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Re: Smullyan's Proof of the Drinkers Principle V3

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The only difference is that incomplete lattices
can be also finite. For example if you take
this complete lattice:

___{Anna, Bert}
___/ ____________\
{Anna}________{Bert}
___\____________/
_________{}

https://en.wikipedia.org/wiki/Hasse_diagram

And remove {Anna, Bert} you get an
incomplete lattice, also a semi-lattice:

{Anna}________{Bert}
___\____________/
_________{}
https://en.wikipedia.org/wiki/Hasse_diagram

On the other hand the extension of your DC Poop
Set(_) is always infinite because you have the
powerset axiom. Because of the union axiom of

set theory, the lattice has also arbitrary meets,
And by Cantors theorem, you can prove:

|A| < |𝒫(A)|

So I guess there is no way to make the
extension Set(_) finite. Just Cantors theorem
will say that it is finite, and

we cannot make it finite by some loops?

Mostowski Collapse schrieb:
> Some info for the school skipper:
> 
> So what was before Rusells Paradox (1901)?
> It was Cantor who banged his head here,
> the same thing:
> 
> If we start from the notion of a definite
> multiplicity [[Vielheit]] (a system, a totality)
> of things, it is necessary, as I discovered,
> to distinguish two kinds of multiplicities
> (by this I always mean definite multiplicities).
> 
> For a multiplicity can be such that the assumption
> that all of its elements " are together " leads
> to a contradiction, so that it is impossible to
> conceive of the multi-plicity as a unity, as " one
> finished thing ". Such multiplicities I call
> absolutely infinite or inconsistent multiplicities.
> 
>  From Frege to Gödel: A Source Book in Mathematical Logic, 1879-1931
> https://books.google.ch/books?id=v4tBTBlU05sC
> 
> After Russell there were more mondaine
> names. You can also call it an incomplete
> lattice, etc.. etc..
> 
> Mostowski Collapse schrieb:
>> Well you might think its irrelevant.
>> But you just proved something about the
>> extensions of Set(_).
>>
>> So even if you don't know what you are
>> doing, you are yourself a lattice researcher
>> right now. What you prove is that
>>
>> Set(_), the extension of it, is not a complete
>> lattice. It doesn't have a top element.
>> This lead Cantor to label the "absolute infinite"
>>
>> as the "inconsistent multiplicity". Since like
>> in the expectation of Rusells Paradox, this
>> here is not element of the extension of Set(_):
>>
>> U = { x | x = x }
>>
>> You might also don't know what the terms
>> extension/intension mean. Don't worry. There is
>> a first time for everything. Maybe you know
>>
>> what a door knob is? I don't want to say a door
>> knob has the higher IQ like you. But if a door knob
>> is connected to the internet, via some smart home
>>
>> appliance, it might know what extension/intension means.
>> Just google it, if you don't have a logic book at home.
>>
>> https://letmegooglethat.com/?q=extension+intension
>>
>>
>> Dan Christensen schrieb:
>>> On Sunday, May 7, 2023 at 11:31:11 AM UTC-4, Mostowski Collapse wrote:
>>>
>>> [snip irrelevant discussion of classes and lattices]
>>>
>>>> ALL(s):[Set(s) => EXIST(a):~a e s]
>>>> http://www.dcproof.com/UniversalSet.htm
>>>
>>>> So when you assume drinkers comes from Set(_),  and
>>>> don't further restrict it, you are dealing with an incomplete
>>>> lattice.
>>>
>>> We start with  the premise :
>>>
>>> 1. Set(u) & ALL(a):a e u
>>> Premise
>>>
>>> We obtain a contradiction from it, so it must be false.
>>>
>>> ~EXIST(s):[Set(s) & ALL(a):a e s]
>>>
>>> Or equivalently...
>>>
>>> ALL(s):[Set(s) => EXIST(a):~a e s]
>>>
>>> Simple as that. There no need to muddy the waters with your talk of 
>>> classes or lattices, Mr. Collapse. As usual, you seem to be 
>>> desperately grasping at straws.
>>>
>>> Dan
>>>
>>> Download my DC Proof 2.0 freeware at http://www.dcproof.com
>>> Visit my Math Blog at http://www.dcproof.wordpress.com
>>>
>>
> 

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Re: Smullyan's Proof of the Drinkers Principle V3 Mostowski Collapse <bursejan@gmail.com> - 2023-05-03 16:16 -0700
  Re: Smullyan's Proof of the Drinkers Principle V3 Mostowski Collapse <janburse@fastmail.fm> - 2023-05-04 20:19 +0200
    Re: Smullyan's Proof of the Drinkers Principle V3 Mostowski Collapse <janburse@fastmail.fm> - 2023-05-04 20:27 +0200
      Re: Smullyan's Proof of the Drinkers Principle V3 Mostowski Collapse <janburse@fastmail.fm> - 2023-05-04 20:32 +0200
        Re: Smullyan's Proof of the Drinkers Principle V3 Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-05-04 12:15 -0700
          Re: Smullyan's Proof of the Drinkers Principle V3 Mostowski Collapse <bursejan@gmail.com> - 2023-05-04 16:33 -0700
            Re: Smullyan's Proof of the Drinkers Principle V3 Mostowski Collapse <bursejan@gmail.com> - 2023-05-04 16:50 -0700
            Re: Smullyan's Proof of the Drinkers Principle V3 Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-05-04 16:54 -0700
              Re: Smullyan's Proof of the Drinkers Principle V3 Mostowski Collapse <bursejan@gmail.com> - 2023-05-04 17:09 -0700
                Re: Smullyan's Proof of the Drinkers Principle V3 Mostowski Collapse <bursejan@gmail.com> - 2023-05-04 17:12 -0700
                Re: Smullyan's Proof of the Drinkers Principle V3 Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-05-04 22:34 -0700
                Re: Smullyan's Proof of the Drinkers Principle V3 Mostowski Collapse <bursejan@gmail.com> - 2023-05-05 03:35 -0700
                Re: Smullyan's Proof of the Drinkers Principle V3 Mostowski Collapse <bursejan@gmail.com> - 2023-05-05 14:37 -0700
                Re: Smullyan's Proof of the Drinkers Principle V3 Mostowski Collapse <bursejan@gmail.com> - 2023-05-06 03:09 -0700
                Re: Smullyan's Proof of the Drinkers Principle V3 Mostowski Collapse <bursejan@gmail.com> - 2023-05-06 03:43 -0700
                Re: Smullyan's Proof of the Drinkers Principle V3 Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-05-06 10:29 -0700
                Re: Smullyan's Proof of the Drinkers Principle V3 Mostowski Collapse <bursejan@gmail.com> - 2023-05-07 02:41 -0700
                Re: Smullyan's Proof of the Drinkers Principle V3 Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-05-07 06:59 -0700
                Re: Smullyan's Proof of the Drinkers Principle V3 Mostowski Collapse <bursejan@gmail.com> - 2023-05-07 08:31 -0700
                Re: Smullyan's Proof of the Drinkers Principle V3 Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-05-07 11:19 -0700
                Re: Smullyan's Proof of the Drinkers Principle V3 Mostowski Collapse <janburse@fastmail.fm> - 2023-05-07 20:34 +0200
                Re: Smullyan's Proof of the Drinkers Principle V3 Mostowski Collapse <janburse@fastmail.fm> - 2023-05-07 20:41 +0200
                Re: Smullyan's Proof of the Drinkers Principle V3 Mostowski Collapse <janburse@fastmail.fm> - 2023-05-07 20:47 +0200
                Re: Smullyan's Proof of the Drinkers Principle V3 Mostowski Collapse <janburse@fastmail.fm> - 2023-05-07 20:48 +0200
                Re: Smullyan's Proof of the Drinkers Principle V3 Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-05-07 11:51 -0700
                Re: Smullyan's Proof of the Drinkers Principle V3 Mostowski Collapse <bursejan@gmail.com> - 2023-05-08 05:36 -0700
                Re: Smullyan's Proof of the Drinkers Principle V3 Mostowski Collapse <bursejan@gmail.com> - 2023-05-08 07:22 -0700
                Re: Smullyan's Proof of the Drinkers Principle V3 Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-05-11 14:34 -0700
                Re: Smullyan's Proof of the Drinkers Principle V3 Mostowski Collapse <bursejan@gmail.com> - 2023-05-11 16:10 -0700
                Re: Smullyan's Proof of the Drinkers Principle V3 Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-05-11 17:00 -0700
                Re: Smullyan's Proof of the Drinkers Principle V3 Mostowski Collapse <janburse@fastmail.fm> - 2023-05-12 12:04 +0200
                Re: Smullyan's Proof of the Drinkers Principle V3 Mostowski Collapse <bursejan@gmail.com> - 2023-05-12 03:13 -0700
                Re: Smullyan's Proof of the Drinkers Principle V3 Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-05-12 07:12 -0700
                Re: Smullyan's Proof of the Drinkers Principle V3 Mostowski Collapse <bursejan@gmail.com> - 2023-05-21 06:59 -0700
                Re: Smullyan's Proof of the Drinkers Principle V3 Mostowski Collapse <bursejan@gmail.com> - 2023-05-21 07:10 -0700
                Re: Smullyan's Proof of the Drinkers Principle V3 Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-05-21 08:22 -0700
                Re: Smullyan's Proof of the Drinkers Principle V3 Mostowski Collapse <bursejan@gmail.com> - 2023-05-21 12:14 -0700
                Re: Smullyan's Proof of the Drinkers Principle V3 Mostowski Collapse <bursejan@gmail.com> - 2023-05-21 12:16 -0700
                Re: Smullyan's Proof of the Drinkers Principle V3 Mostowski Collapse <bursejan@gmail.com> - 2023-05-21 12:17 -0700
                Re: Smullyan's Proof of the Drinkers Principle V3 Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-05-21 12:50 -0700
                Re: Smullyan's Proof of the Drinkers Principle V3 Mostowski Collapse <bursejan@gmail.com> - 2023-05-21 12:56 -0700
                Re: Smullyan's Proof of the Drinkers Principle V3 Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-05-21 15:45 -0700
                Re: Smullyan's Proof of the Drinkers Principle V3 Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-05-21 16:01 -0700
                Re: Smullyan's Proof of the Drinkers Principle V3 Mostowski Collapse <bursejan@gmail.com> - 2023-05-21 16:29 -0700
                Re: Smullyan's Proof of the Drinkers Principle V3 Mostowski Collapse <bursejan@gmail.com> - 2023-05-21 16:56 -0700
                Re: Smullyan's Proof of the Drinkers Principle V3 Mostowski Collapse <bursejan@gmail.com> - 2023-05-21 16:59 -0700
                Re: Smullyan's Proof of the Drinkers Principle V3 Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-05-21 17:51 -0700
                Re: Smullyan's Proof of the Drinkers Principle V3 Mostowski Collapse <janburse@fastmail.fm> - 2023-05-22 02:51 +0200
    Re: Smullyan's Proof of the Drinkers Principle V3 Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-05-04 11:40 -0700
      Re: Smullyan's Proof of the Drinkers Principle V3 Mostowski Collapse <bursejan@gmail.com> - 2023-05-04 11:43 -0700
        Re: Smullyan's Proof of the Drinkers Principle V3 Mostowski Collapse <bursejan@gmail.com> - 2023-05-04 11:49 -0700

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