
Re: Foundations of mathematics... the order of bootstrapping the foundations
Posted:
Aug 21, 2013 8:50 PM


On Tuesday, August 20, 2013 6:58:12 PM UTC7, 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 / FirstOrder 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 unusuable and it has to emulate a dictionary of strings to start again on that higher foundation level without needing the nullset architecture from level 3 up!
so which came first...
the STRING OF ALPHABET SYMBOLS or the HIERARCHY OF NOTHING?
Herc  www.tinyurl.com/HOWPROLOGWORKS

