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(This memoir is here placed, or perhaps better before No. 9, for
the sake of perspicuity of exposition. The matter of it will have to
be somewhat transformed at a later stage.)
If the logician is to talk of mind and its operations at all, it must be in a different sense from that in which modern psychologists study the mind. This conception of mind, which is needed in our studies, will be developed in its four successive grades of clearness.
It is almost universally held that logic is a science of thought (so far as it is a science at all), that thought is a modification of consciousness, and that consciousness is the object of the science of psychology. The effect of this, were it perceived, is to make logic logically dependent upon the very one of all the special sciences which most stands in logical need of a science of logic. Accordingly, we find that some logicians deny that logic is a science, while others maintain that it is a mere description of our feelings. Each of these views has had disastrous effects upon several branches of science. It has occurred to me that perhaps logic relates to mind in one sense of the word "mind", and that the psychologists inquire into the phenomena of mind in another sense of "mind". It is beyond my province to say what the psychologists aim to study; but it is perfectly proper for me to determine by analysis what mind is in the sense in which logic is concerned with it. I have performed this analysis; and I believe that it will be found convincing, somewhat novel, highly interesting, and decidedly elevating. Indeed, I promise myself that if ever this memoir receives the attention that it ought, it will do something appreciable to aid the movement now beginning to extricate science from the slough of materialism. I undertake to show that when a man performs the simplest voluntary act, the nature of his efficiency upon matter is precisely the same as that which we attribute to truth when we say "Truth, crushed to earth, shall rise again," in which most scientific men have more or less faith. I will further make it mathematically evident that to say that while matter can act immediately only upon matter and mind can immediately act only upon mind, and yet each can act upon the other without the intervention of a tertium quid, does not involve the self-contradiction which it appears at first blush to express. At the same time, I show that there is nothing which it properly belongs to the logician to say about mind, in his sense, which cannot be established on the basis of universal experience, without appealing to any special science whatever.
Logic will here be defined as formal semiotic. A definition of a sign will be given which no more refers to human thought than does the definition of a line as the place which a particle occupies, part by part, during a lapse of time. Namely, a sign is something, A, which brings something, B, its interpretant sign determined or created by it, into the same sort of correspondence with something, C, its object, as that in which itself stands to C. It is from this definition, together with a definition of "formal", that I deduce mathematically the principles of logic. I also make a historical review of all the definitions and conceptions of logic and show not merely that my definition is no novelty, but that my non-psychological conception of logic has virtually been quite generally held, though not generally recognized.
I define logic very broadly as the study of the formal laws of
signs, or formal semiotic. I define a sign as something, A, which
brings something, B, its interpretant, into the same sort of
correspondence with something, C, its object, as that in which itself
stands to C. In this definition I make no more reference to anything
like the human mind than I do when I define a line as the place within
which a particle lies during a lapse of time. At the same time, a
sign, by virtue of this definition, has some sort of meaning. That is
implied in correspondence. Now meaning is mind in the logical sense.
But many will object that the only signs we can study are signs
interpreted in human thought. I reply that by the definition thoughts
are themselves signs, and that if it happens to be a fact that all
other signs are ultimately interpreted in thought-signs, then that
fact is irrelevant to logic. The proof that it is irrelevant is that
all the principles of logic are deducible from my definition without
taking any account of the alleged fact, much more clearly than if any
attempt is made to introduce this allegation as a premiss. Therefore,
unless this allegation be regarded as itself a truth of logic, which
it is not, since it is not of a formal nature, it is perfectly
irrelevant to logic. I also define very carefully what I mean by a
"formal" law. I say nothing in the definition about normative
principles, because not all the principles of logic are normative.
Indeed, it is only the connection of logic with esthetics through
ethics which causes it to be a normative science at all.
We cannot safely employ in logic any kind of reasoning which is
subject to doubts which a science of logic is needed to remove. We
are, therefore, restricted to mathematical reasoning. Now
mathematical reasoning requires a diagrammatic or pure constructive
notion of the thing reasoned about. But the ordinary logicians talk
of acts of the mind, concepts, judgments, acts of concluding, which
are mixed ideas into which enter all sorts of elements in a manner
which prevents any strict mathematical reasoning about them. All
these ideas of the mind are, however, representations, or signs. We
must begin by getting diagrammatic notions of signs from which we
strip away, at first, all reference to the mind; and after we have
made those ideas just as distinct as our notion of a prime number or
of an oval line, we may then consider, if need be, what are the
peculiar characteristics of a mental sign, and in fact may give a
mathematical definition of a mind in the same sense in which we can
give a mathematical definition of a straight line. We cannot by any
purely mathematical definition build up the peculiar idea of
straightness, since that is nothing but a feeling. We can only define
a straight line as one of a continuous family of lines having certain
relations to one another. But there might be just such a family
composed of lines none of which would appear straight to us. In like
manner, we can define the formal character of mind in a manner
perfectly adequate to all the purposes of logic. But there is nothing
to compel the object of such a formal definition to have the peculiar
feeling of consciousness. That peculiar feeling has nothing to do
with the logicality of reasoning, however; and it is far better to
leave it out of account.
By an application of categoric, I show that the primary division of logic should be into stechiology, critic, and methodeutic. There is a cross-division into the doctrines of terms, propositions, and arguments, to which three kinds of signs, however, stechiology, critic, and methodeutic are quite differently related. The various historical divisions of logic are considered.
Logic is primarily divided into stechiologic, critic, and
methodeutic, which are defined in terms of the categories. Logic
relates to terms, propositions, and arguments. Stechiologic treats of
every variety. Critic has no direct bearing upon terms, upon
analytic, or explicatory, propositions, nor upon necessary reasoning
as such. It does, however, treat of meaningless and absurd terms, of
irrelevant definitions, of fallacious demonstrations and of probable
deductions. Methodeutic has no direct bearing upon any terms or
propositions or upon any kind of reasoning except that which starts
hypotheses. After critical logic has pronounced a hypothesis to be
justifiable (being a verifiable hypothesis which explains the
surprising fact), it remains to submit the hypothesis to methodeutic
in order to determine whether it should be the first among the
justifiable hypotheses to be considered. No such supplementary
inquiry is called for in the case of a deductive or an inductive
conclusion. Indirectly, however, methodeutic treats of all kinds of
signs.
By virtue of the categories, anything whatever may be considered
under three aspects; first, in its peculiar flavor; second, as
reacting with an object; and third, as represented. The peculiar
flavor which belongs to a sign, as such, is its imputed flavor, or
meaning. The object upon which a sign as such reacts is the object to
which it corresponds, or denotes. The representamen which belongs to
a sign as such is its interpretant. Consequently, formal semiotic
falls into three departments, the study of those laws to which a sign
must conform in order to mean what it is to mean, the study of the
laws to which a sign must conform in order really to correspond to the
object to which it is intended to conform, that is, to be true, and
those laws to which a sign must conform in order to determine the
interpretant to which it is intended to appeal, that is, to advance
knowledge. These three departments have been called stechiologic,
critic, and methodeutic. I regard this division as primary, because
it depends upon a principle which is applicable to anything
whatsoever.
AND ESTABLISHING THE TRUTHS OF LOGIC
I shall here show that no less than thirteen different methods
of establishing logical truth are in current use today, and mostly
without any principle of choice and in a deplorably uncritical manner.
It need not be said that a science whose methods are all at
sixes and sevens is in poor case. I shall show that there are at
present actually in use six plus seven, or thirteen methods in use for
establishing logical truth, without counting the method of authority
which is really operative, although unavowed. While there are some
logicians who are more or less scrupulous in their choice of methods,
most of them resort indifferently to any one of twelve, the only one
they scrupulously avoid being the only one that is generally valid.
For I shall prove conclusively that the majority of the methods are
absolutely worthless, and that of the others only one is properly
applicable in all parts of logic. That one method consists in
proceeding from universally observed facts, formulated abstractly, and
deducing their consequences by mathematical reasoning. We are here
with certain objections which weigh with almost all logicians but
which I shall undertake to show are merely due to a feeble grasp of
the conceptions of logic. This first of these objections, which lies
behind them all, is that, logic being the science which establishes
the validity of reasoning, it begs the question to employ reasoning to
establish the principles of logic. To this I reply that as long as
all doubt is removed by a method, nothing better can be demanded. But
owing to the confused state of mind of logicians, they make various
attempts to answer this, such as that doubt is not removed if we
question the validity of the reasoning. The rejoinder is obvious
enough. Of course, it follows that pure mathematics does not stand in
need of any science of logic to determine whether a reasoning is good
or not; and by a review of the different disputes which have arisen
between mathematicians, I show that this is the case; and I contrast
this with a number of instances in the history of other sciences,
where logical doctrines were sadly needed.
No less than thirteen different ways are employed by different
logicians for ascertaining what is good reasoning and what is bad
reasoning. Only one of these thirteen methods is generally employed
by me, although there are one or two of the others which I apply to a
very limited extent as confirmatory only in settling minute details.
The great mass of the twelve methods I regard as altogether
unscientific and worthless in scientific logic, though there are
certain unscientific and inexact parts of logic, where reasoning is
mainly regulated by the logical instinct, where there is no particular
objection to their use. In particular, I hold the ordinary subjective
method of the German logicians--which bases logic upon the feeling of
logicality to such an extent that good reasoning is defined as such
reasoning as we deliberately approve as satisfying that feeling--to be
simply disastrous to science, to be much worse than leaving the whole
question to the direct decision of instinct, and to be responsible for
grave errors of procedure in the German psychical science, as for
example in linguistics, in the historical criticism of documents, etc.
[I] will give some preliminary idea of the present state of
logical inquiry. It will be shown that thirteen different ways of
determining whether reasoning is good or bad are now in use, to my
knowledge. Most of these will be shown to be worthless. A few may be
sparingly employed in special cases to which they are adapted. But
one sole method is generally valid. Namely, it must be shown that
whatever be the constitution of the universe, the method of reasoning
adopted, if it leads to any conclusion, and if there is any such thing
as the Truth to be reached, must in the long run reach a true
conclusion. The doctrine to which this is prominently opposed is that
the only way of judging of the validity of a reasoning is by means of
our instinctive feeling of rationality. My position against this
subjective logic is this. The instinct of rationality is not a simple
feeling. It is a faculty which produces distinct judgments; and the
matter of any such judgment is that a given method of reasoning is
good or bad, that is, will or will not answer its purpose as certainly
and completely as any that can be found. The instinctive judgment of
rationality, therefore, makes its pronouncement relative to the
reasoner's purpose. For that reason, it is necessary to consider
separately theoretical reasonings, the reasonings of pure science, and
practical reasonings, the reasonings of a person about the affairs of
life. The latter proposes to act speedily upon his conclusion; so
that the question must be settled with some degree of promptitude.
Science, on the other hand, may be a century, or five centuries,
engaged upon an investigation. Indeed, there is no definite period
within which science must reach its final conclusion. Therefore, if
it is quite evident that a method of reasoning is such that it must
reach the truth in the long run of probabilities, while it may not be
so good a method as some other where the approximation is more rapid,
yet it cannot be pronounced absolutely bad for scientific purposes.
The voice of instinct itself, when closely cross-questioned, assents
to this. For if we consider two methods of reasoning which the
instinctive sense of rationality in the first instance pronounces to
be upon a par, and if we show, as we can, that one of these will
evidently lead to the truth in the long run, if it leads to any
conclusion and if there is any truth, while as to the other, it is
evident that there is no such necessity, instinct will change its mind
and prefer the method which the objective criterion prefers. Indeed,
instinct confesses its own inadequacy to decide upon reasonings which
may be continued through many ages. But in the case of a person's
practical reasonings the case is different. For an individual whose
purse is finite, there really is no such thing as the "long run" of
probabilities. The objective theory is not strictly applicable.
Besides, here instinct is within its own proper domain; and instinct,
within its proper domain is far keener and surer than any human theory
whatever. Practical reasonings, therefore, ought not to be guided by
scientific logic, but by instinct; and the only logic which is
applicable to them consists in unsystematic generalizations of
instinct. But in proportion as the person practices a true ethics and
is animated by the purpose behind Nature at large, in that proportion
will it be possible for his reasonings to become scientifically
logical.
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Dept of
Philosophy
