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What are numbers?

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Postby at1with0 » Fri Sep 07, 2012 5:05 pm

I may be making a mistake in thinking that you are using the word relation the same way I would.

To me, a relation is a set of pairs where a pair (x,y) is a member of the relation if x is related to y. For example, the relation could be "is a parent of" and so (son, son's father) is a member of the relation while (nephew, cousin's father) is not.

All kinds of relations exist without quantification. Or perhaps you can tell me what you mean by relation and maybe then I will understand how quantification is always involved in relations.
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Postby DIss0n80r » Fri Sep 07, 2012 6:03 pm

All referenceables are numerable. Numeric designations are essentially tags for relational valuation. You are arbitrarily narrowing relation to set-pair correspondence, but numeration is still implicit. Numeration is always going to be implicit, because it is an essential feature of any relation example you could give.
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Postby at1with0 » Fri Sep 07, 2012 6:20 pm

DIss0n80r wrote:All referenceables are numerable. Numeric designations are essentially tags for relational valuation. You are arbitrarily narrowing relation to set-pair correspondence, but numeration is still implicit. Numeration is always going to be implicit, because it is an essential feature of any relation example you could give.



How is numeration an essential feature of the relation example I gave?
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Postby DIss0n80r » Fri Sep 07, 2012 6:31 pm

Any referenceable is inherently a count for one. Relation is both singular and pluralistic.
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Postby at1with0 » Fri Sep 07, 2012 7:39 pm

What do you mean?

A count for one?
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Postby DIss0n80r » Fri Sep 07, 2012 7:56 pm

Never mind.
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Postby Island_Girl » Sat Sep 08, 2012 12:24 am

Music explains most things to me.

May I offer this to add flavor to
the discussion? :)

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Postby at1with0 » Sat Sep 08, 2012 8:35 am

Music and math are closely connected... Perhaps numbers can be "visualized" as notes or melodies or chords.
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Postby DIss0n80r » Sat Sep 08, 2012 9:32 am

"Abstraction consists essentially in the creation and utilization of ambiguity."

"Logic moves in one direction, the direction of clarity, coherence and structure. Ambiguity moves in the other direction, that of fluidity, openness, and release. Mathematics moves back and forth between these two poles. [...] It is the interaction between these different aspects that gives mathematics its power." - William Byers How Mathematicians Think
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Postby at1with0 » Sat Sep 08, 2012 9:41 am

Reminds me of the set concept. I haven't come across a definition of the word set that depends on more primary notions. In what I've seen, sets are defined in ways that are ambiguous or not defined at all.
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