Gary F, Jon, John, list, I have just recently returned from a trip abroad where I had little Internet access, and so I have only today read through once all the posts in this thread. I have found yours, Jon's and John's of particular interest. Your post today was especially valuable in helping to clarify for me some of the matters concerning EGs about which I've had some considerable confusion. In particular, I found these comments of yours especially helpful.
GF: The “Bedrock” draft seems to represent the end of this process, where Peirce finally had to admit that modalities could not be *iconically* represented in the EG system, especially if *cuts* and the *areas* inside them had to represent *both modality and negation*. The problem with cuts as modalities is the same as the problem with Selectives, that they were symbolic rather than iconic: their interpretation had to be guided by explicitly verbalized rules and conventions rather than the nonverbal iconicity which was supposed to be the main advantage of of Existential Graphs over other notation systems. From 1908 on, as far as I can tell, his presentations of EGs used the cuts for negation only, and dropped the issue of modality altogether. and GF: As you can see, Peirce introduces this argument with a reference to “failure of Selectives to be as analytical as possible,” but it goes deeper than that: it shows the failure of *the scroll*, or cut within a cut, to be as analytical as possible. But it was from the scroll that the interpretation of cuts as negations was derived. This implies that the cuts, as a feature of EGs, were themselves neither as analytical nor as iconic as Peirce had thought they were in 1903. They are symbolic, in that it has to be stipulated that they should be read as negations, as this is not visually (or in an optico-muscular way) evident to anyone who looks at them. It is not surprising, then, that EGs underwent no further development after this point (although Peirce continued to recommend them, for instance to Lady Welby, as useful for the purpose of logical analysis). At the moment I will only remark that it is is becoming increasingly clear to me from just the above comments (most especially the first, and the Peirce quotes you were commenting on there) that Peirce would necessarily have had to abandon EGs for his attempted *proof of pragmatism*. After all, isn't it very much concerned with modality? One other matter which I also haven't had much time yet to reflect on has to do with a distinction Jon's been making for some time now between the three Universal Categories (1ns, 2ns, 3ns) discovered in Phenomenology and three Universes of Experience mentioned near the opening of "A Neglected Argument. . ." In a note yesterday to the members of a NYC philosophy club I belong to, I wrote: One matter being considered in that discussion [i.e., this thread], and which I'd be interested in your thoughts on at our next meeting, is whether the Three Universal Categories are transmuted into Three Universes of Experience in sciences further down in Peirce's Classification of Sciences, or whether (by "the principle of principle") Phenomenology is but providing a trichotomic principle to other sciences [further down in the classification]. Also, if Peirce does intend to establish three Universes of Experience in some sense [significantly] different from the categories, are these first located in Logic as Semeiotic [as Jon seems to be saying] or are they best located in Metaphysics (suggested by Peirce's using that phrase in the Neglected Argument). Or both? In any event, I for one am finding this on-going discussion both of interest and value. Best, Gary R *Gary Richmond* *Philosophy and Critical Thinking* *Communication Studies* *LaGuardia College of the City University of New York* On Wed, Mar 6, 2019 at 11:37 AM <[email protected]> wrote: > List, > > Peirce’s most complete draft of “The Bed-Rock Beneath Pragmaticism” ( > http://gnusystems.ca/Bedrock.htm) includes a long section beginning on p. > {31} about the problems with *Selectives* as components of the system of > Existential Graphs. *Selectives* were introduced in the 1906 *Prolegomena* > at http://gnusystems.ca/ProlegomPrag.htm#4561 to deal with notational > problems arising from a Line of Identity (or Ligature) crossing a cut (or > another Ligature). But as Peirce explained in “Bedrock”: > > [[ Selectives violate the essential idea, or {33} purpose of The System, > Existential Graphs, as it is stated in the *Prolegomena*; namely, to > afford a method (1) as *simple* as possible (that is to say, with as > small a number of arbitrary conventions as possible), for representing > propositions (2) as *iconically*, or diagrammatically and (3) as > *analytically* as possible. … These three essential aims of the system > are, every one of them, missed by Selectives. ]] > > One of the problems Peirce pointed out pertains not only to Selectives but > to the interpretation of the cuts themselves. Up until April of 1906, a cut > (a lightly drawn line around a graph) was to be interpreted as *negation*. > This interpretation was considered iconic by Peirce because it was derived > from the *scroll* — the most basic of all diagrams in the EG system — as > Peirce explained in Lowell Lecture 2 (1903), at > http://gnusystems.ca/Lowell2.htm#scrl . The gist of his argument, using > the example he gives there, is as follows: > > Suppose we want to make a graph-replica asserting a conditional > proposition such as [If it rains, a pear is ripe.] This is intended to be a > conditional *de inesse*, i.e. no modality is involved in the logical > relation. We make a cut on the sheet of assertion which separates the *area > inside the cut* from whatever is *asserted* on the sheet. This area > represents a “universe of supposition” as opposed to the “universe of > discourse” represented by the sheet of assertion itself; and this implies > that anything scribed on the area inside the cut is thereby *denied*. > > Now we scribe on that area [It rains], *and* another cut inside the first > cut but *not* including [it rains]. On the area inside this inner cut we > scribe [a pear is ripe]. The inner cut being scribed on the area of the > outer cut amounts to a *denial of the denial* — and since no modality is > involved, a denial of a denial amounts to an *assertion*. So we read the > whole graph as saying that [a pear is ripe] can be asserted on the > condition that the area in which it is written is *enclosed *by the area > in which we *suppose* that [it rains.] By reading both cuts as signifying > negation, we can translate the whole graph into English this way: “It is > not true that it rains and that no pear is ripe.” This is logically > equivalent to saying that “If it rains, a pear is ripe” — assuming that we > treat it that statement as a conditional *de inesse* (not as a fallible > observation of empirical causation). > > The above paragraph is all about Alpha graphs. In Beta graphs we introduce > the icon of the Line of Identity, and this introduces a problem: how do we > interpret a line of identity that crosses a cut, if the cut signifies > negation? Peirce was stumped by this at first, so he made a rule in 1903 > that a graph, such as a line of identity, simply *cannot *cross a cut. > But he changed his mind in writing up a presentation to the National > Academy of Science given in April 1906 (CP 4.573-84, but see Roberts 1973, > 88 ff. for the date). Here he began calling the area inside a single cut > the *verso*, and rethinking what it represented. This led to a subtly > different explanation of why it signified negation of its contents: > > [[ The *verso* is usually appropriated to imparting information about > *subjective > possibilities* or what may be true for aught we know. To scribe a graph > is to impart an item of information; and this item of information does one > of two things. It either adds to what we know to exist or it cuts off > something from our list of subjective possibilities. Hence, it must be that > a graph scribed on the *verso* is thereby denied. ] CP 4.574 ] > > But it also led Peirce to a “new discovery” about the interpretation of > EGs: > > [[ The new discovery which sheds such a light is simply that, as the main > part of the sheet represents existence or actuality, so the area within a > cut, that is, the *verso* of the sheet, represents a kind of possibility. > > From thence I immediately infer several things that I did not understand > before, as follows: > > First, the cut may be imagined to extend down to one or another depth into > the paper, so that the overturning of the piece cut out may expose one > stratum or another, these being distinguished by their tints; the different > tints representing different kinds of possibility. > > This improvement gives substantially, as far as I can see, nearly the > whole of that Gamma part which I have been endeavoring to discern. ]] > > Peirce jumped to the conclusion that he could use various kinds of cuts to > represent various *modalities* as well as negation. Over the next year or > so he experimented with various ways of doing this, including the > “tinctures” of the 1906 *Prolegomena* and several types of “broken cuts.” > This coincided with a change of plan for his *Monist* series on > Pragmatism: he decided to base his “proof” of pragmaticism on the > Existential Graphs, specifically the Gamma graphs which he thought capable > of analyzing modal logic. > > The “Bedrock” draft seems to represent the end of this process, where > Peirce finally had to admit that modalities could not be *iconically* > represented in the EG system, especially if *cuts* and the *areas* inside > them had to represent *both modality and negation*. The problem with cuts > as modalities is the same as the problem with Selectives, that they were > symbolic rather than iconic: their interpretation had to be guided by > explicitly verbalized rules and conventions rather than the nonverbal > iconicity which was supposed to be the main advantage of of Existential > Graphs over other notation systems. From 1908 on, as far as I can tell, his > presentations of EGs used the cuts for negation only, and dropped the issue > of modality altogether. > > In my opinion, the part of the Bedrock draft which makes the point most > clearly is the part in which Peirce explains why he regards logical > *sequence* as simpler than logical *negation*. This implies that the > *scroll*, read like the one above (“It is not true that A is true and B > is false”), is *not analytical enough* as a representation of “If A then > B.” Here is the passage from “Bedrock”: > > [[ The second failure of Selectives to be as analytical as possible lies > in their encouraging the idea that negation, or denial, is a relatively > simple concept, and that the concept of Consequence, is a special composite > of two negations, so that to say, “If in the actual state of things A is > true, then B is true,” is correctly analyzed as the assertion, “It is false > to say that A is true while B is false.” I fully acknowledge that, for most > purposes and in a preliminary explanation, the error of this analysis is > altogether insignificant. But when we come to the first analysis the > inaccuracy must not be passed over. All my own writings upon formal logic > have been based on the belief {48} that the concept of Sequence, alike in > reasonings and in judgments, whether the latter be conditional or > categorical, could in no wise be replaced by any composition of ideas. For > in reasoning, at least, when we first affirm, or affirmatively judge, the > conjugate of premisses, the judgment of the conclusion has not yet been > performed. There then follows a real movement of thought in the mind, in > which that judgment of the conclusion comes to pass. Now surely, speaking > of the same A and B as above, it were absurd to say that a real change of A > into a sequent B consists in a state of things that should consist in there > not being an A without a B. For in such a state of things there would be no > change at all. {49} This judgment is, at first, no more than a copy, or > “generalized” icon (with a symbolic “legend,” or label, indexically > attached to it), of that experience of having been constrained by the > supposition of A to join to that the acknowledgment of the truth (in the > case supposed), of B. Consequently, since the real sequence, as we have > seen, cannot be adequately represented as merely a composite of two > negations, no more can the copy [of] it, which is substantially the > *concept* of the sequence. It is but very rarely that a proof as > satisfactory as this, that a given concept is not composite, can be > obtained. ]] > > As you can see, Peirce introduces this argument with a reference to > “failure of Selectives to be as analytical as possible,” but it goes deeper > than that: it shows the failure of *the scroll*, or cut within a cut, to > be as analytical as possible. But it was from the scroll that the > interpretation of cuts as negations was derived. This implies that the > cuts, as a feature of EGs, were themselves neither as analytical nor as > iconic as Peirce had thought they were in 1903. They are symbolic, in that > it has to be stipulated that they should be read as negations, as this is > not visually (or in an optico-muscular way) evident to anyone who looks at > them. It is not surprising, then, that EGs underwent no further development > after this point (although Peirce continued to recommend them, for instance > to Lady Welby, as useful for the purpose of logical analysis). > > I’ll stop here and invite comments, and (finally!) get back to responding > to Jon’s posts in this thread. > > Gary f. > > > > ----------------------------- > PEIRCE-L subscribers: Click on "Reply List" or "Reply All" to REPLY ON > PEIRCE-L to this message. PEIRCE-L posts should go to > [email protected] . 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