[port-peer-review] The Social Theory of Logic
Hi, here's something that I will eventually post on PORT, but thought you
might like an advance look? We must always be aware of the dates of his
writings, but this account stays pretty firm in his later work, I think.
Remember, Peirce's challenge is to get abduction and induction included in
our understanding of logic, and that amounts to explaining the
individual's relationship to the world (in essence), so that that
relationship can be progressively clarified in our thought (or reasoning)
by deduction. See what you can get from this section of an essay? [will
print on maybe 5 pages]. --M. (01)
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A section from "Grounds of Validity of the Laws of Logic," originally
published in Journal of Speculative Philosophy, (1868); intended as Essay
V of the "Search for a Method," 1893.
In CP Vol. 5. (02)
THE SOCIAL THEORY OF LOGIC (03)
341. The difficulty of showing how the law of deductive reasoning
is true depends upon our inability to conceive of its not being true. In
the case of probable reasoning the difficulty is of quite another kind;
here, where we see precisely what the procedure is, we wonder how such a
process can have any validity at all. How magical it is that by examining
a part of a class we can know what is true of the whole of the class, and
by study of the past can know the future; in short, that we can know what
we have not experienced! (04)
Is not this an intellectual intuition! Is it not that besides
ordinary experience which is dependent on there being a certain physical
connection between our organs and the thing experienced, there is a second
avenue of truth dependent only on there being a certain intellectual
connection between our previous knowledge and what we learn in that way?
Yes, this is true. Man has this faculty, just as opium has a somnific
virtue; but some further questions may be asked, nevertheless. How is the
existence of this faculty accounted for? In one sense, no doubt, by
natural selection. Since it is absolutely essential to the preservation of
so delicate an organism as man's, no race which had it not has been able
to sustain itself. This accounts for the prevalence of this faculty,
provided it was only a possible one. But how can it be possible? What
could enable the mind to know physical things which do not physically
influence it and which it does not influence? The question cannot be
answered by any statement concerning the human mind, for it is equivalent
to asking what makes the facts usually to be, as inductive and hypothetic
conclusions from true premisses represent them to be? Facts of a certain
kind are usually true when facts having certain relations to them are
true; what is the cause of this? That is the question. (05)
342. The usual reply is that nature is everywhere regular; as
things have been, so they will be; as one part of nature is, so is every
other. But this explanation will not do. Nature is not regular. No
disorder would be less orderly than the existing arrangement. It is true
that the special laws and regularities are innumerable; but nobody thinks
of the irregularities, which are infinitely more frequent. Every fact true
of any one thing in the universe is related to every fact true of every
other. But the immense majority of these relations are fortuitous and
irregular. A man in China bought a cow three days and five minutes after a
Greenlander had sneezed. Is that abstract circumstance connected with any
regularity whatever? And are not such relations infinitely more frequent
than those which are regular? But if a very large number of qualities were
to be distributed among a very large number of things in almost any way,
there would chance to be some few regularities. If, for example, upon a
checker-board of an enormous number of squares, painted all sorts of
colors, myriads of dice were to be thrown, it could hardly fail to happen,
that upon some color, or shade of color, out of so many, some one of the
six numbers should not be uppermost on any die. This would be a
regularity; for, the universal proposition would be true that upon that
color that number is never turned up. But suppose this regularity
abolished, then a far more remarkable regularity would be created, namely,
that on every color every number is turned up. Either way, therefore, a
regularity must occur. Indeed, a little reflection will show that,
although we have here only variations of color and of the numbers of the
dice, many regularities must occur. And the greater the number of objects,
the more respects in which they vary, and the greater the number of
varieties in each respect, the greater will be the number of regularities.
Now, in the universe, all these numbers are infinite. Therefore, however
disorderly the chaos, the number of regularities must be infinite. The
orderliness of the universe, therefore, if it exists, must consist in the
large proportion of relations which present a regularity to those which
are quite irregular. But this proportion in the actual universe is, as we
have seen, as small as it can be; and, therefore, the orderliness of the
universe is as little as that of any arrangement whatever. (06)
343. But even if there were such an orderliness in things, it
never could be discovered. For it would belong to things either
collectively or distributively. If it belonged to things collectively,
that is to say, if things formed a system, the difficulty would be that a
system can only be known by seeing some considerable proportion of the
whole. Now we never can know how great a part of the whole of nature we
have discovered. If the order were distributive, that is, belonged to all
things only by belonging to each thing, the difficulty would be that a
character can only be known by comparing something which has it 1 with
something which has it not. Being, quality, relation, and other universals
are not known except as characters of words or other signs, attributed by
a figure of speech to things. Thus, in neither case could the order of
things be known. But the order of things would not help the validity of
our reasoning -- that is, would not help us to reason correctly -- unless
we knew what the order of things required the relation between the known
reason from to the unknown reasoned to, to be. (07)
344. But even if this order both existed and were known, the
knowledge would be of no use except as a general principle, from which
things could be deduced. It would not explain how knowledge could be
increased (in contradistinction to being rendered more distinct), and so
it would not explain how it could itself have been acquired. (08)
345. Finally, if the validity of induction and hypothesis were
dependent on a particular constitution of the universe, we could imagine a
universe in which these modes of inference should not be valid, just as we
can imagine a universe in which there would be no attraction, but things
should merely drift about. Accordingly, J.S. Mill, who explains the
validity of induction by the uniformity of nature, P1 maintains that he
can imagine a universe without any regularity, so that no probable
inference would be valid in it. P2 In the universe as it is, probable
arguments sometimes fail, nor can any definite proportion of cases be
stated in which they hold good; all that can be said is that in the long
run they prove approximately correct. Can a universe be imagined in which
this would not be the case? It must be a universe where probable argument
can have some application, in order that it may fail half the time. It
must, therefore, be a universe experienced. Of the finite number of
propositions true of a finite amount of experience of such a universe, no
one would be universal in form, unless the subject of it were an
individual. For if there were a plural universal proposition, inferences
by analogy from one particular to another would hold good invariably in
reference to that subject. So that these arguments might be no better than
guesses in reference to other parts of the universe, but they would
invariably hold good in a finite proportion of it, and so would on the
whole be somewhat better than guesses. There could, also, be no
individuals in that universe, for there must be some general class -- that
is, there must be some things more or less alike -- or probable argument
would find no premisses there; therefore, there must be two mutually
exclusive classes, since every class has a residue outside of it; hence,
if there were any individual, that individual would be wholly excluded
from one or other of these classes. Hence, the universal plural
proposition would be true, that no one of a certain class was that
individual. Hence, no universal proposition would be true. Accordingly,
every combination of characters would occur in such a universe. But this
would not be disorder, but the simplest order; it would not be
unintelligible, but, on the contrary, everything conceivable would be
found in it with equal frequency. The notion, therefore, of a universe in
which probable arguments should fail as often as hold true, is absurd. 1
We can suppose it in general terms, but we cannot specify how it should be
other than self-contradictory. [Footnote: Boole (Laws of Thought, p. 370)
has shown, in a very simple and elegant manner, that an infinite number of
balls may have characters distributed in such a way, that from the
characters of the balls already drawn, we could infer nothing in regard to
that of the characters of the next one. The same is true of some
arrangements of a finite number of balls, provided the inference takes
place after a fixed number of drawings. But this does not invalidate the
reasoning above, although it is an important fact without doubt.] (09)
346. Since we cannot conceive of probable inferences as not
generally holding good, and since no special supposition will serve to
explain their validity, many logicians have sought to base this validity
on that of deduction, and that in a variety of ways. The only attempt of
this sort, however, which deserves to be noticed is that which seeks to
determine the probability of a future event by the theory of
probabilities, from the fact that a certain number of similar events have
been observed. Whether this can be done or not depends on the meaning
assigned to the word probability. But if this word is to be taken in such
a sense that a form of conclusion which is probable is valid; since the
validity of an inference (or its correspondence with facts) consists
solely in this, that when such premisses are true, such a conclusion is
generally true, then probability can mean nothing but the ratio of the
frequency of occurrence of a specific event to a general one over it. In
this sense of the term, it is plain that the probability of an inductive
conclusion cannot be deduced from the premisses; for from the inductive
premisses (010)
S', S'', S''' are M,
S', S'', S''' are P, (011)
nothing follows deductively, except that any M, which is S', or S'', or
S''' is P; or, less explicitly, that some M is P. (012)
347. Thus, we seem to be driven to this point. On the one hand, no
determination of things, no fact, can result in the validity of probable
argument; nor, on the other hand, is such argument reducible to that form
which holds good, however the facts may be. This seems very much like a
reduction to absurdity of the validity of such reasoning; and a paradox of
the greatest difficulty is presented for solution. (013)
348. There can be no doubt of the importance of this problem.
According to Kant, the central question of philosophy is "How are
synthetical judgments a priori possible?" But antecedently to this comes
the question how synthetical judgments in general, and still more
generally, how synthetical reasoning is possible at all. When the answer
to the general problem has been obtained, the particular one will be
comparatively simple. This is the lock upon the door of philosophy. 1 (014)
349. All probable inference, whether induction or hypothesis, is
inference from the parts to the whole. It is essentially the same,
therefore, as statistical inference. Out of a bag of black and white beans
I take a few handfuls, and from this sample I can judge approximately the
proportions of black and white in the whole. This is identical with
induction. Now we know upon what the validity of this inference depends.
It depends upon the fact that in the long run, any one bean would be taken
out as often as any other. For were this not so, the mean of a large
number of results of such testings of the contents of the bag would not be
precisely the ratio of the numbers of the two colors of beans in the bag.
Now we may divide the question of the validity of induction into two
parts: first, why of all inductions premisses for which occur, the
generality should hold good, and second, why men are not fated always to
light upon the small proportion of worthless inductions. Then, the first
of these two questions is readily answered. For since all the members of
any class are the same as all that are to be known; and since from any
part of those which are to be known an induction is competent to the rest,
in the long run any one member of a class will occur as the subject of a
premiss of a possible induction as often as any other, and, therefore, the
validity of induction depends simply upon the fact that the parts make up
and constitute the whole. This in its turn depends simply upon there being
such a state of things that any general terms are possible. But it has
been shown in 311 that being at all is being in general. And thus this
part of the validity of induction depends merely on there being any
reality. (015)
350. From this it appears that we cannot say that the generality
of inductions are true, but only that in the long run they approximate to
the truth. This is the truth of the statement, that the universality of an
inference from induction is only the analogue of true universality. Hence,
also, it cannot be said that we know an inductive conclusion to be true,
however loosely we state it; we only know that by accepting inductive
conclusions, in the long run our errors balance one another. In fact,
insurance companies proceed upon induction; -- they do not know what will
happen to this or that policyholder; they only know that they are secure
in the long run. (016)
351. The other question relative to the validity of induction, is
why men are not fated always to light upon those inductions which are
highly deceptive. The explanation of the former branch of the problem we
have seen to be that there is something real. Now, since if there is
anything real, then (on account of this reality consisting in the ultimate
agreement of all men, and on account of the fact that reasoning from parts
to whole, is the only kind of synthetic reasoning which men possess) it
follows necessarily that a sufficiently long succession of inferences from
parts to whole will lead men to a knowledge of it, so that in that case
they cannot be fated on the whole to be thoroughly unlucky in their
inductions. This second branch of the problem is in fact equivalent to
asking why there is anything real, and thus its solution will carry the
solution of the former branch one step further.
Peirce: CP 5.352 Cross-Ref: (017)
352. 1 The answer to this question may be put into a general and
abstract, or a special detailed form. If men were not to be able to learn
from induction, it must be because as a general rule, when they had made
an induction, the order of things (as they appear in experience), would
then undergo a revolution. Just herein would the unreality of such a
universe consist; namely, that the order of the universe should depend on
how much men should know of it. But this general rule would be capable of
being itself discovered by induction; and so it must be a law of such a
universe, that when this was discovered it would cease to operate. But
this second law would itself be capable of discovery. And so in such a
universe there would be nothing which would not sooner or later be known;
and it would have an order capable of discovery by a sufficiently long
course of reasoning. But this is contrary to the hypothesis, and therefore
that hypothesis is absurd. This is the particular answer. But we may also
say, in general, that if nothing real exists, then, since every question
supposes that something exists -- for it maintains its own urgency -- it
supposes only illusions to exist. But the existence even of an illusion is
a reality; for an illusion affects all men, or it does not. In the former
case, it is a reality according to our theory of reality; in the latter
case, it is independent of the state of mind of any individuals except
those whom it happens to affect. So that the answer to the question, Why
is anything real? is this: That question means, "supposing anything to
exist, why is something real?" The answer is, that that very existence is
reality by definition. (018)
All that has here been said, particularly of induction, applies to
all inference from parts to whole, and therefore to hypothesis, and so to
all probable inference.
Peirce: CP 5.352 Cross-Ref: (019)
Thus, I claim to have shown, in the first place, that it is
possible to hold a consistent theory of the validity of the laws of
ordinary logic.
Peirce: CP 5.353 Cross-Ref: (020)
353. But now let us suppose the idealistic theory of reality,
which I have in this paper taken for granted to be false. In that case,
inductions would not be true unless the world were so constituted that
every object should be presented in experience as often as any other; and
further, unless we were so constituted that we had no more tendency to
make bad inductions than good ones. These facts might be explained by the
benevolence of the Creator; but, as has already been argued, they could
not explain, but are absolutely refuted by the fact that no state of
things can be conceived in which probable arguments should not lead to the
truth. This affords a most important argument in favor of that theory of
reality, and thus of those denials of certain faculties from which it was
deduced, as well as of the general style of philosophizing by which those
denials were reached. (021)
354. Upon our theory of reality and of logic, it can be shown that
no inference of any individual can be thoroughly logical without certain
determinations of his mind which do not concern any one inference
immediately; for we have seen that that mode of inference which alone can
teach us anything, or carry us at all beyond what was implied in our
premisses -- in fact, does not give us to know any more than we knew
before; only, we know that, by faithfully adhering to that mode of
inference, we shall, on the whole, approximate to the truth. Each of us is
an insurance company, in short. But, now, suppose that an insurance
company, among its risks, should take one exceeding in amount the sum of
all the others. Plainly, it would then have no security whatever. Now, has
not every single man such a risk? What shall it profit a man if he shall
gain the whole world and lose his own soul? If a man has a transcendent
personal interest infinitely outweighing all others, then, upon the theory
of validity of inference just developed, he is devoid of all security, and
can make no valid inference whatever. What follows? That logic rigidly
requires, before all else, that no determinate fact, nothing which can
happen to a man's self, should be of more consequence to him than
everything else. He who would not sacrifice his own soul to save the whole
world, is illogical in all his inferences, collectively. So the social
principle is rooted intrinsically in logic. 1 (022)
355. That being the case, it becomes interesting to inquire how it
is with men as a matter of fact. There is a psychological theory that man
cannot act without a view to his own pleasure. This theory is based on a
falsely assumed subjectivism. Upon our principles of the objectivity of
knowledge, it could not be based; and if they are correct, it is reduced
to an absurdity. It seems to me that the usual opinion of the selfishness
of man is based in large measure upon this false theory. I do not think
that the facts bear out the usual opinion. The immense self-sacrifices
which the most wilful men often make, show that wilfulness is a very
different thing from selfishness. The care that men have for what is to
happen after they are dead, cannot be selfish. And finally and chiefly,
the constant use of the word "we" -- as when we speak of our possessions
on the Pacific -- our destiny as a republic -- in cases in which no
personal interests at all are involved, show conclusively that men do not
make their personal interests their only ones, and therefore may, at
least, subordinate them to the interests of the community. (023)
356. But just the revelation of the possibility of this complete
self-sacrifice in man, and the belief in its saving power, will serve to
redeem the logicality of all men. For he who recognizes the logical
necessity of complete self-identification of one's own interests with
those of the community, and its potential existence in man, even if he has
it not himself, will perceive that only the inferences of that man who has
it are logical, and so views his own inferences as being valid only so far
as they would be accepted by that man. But so far as he has this belief,
he becomes identified with that man. And that ideal perfection of
knowledge by which we have seen that reality is constituted must thus
belong to a community in which this identification is complete. (024)
357. This would serve as a complete establishment of private
logicality, were it not that the assumption, that man or the community
(which may be wider than man) shall ever arrive at a state of information
greater than some definite finite information, is entirely unsupported by
reasons. There cannot be a scintilla of evidence to show that at some time
all living beings shall not be annihilated at once, and that forever after
there shall be throughout the universe any intelligence whatever. Indeed,
this very assumption involves itself a transcendent and supreme interest,
and therefore from its very nature is unsusceptible of any support from
reasons. This infinite hope which we all have (for even the atheist will
constantly betray his calm expectation that what is Best will come about)
is something so august and momentous, that all reasoning in reference to
it is a trifling impertinence. We do not want to know what are the weights
of reasons pro and con -- that is, how much odds we should wish to receive
on such a venture in the long run -- because there is no long run in the
case; the question is single and supreme, and ALL is at stake upon it. We
are in the condition of a man in a life and death struggle; if he have not
sufficient strength, it is wholly indifferent to him how he acts, so that
the only assumption upon which he can act rationally is the hope of
success. So this sentiment is rigidly demanded by logic. If its object
were any determinate fact, any private interest, it might conflict with
the results of knowledge and so with itself; but when its object is of a
nature as wide as the community can turn out to be, it is always a
hypothesis uncontradicted by facts and justified by its indispensableness
for making any action rational. (025)