Re: GÖDEL
"'Lee Corbin' [email protected] [Fabric-of-Reality]" <[email protected]> Thu, 13 Nov 2014 18:45:51 -0800
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Those who are interested when G=C3=B6del's theorems should and should *not*=
be applied ought to read Torkel Franzen=E2=80=99s wonderful book, =E2=80=
=9CG=C3=B6del's Theorem: An Incomplete Guide to its Use and Abuse=E2=80=9D.=
Study of his book has convinced me that about 95% of the references one c=
omes across to G=C3=B6del's Theorem are fallacious. Here is just one fascin=
ating fact: The theorem to formal systems that contain =E2=80=9Ca certain a=
mount of arithmetic=E2=80=9D (it=E2=80=99s hard to spell that out in more d=
etail). One example is the formal system containing this axioms for real nu=
mbers. G=C3=B6del's Theorem does not apply, because the real number axioms,=
surprisingly, cannot =E2=80=9Cget their hands=E2=80=9D on integers in the =
sense that you cannot specify =E2=80=9Cfor all integers=E2=80=9D the way th=
at you can in Peano Arithmetic.
Lee
From: mailto:Fabric-of-Reality@yahoo=
groups.com
Sent: Thursday, November 13, 2014 7:24 AM
To: Fabric-of-Reality=
@yahoogroups.com
Subject: Re: GODEL
On 04 Nov 2014, at 22:48, etre2@sbcgl=
obal.net [Fabric-of-Reality] wrote:
I don't think that Hawkins h=
as come close to proving that the existence of God is improbable. His case =
can be summarized when he says....""when one person suffers from a delusion=
it is called insanity. When many people suffer from a delusion it is calle=
d religion."
So the belief in the collapse of the wave is a religion. Why =
not. Feynman already called it a "collective hallucination", if I remember =
well.
.
G=C3=B6del=E2=80=99s mathematical proof is probably the =
strongest case for the IMPROBABLE existence of God, but this proof simply m=
eans that it's just not possible to identify the processes that gave rise t=
o the formation "of all that exists" (or "being")....RobtO
The ancient g=
reeks got this too, by the dream argument, and it was the start of science,=
when we stop to believe that what we see and measure is necessarily the "r=
eal thing", which might be just hidden by the appearance. Note that G=C3=B6=
del provided a proof of the existence of God, but it requires you to accept=
St-Anselmus definition of God, and G=C3=B6del formalization of that defini=
tion, and the alethic modal logic S5. Personally, I don't believe in S5, no=
r do I find the definition of God by St-Anselmus the most enlightening one.=
But his incompleteness theorem, together with his non definability of tru=
th (G=C3=B6del-Tarski) makes somehow the arithmetical truth behaving like t=
he God of the Platonist, which is not much more than the truth we search (a=
s opposed to any truth we might believe to have found).
Bruno
http:=
//iridia.ulb.ac.be/~marchal/
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<DIV style=3D"FONT-SIZE: 12pt;FONT-FAMILY: 'Book Antiqua';COLOR: #000000;">
<DIV>Those who are interested when G=C3=B6del's theorems should and should =
*not* be=20
applied ought to read Torkel Franzen=E2=80=99s wonderful book, =E2=80=9CG=
=C3=B6del's Theorem: An=20
Incomplete Guide to its Use and Abuse=E2=80=9D.</DIV>
<DIV> </DIV>
<DIV>Study of his book has convinced me that about 95% of the references on=
e=20
comes across to G=C3=B6del's Theorem are fallacious. Here is just one fasci=
nating=20
fact: The theorem to formal systems that contain =E2=80=9Ca certain amount =
of=20
arithmetic=E2=80=9D (it=E2=80=99s hard to spell that out in more detail). O=
ne example is the=20
formal system containing this axioms for real numbers. G=C3=B6del's Theorem=
does not=20
apply, because the real number axioms, surprisingly, cannot =E2=80=9Cget th=
eir hands=E2=80=9D on=20
integers in the sense that you cannot specify =E2=80=9Cfor all integers=E2=
=80=9D the way that=20
you can in Peano Arithmetic.</DIV>
<DIV> </DIV>
<DIV>Lee</DIV>
<DIV> </DIV>
<DIV style=3D"FONT-SIZE: small;TEXT-DECORATION: none;FONT-FAMILY: "Cal=
ibri";FONT-WEIGHT: normal;COLOR: #000000;FONT-STYLE: normal;">
<DIV style=3D"FONT: 10pt tahoma;">
<DIV> </DIV>
<DIV style=3D"BACKGROUND: #f5f5f5;">
<DIV><B>From:</B> <A title=3D"[email protected]" href=3D"ma=
ilto:[email protected]">mailto:Fabric-of-Reality@yahoogroup=
s.com</A>=20
</DIV>
<DIV><B>Sent:</B> Thursday, November 13, 2014 7:24 AM</DIV>
<DIV><B>To:</B> <A title=3D"[email protected]" href=3D"mail=
to:[email protected]">[email protected]</A>=
=20
</DIV>
<DIV><B>Subject:</B> Re: GODEL</DIV></DIV></DIV>
<DIV><FONT face=3D"Book Antiqua"></FONT> </DIV></DIV>
<DIV style=3D"FONT-SIZE: small;TEXT-DECORATION: none;FONT-FAMILY: "Cal=
ibri";FONT-WEIGHT: normal;COLOR: #000000;FONT-STYLE: normal;"><SPAN></=
SPAN>
<DIV id=3D"ygrp-mlmsg">
<DIV id=3D"ygrp-msg">
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<DIV>
<DIV>On 04 Nov 2014, at 22:48, <A href=3D"mailto:[email protected]">etre2=
@sbcglobal.net</A> [Fabric-of-Reality]=20
wrote:</DIV><BR class=3D"Apple-interchange-newline">
<BLOCKQUOTE type=3D"cite">
<DIV style=3D"BACKGROUND-COLOR: rgb(255,255,255);"><SPAN> </SPAN>=20
<DIV id=3D"ygrp-text">
<DIV> </DIV>
<P> <STRONG><FONT size=3D"2">I don't think that Hawkins has come clo=
se to=20
proving that the existence of God is improbable. His case can be summariz=
ed=20
when he says....""when one person suffers from a delusion it is called=20
insanity. When many people suffer from a delusion it is called=20
religion."</FONT></STRONG></P></DIV></DIV></BLOCKQUOTE></DIV>
<DIV>So the belief in the collapse of the wave is a religion. Why not. Feyn=
man=20
already called it a "collective hallucination", if I remember well.</DIV>
<DIV> </DIV>
<DIV> </DIV>
<DIV> </DIV>
<DIV> </DIV><BR>
<BLOCKQUOTE type=3D"cite">
<DIV style=3D"BACKGROUND-COLOR: rgb(255,255,255);">
<DIV id=3D"ygrp-mlmsg">
<DIV id=3D"ygrp-msg">
<DIV id=3D"ygrp-text">
<P><STRONG><FONT size=3D"2">.</FONT></STRONG></P><STRONG><FONT size=3D"2"=
></FONT></STRONG>
<P><STRONG><FONT size=3D"2">G=C3=B6del=E2=80=99s mathematical proof is pr=
obably the strongest=20
case for the IMPROBABLE existence of God, but this proof simply means tha=
t=20
it's just not possible to identify the processes that gave rise to the=20
formation "of all that exists" (or "being")....RobtO=20
</FONT></STRONG></P></DIV></DIV></DIV></DIV></BLOCKQUOTE>
<DIV> </DIV>
<DIV>The ancient greeks got this too, by the dream argument, and it was the=
=20
start of science, when we stop to believe that what we see and measure is=20
necessarily the "real thing", which might be just hidden by the appearance.=
Note=20
that G=C3=B6del provided a proof of the existence of God, but it requires y=
ou to=20
accept St-Anselmus definition of God, and G=C3=B6del formalization of that=
=20
definition, and the alethic modal logic S5. Personally, I don't believe in =
S5,=20
nor do I find the definition of God by St-Anselmus the most enlightening on=
e.=20
</DIV>
<DIV>But his incompleteness theorem, together with his non definability of =
truth=20
(G=C3=B6del-Tarski) makes somehow the arithmetical truth behaving like the =
God of the=20
Platonist, which is not much more than the truth we search (as opposed to a=
ny=20
truth we might believe to have found).</DIV>
<DIV> </DIV>
<DIV>Bruno</DIV>
<DIV> </DIV>
<DIV> </DIV><BR>
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<DIV><A href=3D"http://iridia.ulb.ac.be/~marchal/">http://iridia.ulb.ac.be/=
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