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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: 10,311
Registered: 7/15/05
Re: Foundations of mathematics... the order of bootstrapping the foundations
Posted: Aug 21, 2013 12:09 AM
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William Elliot wrote:
>Lax Clarke wrote:
>

>> Please correct me if I'm wrong please:
>> 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
enough to answer that.

>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



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