On 2/14/2012 13:45, Stephen P. King wrote:
On 2/14/2012 5:13 AM, acw wrote:
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.
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 ...)
Dear ACW,
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
smart dude!
Using hypersets to talk about such self-similar concepts sounds fine.
That's a pretty interesting paper. I've read some of Ben Geortzel's
other work before (mostly in the field of AGI), his ideas and work are
quite interesting.
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?
If something does have existence, I will tend to assume it also has a
consistent definition (even if we're not aware of it yet), although some
things might either be undefinable in simpler terms (for example
arithmetic) or they might require stronger theories than themselves to
define them (such as arithmetical truth). The dictionary meaning of the
word is too narrow, a better way of thinking about it is to think about
what 'is' means. More precise definitions of the concept of definition
can be given in more precise languages than English (such as programming
languages), but that might be again too restrictive.
How come that one definition and not some other or even a class of
definitions?
There may be many equivalent definitions, possibly even an infinity of
them.
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?
You're not incorrect, but that's just the act of inferring or inducing a
definition. However, something can have existence and should also have a
proper definition (in some language) even if you haven't reached it.
Someone does some reasoning and gives some pattern some name. I claim
that the pattern's existence is independent of that person giving it a
name. A person might not be able to properly communicate the pattern to
others without introducing the pattern to others, but the pattern exists
- their own bodies, world, knowledge, ... are such patterns.
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...
Okay.
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!
Hmm, you're right! Hypersets and hyperset-like concepts are quite
common, especially in knowledge-representation.
Onward!
Stephen
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