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 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? >
The humans who interpret.

