Faksoko has been suggested as a mnemonic for this method of reduction, k denoting obversion, so that ks demotes obversion followed by conversion (i.e., contraposition).
Whately’s mnemonic Fakoro (Elements of Logic, p. 97) does not indicate the obversion of the minor premiss (r being with him an unmeaning letter).
| Some M is not P, | |
| All M is S, | |
| therefore, | Some S is not P, |
is reducible to Darii by the contraposition of the major premiss and the transposition of the premisses, thus,—
| All M is S, | |
| Some not-P is M, | |
| therefore, | Some not-P is S. |
Some not-P is S is not indeed our original conclusion, but the latter can be obtained from it by conversion followed by obversion. This method of reduction may be indicated by Doksamosk (which again is obviously preferable to Dokamo, suggested by Whately, since the latter would make it appear as if we immediately obtained the original conclusion in Darii.)
260. Extension of the Doctrine of Reduction.—The doctrine of reduction may be extended, and it can be shewn not merely that any syllogism may be reduced to figure 1, but also that it may be reduced to any given mood (not being a subaltern mood) of that figure.[348] This position will obviously be established if we can shew that Barbara, Celarent, Darii, and Ferio are mutually reducible to one another.
[348 ] Compare, further, sections [284], [285].
Barbara may be reduced to Celarent by the obversion of the major premiss and also of the new conclusion thereby obtained. Thus, using arrows, as in the [note] on page 320,