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

Tue Apr 5 03:23:22 EDT 2022

Hello,

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

https://web.stanford.edu/group/cslipublications/cslipublications/site/1881526852.shtml

https://en.wikipedia.org/wiki/Jules_Vuillemin

(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?"
https://www.cambridge.org/core/books/what-are-philosophical-systems/12CC0EEF3C4372B0740E0A1BA74C13B9 

Unfortunately, this work does not seem well known.)

Best wishes,

Jo.

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"
>> http://www.sophia-project.org/uploads/1/3/9/5/13955288/cicero_fate.pdf
>>
>> 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
> (https://en.wikipedia.org/wiki/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:
> http://web.flu.cas.cz/scan/323542882.pdf
> Maybe someone out there will have a link to a fully scanned copy of this book.
> 
> Yours,
> Joao Marcos
> 
> --
> http://sequiturquodlibet.googlepages.com/
> 