Re: Resiliency To New Data Requirements
From: Bob Badour <bbadour_at_pei.sympatico.ca>
Date: Tue, 08 Aug 2006 01:00:20 GMT
Message-ID: <EmRBg.36512$pu3.479885_at_ursa-nb00s0.nbnet.nb.ca>
>
>
> (since similar discussions frequently crop up in sci.logic a
> cross-post might get some interesting input.)
>
> My suggestions for the most general uses only a single
> concept: language. Yours uses three concepts: set, element,
> and zero. :-)
>
> Seriously, giving a concept a name (set for example) doesn't
> make it more or less singular. Determining the singularity
> of concepts is notoriously difficult. Surely you are aware
> that the set concept is often argued and many attempts are
> regularly made to provide a correct and complete definition.
>
> The "element" language you used seems to indicate a concept
> of "set" as a collection of elements with the collection
> regarded as a whole or in Cantor's words "Any collection
> into a whole M of definite and separate objects m of our
> intuition or our thought."
>
> Thus, there are in fact two concepts in this concept of set:
> element and aggregate. The concept of aggregate or wholeness
> being necessary to distinguish {{}}, {{},{}}, etc from {}
> for example. Furthermore, you can't get very far without at
> the additional concept of the empty set (or the concept of
> zero, nothing, etc) or ur-elements or some other atoms.
>
> So you chose element, collection, and zero, while I chose 0,
> 1, and sequence. Which seem equally simple, no? No, I admit
> to also seeing sets as somehow "more simple". Partly because
> the concept of collection seems more simple than sequence
> obviously because collection lacks order. Though as natural
> as order is to humans perhaps the sequence concept does
> not add much if any "conceptual" complexity.
>
> Alas, the question was of "generality" not simplicity. And
> I've never seen set theory represented without the use of
> sequences of symbols ;-) (Loaded statement of course.)
>
> -- Keith -- Fraud 6
Date: Tue, 08 Aug 2006 01:00:20 GMT
Message-ID: <EmRBg.36512$pu3.479885_at_ursa-nb00s0.nbnet.nb.ca>
Keith H Duggar wrote:
> Bob Badour wrote:
>
>>Keith H Duggar wrote:
>>
>>>Bob Badour wrote:
>>>
>>>>Marshall wrote :
>>>>
>>>>>Neo wrote :
>>>>>
>>>>>>That task has been to find the most general method
>>>>>>of representing things.
>>>>>
>>>>>Answering that question is easy. The most general
>>>>>method of representing things is to use bits.
>>>>
>>>>There is a more general method, which is to use
>>>>sets. See formalism as a foundation of mathematics.
>>>>
>>>>{} is the canonical set with zero elements and represents zero or false
>>>>{{}} is the canonical set with one element and represents one or true
>>>>{{},{{}}} is the canonical set with two elements etc.
>>>
>>>I would have said the "most general way of representing
>>>things" is a sequence of symbols from an alphabet. Of
>>>which {}, {{}}, {{}{{}}}, along with the characters I'm
>>>using now to represent English, predicate logic, etc are
>>>all examples. If you limit the alphabet to only two
>>>symbols 0 and 1 then you have binary sequences.
>>
>>Ah, now we are getting into the representations of our
>>representations. My suggestion for most general uses only
>>a single concept: set. Yours uses three concepts: 0, 1 and
>>sequence.
>
>
> (since similar discussions frequently crop up in sci.logic a
> cross-post might get some interesting input.)
>
> My suggestions for the most general uses only a single
> concept: language. Yours uses three concepts: set, element,
> and zero. :-)
>
> Seriously, giving a concept a name (set for example) doesn't
> make it more or less singular. Determining the singularity
> of concepts is notoriously difficult. Surely you are aware
> that the set concept is often argued and many attempts are
> regularly made to provide a correct and complete definition.
>
> The "element" language you used seems to indicate a concept
> of "set" as a collection of elements with the collection
> regarded as a whole or in Cantor's words "Any collection
> into a whole M of definite and separate objects m of our
> intuition or our thought."
>
> Thus, there are in fact two concepts in this concept of set:
> element and aggregate. The concept of aggregate or wholeness
> being necessary to distinguish {{}}, {{},{}}, etc from {}
> for example. Furthermore, you can't get very far without at
> the additional concept of the empty set (or the concept of
> zero, nothing, etc) or ur-elements or some other atoms.
>
> So you chose element, collection, and zero, while I chose 0,
> 1, and sequence. Which seem equally simple, no? No, I admit
> to also seeing sets as somehow "more simple". Partly because
> the concept of collection seems more simple than sequence
> obviously because collection lacks order. Though as natural
> as order is to humans perhaps the sequence concept does
> not add much if any "conceptual" complexity.
>
> Alas, the question was of "generality" not simplicity. And
> I've never seen set theory represented without the use of
> sequences of symbols ;-) (Loaded statement of course.)
>
> -- Keith -- Fraud 6
Of course. ;-) Received on Tue Aug 08 2006 - 03:00:20 CEST