On Friday, February 1, 2013 2:29:21 PM UTC-5, Stephen Paul King wrote:
>
>  On 2/1/2013 8:07 AM, Craig Weinberg wrote:
>  
>
>
> On Friday, February 1, 2013 12:12:17 AM UTC-5, Stephen Paul King wrote: 
>>
>>  On 1/31/2013 6:12 PM, Craig Weinberg wrote:
>>  
>>
>>
>> On Thursday, January 31, 2013 5:38:28 PM UTC-5, Stephen Paul King wrote: 
>>>
>>>  On 1/31/2013 4:46 PM, Telmo Menezes wrote:
>>>  
>>> What's an entity?
>>>
>>>
>>>     Any system whose canonical description can be associated with some 
>>> kind of fixed point theorem.
>>>  
>>
>> Nice. Interestingly this just came up on another list five minutes ago. 
>> Some interesting etymology too:
>>
>> entity (n.)
>>     1590s, from Late Latin entitatem (nom. entitas), from ens (genitive 
>> entis) "a thing," proposed by Caesar as prp. of esse "be" (see is), to 
>> render Greek philosophical term to on "that which is" (from neuter of prp. 
>> of einai "to be;" see essence). Originally abstract; concrete sense in 
>> English is from 1620s.
>>
>> entire (adj.) 
>>     late 14c., from Old French entier "whole, unbroken, intact, 
>> complete," from Latin integrum (nom. integer; see integer).
>>
>>  A slightly different meaning when we formalize it... a literal entity 
>> has a thingness definable by position. A more figurative or casual 
>> reference could mean like a 'the aspect of a presence or representation 
>> which emphasizes its closure'.
>>
>> Craig
>>  
>> Hi Craig,
>>
>>     Position is one kind of dimension that is identifiable via a fixed 
>> point, for example: Craig is at such and such an address.
>>  
>
> Hi Stephen,
>
> I would tend to consider address just another kind of position though. Is 
> there an example of something which fixed point theorem addresses which is 
> not a dimension which can be defined by position? Isn't the act of fixing a 
> point the same as formalizing a position?
>
> Craig
>  
>  Hi Craig,
>
>     No, its about the relation between object and context in a dynamic 
> sense. Look at the variability in fixed points here: 
> http://en.wikipedia.org/wiki/Fixed-point_theorem
>
> Look at what all have in common: Some transformation on a collection, some 
> closure of that which is transformed and some invariant - the fixed point.
>

Oh, sorry I didn't realize that was a specifically defined term.  F-p 
theorem seems too narrow to me to contain the casual use of 'entity', as x 
or f(x) is already an entity regardless of any operations of coordination 
of values. A ghost in a dream can be an entity, or a legal entity can be 
purely conceptual. Unless you are looking at 'entity' as a mathematical 
description only.

Craig


> -- 
> Onward!
>
> Stephen
>
>  

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