  As can be gathered from the foregoing, it was studying with Peirce that focussed Ladd’s attention from mathematics in general to mathematical logic (also called symbolic logic) in particular.  Ladd’s best-known, and most-celebrated work was her paper “On the Algebra of Logic,” published in Studies in Logic by the members of the Johns Hopkins University (C. S. Peirce, editor), Little, Brown, 1883, pp. 17–71. In it, she is (or at least was once) widely regarded as having achieved for the first time in history a completely general and unified account of the Aristotelian syllogism, including a general account of the differences between valid and invalid syllogisms. (Josiah Royce, for example, held this view of Ladd-Franklin’s work in logic.) It is thus worth looking in some detail at how she achieves this result through the algebraizing of the syllogism, but here such detail will not be entered into. Basically, however, we can say that her basic idea is to associate with each possible syllogism a certain “triad”. The syllogism is valid if and only if the “triad” is an “antilogism,” that is to say, is an inconsistent “triad”. Ladd-Franklin wrote on the antilogism as late as 1928 in volume 37 of Mind, pp. 532–534. Whether or not her work is really the first work to unify the theory of the syllogism, and whether or not she ultimately merits the exalted status as a logician that Royce assigns to her must remain a task for future exploration to determine.