I open this intensely interesting question by showing that of
the three types of induction one alone is of any real scientific
value. I then show that all that an induction of this type really
accomplishes is to ascertain the value of a ratio. It follows that
the whole substance of science must come to us by abduction, in the
same sense in which, according to the theory of natural selection in
its extended form, the whole interval between the moner and man has
been traversed by insensible variations in reproduction. Induction,
like natural selection, merely weeds out the unfit. What, then, can
be the justification for a hypothesis? In the first place, abduction
only concludes interrogatively. But that is no sufficient answer to
the question. Idle interrogations are as noxious as can be. The only
justification is that which is often illustrated in playing the game
of whist. Three rounds remain of a hand. How the cards lie, the
leader does not know. But he does know that if they lie in certain
way, a certain lead will save the odd card, while if they do not lie
in that way, no lead will do so. This justifies his assuming, for the
purposes of the lead, that so the cards do lie. For so alone his end
may be gained. The principle is that we are always justified in
presuming, for the purposes of conduct, that our sole end may be
reached. But all belief is belief for the purposes of conduct.
Nothing has any meaning aside from practical purposes. Aside from its
practical aspects a proposition cannot be false, because a meaningless
thing is not a proposition, and as such, has no room to be false. If,
then, it comes to this, that a certain hypothesis must be true or
there is no comprehensible truth, and if, as our ethical and
esthetical discussions have shown is the case, the comprehension of
the universe is the sole aim which a man can deliberately pronounce to
be good, he is justified in unconditionally embracing the hypothesis
which is alone consonant with the attainment of a comprehension of the
truth. It need not be said that the hypotheses which perfectly
fulfill that condition are extremely few. Perhaps the hypothesis that
the universe is governed by a self-conscious mind, in the senses in
which `self-conscious' and `mind' are logically defined, is the only
one there is. Still, practically, the case often comes to that.
Possible hypotheses consist of such hypotheses as we can make. `Can'
is, no doubt, an elastic word. What "can" be done depends on the
amount of effort. Still, the effects of efforts converge toward a
limit. To fix our ideas, take a concrete example. The commander of
an army is in battle. The battle is of such importance that the total
sum of the commander's duty is to win the day. As well as he can make
out, in the limited time he has for considering the question, if a
certain position can be immediately taken, the battle may be won, but
otherwise cannot. Then logic commands him to believe with his whole
heart and soul that that position can be taken, although if he had
time to make a reconnaissance it might be foolhardy and illogical in
the extreme to come to such a conclusion merely from such data as are
actually in his possession. This illustrates how much the time that
is allowed to form an opinion has to do, logically, with that opinion.
Now a scientific investigator is in a double situation. As a unit of
the scientific world, with which he in some measure identifies
himself, he can wait five centuries, if need by, before he decides
upon the acceptability of a certain hypothesis. But as engaged in the
investigation which it is his duty diligently to pursue, he must be
ready the next morning to go on that hypothesis or to reject it. What
logic requires of him is that he should accept that hypothesis which
is the only way that he can, at that time, see in which there should
be any comprehensible truth, and think of the most surprising
observable necessary consequence of it he can, and the next morning
put that consequence to the test of experiment. Being as he is in a
double position, as an individual, and as a representative of the
science of the race, he ought to be in a double state of mind about
the hypothesis, at once ardent in his belief that so it must be, and
yet not committing himself further than to do his best to try the
experiment. If he is merely skeptical, he will not do half justice to
the experiment; if he forgets his relation to general science, he will
shrink from putting his darling theory to such a test. He must
combine the two attitudes. Mendeleef, drawing up his very rough
arrangement of the elements, and upon the basis of that risking his
detailed descriptions of Gallium, Scandium, and Germanium, is the very
exemplar of what the logic of abduction prescribes.
All this is inexact enough. I am here only endeavoring to give
a notion of the contents of this memoir. That I should lay myself
open to any just accusation of loose reasoning is not among the doubts
which trouble me most. I have for myself employed an algebraic
notation to secure the accuracy of my work; but I am not decided to
make use of it in my memoirs.
Upon this theory of the validity of abduction I base certain
rules for the practice of this kind of thought. In comparing these
with those of other logicians I remark that I find in their doctrines
far less that compels my dissent than in regard to induction,
notwithstanding their hard, inelastic conception of this kind of
reasoning. Yet it is here that they find themselves, most of them,
utterly deserted by their general conception of logic, which
it is here that I find mine most efficaciously helpful.
See