Re: Incompleteness vs. Mechanical Reasoning

Marshall wrote:
A few times lately I've had the experience of mentioning
something about mechanical reasoning and then having
someone mention incompleteness as if that had anything
to do with what I was saying. In fact the attitude seems
to be akin to that woman in the penguin-on-the-telly sketch
who says "there; I've run rings around you logically."

It's puzzled me a good deal.

A thought just occurred to me: could this possibly be
the result of people thinking that incompleteness is
something that affects mechanical systems but not
our brain? Is the idea floating around that the human
mind is somehow capable of doing things not only
that no *current* computer can do, but also that no
possible future computer could ever do? Is that
what's going on here?

How do I say this: I do not subscribe to that hypothesis.


Marshall

Machines, and 'programs' made for them, cannot serve as a model for thinking, (or 'the brain' if you like). The distinction is this:

Machines, programs, AND thought/brains can all work with heirarchical systems or frameworks, where each framework supports its own objects. Each framework can also be regarded as an object of a higher type or framework that is further up the ladder of the heirarchy. Thus any framework can be 1) considered as consistent on its own terms but not provable on its own terms, or 2) considered as provable in the total heirarchy of frameworks or systems but not consistent.

Brains, or thoughts, on the other hand, can also, unlike machines and programs, have frameworks that are the manifesting conditions for their objects yet cannot be objects themselves. That is, the manifesting conditions or particular frameworks for certain classes of objects do not form a heirarchical relationship with each other. For example, sound and colour are the manifesting conditions for sounds and colours but the two frameworks cannot, unlike the frameworks for machines and programs, be arranged heirarchically or exhibit relationship.

In summary,
1) the objects that machines and programs deal with are all of one type, in whatever way these objects are structured or organized. They are therefore subject to Godellian limitations.
2) the objects that are manifested by thoughts/the brain, are not all of one type, that is, they can be incommensurable. They are not subject to Godellian limitations.
.

Relevant Pages

  • Re: Incompleteness vs. Mechanical Reasoning
    ... Machines, programs, AND thought/brains can all work with heirarchical ... systems or frameworks, where each framework supports its own objects. ... framework that is further up the ladder of the heirarchy. ... Another way to look a thes combination of these incommensurables is to ...
    (sci.logic)
  • Re: Incompleteness vs. Mechanical Reasoning
    ... Machines, programs, AND thought/brains can all work with heirarchical ... systems or frameworks, where each framework supports its own objects. ... framework that is further up the ladder of the heirarchy. ... have frameworks that are the manifesting conditions for their ...
    (sci.logic)
  • Re: Incompleteness vs. Mechanical Reasoning
    ... Machines, programs, AND thought/brains can all work with heirarchical ... systems or frameworks, where each framework supports its own objects. ... framework that is further up the ladder of the heirarchy. ... and colour are the manifesting conditions for sounds and colours but the ...
    (sci.logic)
  • Re: Incompleteness vs. Mechanical Reasoning
    ... Machines, programs, AND thought/brains can all work with heirarchical ... systems or frameworks, where each framework supports its own objects. ... > thought level we develop ways to commensurate them and arrange them ... > hierarchically or exhibit relationships. ...
    (sci.logic)
  • Re: Incompleteness vs. Mechanical Reasoning
    ... systems or frameworks, where each framework supports its own objects. ... two frameworks cannot, unlike the frameworks for machines and programs, ...  > thought level we develop ways to commensurate them and arrange them ... My own way of looking at what you call incommensurables while I use ...
    (sci.logic)