ls I see that there is a valid conclusion, and that it may be
written in symbol by striking out the two middle parentheses, which gives (
. . ) and reading the two negative dots as an affirmative. And so I see in
( . ) ( . ) that ( ) is the conclusion. This, in full, is the perception
that "all are either Xs or Ys" and "all are either Ys or Zs" necessitates
"some Xs are Zs." Now in Ploucquet's book of 1763, is found, "Deleatur in
praemissis medius; id quod restat indicat conclusionem."[716] In the paper
in which I explain my symbols--which are altogether different from
Ploucquet's--there is found "Erase the symbols of the middle term; the
remaining symbols show the inference." There is very great likeness: and I
would have excused Hamilton for his notion if he had fairly given reference
to the part of the book in which his quotation was found. For I had shown
in my _Formal Logic_ what part of Ploucquet's book I had used: and a fair
disputant would either have strengthened his point by showing that I had
been at his part of the book, or allowed me the advantage of it being
apparent that I had not given evidence of having seen that part of the
book. My good friend, though an honest man, was sometimes unwilling to
allow due advantage to controversial opponents.

But to my point. The only work of Ploucquet I ever saw was lent me by my
friend Dr. Logan,[717] with whom I have often corresponded on logic, etc. I
chanced (in 1865) {338} to turn up the letter which he sent me (Sept. 12,
1847) _with the book_. Part of it runs thus: "I congratulate you on your
success in your logical researches [that is, in asking for the book, I had
described some results]. Since the reading of your first paper I have been
satisfied as to the possibility of inventing a logical notation in which
the rationale of the inference is contained in the symbol, though I never
attempted to verify it [what I communicated, then, satisfied the writer
that I had done and communicated what he, from my previous paper, suspected
to be practicable]. I send you Ploucquet's dissertation....'

It now being manifest that I cannot be souring grapes which have been taken
from me, I will say what I never said in print before. There is not the
slightest merit in making the symbols of the premises yield that of the
conclusion by erasure: _the thing must do itself in every system which
symbolises quantities_. For in every syllogism (except the inverted
_Bramantip_ of the Ari