <flopp...@idirect.com>
wrote:
Oh I forgot to mention, truth is presently being rejected, and the
owner of the truth, GOD, is presently losing the battle because of
this.
If this continues, I suggest you prepare yourself for your eventual
exposure to absolute Evil, which is the consequence of the destruction
of truths.
However, a statistical analysis of this should resolve the problem.
http://www.outersecrets.com/real/biblecode2.htm
Idiot.
OH I forgot something.
You are stinking fucking moronic ***** stupid fucking jackass..
Don't people lives mean anything to you ?
Or are you nothing but a selfish piece of ***** ?
Read the statistics in front of you , you bloody idiot.
http://www.outersecrets.com/real/biblecode2.htm
.
|
|
|
|
|
|
|
|
Related Articles |
|
|
