Hi Bruno Marchal   
Responses indicated by $$$$$$s  

Roger Clough, rclo...@verizon.net   
"Forever is a long time, especially near the end." -Woody Allen   

----- Receiving the following content -----   
From: Bruno Marchal   
Receiver: everything-list   
Time: 2012-10-01, 11:26:24   
Subject: Re: Numbers vs monads   

Hi Roger Clough,   

### ROGER: Quanta are different from particles. They don't move   
from A to B along particular paths through space (or even through space), they 
through all possible mathematical paths - which is to say that they are 
everywhere at once-   
until one particular path is selected by a measurement (or selected by passing 
through slits).   

Do you agree with Everett that all path exists, and that the selection might 
equivalent with a first person indeterminacy?   

$$$$$$$ 1) Well it's an indeterminantcy, but which path is chosen is done by 
the geometry of the location   
or test probe, not the same I would think as logical choice (?)   
So I would say "no."  
Note that intelligence requires the ability to select.   

BRUNO:  OK. But the ability to selct does not require intelligence, just 
interaction and some memory.   
$$$$$$ ROGER:  No, that's where you keep missing the absolutely critical  issue 
of self.   
Choice is exclusive to the autonomous self, and is absolutely necessary. Self  
selects A or B or whatever entirely on its own..  
That's what intelligence is.    
When you type a response, YOU choose which letter to type, etc.  
That's an intelligent action.  

Selection of a quantum path   
(collapse or reduction of the jungle of brain wave paths) produces   
consciousness, according to Penrose et al. They call it orchestrated   
reduction. .   

BRUNO: Penrose is hardly convincing on this. Its basic argument based on G del 
is invalid, and its theory is quite speculative, like the wave collapse, which 
has never make any sense to me.   

ROGER: All physical theories (not mathematical theories)  are speculative until 
validated by data.   

Why would the physical not be infinitely divisible and extensible,   
especially if "not real"?   

#### ROGER: Objects can be physical and also infinitely divisible,   
but L considered this infinite divisibility to disqualify an object to be real 
there's no end to the process, one wouldn't end up with something   
to refer to.   

BRUNO:   In comp we end up with what is similar above the substitution level. 
What we call "macro", but which is really only what we can "isolate".   
The picture is of course quite counter-intuitive.   

> Personally. I substitute Heisenberg's uncertainty principle   
> as the basis for this view because the fundamental particles   
> are supposedly divisible.   

By definition an atom is not divisible, and the "atoms" today are the   
elementary particles. Not sure you can divide an electron or a Higgs   
With comp particles might get the sme explanation as the physicist, as   
fixed points for some transformation in a universal group or universal   
symmetrical system.   
The simple groups, the exceptional groups, the Monster group can play   
some role there (I speculate).   
#### ROGER: You can split an atom because it has parts, reactors do that all of 
the time.   
of this particular point, Electrons and other fundamental particles do not have 
You lost me with the rest of this comment, but that's OK.   

Yes. Atoms are no "atoms" (in greek t??? means not divisible).    
$$$$$$ROGER: The greeks had no means to split the atom, they hadn't even seen 

BRUNO:  But if string theory is correct even electron are still divisible 

I still don't know with comp. Normally some observable have a real continuum 
spectrum. Physical reality cannot be entirely discrete.   

$$$$$$$ROGER: The monads are just points but not physical objects.  
Overlaying them, all of L's reality is just a dimensionless dot.  

> I'm still trying to figure out how numbers and ideas fit   
> into Leibniz's metaphysics. Little is written about this issue,   
> so I have to rely on what Leibniz says otherwise about monads.   

BRUNO: OK. I will interpret your monad by "intensional number".   
$$$$$$$$ROGER: Numbers do not associate to corporeal bodies, so that won't 

BRUNO:  let me be explicit on this. I fixe once and for all a universal   
system: I chose the programming language LISP. Actually, a subset of   
it: the programs LISP computing only (partial) functions from N to N,   
with some list representation of the numbers like (0), (S 0), (S S   
0), ...   

I enumerate in lexicographic way all the programs LISP. P_1, P_2,   
P_3, ...   

The ith partial computable functions phi_i is the one computed by P_i.   

I can place on N a new operation, written #, with a # b = phi_a(b),   
that is the result of the application of the ath program LISP, P_a, in   
the enumeration of all the program LISP above, on b.   

Then I define a number as being intensional when it occurs at the left   
of an expression like a # b.   

The choice of a universal system transforms each number into a   
(partial) function from N to N.   

A number u is universal if phi_u(a, b) = phi_a(b). u interprets or   
understands the program a and apply it to on b to give the result   
phi_a(b). a is the program, b is the data, and u is the computer. (a,   
b) here abbreviates some number coding the couple (a, b), to stay   
withe function having one argument (so u is a P_i, there is a   
universal program P_u).   

Universal is an intensional notion, it concerns the number playing the   
role of a name for the function. The left number in the (partial)   
operation #.   

#### ROGER: Despisers of religion would do well to understand   
this point, as follows:   

Numbers, like all beings in Platonia are intensional and necessary,   
so are not contingent, as monads are. Thus, arithmetical theorems and proofs   
do not change with time, are always true or always false. Perfect, heavenly,   
eternal truths, as they say. Angelic. Life itself. Free spirits.   
Monads are intensional but are contingent, so they change (very rapidly) with 
time (like other   
inhabitants of Contingia). Monads are a bit corrupt like the rest of us.   
Although not perfect, they tend to strive to be so, at least those motivated by 
intellect (the principles of Platonia, so not entropic. Otherwise, those 
dominated by the   
lesser quality, passion, weaken. Entropic. As they say, the wages of sin is 
Those less dominant monads are eaten or taken over by the stronger ones.   
It's a Darwinian jungle down here. Crap happens.   

BRUNO: Crap happens also in arithmetic when viewed from inside.   
Contingency is given by selection on the many computational consistent 
There are different form of contingencies in arithmetic: one for each modal box 
having an arithmetical interpretations.   
In modal logic you can read []p by p is necessary, or true in all (accessible) 
<>p by p is possible or true in one (accessible) world   
~[]p or <>~p by p is contingent (not necessary)   
What will change from one modal logic to another is the accessibility   
or the neighborhood relations on the (abstract) worlds.   

$$$$$ ROGER:  That's correct, I was incorrectly limiting numbers to   
necessary logic.  

> Previously I noted that numbers could not be monads because   
> monads constantly change.   

BRUNO:  They "change" relatively to universal numbers.   

The universal numbers in arithmetic constitutes a sort of INDRA NET,   
as all universal numbers reflects (can emulate, and does emulate, in   
the UD) all other universal numbers.   

Universal numbers introduce many relative dynamics in arithmetic.   

Given that "time is not real", this should not annoy you in any way.   

> Another argument against numbers   
> being monads is that all monads must be attached to corporeal   
> bodies.   


#### ROGER: By atttached I mean associated with. The association is permanent.  
Each monad is an individiaul with individual identity given by the corporeal 
body it is   
associated with. Its soul. All corporeal bodies are different and unique.   

I am OK, in some of the first person perspective. But that is "not real". The 
body is an epistemological construct, yet a every stable one, locally, 
 The mind is not attached or associated to a body, but to an infinity of number 
relations (and the felt body is a construct of the mind).   

$$$$$$ ROGER: To leibniz, matter is not considered to be real, only ideas or 
concepts (monads)  are real,  
but real in a platonic sense.   

> So monads refer to objects in the (already) created world,   
> whose identities persist, while ideas and numbers are not   
> created objects.   

Hmm... They "emanate" from arithmetical truth, so OK.   

The problem is in the "(already)" created world.   

##### ROGER: To some extent there is continuous creation,   
such as the unfolding of subsequent generations of seed--> plant.   
seed----> plant, etc. woman----> baby--> next generation, etc.   
within a particular plant. or woman.   
Yet, according to L, monads cannot be created or destroyed.   
Not to worry as there are an infinite number of them.   

BRUNO: OK in comp, if you accept that the monad are the number coding machine 
relatively to universal numbers.   

(previously)  The existence of a "real physical world" is a badly express 
All we can ask is that vast category of sharable dreams admits some   
(unique?) maximal consistent extension satisfying ... who? All   
universal numbers?   

### ROGER: This is too complex an issue to answer here in great detail..   
The ideas and numbers etc of Platonia can also inhabit the   
minds of men, and there is some limited sharing of ideas   
mentally, as well as some dim knowledge of the past   
and future.   

BRUNO:  Men are in Platonia. But their bodies and consciousness are in the 
limiting internal view of Platonia from inside.   
$$$$$$$ ROGER: No, men are corporeal, extended bodies, so they exist in 
But  anything in platonia is a necessary truth, so it  
should also hold in contingia.  Thus if a contingent man thinks of a necessary  
truth it will appear in his mind, even though it is contingent.  Men have  
access mentally to eternal truths.  

BRUNO:  With comp Platonia is very simple. It is basically the structure (N, 0, 
s, +, *), arithmetic.   
But after G del, we know that such a structure is not simple at all. Indeed, 
unlike physics, there is just no hope to get a complete theory about N, + *.   

$$$$$ Roger: OK, although I haven't a clue as to what it means.   

BRUNO: (previously) I don't know. I mean, I cannot make sense of an "already 
world", nor of objects in there.   

So my attempt to intepret monads by universal number fails, but in   
your definition here you are using concept which I attempt to explain,   
and so I cannot use them.   

####ROGER: Right. Monads and numbers are two different animals,   
although the inhabitants of Platonia can be "thought" or "proved"   
in the minds of men-monads..   

BRUNO:  It looks like you have objects separated from Platonia. In 
Plato-Plotinus and comp,  
Platonia contains the whole of being. That is why Plotinus says that the ONE, 
and the  
MATTERs are not being, as they are not *in* Platonia, and with comp they don't  
belong  properly to Platonia, but are an effect of perspective from inside 

$$$$$ ROGER:  OK, I misunderstand comp, it seems to mean something that is 
calculated, hence contingent.    
OK because Matter is not real if only ideas are real (Leibniz). Matter is in 
And as I show next [in braces, you can skip], Platonia contains the whole of 
[ Necessary truths (platonia) are elite forms of contingent truths (so can also 
exist in contingia)   
But by definition, no  contingent truth is necessary. So there no restriction 
on the  
domain of necessary truths, but there is a glass ceiling on contingent truths.  
So it can be analogously said that God can reach man, but man cannot  
reach God. }   

However, I consider the One, the All, to be permanent features of Platonia.  

BRUNO: But I refute your argument that numbers cannot change, as they do   
change all the time through their arithmetical relations with the   
universal numbers.   

##### ROGER: IMHO By not changing I meant that 1 can never change to 2, it must 
always be 1.   

But I, in some context (added to 3, for example) can be said to be changed or 
to produces 4.   

$$$$ ROGER: Fine.   

(previously) that numbers as numbers cannot change. However....   
IMHO Different numbers can be generated by different calculations, using   
different inputs, or at some different time, but the resulting numbers are 
particulars to that   
particular calculation. And to my mind at least, members of, or belonging to,   
Contingia in some fashion.   

BRUNO:  Yes, exactly. In two very different ways: as being an input, and as 
being a machine, with respect to some universal numbers.   

$$$ ROGER: OK.  

>  (previously)  
> While numbers and ideas cannot be monads, they have to   
> be are entities in the mind, feelings, and bodily aspects   
> of monads.   

Numbers get the two role, at least from the pov of the universal   
numbers. That's the beauty of it.   

##### ROGER: ?   

BRUNO:  Let phi_i an enumeration of all computable functions. In phi_i(j), the 
number i has a role of dynamical machine, and j of passive input.   

ROGERS: OK. That's a much more elegant way to say what a calculation is, if I 
understand you  
from way down here in contingia.  

> For Leibniz refers to the "intellect" of human   
> monads.   

BRUNO: I refer to the "intellect" (terrestrial and divine) of the universal   
numbers, among mainly the L bian one (as the other are a bit too much   
mute on the interesting question).   

ROGER: IMHO Again let me refer to   
a) Numbers themselves. numbers as numbers themselves, and these do not change.  
3 is always 3.   

OK. (Let us hope!)   

b) Calculated numbers. But numbers resulting from calculations obviously can   
differ and change, depending on the type of calculation and varying inputs.   

BRUNO: OK. As input. But they can also be machine---he one who get the input, 
like i in phi_i.   


$$$$$$ROGER: OK.  I overlooked that.  

(previously) And>  similarly, numbers and ideas must be used   
> in the "fictional" construction of matter-- in the bodily   
> aspect of material monads, as well as the construction   
> of our bodies and brains.   

BRUNO: OK. But even truer at another level made possible by comp. As I try to   
illustrate. Arithmetic is full of life and dreams.   


ROGER:  I suppose that calculations, being in contingia, and hence iomperfect,  
can do all sorts of weird things.  


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