The Peirce Blog
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Friday, July 10, 2009

Stanley on Peirce

I've found William A. Stanley's 1978 Peirce essay online at http://www.publicaffairs.noaa.gov/history/peirce.html. (If I had missed it before, so did the Wayback Machine, which still has no record of it, though it does have things from that Website.)

I first learnt of the essay's existence through online searches for books related to Peirce. Here's the info which I had eventually compiled at the Charles Sanders Peirce bibliography:
Stanley, William A. (1978), Charles Peirce, scholar, cartographer, mathematician, and metrologist: An American philosopher, National Oceanic and Atmospheric Administration, NOAA Reprint, v. 8, no. 2, 4 pages. Reprinted 1986, U. S. Department of Commerce.
Stanley, a Peirce Edition Project advisor, headed the NOAA's history division until it was shut down in 1994 http://www.iupui.edu/~peirce/news/1_1/1_1x.htm#surv.

Friday, June 26, 2009

Don't look now, but

Arisbe has been growing. Joseph Ransdell has been adding numerous texts of manuscripts by Peirce. Joe has been tracing the development of Peirce's pragmatic conception of truth back through Peirce's draft texts on logic.

From from Joe's June 17, 2009 peirce-l post:

...for those especially interested in this topic, let me list the manuscripts especially relevant to this, all of which are available from the website ARISBE, with a brief indication of what to look for in them. I list them more or less in the order I will be dealing with them (a number of them being quite short, by the way):
Joe then lists a number of manuscript texts. Here they are in the same order but also with their names (not necessarily assigned by Peirce) and online locations, plus links. Seasons and months of the year are mostly from Joe's peirce-l post. Annotations are Joe's from Arisbe.


  • MS 164 Winter 1869-70: Lessons in Practical Logic. PEP.
  • MS 165a Winter 1869-70: A Practical Treatise on Logic and Methodology. PEP.
  • MS 165b Winter 1869-70: Rules for Investigation. PEP.
    Introductory paragraphs for a logic text based on idea that the aim of reasoning is to arrive at a settled opinion.
  • MS 165c Winter 1869-70: Practical Logic. PEP.
    First formulation of inquiry as settlement of opinion with choice of methods, with only two methods recognized.
  • MS 166 Winter 1869-70: Chapter 2. PEP.
  • MS 171 Spring 1870: Notes for Lectures on Logic to be given 1st term 1870-71. Arisbe.
    Logic described as based on concept of a sign.
  • MS 179 Winter-Spring 1872: Logic, Truth, and the Settlement of Opinion. Arisbe.
    First statement of four methods model
  • MS 189 May-June 1872: Chapter 4: Four Methods of Settling Opinion.
  • MS 209 April 1872: [I can't an MS either 209 or April 1872 at Arisbe.]
  • MS 200 Fall 1872: Of Reality. Arisbe.
  • MS 204 Fall 1872: Chapter IV. Of Reality. Arisbe.
  • MS 208 March 10th, 1873: [I can't find this at Arisbe. Maybe Joe means MS 218? Joe comments on MS 218 below. Anyway, here's the MS 218 title and annotation at Arisbe: MS 218 (March 1873) Chap. 6th.
    Chiefly conncerned with causal connection between sign and object, thought and the thing to which it relates; the hardness of the diamond as what will happen under certan conditions.]
  • MS 233 Spring 1873: Chap. XI. On Logical Breadth and Depth. Arisbe.
Joe then continues:

When I get back, I will be replacing some of these with more legible versions which Jerry Dozoretz and I have been working on, intermittently, in the past year or so; but these will do for the moment. Discussion can be deferred altogether until I get back, but in case anybody wants to go ahead and get into it before then, I will just try to indicate what to look for in them. I suggest that even the early and apparently least informative of these fragments should be read very carefully with a eye to noticing the way in which Peirce initially announces that logic is concerned with the investigation of truth, while at the same time showing much hesitation about the wisdom of thinking of it that way and actually going ahead at first to describe the aim of logic in such a way as to make no use of the concept of truth at all and describing logic instead as being the general theory of inference, sometimes stating more specifically that it is the theory of the syllogism, sometimes that it is the theory of consequences (which was a way of doing logic developed in the 13th Century), which he regarded as an alternatively equivalent way of representing inference. Then when he does first introduce the idea of inquiry as originating in doubt and the insistent need to escape it by a "settlement of opinion", which is where the conception of truth first becomes operative in his account of logic, notice that he at first talks as if treating the aim of inquiry as settlement of opinion is not actually the same as regarding it as pursuit of truth but is to be regarded rather as a substitute for doing so, enabling us to avoid getting lost in the usual philosophical wrangling over what truth is. But this reticence doesn't last, as you will see.

MS 218 is the most extensively developed account of the pragmatic conception of truth in these manuscripts, but I suggest that to get the hang of his thinking you bear down instead very closely on what he is saying in the first few items in the list above, for it is in doing this that you can see his thought in the process of development from a quite crude and implausible initial statement to an increasingly careful one as he reformulates the conception again and again.

MS 171 is also worth special mention. It is not actually a part of the MS material for the projected logic book, but rather a page of lecture notes for a course he was to teach; but it is conceptually of a piece with the Logic book and in it he makes the peculiar (and mind-boggling) nature of his idealism clear when he concludes by saying:

"The real thing is the ultimate opinion about it. About IT, that is, about the ultimate opinion, but not involving the reflection that the opinion is itself that ultimate opinion and is the real thing."
Joe has also added a number of things by Peirce which he doesn't mention in the peirce-l post. If you haven't gone there lately, you might wish to take a look.

Update June 27, 2009: MS 165 contains an untranslated Latin quote from Summulae Logicales written circa the early 1230s by Petrus Hispanus (who became Pope John XXI):

Dialectica est ars artium scientia scientiarum, ad omnium methodorum principia viam habens. Sola enim dialectica probabiliter disputat de principiis omnium aliarum scientiarum.
The word summulae means "small sums." Hispanus intends by it "small summaries." Anyway here is my amateur translation of the passage, as close to word-for-word as I can make it (enim means "for indeed"):
Dialectic is [the] art of arts, science of sciences, having [the] way to all methods’ principles [or sources] . For alone indeed dialectic credibly argues about [or from] principles of all other sciences.
Update June 27, 2009, around 10pm ET: MS165b "Rules for Investigation" says
If a sufficiently long course of experience and reasoning will produce a settlement of opinion, this final opinion is the only legitimate aim of experience and reasoning. For this is all that experience and reasoning really tend to. If experience and reasoning will not lead to a final settlement of opinion, they lead to nothing, and can have no legitimate object. In any case, therefore, the only legitimate aim of experience and reasoning is to reach the final opinion, or in other words to ascertain what would be the ultimate result of sufficient experience and reasoning.
It makes you wonder what Peirce means by "experience." There are the definitions of Experience from the 1900s in the Commens Dictionary of Peirce's Terms. Then there is the definition of "Experience," also viewable at http://peircematters.blogspot.com/#experience_n, in the Century Dictionary. It appears under "E" in PEP UQÀM's list of words whose definitions Peirce wrote or reviewed. Here are excerpts:
1. The state or fact of having made trial or proof, or of having acquired knowledge, wisdom, skill, etc., by actual trial or observation; also, the knowledge so acquired; personal and practical acquaintance with anything; experimental cognition or perception: as, he knows what suffering is by long experience; experience teaches even fools.

2. In philos., knowledge acquired through external or internal perception; also, the totality of the cognitions given by perception, taken in their connection; all that is perceived, understood, and remembered. Locke defines it as our observation, employed either about external sensible objects or about the internal operations of our minds, perceived and reflected upon by ourselves. The Latin experientia was used in its philosophical sense by Celsus and others, and in the middle ages by Roger Bacon. It translates the Greek empeiría of the Stoics. See empiric.

Specifically—3. That which has been learned, suffered, or done, considered as productive of practical judgment and skill; the sum of practical wisdom taught by all the events, vicissitudes, and observations of one's life, or by any particular class or division of them.

4. An individual or particular instance of trial or observation.

5 (Obs.). An experiment.

6. A fixed mental impression or emotion; specifically, a guiding or controlling religious feeling, as at the time of conversion or resulting from subsequent influences.

= Syn. Experience, Experiment, Observation.

Experience is strictly that which befalls a man, or which he goes through, while experiment is that which one actively undertakes. Observation is looking on, without necessarily having any connection with the matter: it is one thing to know of a man's goodness or of the horrors of war by observation, and quite another to know of it or them by experience. To know of a man's goodness by experiment would be to have put it to actual and intentional test. See practice.

Peirce in "Lectures on Pragmatism", CP 5.51, 1903 (see the Commens "Experience" link above), says of experience:

In all the works on pedagogy that ever I read — and they have been many, big, and heavy — I don't remember that any one has advocated a system of teaching by practical jokes, mostly cruel. That, however, describes the method of our great teacher, Experience. She says,
  Open your mouth and shut your eyes
  And I'll give you something to make you wise;
and thereupon she keeps her promise, and seems to take her pay in the fun of tormenting us." ('Harvard )
Reviewing the Century Dictionary and Commens Dictionary definitions, my sense of it is that Peirce uses the word "experience" with some variation in feeling, but still with a narrower sense than the word came to have during the 20th Century, such that it could easily refer to whatever a person is cognitively or affectively aware of undergoing, or to the raw subjective undergoing itself.

Friday, May 8, 2009

Peirce and the problem of the single case

I just ran into this April 30, 2009 post "Peirce and the Problem of the Single Case" by Jonah Schupbach at the blog Choice & Inference. It's always fun to take a look at what people are saying about Peirce's ideas, and there are a number of comments on the thread there.

The question is that of how probabilities can be meaningful in a single case. Peirce's example is that of a man who must pick one card either (1) from a deck correctly identified to him as containing 25 white cards and 1 black card or (2) from a deck correctly identified to him as containing 25 black cards and 1 white card. The man will go straight to heaven if he picks a white card and straight to hell if he picks a black card, so there will be no repetition by him of the "experiment." Obviously he should pick from the deck with 25 white cards and 1 black card but, Peirce asks, what consolation can be given to the man if he mischances to draw the single black card from the deck with 25 white cards and 1 black card? Peirce says ("The Doctrine of Chances", 1878, CP 2.652, EP 1:142-154), "He might say that he had acted in accordance with reason, but that would only show that his reason was absolutely worthless." Peirce goes on to say:
[...] in the case supposed, which has no parallel as far as this man is concerned, there would be no real fact whose existence could give any truth to the statement that, if he had drawn from the other pack, he might have drawn a black card. Indeed, since the validity of an inference consists in the truth of the hypothetical proposition that if the premisses be true the conclusion will also be true, and since the only real fact which can correspond to such a proposition is that whenever the antecedent is true the consequent is so also, it follows that there can be no sense in reasoning in an isolated case, at all.
This ties into Peirce's theme that logic is rooted in the social principle and that one must identify oneself with a larger community, even though, as Peirce says elsewhere with possibly a pun alluding to himself, "For an individual whose purse is finite, there really is no such thing as the 'long run' of probabilities."

Now, maybe I'm a dumb bunny, but I must confess that I've never seen the sting of the single-case probability problem, aside from the sting of losing suffered by the man who bets wisely in the scenario. In a universe anything like ours, there will be indefinitely many situations involving 25-1 odds. I don't see why the drawing by a particular individual of a card from a particular deck should be considered a unique instantiation of 25-1 odds even though he cannot repeat the act; and it seems to me that he and anybody else would take all such cases into account, howsoever multiform such cases are, as being governed, in their collective run, by the law of probability; The repetition of exact same actual conditions for a coin flip or a card draw is impossible anyway. One considers idealized cases to which the actual approximates. And if there were not indefinitely many such actual cases, what practical assurance would one have about how the deck is stacked in one way or another in this case? As in Peirce's example, one would need a divine revelation.

So I come to a conclusion, not only like Peirce, that there can be no sense in reasoning about probability in a genuinely isolated case, but also that in a sufficiently isolated case no probability is involved. The conception of a simple, isolated universe consisting of nothing 26 equiprobable options for just one choice ever to be made, implies a degree of determination within that universe which bursts the bounds of that supposed simplicity; the conception merely veils it, or so I figure. So, one needs to take the view not only of an indefinitely large community, but of being ultimately in an indefintitely large universe, which sounds almost like a tautology now that I say it; I mean, one won't find an indefinitely large community in a universe that isn't indefinitely large.

Well, the thought of having actually to defend certain of the ideas that I've stated here makes me feel unsure of my chances. But I'll post it anyway, nobody's posted here for over two weeks!

Saturday, April 18, 2009

What is meant by 'in the mind'? (part 3)

In the third of his 1903 Lowell Lectures, Peirce has the highest praise for Kant (CP 1.522). Yet he includes Kant in his remark that ‘all modern philosophy of every sect has been nominalistic’ (CP 1.19). ‘Kant was a nominalist; although his philosophy would have been rendered compacter, more consistent, and stronger if its author had taken up realism, as he certainly would have done if he had read Scotus’. Of course Peirce himself was a realist, as he went on to explain (CP 1.20):

In a long notice of Frazer's Berkeley, in the North American Review for October, 1871, I declared for realism. I have since very carefully and thoroughly revised my philosophical opinions more than half a dozen times, and have modified them more or less on most topics; but I have never been able to think differently on that question of nominalism and realism.

According to Peirce's Berkeley review, a realist like himself will ‘deny that there is any reality which is absolutely incognizable in itself, so that it cannot be taken into the mind’ (CP 8.13). Thus he would reject the idea of a ‘Kantian thing-in-itself’ (CP 6.108, 1892). Is this where Peirce parted company with Kant? He wrote in 1905 that the ‘Kantist has only to abjure from the bottom of his heart the proposition that a thing-in-itself can, however indirectly, be conceived; and then correct the details of Kant's doctrine accordingly, and he will find himself to have become a Critical Common-sensist’ (CP 5.452).

Yet Peirce appears to take a different perspective on Kant in the 1871 Berkeley review itself (CP 8.15):

what Kant called his Copernican step was precisely the passage from the nominalistic to the realistic view of reality. It was the essence of his philosophy to regard the real object as determined by the mind. That was nothing else than to consider every conception and intuition which enters necessarily into the experience of an object, and which is not transitory and accidental, as having objective validity. In short, it was to regard the reality as the normal product of mental action, and not as the incognizable cause of it.

Is this compatible with Peirce's later remarks about Kant's nominalism and the ‘Kantian thing-in-itself’? We might try to account for the differences by guessing that he changed his mind about Kant after 1871. But in a later lecture from the same 1903 Lowell series quoted above, Peirce returned to the subject of Kant in a fashion very similar to his 1871 remarks. He did so in a passage which he described in advance as ‘so brief that only the most thorough student of philosophy could fully grasp the meaning of it at the single hearing.’ Since it is so brief, i will quote it here in full:

The first thing to be taken into consideration is the general upshot of Kant's Critic of the Pure Reason. The first step of Kant's thought – the first moment of it, if you like that phraseology – is to recognize that all our knowledge is, and forever must be, relative to human experience and to the nature of the human mind. That conception being well digested, the second moment of the reasoning becomes evident, namely, that as soon as it has been shown concerning any conception that it is essentially involved in the very forms of logic or other forms of knowing, from that moment there can no longer be any rational hesitation about fully accepting that conception as valid for the universe of our possible experience. To repeat an example I have given before, you look at an object and say ‘That is red.’ I ask you how you prove that. You tell me you see it. Yes, you see something; but you do not see that it is red; because that it is red is a proposition; and you do not see a proposition. What you see is an image and has no resemblance to a proposition, and there is no logic in saying that your proposition is proved by the image. For a proposition can only be logically based on a premiss and a premiss is a proposition. To this you very properly reply, with Kant's aid, that my objections allege what is perfectly true, but that instead of showing that you have no right to say the thing is red they conclusively prove that you are logically justified in doing so. At this point, the idealist appears before the tribunal of your reason with the suggestion that since these metaphysical conceptions, that repose upon their being involved in the forms of logic, are only valid for experience and since all our knowledge is relative to the human mind, they are not valid for things as they objectively are; and since the conception of existence is preeminently a conception of that description, it is a mere fairy tale to say that outward objects exist, the only objects of possible experience being our own ideas. Hereupon comes the third moment of Kant's thought, which was only made prominent in the second edition, not, as Kant truly says, that it was not already in the book, but that it was an idea in which Kant's mind was so completely immersed that he failed to see the necessity of making an explicit statement of it, until Fichte misinterpreted him. It is really a most luminous and central element of Kant's thought. I may say that it is the very sun round which all the rest revolves. This third moment consists in the flat denial that the metaphysical conceptions do not apply to things in themselves. Kant never said that. What he said is that these conceptions do not apply beyond the limits of possible experience. But we have direct experience of things in themselves. Nothing can be more completely false than that we can experience only our own ideas. That is indeed without exaggeration the very epitome of all falsity. Our knowledge of things in themselves is entirely relative, it is true; but all experience and all knowledge is knowledge of that which is, independently of being represented. Even lies invariably contain this much truth, that they represent themselves to be referring to something whose mode of being is independent of its being represented. This is true even if the proposition relates to an object of representation as such. At the same time, no proposition can relate, or even thoroughly pretend to relate, to any object otherwise than as that object is represented. These things are utterly unintelligible as long as your thoughts are mere dreams. But as soon as you take into account that Secondness that jabs you perpetually in the ribs, you become awake to their truth. Duns Scotus and Kant are the great assertors of this doctrine, for which Thomas Reid deserves some credit too. But Kant failed to work out all the consequences of this third moment of thought and considerable retractions are called for, accordingly, from some of the positions of his Transcendental Dialectic. Nor in other respects must it be supposed that I assent to everything either in Scotus or in Kant. We all commit our blunders.
(CP 6.95)

Perhaps it is my blunder to suggest that the various remarks about Kant quoted above are somehow incompatible. But i confess that i don't quite see how they can all be included in a single consistent view. On the other hand, i can't take very seriously the idea that Peirce changed his mind about Kant's nominalism and then changed it back again. Probably i am missing some nuances of Peirce's logic here, or just don't understand how his realism relates to Kant's nominalism. If so, maybe some intrepid blog reader (nobody else would have got this far!) can straighten it all out for me (and possibly for others too).

Even if that doesn't happen, i think the long quote just above (CP 6.95) is worth several readings, as an elucidation of Peirce's realism. So maybe that's enough to justify this post.

Monday, April 13, 2009

The Peirce Pages

In the sidebar you'll find links to a Peirce Blog adjunct The Peirce Pages at http://sites.google.com/site/cspmem/ . (I would have put "csp3" into the URL but Google Sites demands at least six characters for the folder name. The "mem" is for "memory".) Right now there are just a few things there, and I've been wondering what else I could put or start there in the short term.

Joe gave me an idea with his recent post here when he said, "...this is an excellent definition of "normal" and it should be picked up on for the Commens definitions of Peirce's terminology." If I gather enough such definitions I could start a miniature supplement to the Commens Dictionary of Peirce's Terms with the understanding that the definitions in the "supplement" would not necessarily reflect, as the Commens entries seem to reflect, a thoroughgoing search for definitions of a given word. They would be material for such, that's all.

Umm...does anybody have any other ideas? If so, please post a comment on it.

Sunday, April 12, 2009

What is meant by 'in the mind'? (part 2)

Ben's post of last Wednesday quotes a key passage from Peirce's 1871 review of a new edition of Berkeley, in which he explained the scholastic debate between realists and nominalists on the reality of universals. According to Peirce, nominalists and realists differ in their concept of reality, and ‘the distinction between these two views of the real – one as the fountain of the current of human thought, the other as the unmoving form to which it is flowing – is what really occasions their disagreement on the question concerning universals’ (EP1:91). For the nominalist, anything real must be external to the mind, and anything internal to the mind can't be also external to it. The realist also believes in an external reality, but not that an object's being internal to the mind necessarily disqualifies it as real. ‘When a thing is in such a relation to the individual mind that that mind cognizes it, it is in the mind; and its being so in the mind will not in the least diminish its external existence.’

In one of his last writings on logic, Peirce returned to the difference between reality and externality. According to the CP editors, this was written for the 1908-9 Monist series ‘Some Amazing Mazes’, but not published at the time. I would recommend reading the whole text beginning at CP 6.318, but that's a bit much for a blog post, so i will jump to CP 6.327-8:

What is meant by calling anything real? I can tell you in what sense I always use the word. According to my use of it, there is a certain resemblance between the Real and the External which renders the discrimination of each from the other important for right reason. Any object whose attributes, i.e. all that may truly be predicated, or asserted, of it, will, and always would, remain exactly what they are, unchanged, though you or I or any man or men should think or should have thought as variously as you please, I term external, in contradistinction to mental. For example, a dream is mental, because it depends upon what passed in the thoughts of the dreamer whether it be true that the dream was of a dog or was of the Round Table of King Arthur or of anything else. On the other hand, the colors of objects of human experience and in particular the contrast between the color of the petals of a Jaqueminot rose and that of the leaves of the bush, although it is relative to the sense of sight, is not mental, in my sense of that word.

[I omit here Peirce's discussion of the ‘difference between a color and a sensation of color’.]

Color, therefore, is a quite remarkably vague quality, as well as being relative to the normal sense of sight. If by ‘normal’ were meant merely the average (or any other kind of mean) of actually occurring instances, say the average sensation of all the inhabitants of the globe on a certain date, then this might have been modified by some disease affecting a large part of the people who happened to be living at the time; and since ‘color’ refers to normal chromatic sense, it would depend upon what passed in the minds of a certain body of men. But, in fact, the ‘normal’ is not the average (or any other kind of mean) of what actually occurs, but of what would, in the long run, occur under certain circumstances. Now what would be, can, it is true, only be learned through observation of what happens to be; but nevertheless no collection of happenings can constitute one trillionth of one per cent of what might be, and would be under supposable conditions; and therefore, though it might conceivably prevent many generations from rightly determining what is normal, it could not affect the true – and ultimately ascertainable (provided there were anybody to ascertain it) – mean and normal; and thus, the result is that no such accident could affect the normal or the true color. So, in general, what I mean by the external might vary with how persons of a given general description would think under supposable circumstances; but it will not vary with how any finite body of individuals have thought, do now think, or will actually think.

So much for what I mean by the external. The main difference between the external, as I use the term, and the real, as I employ that term, seems to be that the question whether anything is external or not is the question of what a word or other symbol or concept (for thinking proper is always conducted in general signs of some sort) is, I say, a question of what a symbol signifies; while the question of whether anything is real or is a figment is the question what a word or other symbol or concept denotes. If the attributes of or possible true assertions about an object could vary according to the way in which you or I or any man or actual body of single men, living at any time or times, might think about that object, then that object is what I call a figment. But if even although its attributes, or what is true of it, should possibly vary according to what some man or men might think, yet if no attribute could vary between being true and being false, according to what any plural of single men could think about that thing, then, and though it were accordingly not external but mental, it would nevertheless be real, since precisely that is what I mean by calling an object real.



This might have some bearing on the question Ben posed in the Addendum to his message: ‘what would be the practical difference between the immediate object and the dynamic object of a TRUE proposition?’ My guess is that there would be no difference at the end of inquiry, but the difference does make a difference in the actual practice of inquiry, because that process can never be known to have reached its end, which is truth itself.

I have another question arising from Peirce's Berkeley review, specifically his comments about Kant's view of reality as Peirce describes it there and in some later writings. But i'd better save that for another post.

Saturday, April 11, 2009

Peirce-picacity

My fellow four-ist (though not always the same fours!), Hyatt Carter, aware of my Peircean proclivities, has alerted me, by an email titled like this post, to an article appearing in the current issue (45.2) of The James Joyce Quarterly:
“The Index Nothing Affirmeth”: The Semiotic Formation of a Literary Mandate in James Joyce’s “The Sisters”

by Murray McArthur

My purpose in this essay is to consider certain aspects of the way James Joyce discovers and deploys the central semiotic resource of literary language, indexicality, to stage in “The Sisters” the—to adapt a Hollywoodism to Giambattista Vico’s writing—precorso of his literary mandate. [….] Specifically, I am interested in that “certain signifying formation” as it manifests itself in the disposition of the index in Joyce’s opening frame. To focus on this disposition, I want to examine closely three scenes: the first from Stephen Hero that represents directly the “certain signifying formation” of the artistic mandate and the second and third from “The Sisters.” In these scenes, the “signifying formation” disposes itself in a triune or trinitarian structure of the sign that C. S. Peirce, an American forty years older than Joyce and completely unknown to him, was defining, in his major contribution to semiotics, as the index. The index, as Peirce so strikingly describes it in the passage cited below, is itself the sign type that compels attention.

In 1903 and 1904, Peirce was beginning the last great revision of and addition to his triadic classification of the sign, starting with his Lowell Institute Lectures in Cambridge, Massachusetts, in October 1903. Peirce divided semiosis or sign-making and sign-interpreting into a firstness or icon or resemblance, a secondness or index or indication, and a thirdness or symbol or arbitrariness [….]
Quibble: (There's always a quibble.) McArthur's version of Peirce's conception of the symbol sounds more like Saussure's than Peirce's but you can't have everything. The symbol is any sign which is "arbitrary" or independent with respect to resemblance or actual connection to its object. It signifies, nevertheless, because of how it will be interpreted, that is to say that it signifies as an interpretive norm or habit (in a system of same) and is not eminently arbitrary or independent with respect either to itself, or to the symbol system in which it participates, or to logical / semiotic / representational relations to its object

Anyway, let me attempt a self-fulfilling prophecy (why should only Joe Ransdell be able to do them?). A Joycean among us desires to look into Murray McArthur's article and report back!