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

Joseph Vidal-Rosset joseph.vidal.rosset at
Tue Apr 5 03:23:22 EDT 2022


About Chrysippus and logic, see chap. 5 of "Necessity and Contingency, 
The Master Argument", from Jules Vuillemin. Here are the useful links:

(In my opinion, the most important work of Vuillemin is his 
classification of philosophical systems, explained both in this book and 
mainly in "What are philosophical systems?" 

Unfortunately, this work does not seem well known.)

Best wishes,


Le 03/04/2022 à 18:22, Joao Marcos a écrit :
>> 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
> contents:
> Maybe someone out there will have a link to a fully scanned copy of this book.
> Yours,
> Joao Marcos
> --

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