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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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 fom Posts: 1,968 Registered: 12/4/12
Re: Foundations of mathematics... the order of bootstrapping the
foundations

Posted: Aug 21, 2013 9:04 PM

On 8/21/2013 7:50 PM, grahamcooper7@gmail.com wrote:
> On Tuesday, August 20, 2013 6:58:12 PM UTC-7, Lax Clarke wrote:
>>
>>
>>
>> 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?
>

The humans who interpret.

Date Subject Author
8/20/13 Lax
8/20/13 William Elliot
8/20/13 Tucsondrew@me.com
8/20/13 William Elliot
8/20/13 Lax
8/21/13 William Elliot
8/21/13 Tucsondrew@me.com
8/20/13 Virgil
8/21/13 quasi
8/21/13 Peter Percival
8/21/13 William Elliot
8/21/13 Peter Percival
8/21/13 Graham Cooper
8/21/13 fom