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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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Graham Cooper

Posts: 4,227
Registered: 5/20/10
Re: Foundations of mathematics... the order of bootstrapping the foundations
Posted: Aug 21, 2013 8:50 PM
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On Tuesday, August 20, 2013 6:58:12 PM UTC-7, 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).
>
> 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.



I think this is roughly accurate!

Let's draw a PYRAMID of the Foundations of Set Theoretic Mathematics.




* MATHS SOLVER *
* LOGIC DATABASE *
* COMPUTING MODELS *
* {a{a b}} {{{}} {}} * s>t>r>i>n>g>s & n^u^m^b^e^r^s
* {{{}}{}{{{{}{}}}}}}} *
* HIERARCHY OF NULL SETS *



Frankly I think {1,{1,2}} <=> <1 2>

is taken a little too far here, note the BASE LEVEL SETS
are practically un-usuable and it has to emulate a dictionary
of strings to start again on that higher foundation level
without needing the null-set architecture from level 3 up!

so which came first...

the STRING OF ALPHABET SYMBOLS or the HIERARCHY OF NOTHING?



Herc
--
www.tinyurl.com/HOW-PROLOG-WORKS




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