Re: Whoopie ! The natural INTEGERS are indeed monads

```Bruno:

how about expanding our closed (mathematical) minds into not only decimal,
binary, etc., but also a (hold on fast!) 12/17ary number systems?
in that case 17 would be non-primary, divisible by 2,3,4,6 besides the 1.
Just playing my mind on math. (You may have an even wider mind). Also zero
can be "thought of" in non-human logic as participant in calculations.```
```
John M
PS: no response required indeed. My agnosticism at work.

On Sat, Dec 8, 2012 at 5:06 AM, Bruno Marchal <marc...@ulb.ac.be> wrote:

>
> On 07 Dec 2012, at 14:33, Roger Clough wrote:
>
>
>> Obviously, I meant the natural integers, not the natural numbers,
>> whatever they be.
>>
>
> Natural numbers = the non negatiove integers: 0, 1, 2, 3, ....
> or 0, s(0), s(s(0)), ...
>
> Bruno
>
>
>
>
>>
>> ----- Have received the following content -----
>> Sender: Roger Clough
>> Time: 2012-12-07, 08:18:36
>> Subject: Whoopie ! The natural numbers are indeed monads
>>
>>
>> Hi Bruno Marchal
>>
>>
>> 1) We in fact agree about what 1p is, except IMHO it is the
>> Supreme Monad viewing the world THROUGH an individual's
>> 1p that I would call the inner God. Or any God.
>>
>> 2) Previously I dismissed numbers as being monads because I
>>
>> But natural numbers are different because
>> even though they are only mental substances, they're still
>> substances, by virtue of the fact that they can't be subdivided.
>> So they are of one part each.
>>
>> Thus the natural numbers are monads, even though they have no
>> physical correlates. Sorry I've be so slow to see that.
>>
>> That reallyiopens doors Then numbers can see each other with 1p.
>>
>> WHOOPEE !
>>
>> [Roger Clough], [rclo...@verizon.net]
>> 12/7/2012
>> "Forever is a long time, especially near the end." -Woody Allen
>>
>> ----- Receiving the following content -----
>> From: Bruno Marchal
>> Time: 2012-12-06, 12:44:46
>> Subject: Re: On the need for perspective and relations in modelling the
>> mind
>>
>>
>>
>>
>> On 05 Dec 2012, at 11:05, Roger Clough wrote:
>>
>>
>> Hi Bruno Marchal
>>
>> Indeed, we can not code for [1p].  But we need not abandon
>> itr entirely, as you seem to have done, and as cognitive
>> theory has done.
>>
>>
>> On the contrary, I define it is a simple way (the owner of the diary) the
>> the self-multiplication thought experiment (UDA). It is enough to
>> understand that physics emerge from the way the "numbers see themselves".
>>
>>
>> But in the math part, I define it by using the fact that the
>> incompleteness phenomenon redeemed the Theatetus definition. The Bp & p
>> definition. It is a bit technical.
>>
>>
>> Don't worry. The 1p is the inner god, the first person, the knower, and
>> it plays the key role for consciousness and matter.
>>
>>
>>
>>
>>
>>
>>
>>
>>  We can replace [1p] by its actions -
>> those of perception,  in which terms are relational (subject: object).
>> You seem to deal with everything from the 3p perspective.
>>
>>
>> That's science. But don't confuse the level. My object of study is the
>> 1p, that we can attribute to machine, or person emulated by machines. I
>> describe the 3p and the 1ps (singular and plural), and indeed their
>> necessary statistical relation at some level.
>>
>>
>>
>>
>>
>>
>>
>> That is my argument for using semiotics, which includes 1p (or
>> interprant) as a necessary and natural part of its triad of relations.
>> Your responses seem to leave out such relations.  I cannot find
>> again the quote I should have bookmarked, but in an argument
>> for using semiotics on the web, it was said that modern cognitive
>> theory has abandoned the self in an effort to depersonalize
>> cognition.  While this is a valid scientific reason, it doesn't work
>> when living breathing humans are concerned.
>>
>>
>> I use computer and mathematical logic semantic. That's the advantage of
>> comp. You have computer science.
>>
>>
>>
>>
>>
>> IMHO leaving out [1p ] in such a way will forever prevent
>> computer calculations from emulating the mind.
>>
>>
>> The 1p is not left out. Eventually comp singles out eight person points
>> of view. If you think comp left out the person, you miss the meaning of the
>> comp hope, or the comp fear.
>>
>>
>> Bruno
>>
>>
>>
>>
>>
>>
>>
>>
>> [Roger Clough], [rclo...@verizon.net]
>> 12/5/2012
>> "Forever is a long time, especially near the end." -Woody Allen
>>
>> ----- Receiving the following content -----
>> From: Bruno Marchal
>> Time: 2012-12-03, 13:03:12
>> Subject: Re: Semantic vs logical truth
>>
>>
>>
>>
>> On 03 Dec 2012, at 00:04, meekerdb wrote:
>>
>>
>> On 12/2/2012 7:27 AM, Bruno Marchal wrote:
>> The 1p truth of the machine is not coded in the machine. Some actual
>> machines knows already that, and can justified that If there are machine
>> (and from outside we can know this to correct) then the 1p-truth is not
>> codable.  The 1p truth are more related to the relation between belief and
>> reality (not necessarily physical reality, except for observation and
>> sensation).
>>
>>
>> Even the simple, and apparently formal Bp & p is NOT codable.
>> Most truth about machine, including some that they can know, are not
>> codable.
>> Many things true about us is not codable either.
>>
>> Let me see if I understand that.  I think you are saying that p, i.e.
>> that "p" describes a fact about the world, a meta-level above the coding of
>> a machine.
>>
>>
>> No, p is for some statement at the base level, like 1+1 = 2.
>>
>>
>>
>>
>>
>>
>>
>>
>>
>>
>> That the Mars Rover believes it is south of it's landing point is
>> implicit in its state and might be inferred from its behavior, but there is
>> no part of the state corresponding to "I *believe* I am south of my landing
>> point."
>>
>>
>> Then Mars Rover is not L?ian. But I am not even sure that Mars Rover is
>> Turing universal, or that it exploits its Turing universality.
>>
>>
>> But PA and ZF can represent "I believe". So we can study the logic of a
>> new 'knowledge" operator defined (at the meta level, for each arithmetical
>> proposition) by Bp & p. For example if p is "1+1=2", it is
>>
>>
>> Believe"("1+1=2") & 1+1 = 2.
>>
>>
>> We cannot define such operator in arithmetic. We would need something
>> like Believe"("1+1=2") & True("1+1 = 2"), but True, in general cannot
>> defined in arithmetic. Yet, we can metadefine it and study its logic, which
>> obeys a soprt of temporal intuionistic logic (interpreting the S4Grz logic
>> obtained).
>>
>>
>>
>>
>>
>>
>>
>>
>>
>>
>> One could include such second-level states (which one might want to
>> communicate to Pasadena) but then that state would be just another
>> first-level state. Right?
>>
>>
>>
>> Not sure I see what you mean. The meta, available by the machine is in
>> the "I believe". It is the 3-I. The presentation of myself to myself. The
>> 1-I will be the non definable operator above. We connect the believer to
>> the truth. It is easy to do for the sound correct machine.
>>
>>
>> Bruno
>>
>>
>>
>>
>>
>>
>>
>>
>>
>> Brent
>>
>>
>>
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