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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 2:36 AM
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Lax Clarke wrote:
> Please correct me if I'm wrong please:
> This is the order of bootstrapping the foundations of mathematics:
> 1) Naive logic (like the ones the Greeks played with).

The Greeks had no theory of n-ary relations, did they? Not even n=2 iirc.

Was it Boole or De Morgan or one of those fellows who pointed out that
the valid inference

A horse is animal
Therefore the head of a horse is the head of an animal

cannot be handled by Greek logic?

> 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.

One might begin by asking if mathematics has a foundation, or if it
needs one.

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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