Home Page      Peirce Papers      Intro to L75      L75 Version 2



  Final Version - MS L75.366  



      This will contain especially a discussion of Erkenntnisslehre, what it must be, if it is an indispensable preparatory doctrine to critical logic.

* * *

  From Draft D - MS L75.247-248  

      Conceiving of stechiologic, not as above defined, but as whatever doctrine is requisite as a preparation for critical logic, we are met with the fact that some of the best German logicians maintain that it should be what is known as a theory of cognition, or Erkenntnisslehre. This doctrine is supposed to be built, in part, upon truths discovered by the psychologists, such as the association of ideas. In this memoir, I show by careful analysis that psychological truths are not relevant to the theory of cognition, but on the contrary that the establishment of those truths depends upon special points of the doctrine of logic. I undertake to show what a theory of cognition becomes when it is stripped of everything irrelevant and inadmissable, and that it then becomes a sort of grammatica speculativa. I then examine universal grammar as it is generally conceived, and show that most of its propositions are merely matters of certain special languages, some of the indo-european languages, with such others as happen to resemble them. I then show that there is a way, and but one way, of reaching a sort of grammatica speculativa, and that this is simply stechiology as I have defined it.


  Final Version - MS L75.366  



EDITORIAL NOTE: Peirce had no comment on this in any version. The term "stechiologic"—sometimes "stechiology"—is used here for what he more typically refers to as "speculative grammar" (or "grammatica speculativa"), which means literally "theoretical grammar" but is perhaps most aptly referred to by the term "philosophical grammar" or as Peirce himself indicate,"universal grammar". I prefer the term "philosophical grammar" myself because one of the collections of Wittgenstein's notes has been given that title, and this helps to situate Peirce in the proper context.




  Final Version - MS L75.366  



      This memoir will be based on my paper of November 1867.*

* EDITORIAL NOTE: "Upon Logical Comprehension and Extension," Proceedings of the American Academy of Arts and Sciences 7, 1867 (reprinted in Vol. 2 of the Collected Papers, Vol. 2 of the Chronological Edition, and in Vol. 1 of Houser and Kloesel's The Essential Peirce. If you think of Frege as the discoverer of the sense/reference or Sinn/Bedeutung distinction, you will find Peirce's depth/breadth or comprehension/extension distinction, and his tracing of this back to Aristotle, unusually interesting. Peirce also provides a formal definition of "information" in terms of this distinction.

      Practice has shown that that paper needs extension in several directions. Besides, account has to be taken of important classes of terms there barely mentioned. The historical part, too, needs great amplification. My very conception of what a term is has been much improved by studies subsequent to that paper, and altogether original. The study of "agglutinative" languages has been an aid to me.

* * *

  From Draft D - MS L75.249  

      [This memoir will develop] the doctrine of logical depth and breadth, in a much more thorough working out of my paper of November 1867, and taking into consideration all kinds of terms.



  Final Version - MS L75.367  



      The question of the nature of the judgment is today more actively debated than any other. It is here that the German logicians are best worthy of attention; and I propose to take occasion to give here an account of modern German logic. Although this seems rather the subject for a book than for a single paper, yet I think, by stretching this memoir, I can bring into it all that is necessary to say about these treatises, which belong to near a dozen distinct schools.

      I shall then show how my own theory follows from attention to the three categories; and shall pass to an elaborate analysis, classification, symbolization, and doctrine of the relations of propositions. This will probably be the longest of all the memoirs, and will balance No. 16, which will be short. I think I shall treat No. 16 as a supplement to No. 15 and divide No. 21 into two parts to be handed in separately.

* * *

  From Draft D - MS L75.249-250  

      No question of logic has of late years received more attention than that of the nature of the judgment. I here propose to show that my method satisfies all conditions. The doctrine is that the proposition, that is, the meaning of the matter of a judgment, is a sign (regarded as identical with any full interpretation of it) which separately designates its object. Thus a portrait with the name of the person portrayed under it expresses a proposition. This proposition need not be asserted. Assertion is a separate act by which a person makes himself responsible for the truth of the proposition. Interrogation, command, etc., equally involve easily defined acts. The question then arises whether a proposition does not involve a peculiar and indefinable element. I show that it does so. But although this element is indefinable, it is easily identified with my second category, and the precise manner in which reaction enters into it is also clear.

      I then examine the principal discussions of the nature of the judgment, and show exactly wherein they are right and wherein wrong.

      I further give a classification of propositions.

* * *

  From Draft A - MS L75.43-45  

      It is necessary to distinguish between a proposition and the assertion of it. To confound those two things is like confounding the writing of one's name idly upon a scrap of paper, perhaps for practice in chirography, with the attachment of one's signature to a binding legal deed. A proposition may be stated without being asserted. I may state it to myself and worry as to whether I shall embrace it or reject it, being dissatisfied with the idea of doing either. In that case, I doubt the proposition. I may state the proposition to you and endeavor to stimulate you to advise me whether to accept or reject it, in which [case] I put it interrogatively. I may state it to myself and be deliberately satisfied to base my action on it whenever occasion may arise, in which case I judge it. I may state it to you and assume a responsibility for it, in which case I assert it. I may impose the responsibility of its agreeing with the truth upon you, in which case I command it. All of these are different moods in which that same proposition may be stated. The German word Urtheil confounds the proposition itself with the psychological act of assenting to it. This confusion is a part of the general refusal of idealism, which still considerably affects almost all German thought, to acknowledge that it is one thing to be and quite another to be represented.

* * *

  From Draft D - MS L75.323-324  

      An assertion is an act which represents that an icon represents the object of an index. Thus, in the assertion, "Mary is red-headed","red-headed" is not an icon itself, it is true, but a symbol. But its interpretant is an icon, a sort of composite photograph of all the red-headed persons one has seen. "Mary" in like manner, is interpreted by a sort of composite memory of all the occasions which forced my attention upon that girl. The putting of these together makes another index which has a force tending to make the icon an index of Mary. This act of force belongs to the second category, and as such, has a degree of intensity. Not that degree in itself belongs to the second category: on the contrary, it belongs to the third. Degree is not a reaction, or effort, but a thought. But degree attaches to every reaction. Consequently, every assertion has a degree of energy.



  Final Version - MS L75.368-372  



      I first examine the essential nature of an argument, showing that it is a sign which separately signifies its interpretant. It will be scrutinized under all aspects.

      I shall then come to the important question of the classification of arguments. My paper of April 1867 on this subject divides arguments into deductions, inductions, abductions (my present name, which will be defended), and mixed arguments. I consider this to be the key of logic. In the following month, May 1867, I correctly defined the three kinds of simple arguments in terms of the categories. But in my paper on probable inference in the Johns Hopkins Studies in Logic, owing to the excessive weight I at that time placed on formalistic considerations, I fell into the error of attaching a name, the synonym I then used for abduction, to a probable inference which I correctly described, forgetting that according to my own earlier and correct account of it, abduction is not of the number of probable inferences. It is singular that I should have done that, when in the very same paper I mention the existence of the mode of inference which is true abduction. Thus, the only error that paper contains is the designation as abduction of a mode of induction somewhat resembling abduction, which may properly be called "abductive induction". It was this resemblance which deceived me, and subsequently led me into a further error contrary to my own previous correct statement, namely, to confound abduction and abductive induction. In subsequent reflections upon the rationale of abduction, I was led to see that this rationale was not that which I had in my Johns Hopkins paper given of induction; and in a statement I published in the Monist, I was led to give the correct rationale of abduction as applying to abductive induction and so, in fact, to all induction. All the difficulties with which I labored are now completely disposed of by recognizing that abductive induction is quite a different thing from abduction. It is a very instructive illustration both of the dangers and of the strength of my heuretic method. Similar errors may remain in my system. I shall be very thankful to whomever can detect them. But if its errors are confined to that class, the general fabric of the doctrine is true. I at first saw that there must be three kinds of arguments severally related to the three categories; and I correctly described them. Subsequently studying one of these kinds, I found that besides the typical form, there was another, distinguished from the typical form by being related to that category relation to which distinguishes abduction. I hastily identified it with abduction, not being clear-headed enough to see that, while related to that category, it is not related to it in the precise way in which one of the primary divisions of arguments ought to be, according to the theory of the categories. This is the form of error to which my method of discovery is peculiarly liable. One sees that a form has a relation to a certain category, and one is unable for the time being to attain sufficient clearness of thought to make quite sure that the relation is of the precise nature required. If only one point were obscure, it would soon be cleared up; but the difficulty is at first that one is sailing in a dense fog, through an unknown sea, without a single landmark. I can only say that if others, after me, can find some way of making as important discoveries in logic as I have done while falling into less error, nobody will be more intensely delighted than I shall be. My gratitude to the man who will show me where I am wrong in logic will have no bounds. Thus far, I have had to find out for myself as well as I could. Meantime, be it observed that the kind of error which I have been considering can never amount to anything worse than a faulty classification. All that I asserted about probable inference in my Johns Hopkins paper and in my Monist paper was perfectly true.

      In this paper, besides very important improvements in the subdivision of the three kinds of simple arguments, with several hitherto unrecognized types, and far greater clearness of exposition, I shall have much that is new to say about mixed arguments, which present many points of importance and of interest that have never been remarked. I shall give a new classification of them based, not upon the nature of their elements, but upon their modes of combination. Besides setting forth my own doctrine of the stechiology of argument, I shall examine the most important of those which are opposed to it.

* * *

  From Draft D - MS L75.250-252  

      Most of the German logicians who are free from traditional influences have regarded the judgment as the logical element, because they find in it something sui generis. They find nothing of the sort in the argument. I show just how much truth there is in this, and that there really is a peculiar element in the argument; to wit, the third category. I show what the peculiarity of the German mind which leads to this and a number of other analogous views consists in. I then analyze the nature of the argument, and show among other things that in all reasoning there is a logica utens, or an appeal to a vaguely defined logical doctrine. I show that it follows from the definition of an argument, as a sign which definitely signifies its intended interpretant, that an argument must be a self-conscious sign, and I formally define this self-consciousness, without any resort to psychology or to the peculiar flavor of human self-consciousness. I further show that properly, an argument is self-controlled, although a sign may be quite similar to an argument without being self-controlled. I then show that from the definition of an argument it follows mathematically that every argument is either a deduction, an induction, an abduction, or an argument which mixes these characters. I proceed to show what the chief varieties of these [are], which will be one of the parts of this memoir most emphasized. In particular I distinguish deduction into two types, the corollarial and the theorematic, and induction into three types of widely different natures. This division is specially significant, and has never been published.

* * *

  From Draft A - MS L75.35-39  

      There are three different ways in which a method may be calculated to lead to the truth, these three senses constituting three great classes of reasonings. Deduction is reasoning which professes to pursue such a method that if the premisses are true the conclusion will in every case be true. Probable deduction is, strictly speaking, necessary; only, it is necessary reasoning concerning probabilities. Induction is reasoning which professes to pursue such a method that, being persisted in, each special application of it (when it is applicable) must at least indefinitely approximate to the truth about the subject in hand, in the long run. Abduction is reasoning which professes to be such that in case there is any ascertainable truth concerning the matter in hand, the general method of this reasoning, though not necessarily each special application of it, must eventually approximate to the truth.

      Of these three classes of reasonings abduction is the lowest. So long as it is sincere, and if it be not, it does not deserve to be called reasoning, abduction cannot be absolutely bad. For sincere efforts to reach the truth, no matter in how wrong a way they may be commenced, cannot fail ultimately to attain any truth that is attainable. Consequently, there is only a relative preference between different abductions; and the ground of such preference must be economical. That is to say, the better abduction is the one which is likely to lead to the truth with the lesser expenditure of time, vitality, etc.

      Deduction is only of value in tracing out the consequences of hypotheses, which it regards as pure, or unfounded, hypotheses. Deduction is divisible into sub-classes in various ways, of which the most important is into corollarial and theorematic. Corollarial deduction is where it is only necessary to imagine any case in which the premisses are true in order to perceive immediately that the conclusion holds in that case. Ordinary syllogisms and some deductions in the logic of relatives belong to this class. Theorematic deduction is deduction in which it is necessary to experiment in the imagination upon the image of the premiss in order from the result of such experiment to make corollarial deductions to the truth of the conclusion. The subdivisions of theorematic deduction are of very high theoretical importance. But I cannot go into them in this statement.

      Induction is the highest and most typical form of reasoning. In my essay of 1883, I only recognized two closely allied logical forms of pure induction, one of which in undoubtedly the highest. I have since discovered eight other forms which include those almost exclusively used by reasoners who are not adepts in logic. In fact, Norman Lockyer is the only writer I have met with who in his best work, especially his last book, habitually restricts himself to the highest form. Some of his work, however, as for example, that on the orientation of temples, is logically poor.

      Besides these three types of reasoning there is a fourth, analogy, which combines the characters of the three, yet cannot be adequately represented as composite. There are also composite reasonings where an argument of one type is joined to an argument of another type. Such for example, is an induction fortified by the consideration of some known uniformity. Uniformities are of four principal kinds of which Mill distinctly recognizes only a single one.

      Mill's four methods of induction is a heterogeneous division, not at all scientific, and, in part, of very trifling utility. Still, it is better than no classification of inductions at all.

  From Draft A - MS L75.35, 53  

      Necessary deduction, in the narrower sense, is either corollarial or theorematic.*

* EDITORIAL NOTE: By "in the narrower sense," Peirce apparently means "leaving probable deduction aside." In the MS this paragraph actually begins right after the sentence near the beginning of the above segment in which probable deduction is characterized. It is displaced here because it was marked as rejected by Peirce.

Corollarial reasoning is that in which it is only necessary to consider what the premisses mean in order to find that the conclusion is as true as they. Theorematic reasoning is reasoning in which this is not enough, but it is needful to perform experiments in the imagination in order to assure ourselves that the conclusion is true. For example, in order to prove that if all triangles of equal area have the sums of their angles equal, then the difference of the sum from two right angles must be proportional to the area of the triangle, we shall imagine a triangle to be cut into any number of equal triangles. Then we easily satisfy ourselves by experiment that when a triangle is added to a polygon so as to increase the number of sides by n, the sum of the angles will be increased by n-2 times 2 right angles. Consequently, if m triangles be added so as to increase the number of sides by n the sum of the angles will be increased by n-m times 2 right angles. Now when a large triangle is cut into a small triangles, a-1 triangles are joined to a triangles so as not to increase the number of sides. Hence the large triangle will have the sum of its angles equal to that of one of the small triangles diminished by a-1 times 2 right angles or the sum of the angles of the large triangle less 2 right angles will be a times the sum of the angles of the small triangles after each of the a-sums has been diminished by two right angles, which was the proposition to be proved.*

* EDITORIAL NOTE: The argument in the above passage is intended to show that recourse to diagrammatic experimentation is both required and sufficient in the case in question to establish the conclusion, the point being to show why mathematical reasoning is theorematic and not merely corollarial. This is an important and controverted thesis, put forward by Peirce—against the grain, as always—at a time when the formalist conception of mathematics, which holds that all mathematical reasoning is reducible to what Peirce calls "corollarial" reasoning, was in the ascendancy. The formalist David Hilbert's famous lecture in which his list of questions for 20th Century mathematics was put forth (which both Gödel and Turing later addressed) was given in 1900, for example. Unfortunately, this page of the manuscript is difficult to read in several places and I don't understand the argument well enough myself to be certain that I am transcribing it properly. I haven't seen him use this particular one elsewhere. It would be helpful if anyone who feels competent to assess the argument would address the question of whether it really adds up as it should. It is possible that Peirce himself didn't think so since it occurs in a paragraph the beginning part of which is marked through in a way indicating rejection; but then Peirce's reason for rejecting the paragraph may have had nothing to do with his view of the validity of that argument.

* * *

  From Draft E - MS L75.163-173  

      The nature of argument [is] fully examined in all its aspects. All arguments are either deductions, inductions, abductions, or mixed arguments. My earliest statements were correct in this respect. But in my paper in the Johns Hopkins Studies in Logic, overemphasizing formalities, I failed to distinguish between abduction and a previously overlooked or little noticed variety of induction which may be called "abductive induction"; in consequence of which, that paper, although correct as far as it goes, and although fully covering the subject of which it professed to treat, entirely overlooked an indispensable mode of inference, abduction, I myself having previously described the inference correctly. Deduction is necessary inference; but if it is applied to probability, then, while remaining in itself necessary, it concludes a probability. That gives the doctrine of chances. Induction is a totally different sort of inquiry, proceeding, by means of experiment, to obtain an answer to a previously propounded question. It has two species: the extensive, where the question is how much, and the comprehensive, or abductive, where the question is to be answered by yes or no (or else is merely susceptible of a vague answer). Abduction is distinguished from abductive induction in not being, properly speaking, experimental, that is, it makes its observations without reference to any previously propounded question, but, on the contrary, itself starts a question, or problematically propounded hypothesis, to explain a surprising observation. Since I barely escaped error on this matter, I will in this present note illustrate the difference between abduction, abductive induction, and probable deduction.

      Suppose, then, that, being seated in a street car, I remark a man opposite to me whose appearance and behavior unite characters which I am surprised to find together in the same person. I ask myself, How can this be? Suppose I find this problematic reply: Perhaps he is an ex-priest. He is the very image of such a person; he presents an icon of an ex-priest. Here is an iconic argument, or abduction of it. Secondly, it now occurs to me that if he is an ex-priest, he should be tonsured; and in order to test this, I say something to him calculated to make him take off his hat. He does so, and I find that he is indeed tonsured. Here at last is an indication that my theory is correct. I can now say that he is presumably an ex-priest, although it would be inaccurate to say that there is any definite probability that he is so, since I do not know how often I might find a man tonsured who was not an ex-priest, though evidently far oftener than he would be one. The supposition is, however, now supported by an inductive induction, a weak form of symptomatic or indexical argument. It stands on a widely different basis from that on which it stood before my little experiment. Before, it rested on the flimsy support of similarity, or agreement in "flavor." Now, facts have been constrained to yield confirmation to it by bearing out a prediction based upon it. Belief in the theory rests now on factual reaction to the theory. Thirdly, while the man's hat is off, I read in the crown of it a name that has been pasted into it. I have no doubt whatever that it is the man's name. I do not go into the question of how I come to be so confident of that. As long as I have no doubt, it matters not how doubt came to be destroyed. I get out of the car, and go to call upon the chancellor of the diocese; and that he will tell me the truth I equally believe implicitly. I ask the chancellor, "Who is Michael Wo-Ling Ptah-Hotep Jerolomon?" (Pardon my nonsense.) He replies, "He is an ex-priest." "Is he the only man of that name?" "No, there are, or may be, fifteen. Fourteen of them reside in this town and are ex-priests. The fifteenth went, twenty years ago, to High Thibet, and has never been heard of since." It thus appears that the name read in the hat, though having no striking "flavor" of ex-priest about it, nor any such causal connection with the man's being an ex-priest as was the tonsure, yet in consequence of this knowledge becomes a symbol of the man's being an ex-priest; for a symbol is a sign which becomes significant simply by virtue of the fact that it will be so interpreted. So, it might conceivably have been an accident that the man was tonsured, but now that the name Michael Wu-Ling Ptah-Hotep Jerolomon signifies for me a probability of more than fourteen to one of being an ex-priest, I must think that the probability on that ground alone is over fourteen to one that he is an ex-priest. There is no escape from that. It is what I consider myself certain of. It is only a probability. Yet now, fourthly, combining the arguments into one mixed argument, and considering, what is logically relevant, that I have no serious stake in the question, I am satisfied to consider the mixed argument as proof, and to dismiss the question until it may acquire more importance. (Although the illustration is silly, it all the better covers the case.)

      Mixed arguments are of three kinds. The first consists of those which tend to establish the same conclusion or contradictory conclusions, or to establish two premisses from which, taken together, a conclusion can be inferred; second, arguments consisting of two parts of which one taken by itself lends no support to the conclusion of the other, but tends to establish a fact which makes the other a stronger or weaker argument. For example, I see two men wearing both the same badge going to the polls together talking with great delight over the effect of their vote; and I learn that one of them voted the Democratic ticket. I infer that the other did so, too. But subsequently, I learn that that badge is the symbol of membership of a society which decided that its members should go to the polls in pairs and that one of each pair should vote Democratic and the other Republican. I consequently reverse my previous inference. Under this head come inductions supported by uniformities, of which there are four simple types. The third kind of mixed arguments are those in which the same premisses form two different kinds of arguments. Important subdivisions of induction and deduction will be defined and illustrated.

      Having thus set forth my own doctrine of the stechiology of argument, I examine other doctrines.



  Final Version - MS L75.372  



      A thorough discussion of the nature, division, and method of critical logic.


End of PART 6 of 10 of MS L75


Queries, comments, and suggestions to
Joseph Ransdell -- Dept of Philosophy
Texas Tech University, Lubbock Texas 79409

Scholarly quotation from or reference to
the content of this website will mention
the URL of the web-page where the content occurs.

The URL of the present page, which is part of the Arisbe website, is

Page last modified June 15, 1998

Top of the Page