Hi Bruno Marchal 

Yes, the Greeks had some kind of Trinity. So did the
Hindus. But the meanings are different than those of the Christian trinity.
The meanings of the Greek trinity figures
include the Demiurge (Satan, sort of) so are not identical to the Christian 
trinity.
And the Hindu Trinity are creator, maintainer, destroyer. 
The Christian trinity has no destroyer. 

Also, Augustine didn't invent the Christian trinity,
no dou9bt he got it from the gorgeous beginning 
of the gospel of John:

In the beginning was the Word 
And the Word was with God 
and the Word was God.

Which are, respectively, Jesus, the Holy Spirit
and God. God in the flesh, God in the world, and the
transcendent God.

The trinity is also displayed at Jesus' baptism by
Jesus, a dove (holy spirit) landing on his shouder,
and his father (God) speaking from Heaven.


[Roger Clough], [rclo...@verizon.net]
12/1/2012 
"Forever is a long time, especially near the end." -Woody Allen

----- Receiving the following content ----- 
From: Bruno Marchal 
Receiver: everything-list 
Time: 2012-12-01, 08:19:11
Subject: Re: the many faces of truth




On 30 Nov 2012, at 15:05, Roger Clough wrote:


the many faces of truth 

I believe that there are many forms of truth,
each form depending on how it is defined.
So I guess I am a nominalist. Or a pragmatist.
Same difference.

Russell's and Aristotle's form of truth would
be "truth by correspondence".

There is also "pragmatic truth", which has
nothing to do with correpondence,  it is
what results when a well-defined protocol,
such as a scientific experiment, is carried out.
Scientific truth would then be pragmatic,
such as a force is the reaction obtained
when a mass is accelerated.

Then there is the Christian trinity,  which
gives us three more faces of truth.


Then there is the Machine Octality, which gives 8 "faces of arithmetical truth":


Truth, belief, knowledge, observation, sensation, that is


p,  Bp,  Bp & p,  Bp & Dt,  Bp & Dt & p. 


8, because three of them inherit the G/G* incompleteness splitting.


A case can been made that the first three one correspond to the "Greek 
trinity", that Augustin has used to refine the Christian trinity.


Bruno










[Roger Clough], [rclo...@verizon.net]
11/30/2012 
"Forever is a long time, especially near the end." -Woody Allen

----- Receiving the following content ----- 
From: Stephen P. King 
Receiver: everything-list 
Time: 2012-11-02, 18:07:35
Subject: Re: Communicability


On 11/2/2012 1:08 PM, Bruno Marchal wrote:


On 01 Nov 2012, at 22:34, Stephen P. King wrote: 


On 11/1/2012 11:47 AM, Bruno Marchal wrote: 


On 01 Nov 2012, at 01:01, Stephen P. King wrote: 


Dear Bruno, 

  Exactly what do these temporal concepts, such as "explain", "solve", 
"interacting" and " emulating", mean in an atemporal setting? You are mixing 
temporal and atemporal ideas. ... 


Study a good book in theoretical computer science. You told me that you have 
the book by Matiyazevich. he does explicitly emulate Turing machine, which have 
a quite physical look, with a moving head, and obeying instruction is a 
temporal manner, and yet they can be shown to be emulated by a the existence or 
non existence of solution of Diophantine equations. 


Dear Bruno, 

   That book, full of wonderful words and equations, is a physical object. 


True, but non relevant. 


Dear Bruno,

    Yes it is relevant as it is the essence of my proof. But let me quote 
Russell: http://www.ditext.com/russell/rus12.html


"..a belief is true when it corresponds to a certain associated complex, and 
false when it does not. Assuming, for the sake of definiteness, that the 
objects of the belief are two terms and a relation, the terms being put in a 
certain order by the 'sense' of the believing, then if the two terms in that 
order are united by the relation into a complex, the belief is true; if not, it 
is false. This constitutes the definition of truth and falsehood that we were 
in search of. Judging or believing is a certain complex unity of which a mind 
is a constituent; if the remaining constituents, taken in the order which they 
have in the belief, form a complex unity, then the belief is true; if not, it 
is false. 
Thus although truth and falsehood are properties of beliefs, yet they are in a 
sense extrinsic properties, for the condition of the truth of a belief is 
something not involving beliefs, or (in general) any mind at all, but only the 
objects of the belief. A mind, which believes, believes truly when there is a 
corresponding complex not involving the mind, but only its objects. This 
correspondence ensures truth, and its absence entails falsehood. Hence we 
account simultaneously for the two facts that beliefs (a) depend on minds for 
their existence, (b) do not depend on minds for their truth. 
We may restate our theory as follows: If we take such a belief as 'Othello 
believes that Desdemona loves Cassio', we will call Desdemona and Cassio the 
object-terms, and loving the object-relation. If there is a complex unity 
'Desdemona's love for Cassio', consisting of the object-terms related by the 
object-relation in the same order as they have in the belief, then this complex 
unity is called the fact corresponding to the belief. Thus a belief is true 
when there is a corresponding fact, and is false when there is no corresponding 
fact. 
It will be seen that minds do not create truth or falsehood. They create 
beliefs, but when once the beliefs are created, the mind cannot make them true 
or false, except in the special case where they concern future things which are 
within the power of the person believing, such as catching trains. What makes a 
belief true is a fact, and this fact does not (except in exceptional cases) in 
any way involve the mind of the person who has the belief. "

    I do not see Russell accepting the idea that Truths have definite valued in 
the absence of beliefs and the definiteness of belief in the absence of minds. 
Why do you accept such an idea? Facts require possible worlds.




That physical object is, in my thinking, an example of an implementation of the 
"emulation of a Turing Machine..." just as the image on my TV of Rainbow Dash 
and her friends is a physical implementation of magical Ponies. You seem to 
ignore the obvious... 


You assume physical objects, but this contradict your own theory (on which you 
point to, but without ever giving it). 


    I do not pretend to have a "theory of Everything". I am merely trying to 
show you where there is an obstruction in your result that results in the 
problem of an arithmetic body. It is strange that you openly admit to a problem 
but do anything to prevent its solution!
    







But this is already no more an enigma for many physicists which agree that 
temporality is just an illusion resulting from projection from higher 
dimension. 


   Those physicists are wrong in their belief. This is argued well in this 
paper http://xxx.lanl.gov/abs/gr-qc/9708055 and in any other places. I recall a 
long chat that I had with Julian Barbor. In it I tried to ask him about the 
computational complexity of implementing his 'time capsule' and 'best matching' 
ideas, he seemed to not understand what the heck I was talking about and yet 
bemoaned the very problem at length in one of his papers on the idea! 

>From pg 52 of http://www.platonia.com/barbour_hrp2003.pdf 

"About ten years ago, I did some computer calculations to find such 
configurations with the Macintosh computer I then possessed. I was able to 
do exhaustive calculations up to N = 27, which took the computer about three 
days. Because the number of combinations that must be checked out grows 
exponentially with N, even with a modern supercomputer I doubt that 
calculations much beyond N = 50 would be feasible." 

   BTW, it was reading this paper that opened my eyes to the NP-Hard problem of 
Leibniz' Pre-Established Harmony. 




I thought you agree that physics (and thus time) is not primitive. 


   I agree, physics (and all that it such as particles, forces, matter, energy) 
impels cannot be ontologically primitive. But it must exist nonetheless. My 
challenge is showing how. I start with a notion of a property neutral "totality 
of all that exists" 


But what exists has properties, and besides, we don't know what exists (beside 
our consciousness), so you take for granted much too much, exactly what we have 
to explain. 


    No. Mere existence does not inform properties, it merely denote necessary 
possibility. You are using a materialist's definition of "existence" and not a 
philosophical definition. It seems that you need some remedial education in 
philosophical concepts!

    Existence is not a property that can be measured or otherwise determined by 
some means. This is because existence is not contingent nor supervening on 
anything else. Existence is ontological and axiomatic. When we observe, measure 
or infer the possibility of such, we are denoting the properties of objects. 
When we think of or deduce a concept, we are not "causing the concept to come 
into existence", we are merely determining its properties. Existence is not a 
property, it is the only a priori synthetic as all other considerations demand 
it.

    If we consider properties, such as the oneness and unity of 1, and the 
twoness of 2, etc. we are apprehending the proprieties of concepts and not 
magically gaining information of some immaterial object. My proof of this claim 
is the simple demonstration that if you cannot represent a concept or an object 
to both yourself and some other entity, then you cannot know anything at all 
about it, nor can you even conceptualize it. This undermines the very idea that 
there exists object outside of our ability to know of them, at least in the 
potential sense of a priori, since we cannot even speculate about their 
existence.
    Truth is not an object, it is the result of an evaluation by a mind, but it 
is such that it does not depend on any particular mind. There is no such thing 
as a "private truth" other than the 1p aspect of the apprehension of qualia.




and consider how from that ground two aspects emerge simultaneously, the 
physical and the mental as mutually distinct dual aspects that when added 
together yield back the neutrality. This idea is very similar to Russell 
Standish's Theory of Nothing. 


I have no clue what you mean. 


    Try harder, it is not that difficult. What is the basic result of 
Standish's thesis? http://www.hpcoders.com.au/theory-of-nothing.pdf

"There is a mathematical equivalence between the
Everything, as represented by this collection of all possi-
ble descriptions and Nothing, a state of no information.
That some of the descriptions must describe conscious
observers who obviously observe something, gives us a
mechanism for getting Something from Nothing: Some-
thing is the "inside view" of Nothing."

and

"The ontology of bitstrings has no possible "God's
eye" viewpoint. Since the ensemble of bitstrings
have zero information, nothing can be learnt from
observing it from the outside."

    There is no external Truth other than what might be possibly known by some 
entity within the totality of what exists and thus truth does not 'float-free' 
of the means that could exist of determining it.










This means that they can and need to be explain from non temporal notion. 

Arithmetic is the bloc mindspace. 


   Is it a Singleton? 


No. 


    Then what partitions it into mutually exclusive statements?




Can it be exactly represented by a Boolean Algebra? 


Yes. 


    Then it has a dual that is a topological space. My thesis is that "physical 
worlds" are nothing more that elaborations and relations on these topological 
spaces that are dual to arithmetics. This makes arithmetics and physical worlds 
(representable by Stone spaces) to be co-existent and dual aspects of a 
fundamental ontological primitive that has no particular properties nor truth 
values.




I see 'mindspace" as one half of the dual aspects. 


You pretend to see a flaw. I am not interested in your "theory". You have to 
work in the theory you are criticizing, to find the flaw in that theory. If not 
you are like someone pretending that abelian group are ridiculous as you know a 
non abelian group. Use comp, without adding any other axioms, please. 


    The fact that your result has a "arithmetic body" problem is my proof of a 
flaw in comp. It is the same problem that Berkeley's Immaterialism has. There 
is nothing new in your work other than 1) a brilliant refutation of material 
monism, 2) a wonderful modal logical derivation of the relations of within a 
mind and 3) a fatal flaw of assuming what cannot be known to be the subject of 
a theory. Truth is not an a priori definite. Only existence can be a priori.






There is nothing more dynamical than the notion of computations, yet, they have 
been discovered in statical math structure. 


   Mathematical objects are the epitome of static objects. I think that this 
view of math is blinkered. A description of a dynamic process may be static, 
but the evolutionaly Becoming aspect is still there, just hidden. Just as a 
photograph acts to freeze a moment in time... 


So you assume a primitive time.

    How so? I have repeatedly discussed how time is a measure of change. Change 
can exist without a measure. You are conflating the act of sequencing events 
with the ordering that this action induces.


This contradicts your "theory" (the few I ahve grasped, but which becomes more 
and more confused, when you try to escape some comp's consequence, for reason 
which eludes me, as in some post you seem to have agreed with them. 


    Well, I cannot be held responsible for the mistakes and misunderstanding of 
others. ;-) I can agree with some comment of almost all people without 
wholesale agreement with them. I agree with most of your ideas, Bruno. We fight 
over a tiny concept, but it is the linchpin of your entire thesis. You claim 
that truth is a priori and I claim that truth is a posteriori. You claim that 
numbers have particular values independent of the means to manifest those 
values and I claim that they cannot.
    I can explain your ideas to other people to the point of their 
understanding of them, but you cannot even understand the basic idea of what is 
"existence"!! 






This is made possible as the statical sequence 0, 1, 2, 3, ... reintroduces a 
lot of quasi-time notion, and it is explained how some of them will play the 
role of the "observable timing of events" locally, by relative numbers. 


   This is where you make the mistake. You are assuming that the ordering of 
numbers *is* the dynamic. 


No. 


    Then how can you claim that the ordering of numbers can "run" or 
"implement" a computation?




I claim that the ordering of numbers *is a representation* of the dynamic. 


It can be. But the confusion is not made in comp, or in my posts.

    Where is it then? 




We should be very careful when we identify the map with the territory! I agree 
that there are situations when there is an exact isomorphism between map and 
territory, but that is only in the case of  automorphisms and fixed points. 
   We can use sequences of relative numbers, surely, but only when the 
conditions to define them occur. 


This makes no sense. It leads directly to infinite regress, as the condition 
will usually be much more complex than the definition of the numbers. You are 
asking to the centipede to understand how its brain and legs function before 
walking. 


    No! Infinite regress is only a problem if it is part of an explanation. 
Non-well founded sets are perfectly logical and non-pathological and include 
all kinds of infinite regress!




We cannot assume that the properties of relative numbers exist in the absence 
of the means to define the "timing", "locality" and "relations" required. 


Then give me your theory of numbers. And make sure it is simpler than the first 
order usual arithmetical theories. Good luck ... 


    Any particular number is the equivalence class of its possible 
manifestations. Alternatively, a numbers is the bundle of the properties that 
it induces on other numbers and/or objects.

0 = 1-1, 2-2, 3-3, 4-4, ..., the additive identity in some model of arithmetic, 
..., the absence of values, ...  
1 = 2-1, 3-2, 4-3, 5-4, ... , the multiplicative identity in some model of 
arithmetic, ...
3 = 4-5, 5-4, ..., the observer independent quantitative value of three 
objects, ..
...

    I assume that truth is something that cannot be communicated but it can be 
agreed upon. Truth is 1p. ;-)


-- 
Onward!

Stephen


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