The first rampart is destroyed; our adversaries take refuge behind the
second--the Theory of Proof. This theory has passed for two thousand
years for a substantiated, definite, unassailable truth. Many have
deemed it useless, but no one has dared to call it false. On all sides
it has been considered as an established theorem. Let us examine it
closely and attentively. What is a proof? According to logicians, it is
a syllogism. And what is a syllogism? A group of three propositions of
this kind: "All men are mortal; Prince Albert is a man; therefore Prince
Albert is mortal." Here we have the type of a proof, and every complete
proof is conformable to this type. Now what is there, according to
logicians, in this proof? A general proposition concerning all men,
which gives rise to a particular proposition concerning a certain man.
From the first we pass to the second, because the second is contained in
the first; from the general to the particular, because the particular is
comprised in the general. The second is but an instance of the first;
its truth is contained beforehand in that of the first, and this is why
it is a truth. In fact, as soon as the conclusion is no longer contained
in the premises, the reasoning is false, and all the complicated rules
of the Middle Ages have been reduced by the Port-Royalists to this
single rule, "The conclusion must be contained in the premises." Thus
the entire process of the human mind in its reasonings, consists in
recognizing in individuals what is known of a whole class; in affirming
in detail what has been established for the aggregate; in laying down a
second time, and piecemeal, what has been laid down once for all at
first.
By no means, replies Mill; for if it were so, our reasoning would be
good for nothing. It would not be a progress, but a repetition. When I
have affirmed that all men are mortal, I have affirmed implicitly that
Prince Albert is mortal. In speaking of the whole class, that is to say,
of all the individuals of the class, I have spoken of each individual,
and therefore of Prince Albert, who is one of them. I say nothing new,
then, when I now mention him expressly. My conclusion teaches me
nothing; it adds nothing to my positive knowledge; it only puts in
another shape a knowledge which I already possessed. It is not fruitful,
but purely verbal. If, then, reasoning be what logicians represent it,
it is not instructive. I know as much of the subject at the beginning of
my reasoning as at the end. I have transformed words into other words; I
have been moving, without gaining ground. Now this cannot be the case;
for, in fact, reasoning does teach us new truths. I learn a new truth
when I discover that Prince Albert is mortal, and I discover it by dint
of reasoning; for, since he is still alive, I cannot have learnt it by
direct observation. Thus logicians are mistaken; and beyond the
scholastic theory of syllogism, which reduces reasoning to substitutions
of words, we must look for a positive theory of proof, which shall
explain how it is that, by the process of reasoning, we discover facts.
For this purpose, it is sufficient to observe that general propositions
are not the true proof of particular propositions. They seem so, but are
not. It is not from the mortality of all men that I conclude Prince
Albert to be mortal; the premises are elsewhere, and in the background.
The general proposition is but a memento^ a sort of abbreviative
register, to which I have consigned the fruit of my experience. This
memento may be regarded as a notebook, to which we refer to refresh our
memory; but it is not from the book that we draw our knowledge, but from
the objects which we have seen. My memento is valuable, only for the
facts which it recalls. My general proposition has no value, except for
the particular facts which it sums up.
"The mortality of John, Thomas, and company, is, after all, the whole
evidence we have for the mortality of the Duke of Wellington. Not one
iota is added to the proof by interpolating a general proposition. Since
the individual cases are all the evidence we can possess, evidence which
no logical form into which we choose to throw it can make greater than
it is; and since that evidence is either sufficient in itself, or, if
insufficient for the one purpose, cannot be sufficient for the other; I
am unable to see why we should be forbidden to take the shortest cut
from these sufficient premisses to the conclusion, and constrained to
travel the 'high priori road' by the arbitrary fiat of logicians."[406]
"The true reason which makes us believe that Prince Albert will die is,
that his ancestors, and our ancestors, and all the other persons who
were their contemporaries, are dead. These facts are the true premises
of our reasoning." It is from them that we have drawn the general
proposition; they have taught us its scope and truth; it confines itself
to mentioning them in a shorter form; it receives its whole substance
from them; they act by it and through it, to lead us to the conclusion
to which it seems to give rise. It is only their representative, and on
occasion they do without it. Children, ignorant people, animals, know
that the sun will rise, that water will drown them, that fire will burn
them, without employing this general proposition. They reason, and we
reason, too, not from the general to the particular, but from particular
to particular:
"All inference is from particulars to particulars; general propositions
are merely registers of such inferences already made, and short formulæ
for making more: The major premiss of a syllogism, consequently, is a
formula of this description: and the conclusion is not an inference
drawn from the formula, but an inference drawn according to the formula:
the real logical antecedent, or premisses, being the particular facts
from which the general proposition was collected by induction. Those
facts, and the individual instances which supplied them, may have been
forgotten; but a record remains, not indeed descriptive of the facts
themselves, but showing how those cases may be distinguished respecting
which the facts, when known, were considered to warrant a given
inference. According to the indications of this record we draw our
conclusion; which is to all intents and purposes, a conclusion from the
forgotten facts. For this it is essential that we should read the record
correctly: and the rules of the syllogism are a set of precautions to
ensure our doing so."[407]
"If we had sufficiently capacious memories, and a sufficient power of
maintaining order among a huge mass of details, the reasoning could go
on without any general propositions; they are mere formulae for
inferring particulars from particulars."[408]
Here, as before, logicians are mistaken: they gave the highest place to
verbal operations, and left the really fruitful operations in the
background. They gave the preference to words over facts. They
perpetuated the nominalism of the Middle Ages. They mistook the
explanation of names for the nature of things, and the transformation of
ideas for the progress of the mind. It is for us to overturn this order
in logic, as we have overturned it in science, to exalt particular and
instructive facts, and to give them in our theories that superiority and
importance which our practice has conferred upon them for three
centuries past.