Re: Contradiction or paradox

On May 18, 5:15 pm, MoeBlee <jazzm...@xxxxxxxxxxx> wrote:
On May 18, 12:33 pm, Charlie-Boo <shymath...@xxxxxxxxx> wrote:

Do you deny that CBL is a Computationally Based Logic? Do you know of
any more standard Computationally Based Logics?

Define 'computationally based logic'.

*sigh*

A Propositionally Based Logic (e.g. PA) expresses assertions about
relationships among objects in a universal set. Call this an N-N
system where N is the cardinality of the universal set. This model is
suitable for expressing only mathematics.

In contrast, a Computationally Based Logic (e.g. CBL) expresses
relationships among disparant sets, of differing cardinalities.
Relating these sets (e.g. the set of Turing Machines and the set of
one-place functions from N to N) requires computing so that the
smaller set can equate with a subset of the larger set that includes
elements arbitrarily close to every element of the larger set.

Then assertions in a Computationally Based Logic are about the
computing power of various systems. Primitive assertions are not that
one element is less than another, but about the nature of the less
than relation itself. We can express assertions about sets being
expressible, representable, recursive, recursively enumerable,
defining a set, stateable in English, and a whole host of
metamathematical notions. CBL's are ideal for metamathematics.

Ok so far?

C-B

MoeBlee


.

Relevant Pages

  • WoLLIC 2008 - Call for Participation
    ... involving formal logic, computing and programming theory, and natural ... The Fifteenth WoLLIC will be held in the campus of Heriot-Watt Univ, ... and Applied Logics, the European Association for Logic, ...
    (comp.specification.z)
  • Re: Contradiction or paradox
    ... any more standard Computationally Based Logics? ... A Propositionally Based Logic expresses assertions about ... system where N is the cardinality of the universal set. ... computing power of various systems. ...
    (sci.logic)
  • Re: [opensuse] Re: [SLE] Novell-Microsoft: What They Arent Telling You
    ... but a variety of logics nonetheless. ... The only problem with current logical formalisms is how low-level they ... He insisted programming belonged in the Math department. ... and theoretical underpinnings of computing. ...
    (SuSE)