Chrysippus and incompleteness (correction of the title in the submission)

Joao Marcos botocudo at
Sun Apr 3 12:22:15 EDT 2022

> I would like to share the following quote due to the great Ancient logician
> Chrysippus of Soli (279 ? c. 206 BC), found in a book written by Marcus
> Tullius Cicero (106 BC ? 43 BC):
> if uncaused motion exists, it will not be the case that every proposition
> > [...] is either true or false, for things no possesing efficient causes
> > will never be true nor false
> page 5 in: M. T. Cicero, "On Fate"
> Is there any formalization of Chrysippus's claim?

This may not be the answer you're looking for, but it might be of
general interest to point out that one of the earliest researchers
with an algebraic approach to *many-valued logics*, Grigore Moisil
(, used to call them
"non-Chrysippian logics", precisely for the reasons alluded in the
above quote.

In this respect, by the way, you might want to check the book "Essais
sur les logiques non chrysippiennes", which has the following table of
Maybe someone out there will have a link to a fully scanned copy of this book.

Joao Marcos


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