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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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Registered: 5/24/13
Re: Foundations of mathematics... the order of bootstrapping the foundations
Posted: Aug 21, 2013 12:03 AM
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On Tuesday, August 20, 2013 8:38:24 PM UTC-7, Lax Clarke wrote:
> Ok. I just want to know the order of learning I guess. Or say a really smart and "rigor-loving" alien landed in our backyard, in what order would we explain thing to him in (assuming the alien learns English first).

I find it more of a Dialectic process between Logic and Mathematics.
We learn simple Arithmetic, which is a very Logical Structure.
Next comes basic Algebra and Geometry. Here we enrich our
knowledge of Logical System.
When these Logical Ideas are firm enough, usually by being
exposed to many Mathematical and Logical Systems, we are
at the point where we can Define our Mathematical Objects in
a Logical Axiomatic System.
After that we investigate the Logical Implications of having such
a Mathematical System, and develop Meta-Theories and the such.

The two are intimately interconnected.


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