anapodeictic

is a fairly obscure word. It is used in The Plebs, a student magazine from 1912 in a story called "The Gold Making Angel", in a satrical postcard, where it is intended to be obscure.

Austin Phelps (in 1883) claims that Longinus (the centurion who pierced Jesus's side, immortalized by Bernini?) used the term to described St Paul's Epistles, suggesting it means "the style of one, not in search of, but in possession of, truth, and using it eagerly for an object." There is no evidence that Longinus did so that I am aware of.

Withrop Sheldon used the term in his translation of Lucian of Samosata's, "The Auction of Philosophers" and footnotes it as meaning "not requiring demonstration". Chrysippus, whil on the auction block, threatens to shoot someone with the "second anapodeictic syllogism".

It is used by two philosophers to refer to syllogisms as an alternate translation of Sextus Empirus. He is usually quoted as "[Chrysippus] declares that the dog makes use of the fifth complex indemonstrable syllogism when, ... ", but Floridi (in 1997) used "anapodeictic" as an alternate term. Mauro Nasti De Vincentis uses it to refer to Chrysippus' first syllogism.

Keifer (in 2002) claims "anapodeictic knowledge" means "an immediate, necessary and true statement".

These six uses are all I find. Three of them use it in idiosyncratic ways. I suppose the only shared use of it is a description of Chrysippus' indemonstrable syllogisms.

Does anyone have any theories as to what Chrysippus's inference rules were (other than Cut and if A and B -> C then A and not C -> not B)?