On 10/14/2015 6:59 PM, Jason Resch wrote:
On Wed, Oct 14, 2015 at 4:01 AM, Bruno Marchal <[email protected]
<mailto:[email protected]>> wrote:
Actually, Robinson Arithmetic is consistent with ultrafinitism.
So, logically, ultrafinitism is not a threat for comp at the
ontological level. Of course, to get physics, we need to interview
non ultra-finitist observers, as they are mute on almost all
interesting questions, so Peter Jones argument could still be
recuperated by NOT listening or taking into account most observers
existing in the least model of RA. But this met your critics.
I just point to the fact that a biggest number is not so much a
logical threat that I thought once.
A good exercise: find a model of RA with a biggest natural number
(of course such a model will not please to an ultrafinitist).
1. 0 is not the predecessor of any number
2. predecessor of x = predecessor of y -> x = y
3. Every number is 0 or a predecessor of a number
4. x - 0 = x
5. x - predecessor of y = predecessor of (x - y)
?? x - predecessor of x = predecessor of (x - x)
Brent
6. x * 0 = 0
7. x * predecessor of y = (x * y) - x
Nelson wrote a book on predicative arithmetic, and defends the
idea that the exponentiation function n^x is not total. It can be
interesting in showing that ultrafinitism is really not relevant
for any mechanistic account of mind and nature.
What about when the biggest number isn't big enough to contain enough
information to realize a conscious state?
Jason
4. Bruno leans heavily on saying his theory explains QM, but
it's not clear to me that it's even consistent with QM. For
example how is the operation of Shor's algorithm consistent
with the multiple threads of the UDA?
I think Bruce Kellet has also made some critiques of Bruno's
argument.
Bruce's argument is that computationalism is false, and
arithmetical realism is false. If you reject these, it is no
conflict with the UDA, whose logic depends on those assumptions.
Your argument in #1 and #2, also rests implicity on a rejection
of computationslim. #1 implies the computations don't matter, and
#2 implies the right computations don't matter if they are isolated.
It is a red herring to ask "where is the error" because I
don't think his argument is a fallacy; I think it is less
than logic entailment.
You can dispute the assumptions (computationalism, infinity,
arithmetical realism, etc.) but if you reject infinity or
arithmetical realism, you must also reject Church-Turing's
thesis, and it's difficult to make sense of computationalism if
you can no longer define computation or computability. So if you
accept computationalism, you are implicitly accepting infinity
and arithmetical realism. Given this, the rest of Bruno's result
is a logical proof, which is either correct or has an error.
Jason
--
You received this message because you are subscribed to the
Google Groups "Everything List" group.
To unsubscribe from this group and stop receiving emails from it,
send an email to [email protected]
<mailto:[email protected]>.
To post to this group, send email to
[email protected]
<mailto:[email protected]>.
Visit this group at http://groups.google.com/group/everything-list.
For more options, visit https://groups.google.com/d/optout.
http://iridia.ulb.ac.be/~marchal/
<http://iridia.ulb.ac.be/%7Emarchal/>
--
You received this message because you are subscribed to the Google
Groups "Everything List" group.
To unsubscribe from this group and stop receiving emails from it,
send an email to [email protected]
<mailto:[email protected]>.
To post to this group, send email to
[email protected]
<mailto:[email protected]>.
Visit this group at http://groups.google.com/group/everything-list.
For more options, visit https://groups.google.com/d/optout.
--
You received this message because you are subscribed to the Google
Groups "Everything List" group.
To unsubscribe from this group and stop receiving emails from it, send
an email to [email protected]
<mailto:[email protected]>.
To post to this group, send email to [email protected]
<mailto:[email protected]>.
Visit this group at http://groups.google.com/group/everything-list.
For more options, visit https://groups.google.com/d/optout.
--
You received this message because you are subscribed to the Google Groups
"Everything List" group.
To unsubscribe from this group and stop receiving emails from it, send an email
to [email protected].
To post to this group, send email to [email protected].
Visit this group at http://groups.google.com/group/everything-list.
For more options, visit https://groups.google.com/d/optout.
