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.


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  

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
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  

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.




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