logician graham priest takes leibniz's principle of sufficient reason in "infinite parts" p. 33 of his beyond the limits of thought.
The fundamental principle of reasoning is that there is nothing without a reason; or to explain the matter more distinctly that there is no truth for which reason does not subsist.and here is priest's answer to dispatch PSR, i.e., Leibniz's Principle of Sufficient Reason):
By the PSR we can apply the operator to this to produce a reason for σ. Assuming that nothing can be a reason for itself, this reason cannot be a member of σ (Transcendence). But the cause of σ is exactly one of the things generated by applying the operator into the prescribed fashion. Hence it is in σ (Closure) and hence we have a contradiction at the limit of the iterable.priest thinks he dispatches what he calls "weaker" version of PSR by appealing to quantum mechanics's transitions, as "completely spontaneous." but i don't see why leibniz would have a problem with stochastic events.
Leibniz's PSR states is that no state of affairs (facts) can hold which is not completely accounted for and made fully explicable by reference to something else, i.e., random events explained by quantum mechanics.
let's take priest's idea of "iterable".
1- indeed any reason generated within PSR is iterable. priest suggests:
... the reason of σ is exactly one of the things generated by applying the operator...
alas! σ (as operator) has to be inside PSR to be! (if it was outside it would not be an σ-perator).
now leibniz bites the bullet: invoking any σ inside PSR is guilty of circularity?
in a perverse way, priest is prevented from employing PSR to debunk PSR.
2- further, leibniz wouldn't mind circularity as long as it's virtuous!
(which is precisely the secret of the baroque)
stairs @ palazzo barberini, by franciscus borromini
by leibniz's own admission, any operator inside PSR is, itself, implicitly "operated."
PSR is a super-operator.
can supervinience be retrofitted? aber natürlich!