Quentin Anciaux wrote:
> Hi Brent,
>
> On Friday 16 March 2007 00:16:13 Brent Meeker wrote:
>> Stathis Papaioannou wrote:
>>> On 3/15/07, *Brent Meeker* <meekerdb.domain.name.hidden
>>>
>>> <mailto:meekerdb.domain.name.hidden>> wrote:
>>> > But these ideas illustrate a problem with
>>> > "everything-exists". Everything conceivable, i.e. not
>>> > self-contradictory is so ill defined it seems impossible to
>>>
>>> assign
>>>
>>> > any measure to it, and without a measure, something to pick
>>>
>>> out this
>>>
>>> > rather than that, the theory is empty. It just says what is
>>> > possible is possible. But if there a measure, something
>>>
>>> picks out
>>>
>>> > this rather than that, we can ask why THAT measure?
>>> >
>>> >
>>> > Isn't that like arguing that there can be no number 17 because
>>>
>>> there is
>>>
>>> > no way to assign it a measure and it would get lost among all the
>>>
>>> other
>>>
>>> > objects in Platonia?
>>> >
>>> > Stathis Papaioannou
>>>
>>> I think it's more like asking why are we aware of 17 and other small
>>> numbers but no integers greater that say 10^10^20 - i.e. almost all
>>> of them. A theory that just says "all integers exist" doesn't help
>>> answer that. But if the integers are something we "make up" (or are
>>> hardwired by evolution) then it makes sense that we are only
>>> acquainted with small ones.
>>>
>>>
>>> OK, but there are other questions that defy such an explanation. Suppose
>>> the universe were infinite, as per Tegmark Level 1, and contained an
>>> infinite number of observers. Wouldn't that make your measure
>>> effectively zero? And yet here you are.
>>>
>>> Stathis Papaioannou
>> Another observation refuting Tegmark! :-)
>>
>> Seriously, even in the finite universe we observe my probability is almost
>> zero. Almost everything and and everyone is improbable, just like my
>> winning the lottery when I buy one a million tickets is improbable - but
>> someone has to win. So it's a question of relative measure. Each integer
>> has zero measure in the set of all integers - yet we are acquainted with
>> some and not others. So why is the "acquaintance measure" of small
>> integers so much greater than that of integers greater than 10^10^20 (i.e.
>> almost all of them). What picks out the small integers?
>>
>> Brent Meeker
>
> If you see each integer with a successor notation, 2 is S(1) and 3 is S(2)
> which is S(S(1)) and so on, you see that "big" integers contains the "small"
> integers and the smalls are over represented... just a though ;-)
>
> Quentin
Yes, I think there's a grain of truth in that. The integers aren't *just out there*. By Peano's, or anyone else's, axioms they are generated as needed. We don't want to run out so we (except Torgny) always allow one more, but we never need the whole set at once until we want to make diagonalization arguments.
Brent Meeker
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Received on Thu Mar 15 2007 - 22:52:21 PDT