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\section{Rough argument summary}
I am trying to compute
$P(\mbox{our world}\mid\mbox{there is no Creator})$. I know the probability of our world given that
for it was not created. For any property $p$ such that our world has this property,
$P(\mbox{our world} \mid \mbox{there is no Creator})$ the probability of our world is at most
$P(p \mid \mbox{there is no Creator})$, the probability of $p$, where
$P(p)$ the probability of $p$ is the probability of all worlds having the $p$ property.
Then I will find Then, if there is such a property $p$
for which $P(p \mid \mbox{there whose probability is
no Creator}) = 0$, showing that $P(\mbox{our world}\mid{there $0$ then our world's probability is
no Creator})=0$. $0$. I will also discuss why it is enough to use that property.
The property $p$ for which I will attempt to show that
$P(p \mid \mbox{there is no Creator}) = 0$ it has a $0$ probability is \ghilimele{There is a mathematical theory that has a finite definition and is useful for making approximate predictions in a non-trivial part of our universe}.
The For clarity, I have split the argument
is presented then in two parts.
The first one uses "There is a mathematical theory that has a finite definition and fully models the universe" as the above property and shows that the probability of a non-created universe to have this property is 0. However, this
is result is not really useful for a number of reasons, including that we may need to have an infinite definition only if we want infinite precision in our predictions, but for most or even all practical purposes we could not tell the difference between predictions with extremely good precision and predictions with infinite precision.
In the second part I will also consider theories which do not fully model the universe and I will show that in a non-created universe we can't have a non-zero probability for a finite theory that works in a non-trivial part of a universe.
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Then the first part argument has the following steps:
1. \begin{ennumerate}
\item If our world is not created then either there are other worlds, or our world could have been different.
2. \item We will consider only worlds which are "well behaved", e.g. they can be modelled mathematically (for a reasonable definition of modelling that focuses on predictions), they can have intelligent life, there is a concept of time and so on.
3. \item We will consider all the possible theories that could model such worlds. Their set has the same cardinal as the real numbers.
4. \item For any reasonable statistical distribution, the set of finite theories has zero probability.
5. \item Therefore
P(p | there the probability of $p$ is
no Creator) = 0. $0$.
The second part of the argument reuses steps 1-4 from the first part, rephrased to allow partial modelling, but also has a few extra ones.
6. In order to have intelligent beings one needs finite theories that are useful.