It should however be stated that the question is not about absolute truth
or falsehood. No one denies that anything I call an inference is an
inference: they say that my alterations are _extra-logical_; that they are
_material_, not _formal_; and that logic is a _formal_ science.
The distinction between material and formal is easily made, where the usual
perversions are not required. A _form_ is an empty machine, such as "Every
X is Y"; it may be supplied with _matter_, as in "Every _man_ is _animal_."
The logicians will not see that their _formal_ proposition, "Every X is Y,"
is material in three points, the degree of assertion, the quantity of the
proposition, and the copula. The purely formal proposition is "There is the
probability [alpha] that X stands in the relation L to Y." The time will
come when it will be regretted that logic went without paradoxers for two
thousand years: and when much that has been said on the distinction of form
and matter will breed jokes.
I give one instance of one mood of each of the systems, in the order of the
letters first written above.
_Relative._--In this system the formal relation is taken, that is, the
copula may be any whatever. As a material instance, in which the
_relations_ are those of consanguinity (of men understood), take the
following: X is the brother of Y; X is not the uncle of Z; therefore, Z is
not the child of Y. The discussion of relation, and of the objections to
the extension, is in the _Cambridge Transactions_, Vol. X, Part 2; a
crabbed conglomerate.
_Undecided._--In this system one premise, and want of power over another,
infer want of power over a conclusion. {335} As "Some men are not capable
of tracing consequences; we cannot be sure that there are beings
responsible for consequences who are incapable of tracing consequences;
therefore, we cannot be sure that all men are responsible for the
consequences of their actions."
_Exemplar._--This, long after it suggested itself to me as a means of
correcting a defect in Hamilton's system, I saw to be the very system of
Aristotle himself, though his followers have drifted into another. It makes
its subject and predicate examples, thus: Any one man is an animal; any one
animal is a mortal; therefore, any one man is a mortal.
_Numerical._--Suppose 100 Ys to exist: then if 70 Xs be Ys, and 40 Zs be
Ys, it follows that 10 Xs (at least) are Zs. Hamilton, whose mind could not
generalize on symbols, saw that the word _most_ would come under this
system, and admitted, as valid, such a syllogism as "most Ys are Xs; most
Ys are Zs; therefore, some Xs are Zs."
_Onymatic._--This is the ordinary system much enlarged in propositional
forms. It is fully discussed in my _Syllabus of Logic_.
_Transposed._--In this syllogism the quantity in one premise is transposed
into the other. As, some Xs are not Ys; for every X there is a Y which is
Z; therefore, some Zs are not Xs.
Sir William Hamilton of Edinburgh was one of the best friends and allies I
ever had. When I first began to publish speculation on this subject, he
introduced me to the logical world as having plagiarized from him. This
drew their attention: a mathematician might have written about logic under
forms which had something of mathematical look long enough before the
Aristotelians would have troubled themselves with him: as was done by John
Bernoulli,[711] {336} James Bernoulli,[712] Lambert,[713] and
Gergonne;[714] who, when our discussion began, were not known even to
omnilegent Hamilton. He retracted his accusation of _wilful_ theft in a
manly way when he found it untenable; but on this point he wavered a
little, and was convinced to the last that I had taken his principle
unconsciously. He thought I had done the same with Ploucquet[715] and
Lambert. It was his pet notion that I did not understand the commonest
principles of logic, that I did not always know the difference between the
middle term of a syllogism and its conclusion. It went against his grain to
imagine that a mathematician could be a logician. So long as he took me to
be riding my own hobby, he laughed consumedly: but when he thought he could
make out that I was mounted behind Ploucquet or Lambert, the current ran
thus: "It would indeed have been little short of a miracle had he, ignorant
even of the common principles of logic, been able of himself to rise to
generalization so lofty and so accurate as are supposed in the peculiar
doctrines of both the rival logicians, Lambert and Ploucquet--how useless
soever these may in practice prove to be." All this has been sufficiently
discussed elsewhere: "but, masters, remember that I am an ass."
I know that I never saw Lambert's work until after all Hamilton supposed me
to have taken was written: he himself, who read almost everything, knew
nothing about it until after I did. I cannot prove what I say about my
knowledge of Lambert: but the means of doing it may turn up. For, by the
casual turning up of an old letter, I _have_ {337} found the means of
clearing myself as to Ploucquet. Hamilton assumed that (unconsciously) I
took from Ploucquet the notion of a logical notation in which the symbol of
the conclusion is seen in the joint symbols of the premises. For example,
in my own fashion I write down ( . ) ( . ), two symbols of premises. By
these symbols 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 Aristotelians) the conclusion is manifest in this way
without symbols. This _Bramantip_ destroys system in the Aristotelian lot:
and circumstances which I have pointed out destroy it in Hamilton's own
collection. But in that enlargement of the reputed Aristotelian system
which I have called _onymatic_, and in that correction of Hamilton's system
which I have called _exemplar_, the rule of erasure is universal, and may
be seen without symbols.
Our first controversy was in 1846. In 1847, in my _Formal Logic_, I gave
him back a little satire for satire, just to show, as I stated, that I
could employ ridicule if I pleased. He was so offended with the appendix in
which this was contained, that he would not accept the copy of the book I
sent him, but returned it. Copies of controversial works, sent from
opponent to opponent, are not _presents_, in the usual sense: it was a
marked success to make him angry enough to forget this. It had some effect
however: during the rest of his life I wished to avoid provocation; for I
{339} could not feel sure that excitement might not produce consequences. I
allowed his slashing account of me in the _Discussions_ to pass unanswered:
and before that, when he proposed to open a controversy in the _Athenaeum_
upon my second Cambridge paper, I merely deferred the dispute until the
next edition of my _Formal Logic_. I cannot expect the account in the
_Discussions_ to amuse an unconcerned reader as much as it amused myself:
but for a cut-and-thrust, might-and-main, tooth-and-nail, hammer-and-tongs
assault, I can particularly recommend it. I never knew, until I read it,
how much I should enjoy a thundering onslought on myself, done with racy
insolence by a master hand, to whom my good genius had whispered _Ita feri
ut se sentiat emori_.[718] Since that time I have, as the Irishman said,
become "dry moulded for want of a bating." Some of my paradoxers have done
their best: but theirs is mere twopenny--"small swipes," as Peter Peebles
said. Brandy for heroes! I hope a reviewer or two will have mercy on me,
and will give me as good discipline as Strafford would have given Hampden
and his set: "much beholden," said he, "should they be to any one that
should thoroughly take pains with them in that kind"--meaning _objective_
flagellation. And I shall be the same to any one who will serve me so--but
in a literary and periodical sense: my corporeal cuticle is as thin as my
neighbors'.
Sir W. H. was suffering under local paralysis before our controversy
commenced: and though his mind was quite unaffected, a retort of as
downright a character as the attack might have produced serious effect upon
a person who had shown himself sensible of ridicule. Had a second attack of
his disorder followed an answer from me, I should have been held to have
caused it: though, looking at Hamilton's genial love of combat, I strongly
suspected that a retort in kind
{340}
"Would cheer his heart, and warm his blood,
And make him fight, and do him good."
But I could not venture to risk it. So all I did, in reply to the article
in the _Discussions_, was to write to him the following note: which, as
illustrating an etiquette of controversy, I insert.
"I beg to acknowledge and thank you for.... It is necessary that I should
say a word on my retention of this work, with reference to your return of
the copy of my _Formal Logic_, which I presented to you on its publication:
a return made on the ground of your disapproval of the account of our
controversy which that work contained. According to my view of the subject,
any one whose dealing with the author of a book is specially attacked in
it, has a right to expect from the author that part of the book in which
the attack is made, together with so much of the remaining part as is
fairly context. And I hold that the acceptance by the party assailed of
such work or part of a work does not imply any amount of approval of the
contents, or of want of disapproval. On this principle (though I am not
prepared to add the word _alone_) I forwarded to you the whole of my work
on _Formal Logic_ and my second Cambridge Memoir. And on this principle I
should have held you wanting in due regard to my literary rights if you had
not forwarded to me your asterisked pages, with all else that was necessary
to a full understanding of their scope and meaning, so far as the contents
of the book would furnish it. For the remaining portion, which it would be
a hundred pities to separate from the pages in which I am directly
concerned, I am your debtor on another principle; and shall be glad to
remain so if you will allow me to make a feint of balancing the account by
the offer of two small works on subjects as little connected with our
discussion as the _Epistolae Obscurorum Virorum_, or the Lutheran dispute. I
trust that by accepting my _Opuscula_ you will enable me to avoid the {341}
use of the knife, and leave me to cut you up with the pen as occasion shall
serve, I remain, etc. (April 21, 1852)."
I received polite thanks, but not a word about the body of the letter: my
argument, I suppose, was admitted.