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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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Peter Percival

Posts: 2,623
Registered: 10/25/10
Re: Foundations of mathematics... the order of bootstrapping the

Posted: Aug 21, 2013 2:43 AM
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William Elliot wrote:
> On Tue, 20 Aug 2013, 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.

Bootstrapping is a metaphor which is surely common property. In year X
some wit spoke of lifting himself by his own bootstraps. It's a fair
bet that X long preceded the computer (computer as machine not computer
as human calculator).

Didn't Baron Münchhausen lift himself _and_ his horse out of a bog by
his own hair?

>> 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.

> A metalanguage is used to dacribe a formal language.

Sorrow in all lands, and grievous omens.
Great anger in the dragon of the hills,
And silent now the earth's green oracles
That will not speak again of innocence.
David Sutton -- Geomancies

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