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Virgil Șerbănuță edited untitled.tex
over 8 years ago
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Given the definitions above, this is the layout of my argument.
\begin{ennumerate} \begin{enumerate}
\item A possible universe description is a set of mathematical axioms. Any set of noncontradictory mathematical axioms which is at most countable is a possible universe description.
\item There is an infinite and uncountable (of cardinality at least $\reale$) set of possible universe descriptions in which Turing-complete entities could exist, which are fundamentally different and for any two such descriptions their sets of possible universes are disjoint. The Turing-complete entities have access to data which could be used to provide a description of the universe and the descriptions which could be built this way also form an uncountable set. [TODO: maybe replace Turing-complete with intelligent and expand on the descriptions provided by the intelligent entities]. Let us denote this set by $\cal T$.
\begin{ennumerate} \begin{enumerate}
\item There is such a set which has descriptions somehow similar to our universe, making them more plausible.
\end{ennumerate} \end{enumerate}
\item For any sentence $S$ which is true in a countable set of universe descriptions and any probability distribution which is not heavily biased (i.e. any continous probability distribution) the probability of $S$ is zero.
\begin{ennumerate} \begin{enumerate}
\item Given such a probability distribution over $T$, let $\cal T_0$ be the set of all descriptions in $\cal T$ in which there a true sentence $S$ of probability zero. Then the probability of $\cal T_0$ is zero. Note that the sentence is not of the type mentioned above.
\item There set of finite descriptions is countable, so the property "Has a finite description" has a probability 0 in $T$. [TODO: This construction should also work when the descriptions are not disjoint, but they allow full predictions of events in their universes].
\end{ennumerate}
\end{ennumerate} \end{enumerate}
\end{enumerate}
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