On 2/14/2012 5:13 AM, acw wrote:
Soundness and consistency have precise definitions. If you want an
absolute definition of consistency, it could be seen as a particular
machine never halting. Due to circularity of any such definitions, one
has to take some notion of abstract computation fundamental (for
example through arithmetic or combinators or ...)
How does the existence on an entity determine its properties? Please
answer this question. What do "soundness" and "consistency" even mean
when there does not exist an unassailable way of defining what they are?
Look carefully at what is required for a proof, don't ignore the need to
be able to communicate the proof.
I do like this definition of consistency as an (abstract) machine
that never halts (its computation of itself). I like it a lot! We can
use the language of hypersets
<http://en.wikipedia.org/wiki/Non-well-founded_set_theory> to get
consistent definitions in spite of the circularity. Ben Goertzel wrote a
very nice paper that outlines the idea:
goertzel.org/consciousness/consciousness_paper.pdf Ben Goertzel is one
Getting back to my basic question: How is it that the mere
existence of an entity gives it a definition? The usual notion of a
definition of a word is "what is found to the right of a word listed in
a dictionary", but are we going beyond that notion?
How come that one definition and not some other or even a class of
definitions? Am I incorrect in thinking that definitions are a set of
relations that are built up by observers though the process of
observation of the world and communicating with each other about the
possible content of their individual observations? This is, after all,
how dictionaries are formed (modulo the printing process, etc.)... When
I am thinking of the existence of an entity, I am not considering that
it is observed or that observation or measurement by an automated system
occurred or anything else that might yield a definite count of what the
properties of an entity are; I am just considering its existence per se.
So I guess that I am not being clear...
How does the mere existence of an entity act in any way as an
observation of itself? Why that question? B/c it seems to me that that
is what is required to have a consistent notion of an entity having
properties merely by existing. So maybe you are thinking of what a
hyperset is without realizing it!
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