On 8/19/2012 4:30 PM, meekerdb wrote:
On 8/19/2012 12:51 PM, Stephen P. King wrote:
I understand that 2+2 = 4.
I still cannot explain how and why I understand "2+2 = 4".
"2+2=4" is easy.
"I understand 2+2=4" is quasi infinitely more complex.
Dear Bruno,
As I see it, the quasi-infiitely more complex aspect of "I
understand that 2+2=4" follows, at least, from the requirement that
many entities capable of making such statements can point to examples
of 2+2=4 and communicate about such statements with each other
however far away in space and time they are from each other. We can
ignore the fact that there is a collection of entities to whom the
statement "I understand that 2+2=4" has a meaning. You need to get a
grip on the nature of meaningfulness. Searle has tried to do this
with his Chinese Room idea but failed to communicate the concept. :_(
Maybe Bruno will introduce a new modality to his logic Up="Understands
p". :-)
Brent
--
Hi Brent,
That would be wonderful if possible. AFAIK, understanding is
contingent on demonstrability, e.g. I understand p if and only if I can
demonstrate that p implies q and q is not trivial and q is true in the
same context as p. I think that Bruno's idea of "interviewing a machine"
is a form of demonstration as I am trying to define it here. In my
thesis, demonstrability requires that the model to be demonstrated is
actually implemented in at least one possible physical world (i.e.
satisfies thermodynamic laws and Shannon information theory) otherwise
it could be used to implement a Maxwell Demon.
BTW, it was an analysis of Maxwell's Demon that lead me to my
current ideas, that abstract computation requires that at least one
physical system actually can implement it. This is not ultrafinitism
since I am allowing for an uncountable infinity of physical worlds, but
almost none of them are accessible to each other (there exist event
horizons, etc.).
Consider the case where a computation X is generating an exact
simulation of the behavior of molecules in a two compartment tank with a
valve and there exists a computer Y that can use the output of X to
control the valve. We can easily see that X could be a subroutine of Y.
If the control of Y leads to an exact partition of the fast (hot) and
slow (cold) molecules and this difference can be used to run Y then some
might argue that we would have a computation for free situation. The
problem is that for the hot/cold difference to be exploited to do work
the entire apparatus would have to be coupled to a heat reservoir that
would absorb the waste energy generated by the work. Heat Reservoirs
are interesting beasts....
See
http://www.nature.com/news/the-unavoidable-cost-of-computation-revealed-1.10186
for more on this.
We ignore the role played by our physical world in our
philosophical/mathematical/logical discussions to our peril!
--
Onward!
Stephen
"Nature, to be commanded, must be obeyed."
~ Francis Bacon
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