Jerry, Jon, List, The attached file contains the abstract and outline of the article I'm writing and a complete copy of L376.
JLRC: The question is, what aspects of “21st C developments” are you referring to? Except for a few experimental projects, all computer programs and systems that do any kind of modal reasoning use some version of metalanguage. That was a feature that Peirce introduced in 1898 (RLT). He also added a similar notation for metalanguage to his 1903 Lowell lectures on modal logic. And he used a slightly different, but equivalent notation for metalanguage in June 1911 (R514). But the Delta graphs of L376 combine metalanguage with a novel method of organizing the phemic sheet into a growing and evolving structure of multiple "papers" (see the appendix of the attached file), In the IKRIS project (2004 to 2006), a group of researchers built a very rich system of reasoning on top of a logic that that includes a metalanguage feature that is equivalent to Peirce's 1898 addition to EGs. For a brief summary of the IKRIS project, see https://jfsowa.com/ikl . My summary includes links to the original documents for the project and to the IKL logic, which is based on an ISO standard for Common Logic (CL) plus a metalanguage feature added to CL. The IKRIS documents describe developments that use IKL to support science and engineering projects. I believe that those projects demonstrate that Peirce's methods described in L376 can indeed support his methods of pragmatism. JAS: we were having a respectful and substantive discussion despite our ongoing disagreements. I am disappointed that this is no longer the case and inclined to refrain from any further engagement after one more attempt to set the record straight. With all due respect, I believe that you made a serious mistake by ignoring 90% of the only document in which Peirce mentions Delta graphs, as I said in a previous note: JFS: The critical additions [for a proof of pragmatism] are closely related to what Peirce specified in L376. I call that material a specification of Delta graphs. I don't care what you call it. The specifications are important. The names are irrelevant. There is nothing insulting in that note. I have repeatedly cited the texts I mentioned in my reply to Jerry. I tried to explain how important they are to understand what Peirce was writing about Delta graphs. And I offered to help you correct your article. But you refused to look at those references, and you kept insisting that Peirce was not writing about Delta graphs in the only text in which he wrote "I shall NOW have to add a Delta part in order to deal with modals." In the next sentence, he describes how he is "HERE" describing "the Conventions, the Rules, and the working of the System." Then the paragraph that immediately follows that sentence begins to describe the conventions. That is a very clear connection. I cannot imagine how anyone could mistake it. The remainder of L376 (see below) continues to describe a novel version of EGs that uses features (Cayley's writings) that Peirce had discussed with Risteen in the 1890s. (See the comments by Nathan Houser in EP2.) It also discusses issues that are related to IKL and the IKRIS project. (See my reply above to Jerry.) You refused to read the references to Risteen or the references to IKRIS and IKL. And you kept on searching for references to anything other than the contents of L376. I don't believe that you can blame me for being annoyed. John ---------------------------------------- From: "Jon Alan Schmidt" <jonalanschm...@gmail.com> John, List: Up until the off-List message that you sent me late Saturday evening, we were having a respectful and substantive discussion despite our ongoing disagreements. I am disappointed that this is no longer the case and inclined to refrain from any further engagement after one more attempt to set the record straight. JFS: The critical additions [for a proof of pragmatism] are closely related to what Peirce specified in L376. I call that material a specification of Delta graphs. I don't care what you call it. The specifications are important. The names are irrelevant. The name is relevant when it is one that Peirce himself used. If he had never mentioned a Delta part of EGs at all, then anyone would be free to invent one and give it that name. However, he did mention it, albeit in only one sentence-- "I shall now have to add a Delta part in order to deal with modals"--so no one should misleadingly use the name "Delta graphs" for anything that deviates from or goes well beyond this very brief description. As I have explicitly and repeatedly acknowledged, unless additional pages of R L376 turn up that spell it out, no one can know for sure exactly what he had in mind. That is why I have carefully and consistently referred to the notation that he scribed on R 339:[340r] as a candidate for Delta EGs. JFS: I realize that you insist in ignoring everything but the first two paragraphs of L376. I believe that is a serious mistake. You are deliberately putting blinders on your eyes. I think that we can all agree that it's unwise to reject anything Peirce wrote just because of some preconceived notion that it's irrelevant. On the contrary, I am not ignoring anything in R L376, and I have no preconceived notions about it. I am simply reading and explaining what the entire extant text actually says--and does not say. Again, the "many papers" correspond to different subjects that attract "the common attention" of the utterer and interpreter at different times, such that together they represent the entire universe of discourse. This is not new or innovative in 1911--it echoes what Peirce had already written at least twice previously, as I have demonstrated with exact quotations (https://list.iupui.edu/sympa/arc/peirce-l/2024-03/msg00004.html). Nothing precludes using the "many papers" with Alpha, Beta, or Gamma EGs--they do not "deal with modals" and are not otherwise unique to Delta EGs. Cheers, Jon Alan Schmidt - Olathe, Kansas, USA Structural Engineer, Synechist Philosopher, Lutheran Christian www.LinkedIn.com/in/JonAlanSchmidt / twitter.com/JonAlanSchmidtTitle: Delta Abstract
Delta Graphs: The Logic of Pragmatism
John F. Sowa
Abstract, 18 March 2024
Abstract.
In December 1911, C. S. Peirce proposed a major innovation for
existential graphs: I shall now have to add a Delta part in
order to deal with modals. He wrote the draft in an unfinished
letter, but he included enough detail to show how Delta graphs may be
used in an investigation. As an important hint, the intended
recipient of the letter was Allan Risteen. The text of the letter,
supplemented with information about Risteens expertise and Peirces
writings on pragmaticism, indicates that the phemic sheet of a Delta
graph is a tree of multiple papers, each of which use metalanguage
to describe a different time, aspect, or modality of a universe of
discourse. Features in other 1911 manuscripts provide evidence for
missing details. Developments in the future complete the picture.
Peirce’s use of metalanguage for complex reasoning is consistent
with theoretical and computational methods in the late 20th and early
21st centuries. Once again, he had anticipated innovations in logic
by his successors.
1. Logic for a Proof of Pragmatism
2. The Visit by Risteen
3. Specification of Delta Graphs
4. The IKRIS Project and the IKL Logic
Appendix: Letter to Risteen, L376
My dear Risteen:
A Diagrammatic Syntax. I mentioned to you, while you were [here] last year, that I have a diagrammatic syntax which analyzes the syllogism into no less than six inferential steps. I now describe its latest state of development for the first time. I am glad to think that my account of it will have one such a reader as you. C.S.P.
This syntax, which I have hitherto called the “system of Existential Graphs”, was suggested to me in reading the proof sheets of an article by me that was published in the Monist of Jan. 1897; and I at once wrote a full account of it for the same journal. But Dr. Carus would not print it. I gave an oral account of it, soon after, to the National Academy of Sciences; and in 1903 for my audience of a course of Lectures before the Lowell Institute, I printed a brief account of it. An account of slightly further development of it was given in the Monist of Oct. 1906. In this I made an attempt to make the syntax cover Modals; but it has not satisfied me. The description was, on the whole, as bad as it well could be, in great contrast to the one Dr. Carus rejected. For although the system itself is marked by extreme simplicity, the description fills 55 pages, and defines over a hundred technical terms applying to it. The necessity for these was chiefly due to the lines called “cuts” which simply appear in the present description as the boundaries of shadings, or shaded parts of the sheet. The better exposition of 1903 divided the system into three parts, distinguished as the Alpha, the Beta, and the Gamma, parts; a division I shall here adhere to, although I shall now have to add a Delta part in order to deal with modals. A cross division of the description which here, as in that of 1903, is given precedence over the other is into the Conventions, the Rules, and the working of the System.
The Conventions. The ultimate purpose of contriving this diagrammatic syntax, is to enable one with facility to divide any necessary, or mathematical, reasoning into its ultimate logical steps. It is more accurate to call such reasoning “necessary” than to call it “mathematical”; but the latter designation will give a person who recognizes that not all mathematical reasonings have to do with quantity, but who has happily not received any of the sort of instruction in Logic that is now usually given, a better notion of what is meant than if the reasoning of the kind meant were described as “necessary”.
For example, all sound reasoning in applying the doctrine of chances belongs to the class of reasonings meant; and all such reasoning is truly “necessary” reasoning,that is to say, what it concludes must necessarily (i.e. would always) be true, provided its “premisses”, or the hypotheses upon which it is based, be true. But because what it reasons about is probability,concluding that such and such an event would always, under such and such circumstances, have a stated probability, a person unfamiliar with the theory of reasoning might very naturally take it for probable reasoning. But I usually designate the kind of reasoning in question as Deductive Reasoning, or Deduction, so giving this word a broader meaning than many logicians do.
If I am asked how a person can, in deductive reasoning, be absolutely certain that his conclusion is true, if his premisses are so, I answer that in point of fact he is not. One can never be absolutely certain of anything. All men make mistakes in addition and multiplication, for example; and they may repeat the same mistakes in going over the computation a second time. Consequently, however improbable it may be, it is possible, strictly speaking, that the same mistake should be repeated a million of million of times. This may have happened,ridiculous as it would be really to suppose so,every time that anybody undertook to say how many twice two came too. Absolute accuracy is beyond human powers. But a phrase often used in reference to deductive reasoning expresses correctly the nature of such approach to certainty as we can attain. Namely, it is often said that the reasoner must admit the deductive conclusion from his own premisses, or “fall into self-contradiction”. That is precisely the essence of Deduction: the fact which its conclusion asserts, if it is a logically perfect deduction, was already asserted in its premisses,not, usually, in either one, but in the totality of the premisses taken together.
By means of the accurate _expression_ of the meanings of premisses and conclusions in this diagrammatic syntax, it will be made clear whether or not the nature of deductive [reasoning] really be such as I say it is.
One obvious reason for doubting the theory is that it would seem to render any valid deductive conclusion instantaneously evident upon an examination of the premisses; so that mathematics would be almost too simple a thing to be dignified by the name of a science, in strange conflict with the known reputation of that science as being the most difficult of all the sciences. But the theory ought not to be condemned upon this ground alone, without careful analysis of the reasonings of mathematics, since there are two reasons for believing that a science where reasonings should be of the sort that the theory supposes might have all the difficulty that mathematics has.
The first of these reasons is that if certain propositions of such a science were of such extreme complexity, owing to the great number of individual objects almost exactly alike of which the premisses might make assertions, these assertions at the same time each of them dealing with many such objects, the result might be, if there were many such premisses, that almost any mind would become confused in considering them; so that it might readily happen that it should become far from an easy matter for a person to determine offhand whether a given state of things, only describable in a similarly confusing way, had been asserted to exist or not. Now it cannot be denied that one is frequently confronted in mathematics with situations of the character of that which has just been described. Whoever has read or tried to read Jordan’s Traite des Substitutions, or Gauss’s six demonstrations of the fundamental theorem of algebra, or a great deal of the Mecanique celeste must acknowledge it. But this is not all.
My second reason is found in the peculiar character of mathematical postulates. These pronounce that certain things are possible. But these possibles are not, of course, single things, for a single thing must be more or less than possible: they embrace whole infinite series of infinite series of objects in each postulate; and it is upon the statement of the possibility of one single one of those objects or single one for each set of certain others, that some essential part of the conclusion is founded. How many demonstrations, for example, and very simple ones too, as mathematics goes, depend, each of them, upon the possibility of a single straight line; while this possibility is only asserted in the postulate that there is, or may be, a straight line through any two points of space. In that statement the possibility of every single straight line in space is asserted, including the single one whose existence is pertinent and concerning which a similar postulate directly or mediately asserts something which is an essential ingredient of the conclusion.
The Phemic Sheet. Since the sole purpose of the Syntax I am describing is to facilitate the anatomy, and thereby the physiology of deductive reasonings, the reader will have anticipated the fact that no occasion has been found for supplying it with any means of expressing mere feelings or complexes of mere feelings, such as abound in the arts of music and of painting. Nor has any need been found for furnishing it with means of expressing commands,not even such as take the softened forms of requests and inquiries. We need only a mode of indicating that what is “scribed”, i.e. is marked, whether by coveting or drawing or by a mixture of these two arts, is meant, and is not scribed for some other purpose, as, for example, to show how it might be asserted.
Moreover, however minutely we may analyze our assertions, there will never be the slightest need of any such fragment of meaning as that of a noun or that of an English verb. The simplest part of speech which this syntax contemplates, which, as scribed, I shall term a blot (a vocable I choose because it is cognate with Greek [Gr.] floid, for which see L.& S. p. 1692, under [Gr.] flao, where many words containing this root are given; and there are many others in all European languages] is itself an assertion. Ought it to be an affirmation or a denial? A denial is logically the simpler, because it implies merely that the utterer recognizes, however vaguely, some discrepancy between the fact and the speech, while an affirmation implies that he has examined all the implications of the latter and finds no discrepancy with the fact. This is a circumstance to be borne in mind; but since the denial implies recognition of the affirmation, while the affirmation is so far from implying recognition of the denial, that one might imagine a paradisaic state of innocence in which men never had the idea of falsity, and yet might reason, we must admit that affirmation is psychically the simpler. Now I think that upon this point we must prefer psychical to logical simplicity. I therefore make the blot an affirmation. The subject of it must for simplicity be completely indefinite. The simplest blots, which are not relative, are such as `it snows', `it thunders', etc.
All thought, which is the process of forming, under self-control, an intellectual habit, requires two functionaries; an utterer and an interpreter, and though these two functionaries may live in one brain, they are nevertheless two. In order to distinguish the actual performance of an assertion, though it be altogether a mental act, from a mere representation or appearance, the difference between a mere idea jotted down on a bit of paper, from an affidavit made before a notary, for which the utterer is substantially responsible, I provide my system with a phemic sheet, which is a surface upon which the utterer and interpreter will, by force of a voluntary and actually contracted habit, recognize that whatever is scribed upon it and is interpretable as an assertion is to be recognized as an assertion, although it may refer to a mere idea as its subject.
If “snows” is scribed upon the Phemic Sheet, it asserts that in the universe to which a special understanding between utterer and interpreter has made the special part of the phemic sheet on which it is scribed to relate, it sometime does snow. For they two may conceive that the “phemic sheet” embraces many papers, so that one part of it is before the common attention at one time and another part at another, and that actual conventions between them equivalent to scribed graphs make some of those pieces relate to one subject and part to another.
Any visible form which, if it were scribed on the phemic sheet would be an assertion is called a graph. If it actually be so scribed, it would be incorrect to say that the graph itself is put upon the sheet. For that would be an impossibility, since the graph itself [is] a mere form, an abstraction, a “general”, or as I call it a “might be”, i.e. something which might be if conditions were otherwise than they are; and in that respect it [is] just like a “word”, any word, say camel. (Not that it is right to pronounce a might-be to be a fiction, or to deny its reality without other reason than that it is a mere might-be. For what do we mean by real? The legal sense, that in which we speak of “real” estate, is a good deal older than the ordinary sense. This latter, though I have once or twice met with it in older writings,it is such a natural formation from res,may be said with substantial truth to have been introduced by Duns Scotus, who died, if I recollect the exact date (it can only be a few years out) in 1309. It only came slowly into use, outside of the Scotists, because “in re” etc. were used instead. It would be no use quoting Scotus in order to fix the meaning: that would but render confusion worse confounded. The best way is to analyze our own meaning in some of the many common phrases in which we use it. What would a man have in his mind who should inquire whether Sancho Panza was a real person? Observe that his phrase may be “Is Sancho Panza a real character”. He knows well enough that he cannot now be living or existent. But that does not affect his Reality. Is it really true, or, in other words, “is it a Real fact”, that two brothers founded Rome? If the nature of it is such that its being depends upon how ancient historians have thought, that comes pretty nearly to the same thing as its not being “Real”, or “in re”, as the scholastics would have said.)
Yet this would not hold in all cases; since it is certainly a Real fact that I had a dream last night,a pretty rare occurrence with me. Yet the truth of this consisted in my thinking, in a general sense (that is, imagining) something. On the other hand, Kant’s holding that such concepts as cause etc. are merely due to the nature of the human mind is not considered by him, and certainly ought to be considered any reason for pronouncing “cause” etc. not to be Real. Most philosophers, nowadays, would, on the contrary, think, as I certainly do, that if it were absolutely certain that anything,Time, for example,were a mental phenomenon of mental origin due to the structure of the human mind in such a way that no man could ever by any possibility escape from the idea of events owing in time, that would constitute the reality of time. For the real universe in which man lives is the system of those ideas which research, carried far enough, would ultimately establish. If, on the other hand, all that is true concerning a given object is due to how an individual man, or an individual collection of men happened to think, and that not about other things, as in the case of the dream, but how they happened to think about the very fact or thing whose reality is in question, then plainly the very being and truth of that object is a mere accident of thought; and all we have to do is to stop thinking about it, not only to cause the cessation of its being, but to cause it to cease from ever having been; and that sort of thing we all call unreal. Now a great many people believe the laws of nature are little more than that. They think that Sir Isaac Newton not merely discovered gravitation but that he created it. No less a person than Dr. Karl Pearson says so in plain terms in his Grammar of Science. They do not think, and recognize themselves that they do not believe, that there really are any laws, or regularities in Nature. I do not agree with them. John Stuart Mill who thought nearly as Pearson does, so far differed on that point that he thought the whole truth of Inductive reasoning,not the fact that there are such truths, but that our observations afford any good reason for believing Inductive conclusions, to be likely to be more or less true,is that it is a fact, whether the reasoner knows it or not, that under exactly the same circumstances, the same thing always occurs. I think that is no sound reason for believing in induction as a sound way of reasoning, because, in so far as we have any reason for such a pronouncement (and as a general proposition nothing can be more false), we only know it as an inductive conclusion. It is as the veracity of a witness were in question, and in his defence a lot of others were put on the stand, and on cross-examination it were found that all they knew of the suspected witness’s veracity was what he himself had told them. But if I could have had an opportunity of tackling Mill, who had in him the stuff to make a philosopher, but who had taken his philosophic creed ready made from Bentham and from his father, James Mill, having no reading in philosophy to speak of, and who, while he was
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References
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