Re: Some Questions.
- From: "galathaea" <galathaea@xxxxxxxxx>
- Date: 4 Jan 2007 10:56:50 -0800
Bob Kolker wrote:
1. Can mathematics be done without the concept of set (or class or
collection)?
it needs some form of discrete collection
to be able to form strings
2. To what extent is set -theory- necessary to do mathematics?
it is not
performing a process (of describing)
and describing a process of describing
are two separate things
any repeatable and learnable symbology
is doing mathematics
one description is set theory
The questions are slightly different, so please note.
3. Are there alternate foundations of mathematics to sets?
category theory has been used
to describe mathematics in "diagrams"
as an algebraic alternative
the diagrams play the part of the collection
and can replace any set foundations normally used in category theory
f w lawvere did much work on this in the 60s
and books like
"topoi: a categorial analysis of logic"
"sheaves and geometery"
and "algebraic set theory"
show much of these types of development
the advantage of these types of formulations
is that they are intensional
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galathaea: prankster, fablist, magician, liar
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- From: Bob Kolker
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