On 05 Sep 2012, at 21:36, meekerdb wrote:

On 9/5/2012 8:37 AM, Bruno Marchal wrote:Put in another way: there is no ontological hardware. The hardwareand wetware are emergent on the digital basic ontology (which canbe described by numbers or combinators as they describe the samecomputations and the same object: you can prove the existence ofcombinators in arithmetic,I don't think I understand that remark. Doesn't arithmetic *assume*combinators, i.e. + and * ?

Combinators are defined by K is a combinator S is a combinator if x and y are combinator, then (x, y) are combinators. So they are K, S, (K K), (S S), (K S), (S K), (K (K K)), ((K K) K), etc. The left parenthesis are often not written, for reason of readability. The axioms are Kxy = x Sxyz = xz(yz).

`This is Turing universal, and you can define numbers, + and * in that`

`system. See the lovely book by Smullyan "To mock a mocking bird" for`

`more, or my little course on them on this list.`

`Likewise, you can define them, and emulate them, using only 0,`

`s(0), ... and the laws:`

x+0 = x x+s(y) = s(x+y) x*0=0 x*s(y)=(x*y)+x Which is also Turing universal. Bruno

Brentand you can prove the existence of numbers from the combinator Sand K. So the basic ontology is really the same and we can "know"it (betting on comp). It is really like the choice of a base in alinear space.--You received this message because you are subscribed to the GoogleGroups "Everything List" group.To post to this group, send email to everything-list@googlegroups.com.To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com.For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.

http://iridia.ulb.ac.be/~marchal/ -- You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to everything-list@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.