Re: Does all computation generate heat?

'Brent Meeker' via Everything List Wed, 08 May 2019 11:41:40 -0700


On 5/8/2019 9:20 AM, Bruno Marchal wrote:

On 3 May 2019, at 20:17, 'Brent Meeker' via Everything List<[email protected]<mailto:[email protected]>> wrote:
On 5/3/2019 8:47 AM, Bruno Marchal wrote:
On 3 May 2019, at 14:06, Quentin Anciaux <[email protected]<mailto:[email protected]>> wrote:
Pleasure for the all loving god to have creatures to torture ?

But the problem of evil is not that simple.
Indeed.

But note that just the second theorem of Gödel provides a clue.

With provable(p) written []p
consistent(p) = ~provable(~p) = <>p
f = false, t = true
consistent = ~[]f = <>t = consistent(t),

Gödel’s second I. Theorem, put in equivalent version:

<>t -> ~[]<>t

<>t -> <>~<>t
<>t -> <>[]f

It is that last one where the clue is the more apparent:

Said by PA, or ZF, or any sound Löbian machine: it says the following:

If I am consistent, then it is consistent that I am inconsistent
Notice however that this assumes you know what t and f are.
No, that is not assumed. t and f are only boolean constant. In thearithmetical interpretation, you can take any simple theorems of your(Church-Turing universal) theory (that you are supposed to believein). Usually t is interested by “1=1” and f by “~(1=1)”. But in thecombinators t is interpreted by K and f by KI.
With digital mechanism, just to define what is a digital machine, weneed some acknowledgement on elementary arithmetic, for which we dohave a notion of truth, indeed made mathematically precise by Tarski.In the usual mathematical sense, and not definable in arithmetic, likeall good notion of god should be.
In the formalism they are just markers that are invariant under therules of inference.
Yes, except that here they correspond to direct conclusion of thelogical rule. Now “1” is represented by "s(0)” (or its Gödel number),and what you say will apply to all symbols, or symbols of symbols. Theinterpretation is in the truth, that is here is the stantard model ofarithmetic (the structure (N, 0, s, +, x).
Your remark applies also to brain and (physical or not) realities.
In the semantics they refer to some model.
Exactly.
Beware of the priest who tells you he knows the real model.
Exactly.


Above you are telling us the standard model of arithmetic is the real model.

Brent

The universal machine which knows that she is universal say no better,indeed.


Bruno


Brent


Or

If I am consistent then it is consistent that I will prove a falsity

Peano arithmetic, or ZF, remains consistent when adding the axiomthat they are (respectively) inconsistent.


Loosely, this says:

If shit does not happen, shit might happen.

This might be part of the shadow explaining the origin of evil ([]f)in the internal states realised in arithmetic.


Bruno

PS Exercise; show that Gödel’s theorem (in its modal form) is justLöb’s formula with p replaced by false( f).


Solution: Löb’s formula is []([]p -> p) -> []p,

with p = f, this becomes

[]f([]f -> f) -> []f

Which is, as ~p = (p -> f), obvious by truth table of ~ and ->.

[](~[]f) -> []f

By transposition (using the fact that p -> q is equivalent with ~q-> ~p), we get


~[]f -> ~[](~[]f), or,

by using ~[]p = <>~p, and ~f = t, or ~~p -> p.

<>t -> <>([]f)

Le ven. 3 mai 2019 à 12:46, smitra <[email protected]<mailto:[email protected]>> a écrit :


    What's the point of creating criminals and then to torture those
    criminals for eternity in hell?

    On 03-05-2019 04:41, Samiya Illias wrote:
    > Considering how vast we have come to realise the Universe to
    be, do
    > you honestly think our praise or our insults affect God in
    any way? Do
    > you even realise how great the Creator of all this must be?
    Do you
    > think God would need any appreciation from us? Rather, it is
    we who
    > need to appreciate God!
    >
    > God created the entire creation and He governs it flawlessly
    according
    > to His Laws. The entire creation submits to His Laws, except some
    > criminals...
    >
    > The way I understand it, we, humans and snakes, are criminals
    who have
    > been contained on a planet. Our collective crime is that we
    abused our
    > free will to go against the Universal Laws. We have an
    appointment, in
    > the Divine Court, that will be kept as scheduled. We have
    been given a
    > temporal life so that each one of us can generate evidence (data:
    > speech and deeds) for or against ourselves.
    >
    > Remembering God through prayer, and Praising God by repeatedly
    > declaring that God is free from all imperfection, helps us to
    > understand and consequently be pleased with God, contented to
    submit
    > to His Laws and Decrees, and grateful for the guidance, looking
    > forward to an immortal life of luxury and perhaps the most
    prestigious
    > jobs anyone can ever aspire for: in service of Allah, The One
    and Only
    > God, The KIng of the Mighty Throne of The Entire Creation!
    >
    > There is no compulsion to follow God's Laws, but the
    criminals will
    > not be allowed to leave this planet. They will go from living
    upon it
    > to living within it, in The Fire!
    >
    > Related Posts [4]
    >
    > Samiya Illias
    > Signs & Science [5]
    >
    > On Thu, May 2, 2019 at 5:00 PM John Clark
    <[email protected] <mailto:[email protected]>>
    > wrote:
    >
    >> On Thu, May 2, 2019 at 1:54 AM 'Brent Meeker'
    >> <[email protected]
    <mailto:[email protected]>> wrote:
    >>
    >>>> _ _Islam is a religion based almost entirely on threats.
    >>
    >> True, but in all fairness Christianity is also based on
    threats. It
    >> preaches that faith (believing in something when there is no
    good
    >> reason for doing so) is not stupidity but is instead the
    ultimate
    >> virtue, and if you don't believe in all the crap that
    Christianity
    >> (or Islam) says then a good and loving God will torture you most
    >> fiendishly not for 10^100 years but for an infinite number
    of years.
    >> I'm no saint but I wouldn't do that to a unrepentant Hitler,
    and yet
    >> another thing we're suposed to do is constantly flatter God by
    >> telling Him how good He is.
    >>
    >> The Meaning of Life: Praise the Lord [1]
    >>
    >> John K Clark
    >>
    >> --
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Re: Does all computation generate heat?

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