What problem did Ladd-Franklin (think she) solve(d)? (Q2075275)

Having heard that Christine Ladd-Franklin, in her PhD dissertation ``solved a problem first raised by Aristotle which had baffled logicians for two thousand years: how to reduce all forms of the syllogism to one'' the author of this exquisitely written paper, of a very rare directness, a model of engaging writing, sets out to find out what Ladd-Franklin actually did in her dissertation and what she thought she did. She finds out that the main result of Ladd-Franklin's dissertation was: ``The argument of inconsistency, \((a\overline{\vee}b)(\overline{b}\overline{\vee}c)(c \vee a)\overline{\vee}\), is the single form to which all the ninety-six valid syllogisms (both universal and particular) may be reduced.'' On a first reading, neither the formula occurring in it nor the word ``form'' make sense. A deeper look at the possible meaning of ``form'' reveals that it cannot mean ``\textit{figure} (the disposition of the terms within the three categorical propositions that make up the syllogism)'', it cannot mean ``\textit{mood} (the disposition of copulas into a figure, along with the choice of specific major, minor, and middle terms)'', nor can one say that form refers to something else that would have been used by late antique and medieval logicians, who would have expressed some mysterious question that had bothered logicians for millennia, waiting for Christine Ladd-Franklin to solve it. Failing to find a millenia old problem to be solved, the author turns to the painful task of understanding what Ladd-Franklin's algebra of logic was all about. Having made its contents intelligible for a contemporary reader, the author concludes that ``whatever Ladd's solution was for, it was \textit{not} for a problem of Aristotle's.'' Ladd-Franklin herself ``did not think she was solving a problem of Aristotle'' but rather one raised by \textit{W. S. Jevons} in his [Studies in deductive logic. London: Macmillan (1880)], the ``inverse logical problem'', asking ``given certain combinations inconsistent with conditions to determine those conditions.'' The author then studies the twists and turns leading to the confusion regarding a problem left open by Aristotle.