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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