On 10 Jan 2013, at 13:30, Roger Clough wrote:

Hi Bruno Marchal

Could the incompleteness theorem simply be an artifact of
wrong-headedly trying to reach the necessary from the realm of contingency ?

It is as much an artifact than the fact that there is an infinity of primes. Gödel's theorem concerns all sound machines or theories (or relative numbers).

Note also that incompleteness is also a quasi-direct consequence of Church thesis.

I often give the proof, and that might happen again :)

Bruno




That is, trying synthesize a system, whereas it is actually already complete
if deduced analytically ?


[Roger Clough], [rclo...@verizon.net]
1/10/2013
"Forever is a long time, especially near the end." - Woody Allen
----- Receiving the following content -----
From: Bruno Marchal
Receiver: everything-list
Time: 2013-01-09, 12:10:16
Subject: Re: Sensing the presence of God


On 09 Jan 2013, at 17:03, Telmo Menezes wrote:




On Wed, Jan 9, 2013 at 4:29 PM, Bruno Marchal <marc...@ulb.ac.be> wrote:

On 09 Jan 2013, at 13:26, Telmo Menezes wrote:

Where does hate, falsehood and ugliness come from?

I am not quite sure, but it comes probably from the consistency of inconsistency (that is: G鰀el's second incompleteness theorem).

Doesn't the second incompleteness theorem imply that all knowable truths are local and that absolute truth is unrecognisable?

Why?
I don't think so. G鰀el's incompleteness relies on the absoluteness of the elementary arithmetical truth. It only entails that all machine cannot know the whole thing, and not even give it a name. This can be made more precise in "model theory", or "set theory" where we can define "absolute" and "relative".



That makes sense with my empirical understanding of realty: there are things that I find beautiful and others find ugly. Hate groups feel that they just have a correct understanding of reality, and so on.

I am OK with this, except on elementary arithmetic. You need this just to define "formalism", "machine", etc. But even such kind of truth cannot be communicate as such, unless we first agree on some axioms, and on what axioms are.





Actually it comes from the fact that Bf (inconsistency) gives an evolutionary advantage. Like the true Dt, Bf can be used to prove correct arithmetical propositions, to shorten the proofs of non trivial propositions, etc. I am able to conceive, some day, that all axioms of infinity are of this type (but this is a strong statement).

So basically the hate, the falsehood and the ugliness comes from their local evolutionary advantage. A bit like robbing a bank can be justified, when the goal is to make money locally and quickly. A bit like when the "first animal" decided to feed on a vegetal, which is a form of molecules stealing, at some level. Then other animals steal the molecules of those vegetarians, and so on. This has generated the evolutionary heuristic: to eat or to be eaten, and sometimes that hurts.

Ok - at the evolutionary level of abstraction.

Well, OK. It still hurts, and the hurting feeling seems to be something absolute. We cannot doubt a feeling of headache, even if we can doubt the primary existence of the head.

Bruno





In the main line ...

Bruno





On Wed, Jan 9, 2013 at 1:18 PM, Roger Clough <rclo...@verizon.net> wrote:


According to Plato, all love, all truth, and all beauty comes from the One (ie God). That being the case, when I experience love, truth or beauty, I
sense God's presence.


[Roger Clough], [rclo...@verizon.net]
1/9/2013
"Forever is a long time, especially near the end." - Woody Allen

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