Hi John,

On 30 Jun 2009, at 14:32, John Mikes wrote:

> Hi, Bruno
> you know that I am in a different mindset, yet happy to read your  
> train of thoughts. I consider a set a limited model of elements (and  
> conclusions thereof are not applicable to wider domains) -

Well, as Thorgny illustrated correctly, the notion of SET does not  
apply to SETS. usually the collection of all sets is not considered as  
a set, for many good reasons, some of which appear already in the  
treatise on Numbers by Plotinus. To derive from this that infinite  
sets cannot exist, like Thorgny seems to believed is invalid.

> when I read your
> "A set can be described in extension or in intension. "in extension"  
> means that we give all elements of the set, enclosed in accolades."
> I was really happy with the next sentence:
> "When the set is not to complex (meaning big or infinite), we can  
> use the "...".  - "
> (I missed here the exemption of the 'infinite' "set", really a  
> contradiction, to which the 'set' considerations cannot apply - OR  
> can they?

Of course they can. This is done in everyday mathematics all the time  
since Cantor discovered the notion of sets. It can be said that set  
have been exploited especially for the handling of infinities.
Typical infinite sets are the set of natural numbers {0, 1, 2, ...},  
the set of odd numbers {1, 3, 5, 7, ...}, the set of prime numbers {2,  
3, 5, 7, 11, ...} as already proved by Euclid, the set of decimal  
approximation of most real numbers, etc.

> if you have something on that...)

Google on it. The notion of set (finite and especially infinite sets)  
is pervading all modern mathematics.

> "Many" cannot be infinite (by MY definition).

Well, I prefer to use the word in their most used and standard sense.

> I loved your words on QM, the (linear) extension of the figment  
> physical world as described in reductionist physical sciences.
> I also cannot wait for something more about your approach on
> the "self reference" - the basis of physics? -

This is the whole point of the UDA, and AUDA.

> especially as to
> 'self' of what (who)? I hope the answer will not be "machine" or  
> comp, because then I have to continue "and what is that?"

Of course it is comp, although I use comp because it is the simple  
way. Then, digging on mathematical logic, the same result can be  
retrieve from much weaker assumption. But comp is believed by all  
scientist and philosophers, except Penrose. Even John Searle is  
computationalist with my weak definition of it.
"and what is that"? It is the point of the present thread to explain  
that as slowly as possible so that good willing non mathematicians can  
understand the key points.

> (in more than a utilitarian explanation of what it does). ('it?')
> What boils down to my ignorance as to the originating and  
> maintaining to ANY action we speak about. The 'theos' of a non- 
> assumed and non-supernatural factor (system?) yet involved in  
> conducting all we just find natural and proceeding.
> You may substitute 'numbers' for such, but so far did not reply (to  
> my satisfaction at least) WHAT those 'numbers' may be.
> Sorry, I am not of the religious kind.

If you can compute 34+89, or 65*87, then you know enough. My use of  
number in UDA is not religious, it is the same use as those who use  
number to send man on the moon. Too much and premature philosophizing  
makes it hard to proceed. "Religion" appears later, when you say "yes"  
to the digitalist surgeon. Comp asks for an act of faith.

> *
> Maybe my error is in 'believeing' that a REALITY may exist and 'we'  
> have only access to part of it.

Neither science, nor philosophy, nor theology, could develop without  
such assumption. It is because we believe that there is a reality,  
that we can build theories to infer the part on which we have no  
access. science always consist in an attempt to see the invisible, be  
it atoms, far away galaxies, or mathematical constructions. So this is  
not an error.

> Inventing for our comfort (the D. Bohmian idea) 'numbers' at the  
> human level of pre-Platonian thinking. If 'reality' exists only by  
> 'comp' or 'consequences' then I may be in a reversed error, due to  
> brainwashing by in college imprinted  natural sciences - what I try  
> to exceed yet it still sits there.
> Our 'perceived reality' (ColinH) may also provide the numbers.

Sure, but this is independent of the fact that 17 is a prime numbers  
independently of me. That the set of prime numbers is infinite,  
independently of me, etc.

> Now that sounds heretical enough in this thread. Forgive me.
> *
> Waiting for the self-reference, (who's?)

Who's? But the universal number's self-reference of course. Even the  
Lobian one.

> - with thanks so far

You are welcome,


> On Tue, Jun 30, 2009 at 6:45 AM, Bruno Marchal <marc...@ulb.ac.be>  
> wrote:
> Hi Johnathan,
> On 29 Jun 2009, at 17:22, Johnathan Corgan wrote:
> >
> > Bruno,
> >
> > I think you were off to a good start with your planned series of  
> posts
> > about the seven step argument.  I believe your first installment  
> was a
> > discussion of set theory as one of the mathematical preliminaries to
> > the
> > actual argument.
> >
> > I am looking forward to your next installment.
> Well, thanks. I am not sure Kim and Marty are there, but I can provide
> a summary, and recall the motivation.
> Marty, did you come back from holiday? Kim? still interested in
> electronical summer's school on mathematics.
> The goal of the seven step thread is to make clear the seventh step of
> the UDA (Universal Dovetailer Argument). The purpose of the UDA is to
> make clear that the mind-body problem (or the consciousness/reality
> problem, or the first person/third person) problem is reduced, when we
> do the computationalist assumption, to a pure body appearance or
> discourse problem. UDA shows that if we assume the comp. hyp. then we
> have to explain the appearance of matter from machine or number self-
> reference only. The proof is constructive, it shows *how* the laws of
> physics have to be extracted from self-reference.
> Later, much later, I could explain, if everyone is OK with UDA, how we
> can already extract from self-reference the general shape of physics,
> so that we can already refute empirically, or confirm, the comp. hyp.
> And it appears that the empirical quantum mechanics,  currently,
> confirms the comp. hyp. Quantum mechanics confirms the partial
> indetermination of the outcomes of our possible experiences, and the
> "high non booleanity" of the propositions describing those outcomes".
> The object of the "seventh step thread' consists in making the seventh
> step accessible to non mathematicians. So we have to start from zero.
> I have decided to start from elementary "naive" set theory, without
> which we cannot do anything in math. I will avoid all special
> mathematical symbols, and use instead words with capital letters.
> We have not yet done a lot. So I can sum up, with the new "notations".
> Definition. A set is just a "many" considered, when clear enough, as a
> "one". So a set is just a collection of objects, and those objects are
> called the element, or the member, of the set. If some x is an element
> of some set A, we write x BELONGS-TO A, or (x BELONGS-TO A).
> A set can be described in extension or in intension. "in extension"
> means that we give all elements of the set, enclosed in accolades.
> When the set is not to complex (meaning big or infinite), we can use
> the "...". We can give name to a set, to ease or talk about that set,
> like we do all the times in mathematics. Most of the set we will
> consider are set of mathematical object, mainly numbers in the
> beginning, and then set of ... sets.
> Example-exercise:
> 1°) Let A be the set {0, 1, 2, 3}. ("A" is said to be a local name for
> the set {0, 1, 2, 3}. And local means that such a name is used in a
> local context. One paragraph later "A" could designed another, so be
> careful). If "A" names {0, 1, 2, 3}, we will write "A = {0, 1, 2, 3}".
> OK, so with A = {0, 1, 2, 3}. Which of the following propositions are
> true
> 1) the number 2 is a member of A
> 2) the number 12 is a member of A
> 3) the number 12 is not a member of A
> 4) (3 BELONGS-TO A)
> 5) all members of A are numbers
> 6) one element of A is not a number
> 7) A can be defined in intension in the following way A = {x SUCH-THAT
> x is a positive integer little than 4}
> 2°) Same questions with the set A = {0, 1, 2, 3, ... , 61, 62, 63}
> This makes 14 exercises, which should be easy. I intent to keep it
> that way. I continue after I get either answers (correct or wrong), or
> questions.
> Everyone is welcome to participate. Yet, I ask those who are quick to
> respect those who are slow. To be slow in the beginning usually help
> for being deep in the sequel.
> Best,
> Bruno
> http://iridia.ulb.ac.be/~marchal/
> >


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