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Minute Logic: Chapter I. Intended Characters of this Treatise

… the study of Abduction. Upon this subject, my doctrine has been immensely improved since my essay “A Theory of Probable Inference” was published in 1883. In what I there said about “Hypothetic Inference” I was an explorer upon untrodden ground. I committed, though I half corrected, a slight positive error, which is easily set right without essentially altering my position. But my capital error was a negative one, in not perceiving that, according to my own principles, the reasoning with which I was there dealing could not be the reasoning by which we are led to adopt a hypothesis, although I all but stated as much. But I was too much taken up in considering syllogistic forms and the doctrine of logical extension and comprehension, both of which I made more fundamental than they really are. As long as I held that opinion, my conceptions of Abduction necessarily confused two different kinds of reasoning. When, after repeated attempts, I finally succeeded in clearing the matter up, the fact shone out that probability proper had nothing to do with the validity of Abduction, unless in a doubly indirect manner. But now a number of considerations offered themselves as possibly connected with the solution of the problem, and owing to the extreme weakness of this form of inference, it was difficult to make sure that they were irrelevant. I seemed to be lost in a pathless forest, until by minute application of the first principles, I found that the categories, which I had been led to neglect from not seeing how they were to be applied, must and in fact did furnish the clue that guided me through the maze.

Argument is of three kinds: Deduction, Induction, and Abduction (usually called adopting a hypothesis). [—] An originary Argument, or Abduction, is an argument which presents facts in its Premiss which present a similarity to the fact stated in the Conclusion, but which could perfectly well be true without the latter being so, much more without its being recognized; so that we are not led to assert the Conclusion positively but are only inclined toward admitting it as representing a fact of which the facts of the Premiss constitute an Icon. For example, at a certain stage of Kepler’s eternal exemplar of scientific reasoning, he found that the observed longitudes of Mars, which he had long tried in vain to get fitted with an orbit, were (within the possible limits of error of the observations) such as they would be if Mars moved in an ellipse. The facts were thus, in so far, a likeness of those of motion in an elliptic orbit. Kepler did not conclude from this that the orbit really was an ellipse; but it did incline him to that idea so much as to decide him to undertake to ascertain whether virtual predictions about the latitudes and parallaxes based on this hypothesis would be verified or not. This probational adoption of the hypothesis was an Abduction. An Abduction is Originary in respect to being the only kind of argument which starts a new idea.

Arguments are of three kinds, Deduction, Induction, and what I call Abduction [—] If the conclusion is adopted, simply because it suggests itself as a possible fact which, if true, would necessitate ascertained facts, the Argument is Abductive. [—] It will be remarked that in the case of Abduction the only way in which the facts presented in the argument are any sign of the fact inferred is that they are an Icon […] of it.

An Argument is a sign which distinctly represents the Interpretant, called its Conclusion, which it is intended to determine.

An Argument is a Sign which aims to determine a definite Interpretant, called its Conclusion. It must, a fortiori, have a definite subject.

There is no fourth, as will be proved. This list of categories may be distinguished from other lists as the Ceno-Pythagorean Categories, on account of their connection with numbers. They agree substantially with Hegel’s three moments. Could they be attributed to any thinker in well-known history, that would be almost enough to refute their claims to primitivity. It has occurred to me that perhaps Pythagoras brought them from Media or Aria; but careful examination has convinced me that there was not among the Pythagoreans the smallest approach to anything resembling the categories.

I essay an analysis of what appears in the world. It is not metaphysics that we are dealing with: only logic. Therefore, we do not ask what really is, but only what appears to everyone of us in every minute of our lives. I analyze experience, which is the cognitive resultant of our past lives, and find in it three elements. I call them Categories.

That our thoughts are signs is an old and familiar doctrine. I show that it is only in so far as thoughts are signs, and particularly […] symbols, that they become subjects of logic; and further that the rules of logic are applicable to all symbols. Accordingly by regarding logic as a science of signs or formal semeiotic, and in the main as a science of symbols, or formal symbolic, we accurately cover its subject matter, and at the same time insure ourselves against all risk of being led astray into psychology. The word formal, in this connection, signifies that only the general conditions to which signs ought to conform are to be considered.

But those conditions may be distinguished into three kinds, leading to a corresponding distinction between three departments of logic, in its wider sense; or Formal Semeiotic. Namely the conditions are either, first, such as must be fulfilled in order that an object may be a sign at all; second, such as must be fulfilled in order that the sign may refer to the object to which it aims to refer, that is, may be true; and third, such as must be fulfilled in order that the sign may determine the interpretant it aims to determine, that is, may be pertinent. [—] The study of the second series of conditions is Logic in its narrow sense, or, as we may call it, Critical Logic.

Argument is of three kinds: Deduction, Induction, and Abduction (usually called adopting a hypothesis). An Obsistent Argument, or Deduction, is an argument representing facts in the Premiss, such that when we come to represent them in a Diagram we find ourselves compelled to represent the fact stated in the Conclusion; so that the Conclusion is drawn to recognize that, quite independently of whether it be recognized or not, the facts stated in the premisses are such as could not be if the fact stated in the conclusion were not there; that is to say, the Conclusion is drawn in acknowledgment that the facts stated in the Premiss constitute an Index of the fact which it is thus compelled to acknowledge. All the demonstrations of Euclid are of this kind. Deduction is Obsistent in respect to being the only kind of argument which is compulsive.

Arguments are of three kinds, Deduction, Induction, and what I call Abduction [—] If the facts directly asserted in the argument compell or tend to compell the fact asserted in the conclusion, so that the inference takes place by force, the argument is Deductive.

By experience, I do not mean the first impressions of sense merely, I mean all that the history of our lives has forced us to assent to and accept.

No; but there is nothing at all in our knowledge which we have any warrant at all for regarding as absolute in any particular. Absolute infallibility may belong to the pope and the ecumenical councils: it is outside my province to discuss that question. But I am quite confident it does not belong to the multiplication table. If I must make any exception, let it be that the assertion that every assertion but this is fallible, is the only one that is absolutely infallible. But though nothing else is absolutely infallible, many propositions are practically infallible; such as the dicta of conscience. As for those things which are known by everyday experience, let him doubt them who can lay his hand on his heart and say that he does doubt them. For the rest of us, it would be mendacity to say that our degree of assurance of them is unsatisfactory.

Let us now consider what could appear as being in the present instant were it utterly cut off from past and future. We can only guess; for nothing is more occult than the absolute present. There plainly could be no action; and without the possibility of action, to talk of binarity would be to utter words without meaning. There might be a sort of consciousness, or feeling, with no self; and this feeling might have its tone. Notwithstanding what William James has said, I do not think there could be any continuity like space, which, though it may perhaps appear in an instant in an educated mind, I cannot think could do so if it had no time at all; and without continuity parts of the feeling could not be synthetized; and therefore there would be no recognizable parts. There could not even be a degree of vividness of the feeling; for this [the degree of vividness] is the comparative amount of disturbance of general consciousness by a feeling. At any rate, such shall be our hypothesis, and whether it is psychologically true or not is of no consequence. The world would be reduced to a quality of unanalyzed feeling. Here would be an utter absence of binarity. I cannot call it unity; for even unity supposes plurality. I may call its form Firstness, Orience, or Originality. It would be something which is what it is without reference to anything else within it or without it, regardless of all force and of all reason. Now the world is full of this element of irresponsible, free, Originality. [—]We mostly neglect them; but there are cases, as in qualities of feeling, self-consciousness, etc., in which such isolated flashes come to the front. Originality, or Firstness, is another of my Categories.

… the study of Abduction. Upon this subject, my doctrine has been immensely improved since my essay “A Theory of Probable Inference” was published in 1883. In what I there said about “Hypothetic Inference” I was an explorer upon untrodden ground. I committed, though I half corrected, a slight positive error, which is easily set right without essentially altering my position. But my capital error was a negative one, in not perceiving that, according to my own principles, the reasoning with which I was there dealing could not be the reasoning by which we are led to adopt a hypothesis, although I all but stated as much. But I was too much taken up in considering syllogistic forms and the doctrine of logical extension and comprehension, both of which I made more fundamental than they really are.

A Sign degenerate in the greater degree is an Originalian Sign, or Icon, which is a Sign whose significant virtue is due simply to its Quality. Such, for example, are imaginations of how I would act under certain circumstances, as showing me how another man would be likely to act. We say that the portrait of a person we have not seen is convincing. So far as, on the ground merely of what I see in it, I am led to form an idea of the person it represents, it is an Icon. But, in fact, it is not a pure Icon, because I am greatly influenced by knowing that it is an effect, through the artist, caused by the original’s appearance, and is thus in a genuine Obsistent relation to that original. Besides, I know that portraits have but the slightest resemblance to their originals, except in certain conventional respects, and after a conventional scale of values, etc.

…signs must be divided, first, into those which are signs by virtue of facts which be equally true even if their objects and interpretants were away and even non-existent, which are likenesses, or Icons; second, into those which are signs by virtue of facts which would subsist even if their interpretants were away, though not if their objects were away, which are indications, or Indices; and thirdly, into signs which are signs only by virtue of facts which would cease to be true if their interpretants were removed, which are intellectual signs, or Symbols.

A Sign degenerate in the lesser degree, is an Obsistent Sign, or Index, which is a Sign whose significance of its Object is due to its having a genuine Relation to that Object, irrespective of the Interpretant. Such, for example, is the exclamation “Hi!” as indicative of present danger, or a rap at the door as indicative of a visitor.

…signs must be divided, first, into those which are signs by virtue of facts which be equally true even if their objects and interpretants were away and even non-existent, which are likenesses, or Icons; second, into those which are signs by virtue of facts which would subsist even if their interpretants were away, though not if their objects were away, which are indications, or Indices; and thirdly, into signs which are signs only by virtue of facts which would cease to be true if their interpretants were removed, which are intellectual signs, or Symbols.

Argument is of three kinds: Deduction, Induction, and Abduction (usually called adopting a hypothesis). A Transuasive Argument, or Induction, is an Argument which sets out from a hypothesis, resulting from a previous Abduction, and from virtual predictions, drawn by Deduction, of the results of possible experiments, and having performed the experiments, concludes that the hypothesis is true in the measure in which those predictions are verified, this conclusion, however, being held subject to probable modification to suit future experiments. Since the significance of the facts stated in the premisses depends upon their predictive character, which they could not have had if the conclusion had not been hypothetically entertained, they satisfy the definition of a Symbol of the fact stated in the conclusion. This argument is Transuasive, also, in respect to its alone affording us a reasonable assurance of an ampliation of our positive knowledge. By the term “virtual prediction,” I mean an experiential consequence deduced from the hypothesis, and selected from among possible consequences independently of whether it is known, or believed, to be true, or not; so that at the time it is selected as a test of the hypothesis, we are either ignorant of whether it will support or refute the hypothesis, or, at least, do not select a test which we should not have selected if we had been so ignorant.

The discussion of probability naturally brings us to the interesting question of the validity of induction. I undertake to demonstrate mathematically that the validity of Induction, in the proper sense of the term, that is to say, experimental reasoning, follows, through the lemmas of probabilities, from the rudiments of the doctrine of necessary consequences, without any assumption whatever about the future being like the past, or similar results following similar conditions, or the uniformity of nature, or any such vague principle.

Arguments are of three kinds, Deduction, Induction, and what I call Abduction [—] If the conclusion is accepted because, having been hypothetically propounded as a hypothesis, it predicted that experiments would yield results which they have thereupon been found to yield, the argument is Inductive.

Logic is the science of the general necessary laws of Signs and especially of Symbols.

Logic is the science of the general necessary laws of Signs and especially of Symbols. As such, it has three departments. Obsistent logic, logic in the narrow sense, or Critical Logic, is the theory of the general conditions of the reference of Symbols and other Signs to their professed Objects, that is, it is the theory of the conditions of truth. Originalian logic, or Speculative Grammar, is the doctrine of the general conditions of symbols and other signs having the significant character. It is this department of general logic with which we are, at this moment, occupying ourselves. Transuasional logic, which I term Speculative Rhetoric, is substantially what goes by the name of methodology, or better, of methodeutic. It is the doctrine of the general conditions of the reference of Symbols and other Signs to the Interpretants which they aim to determine…

A celebrated treatise is entitled Logic, or Computation, and although not all reasoning is computation, it is certainly true that numerical computation is reasoning. But calculating machines are in everyday use; and Babbage’s analytical engine would perform considerable feats in mathematics. Other logical machines have been constructed. All those instruments perform inferences; and those inferences are subject to the rules of logic. If from true premisses they always yield true conclusions, what more could be desired? Yet those machines have no souls that we know of. They do not appear to think, at all, in any psychical sense; and even if we should discover that they do so, it would be a fact altogether without bearing upon the logical correctness of their operations, which we should still have to assure ourselves of in the same way we do now.

The idea I am endeavoring to convey is difficult to seize. It cannot be seized by a reader who, instead of trying to seize it, puts himself into a resolutely hostile posture of mind toward it. Does he wish to know what I mean? If so, let him postpone criticism until he clearly apprehends what it is that is to be criticized. There are many minds who will be so occupied with a certain objection that it will quite eclipse the sense of what I have been saying. They will urge that those machines do not perform any inference, at all; that it is, on the contrary, we, who, knowing how they are constructed (be it in detail or in a general way, by testimony), infer that the number which is exhibited at the end of the process must be in a certain arithmetical relation to the numbers which determined the setting and working of the machine.

It will further be urged that if those machines were to be regarded as reasoning, there are others which would reason in far higher ways. For the calculating machines only execute variations upon 1 + 1 = 2, while there are machines which may, with as much justice, be said to resolve problems before which generations of able mathematicians have fallen back, repulsed. Such, for example, are the solids of different shapes which yacht-designers drag through the water, and thereby come to the knowledge of arcana of hydrodynamics. Blocks of wood should seem, then, on my principles to be better reasoners than the brains of Gauss and Stokes. And why stop here? Any apparatus whatever used for experimentation would be, on the same principle, a logical machine. A steam-engine would be working out, at every revolution, its problem in thermodynamics; a simple match, scratched on a box, a question that we are unequal to so much as the formulating of.

This sounds crushing. What have I to say to it all? Simply that it is absolutely just. A logical machine differs from any other machine merely in working upon an excessively simple principle which is applied in a manifold and complex way, instead of upon an occult principle applied in a monotonous way. If anybody wishes me to acknowledge that a logical machine reasons no more than any other machine, I do not know why I should not gratify him. That seems to me a matter of words. The result which the logical machine turns out has a relation to the data with which it was fed, which relation may be considered from the point of view of whether the former could be false so long as the latter are true. That is all there is in the facts of the case; and whether it is called reasoning or not I do not care. All that I insist upon is, that, in like manner, a man may be regarded as a machine which turns out, let us say, a written sentence expressing a conclusion, the man-machine having been fed with a written statement of fact, as premiss. Since this performance is no more than a machine might go through, it has no essential relation to the circumstance that the machine happens to work by geared wheels, while a man happens to work by an ill-understood arrangement of brain-cells; and if there be room for less, still less to the circumstance that a man thinks. Say, if you like, that thinking has everything to do with the life of reasoning; I still insist that it has nothing to do with the logical criticism, which is equally applicable to the machine’s performances and to the man’s.

Logic is the science of the general necessary laws of Signs and especially of Symbols. As such, it has three departments. Obsistent logic, logic in the narrow sense, or Critical Logic, is the theory of the general conditions of the reference of Symbols and other Signs to their professed Objects, that is, it is the theory of the conditions of truth. Originalian logic, or Speculative Grammar, is the doctrine of the general conditions of symbols and other signs having the significant character. It is this department of general logic with which we are, at this moment, occupying ourselves. Transuasional logic, which I term Speculative Rhetoric, is substantially what goes by the name of methodology, or better, of methodeutic. It is the doctrine of the general conditions of the reference of Symbols and other Signs to the Interpretants which they aim to determine…

All this brings us close to Methodeutic, or Speculative Rhetoric. The practical want of a good treatment of this subject is acute.

With Speculative Rhetoric, Logic, in the sense of Normative Semeotic, is brought to a close. But now we have to examine whether there be a doctrine of signs corresponding to Hegel’s objective logic; that is to say, whether there be a life in Signs, so that – the requisite vehicle being present – they will go through a certain order of development, and if so, whether this development be merely of such a nature that the same round of changes of form is described over and over again whatever be the matter of the thought or whether, in addition to such a repetitive order, there be also a greater life-history that every symbol furnished with a vehicle of life goes through, and what is the nature of it.

The real thinking-process presumably begins at the very percepts. But a percept cannot be represented in words, and consequently, the first part of the thinking cannot be represented by any logical form of argument. Our logical account of the matter has to start from a perceptual fact, or proposition resulting from thought about a percept – thinking in its own movement presumably of the same nature as that which we represent by arguments and inferences, but not so representable in consequence of a defect in that method of representation.

That which remains of a Proposition after removal of its Subject is a Term (a rhema) called its Predicate.

A Proposition is a Sign which distinctly indicates of what Object (called its Subject) it is the Sign, but which is left to determine what Interpretant it may.

Rhemata are very nearly what are ordinarily designated as Terms. Indeed, they are the same thing more accurately apprehended. A Rhema, or Term, is a Sign which is left to stand for whatever it may stand for.

All experience compels your acknowledgment. What, then, is the fact that is present to you? Ask yourself: it is past. A fact is a fait accompli; its esse is in praeterito. The past compels the present, in some measure, at least. If you complain to the Past that it is wrong and unreasonable, it laughs. It does not care a snap of the finger for Reason. Its force is brute force. So then, you are compelled, brutally compelled, to admit that there is such an element in the world of experience as brute force. […]

Obsistence (suggesting obviate, object, obstinate, obstacle, insistence, resistance, etc.) is that wherein secondness differs from firstness; or, is that element which taken in connection with Originality, makes one thing such as another compels it to be.

That our thoughts are signs is an old and familiar doctrine. I show that it is only in so far as thoughts are signs, and particularly […] symbols, that they become subjects of logic; and further that the rules of logic are applicable to all symbols. Accordingly by regarding logic as a science of signs or formal semeiotic, and in the main as a science of symbols, or formal symbolic, we accurately cover its subject matter, and at the same time insure ourselves against all risk of being led astray into psychology. The word formal, in this connection, signifies that only the general conditions to which signs ought to conform are to be considered.

The categories directly point out that anything may be regarded, first, in the aspect of a simple Quale; secondly, as in Relation to other things; and thirdly, as a Sign, that is as referring to an object in virtue of determining an interpreting sign, which [I] call its interpretant[,] to refer to the object in the same way.

Logic is the science of the general necessary laws of Signs and especially of Symbols. As such, it has three departments. Obsistent logic, logic in the narrow sense, or Critical Logic, is the theory of the general conditions of the reference of Symbols and other Signs to their professed Objects, that is, it is the theory of the conditions of truth. Originalian logic, or Speculative Grammar, is the doctrine of the general conditions of symbols and other signs having the significant character. It is this department of general logic with which we are, at this moment, occupying ourselves. Transuasional logic, which I term Speculative Rhetoric, is substantially what goes by the name of methodology, or better, of methodeutic. It is the doctrine of the general conditions of the reference of Symbols and other Signs to the Interpretants which they aim to determine…

That our thoughts are signs is an old and familiar doctrine. I show that it is only in so far as thoughts are signs, and particularly […] symbols, that they become subjects of logic; and further that the rules of logic are applicable to all symbols. Accordingly by regarding logic as a science of signs or formal semeiotic, and in the main as a science of symbols, or formal symbolic, we accurately cover its subject matter, and at the same time insure ourselves against all risk of being led astray into psychology. The word formal, in this connection, signifies that only the general conditions to which signs ought to conform are to be considered.

But those conditions may be distinguished into three kinds, leading to a corresponding distinction between three departments of logic, in its wider sense; or Formal Semeiotic. Namely the conditions are either, first, such as must be fulfilled in order that an object may be a sign at all; second, such as must be fulfilled in order that the sign may refer to the object to which it aims to refer, that is, may be true; and third, such as must be fulfilled in order that the sign may determine the interpretant it aims to determine, that is, may be pertinent. I call the study of the first series of conditions Speculative Grammar. It is the […] introductory branch of logic…

All this brings us close to Methodeutic, or Speculative Rhetoric. The practical want of a good treatment of this subject is acute.
[—]
In coming to Speculative Rhetoric, after the main conceptions of logic have been well settled, there can be no serious objection to relaxing the severity of our rule of excluding psychological matter, observations of how we think, and the like. The regulation has served its end; why should it be allowed now to hamper our endeavors to make methodeutic practically useful? But while the justice of this must be admitted, it is also to be borne in mind that there is a purely logical doctrine of how discovery must take place, which, however great or little is its importance, it is my plain task and duty here to explore.

Logic is the science of the general necessary laws of Signs and especially of Symbols. As such, it has three departments. Obsistent logic, logic in the narrow sense, or Critical Logic, is the theory of the general conditions of the reference of Symbols and other Signs to their professed Objects, that is, it is the theory of the conditions of truth. Originalian logic, or Speculative Grammar, is the doctrine of the general conditions of symbols and other signs having the significant character. It is this department of general logic with which we are, at this moment, occupying ourselves. Transuasional logic, which I term Speculative Rhetoric, is substantially what goes by the name of methodology, or better, of methodeutic. It is the doctrine of the general conditions of the reference of Symbols and other Signs to the Interpretants which they aim to determine…

That our thoughts are signs is an old and familiar doctrine. I show that it is only in so far as thoughts are signs, and particularly […] symbols, that they become subjects of logic; and further that the rules of logic are applicable to all symbols. Accordingly by regarding logic as a science of signs or formal semeiotic, and in the main as a science of symbols, or formal symbolic, we accurately cover its subject matter, and at the same time insure ourselves against all risk of being led astray into psychology. The word formal, in this connection, signifies that only the general conditions to which signs ought to conform are to be considered.

But those conditions may be distinguished into three kinds, leading to a corresponding distinction between three departments of logic, in its wider sense; or Formal Semeiotic. Namely the conditions are either, first, such as must be fulfilled in order that an object may be a sign at all; second, such as must be fulfilled in order that the sign may refer to the object to which it aims to refer, that is, may be true; and third, such as must be fulfilled in order that the sign may determine the interpretant it aims to determine, that is, may be pertinent. [—] The study of the third series of conditions will be found to coincide nearly with what is termed Methodeutic or Methodology; but I prefer to term it Speculative Rhetoric.

A Genuine Sign is a Transuasional Sign, or Symbol, which is a sign which owes its significant virtue to a character which can only be realized by the aid of its Interpretant. Any utterance of speech is an example. If the sounds were originally in part iconic, in part indexical, those characters have long since lost their importance. The words only stand for the objects they do, and signify the qualities they do, because they will determine, in the mind of the auditor, corresponding signs.

…signs must be divided, first, into those which are signs by virtue of facts which be equally true even if their objects and interpretants were away and even non-existent, which are likenesses, or Icons; second, into those which are signs by virtue of facts which would subsist even if their interpretants were away, though not if their objects were away, which are indications, or Indices; and thirdly, into signs which are signs only by virtue of facts which would cease to be true if their interpretants were removed, which are intellectual signs, or Symbols.

Let us now take up being in futuro. As in the other cases, this is merely an avenue leading to a purer apprehension of the element it contains. An absolutely pure conception of a Category is out of the question. Being in futuro appears in mental forms, intentions and expectations. Memory supplies us a knowledge of the past by a sort of brute force, a quite binary action, without any reasoning. But all our knowledge of the future is obtained through the medium of something else. [—] Intellectual triplicity, or Mediation, is my third category. […]

Transuasion (suggesting translation, transaction, transfusion, transcendental, etc.) is mediation, or the modification of firstness and secondness by thirdness, taken apart from the secondness and firstness; or, is being in creating Obsistence.