[extropy-chat] Analyzing the simulation argument

[Dan Clemmensen]

Russell Wallace wrote:

>On Thu, 17 Feb 2005 04:39:05 -0500, igoddard at umd.edu <igoddard at umd.edu> wrote:
>  
>
>>The hypothesis that the universe could be a computer program
>>is attractive, but Dan may be right that it's unfalsifiable
>>(and thus pseudoscientific).
>>    
>>
>
>Indeed, I'll go further than that.
>
>Consider Newton and Lagrange's formulations of classical mechanics, or
>the wave and matrix formulations of quantum mechanics. In each case we
>have two sets of equations which give the same results - we therefore
>regard the distinction between them as not merely unfalsifiable but
>meaningless; we say that in each case, the two theories are in fact
>the _same_ theory. Preference for one over the other is therefore
>neither true nor false; it's just a matter of what you happen to find
>more convenient to work with.
>
>Now the hypothesis "we are living in a simulation" (if the simulation
>is assumed to be fully accurate) gives the same results as "we are not
>living in a simulation". Therefore it can be argued that they are the
>_same_ hypothesis. So we have a situation where P and not-P are the
>same statement; therefore, P is a null statement; so the simulation
>hypothesis actually _has no truth value_.
>
>  
>
Two points:

1) Undecidable versus unfalsifiable:
 "Undecidable" is a technical term in the predicate calculus. This
is usually what "has no truth value" refers to.

"Unfalsifiable" is a technical term in philosophy. It is related to 
"undecidable," but
philosophy has not yet been reduced to the predicate calculus.


2) A formal basis for Occam's Razor:
Your post has inspired me to create (discover? re-invent?) a formal 
basis for Occam's razor.
(Surely someone has done this in the past?) I have always thought that 
Occam's razor was
grounded primarily in aesthetics: A system with fewer postulates is 
simply more elegant and
is somehow "prettier." You can argue that a logical system X, and a 
logical system X+P that
make exactly the same predictions are in fact the SAME logical system. 
if X->P, then this is
true. If X!->P, (that is, P cannot be inferred from X) then Occam's 
razor says to pick X rather
than X+P. But why?

My thought is to go to information theory: the system X can be expressed 
in fewer bits than
can (X+P). Furthermore, there are an infinite number of systems with 
additional hypotheses
but with the same predictive power X+P1, X+P2, ..., so X is unique. 
Thus, X is not just an
aesthetic choice, it's a unique choice.

Note that a system X+P where X!->P is in fact clearly different from X 
in one regard: in
the system (X+P), P is true. in the system X, P is undecidable. if X->P, 
then P is a superfluous
postulate and is clearly unneeded. If X->!P, then (X+P) is inconsistent 
and therefore worthless.
But there are an infinite number of undecidable propositions (P, P1, 
P2...) in X. Unless one of
them has predicts something useful other than itself, Why add it?


Note:
  I did a cursory search while writing this, and found:
http://mathworld.wolfram.com/topics/GeneralLogic.html
Wow!