Hi Bruno,
                I'm responding to the quiz (see below). What does "high non 
booleanity" mean in the context of para.2?
> ----- Original Message -----
> From: "Bruno Marchal" <marc...@ulb.ac.be>
> To: <everything-list@googlegroups.com>
> Sent: Tuesday, June 30, 2009 6:45 AM
> Subject: Re: The seven step series
> Hi Johnathan,
> 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   True
> 2) the number 12 is a member of A  False
> 3) the number 12 is not a member of A  True
> 4) (3 BELONGS-TO A)    True: but you haven't told us whether the parenthesis 
> cancels the locality of brackets.
> 5) all members of A are numbers  True
> 6) one element of A is not a number  False: we've established that zero is 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}    True...if zero is considered a 
> positive integer.
> 2°) Same questions with the set A = {0, 1, 2, 3, ... , 61, 62, 63}
1. True
2. True
3. False
4. True: same question as 4 above.
5. True
6. False: zero is a number
7. False

> 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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