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Topic: Foundations of mathematics... the order of bootstrapping the foundations
Replies: 13   Last Post: Aug 21, 2013 9:04 PM

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 quasi Posts: 12,067 Registered: 7/15/05
Re: Foundations of mathematics... the order of bootstrapping the foundations
Posted: Aug 21, 2013 12:09 AM

William Elliot wrote:
>Lax Clarke wrote:
>

>> This is the order of bootstrapping the foundations of
>> mathematics:
>>

>Boot strapping has nothing to do with mathematics.
>It's part of computer science.

Firstly bootstrapping is one word, not two.

As to its applicability, it's an idiom, relating potentially
to any process which proceeds in stages, and such that, at
the completion of each stage, something has been created that,
while viable in and of itself, is also a prerequisite to the
next stage.

Also, the term bootstrapping predates the computer era:

<http://en.wikipedia.org/wiki/Bootstrapping>

It seems to me that the OP's usage of the term bootstrapping
fits his intended purpose -- to analyze the stages used in
building the foundations of mathematics.

>> 1) Naive logic (like the ones the Greeks played with).
>> 2) Use 1) to talk about Naive Set theory (like Halmos' book).
>> 3) Use 2) above to define Mathematical Logic / First-Order Logic
>> 4) Use 3) above to define axiomatic set theory.

As to whether his simplified outline based on 4 stages of
development is reasonable or useful, I'm not knowledgable

>A metalanguage is used to dacribe a formal language.

The OP is already doing that when he says:

Use 1) to ...
Use 2) to ...
Use 3) to ...

Also, what language, meta or non-meta, has the word "dacribe"?

quasi

Date Subject Author
8/20/13 Lax
8/20/13 William Elliot
8/20/13 Tucsondrew@me.com
8/20/13 William Elliot
8/20/13 Lax
8/21/13 William Elliot
8/21/13 Tucsondrew@me.com
8/20/13 Virgil
8/21/13 quasi
8/21/13 Peter Percival
8/21/13 William Elliot
8/21/13 Peter Percival
8/21/13 Graham Cooper
8/21/13 fom