Suppose we wish to define an enigmatic property $\Pi(x)$ of a set $x$. We have the condition
\[\Pi(x) \leftrightarrow \Pi_1(x) \vee \exists y \in x. \Pi(y) \]\[ \neg \exists y. y \in x \, \rightarrow \, \Pi(x)\] That is, if $a$ is an atom then $\Pi(a)$. Our question: is it true that $ZFC \vdash \forall x. \Pi(x)$ ? In what sense in ZFC is the whole always 'more' in some special sense than the part ?
This post is an attempt to formalize some aspects of the first proposition of Proclus' Elements of Theology.
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