Gary F., List:
FYI, Ahti-Veikko Pietarinen published a more complete transcription of R
490--as well as R 498, R 499, R 669, and R 670--as "Two Papers on
Existential Graphs by Charles Peirce" in *Synthese*, 192:4 (April 2015),
881-922. The "online first" PDF version is available here
<https://www.researchgate.net/profile/AHTI_Pietarinen2/publication/271419583_Two_Papers_on_Existential_Graphs_by_Charles_Peirce/links/54c753d30cf289f0ceccf607.pdf>.
R 490 is what Peirce actually presented to the National Academy of Sciences
in April 1906, while R 498 and R 499 are earlier drafts, and Pietarinen
also inserted some "alternative pages" from another manuscript (S-36). R
669 and R 670 are two different drafts for a subsequent presentation to the
same body, scheduled for November 1911 but canceled when Peirce suffered
serious injuries in a fall at his home--an incident of which I was not
previously aware.
CSP: ... I have invariably recognized, as one great class of relations,
the class of *references*, as I have called them, where one correlate is an
existent, and another is a mere possibility ... the moment I discovered in
the *verso* of the sheet of Existential Graphs a representation of a
universe of possibility, I perceived that a *reference* would be
represented by a graph which should cross a cut, thus subduing a vast field
of thought to the governance and control of exact logic. (CP 4.579; 1906)
GF: I’m still not sure I ‘get’ what he means by a *reference* in this
context, although phaneroscopically it seems to be a relation between a
First and a Second which is not simply a dyadic relation.
Pietarinen states, "Peirce’s 1906 presentation has a good claim of making
him the founder of modern philosophical logic," citing one of its
accomplishments as establishing "the philosophical significance of ... the
idea of world-lines ('references')." That was frankly not very helpful to
me, so I poked around online and learned that "world line" is a concept in
quantified modal logic, apparently developed by Jaakko Hintikka to address
the problem of maintaining the identity of an individual over multiple
contexts.
That is only *slightly* more clarifying, but suggests to me that a
"reference" is not necessarily a relation between a First (as a
possibility) and a Second (as an actuality). Rather, it is a relation
of *identity
across "possible worlds"* (in modern parlance), such that a Cut would no
longer always be interpreted as negation, depending on the *kind* of
possibility that is represented by the (tinctured or colored) area that it
encloses. In other words, it seems to introduce another aspect to the
notion that every individual is *general* to some degree.
As we have discussed before, Peirce encountered severe limitations in
trying to represent modality (other than true/false) with only two
dimensions. I suspect that those difficulties are what forced him back to
treating a Cut as negation and a Line of Identity that appears to cross one
as a Ligature instead.
Regards,
Jon Alan Schmidt - Olathe, Kansas, USA
Professional Engineer, Amateur Philosopher, Lutheran Layman
www.LinkedIn.com/in/JonAlanSchmidt - twitter.com/JonAlanSchmidt
On Mon, Apr 1, 2019 at 11:29 AM <[email protected]> wrote:
> Jon, list,
>
> Indeed our paths seem to be converging even more than I expected. You’ve
> covered some points here that I intended to make in my next post, and some
> others I hadn’t even thought of, but are fully consistent with the aspects
> of Peirce’s work that I’ve been exploring, as far as I can tell. I’ll need
> to study your post (and your posts in the other thread) in more detail, but
> instead of responding to this one point-by-point, I’m going to ‘cut to the
> chase’ and go straight to the Peirce text which announces the “major shift”
> I’ve been hinting at since the launch of this thread.
>
> The text is R 490, described as follows in the Robin Catalogue: “CSP
> wrote on the cover of the notebook: "For the National Academy of Sci. 1906
> April Meeting in Washington." Published, with omissions, as [CP]
> 4.573-584.” It’s the CP text I’ll be presenting here (I haven’t yet tried
> to find the MS to see what the omissions are). You (Jon) have seen this
> text before, in fact quoted from it a few months ago, so you may not be
> surprised by the comments I’ll insert between parts of it. The CP editors,
> with their usual disregard for chronological order, placed this text after
> the “Prolegomena to an Apology for Pragmaticism,” although it was obviously
> written before, and in fact must have been written shortly after the Welby
> letter dated March 9 of 1906 (
> http://www.gnusystems.ca/PeirceWelbyMarch1906.htm) which I quoted from in
> the previous post. I’ll try to show some of the connections with that
> letter in my comments between parts of the April text.
>
> [[ 573. In working with Existential Graphs, we use, or at any rate
> imagine that we use, a sheet of paper of different tints on its two sides.
> Let us say that the side we call the *recto* is cream white while the
> *verso* is usually of somewhat bluish grey, but may be of yellow or of a
> rose tint or of green. The *recto* is appropriated to the representation
> of existential, or actual, facts, or what we choose to make believe are
> such. The *verso* is appropriated to the representation of possibilities
> of different kinds according to its tint, but usually to that of subjective
> possibilities, or subjectively possible truths. The special kind of
> possibility here called subjective is that which consists in ignorance. If
> we do not know that there are not inhabitants of Mars, it is subjectively
> possible that there are such beings. …
>
> 574. 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. ]]
>
> Peirce seems to be rethinking the very concept of logical *negation*
> here, looking at it as a kind of modality (*subjective possibility*)
> rather than deriving it from the structure of the *scroll* (representing
> the conditional *de inesse*) as he had in the Lowell lectures three years
> earlier. This line of thought follows up from the March letter to Welby,
> where he wrote near the end:
>
> [[ … now we come to the sole feature of the system which may be strongly
> suspected of being arbitrary. Namely, all the objects of graphs, or
> propositions, are of two classes. Every object is either asserted as an
> *actuality*, i.e., as an *object of* positive *knowledge* or it is merely
> suggested as a *possibility*, or as an *object of ignorance* i.e., an
> object of whose existence the proposition written leaves us ignorant. Let
> us write the objects of knowledge on the recto of the sheet and appropriate
> the verso to indications of objects of ignorance. ] SS 201]
>
> It seems clear enough to me that those “objects of ignorance” became the
> “subjective possibilities” of April 1906, but now the *verso* of the
> sheet of assertion has become more complicated because it is “appropriated
> to the representation of possibilities of different kinds according to its
> tint” (CP 4.573). I consider this the germ of the “tinctured” EGs that
> Peirce later presented in the “Prolegomena.” In April, though, only the
> *verso* comes in different colors, while the *recto* is reserved for
> assertions about things that *do* exist in the universe of discourse.
> Continuing with CP 4:
>
> [[ 575. Now the denial of a subjective possibility usually, if not
> always, involves the assertion of a truth of existence; and consequently
> what is put upon the *verso* must usually have a definite connection with
> a place on the *recto*.
>
> 576. In my former exposition of Existential Graphs, I said that there
> must be a department of the System which I called the Gamma part into which
> I was as yet able to gain mere glimpses, sufficient only to show me its
> reality, and to rouse my intense curiosity, without giving me any real
> insight into it. The conception of the System which I have just set forth
> is a very recent discovery. I have not had time as yet to trace out all its
> consequences. But it is already plain that, in at least three places, it
> lifts the veil from the Gamma part of the system.
>
> 577. 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. ]]
>
> This “new discovery” is at the heart of what I’ve been calling a “major
> shift” in Peirce’s thinking. However, now that the cat’s out of the bag,
> I’d better qualify that a bit, because Peirce may have been ‘April Fooling’
> himself with his enthusiasm for this discovery. As he worked out the
> details of it over the next couple of years, his hopes that it would solve
> all the problems of the gamma graph system were not fulfilled (as Don
> Roberts points out in his book on EGs); and beyond that, his intention to
> base his “proof” of pragmaticism on the EGs was never realized. That
> doesn’t mean that Peirce’s new discovery was entirely fruitless; I think it
> led to some lasting changes in his approach to phaneroscopy, semeiotic and
> metaphysics. For now, though, I’ll focus on the April 1906 address itself.
> To continue:
>
> [[ 578. 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.
>
> 579. Second, In a certain partly printed but unpublished “Syllabus of
> Logic,” which contains the only formal or full description of Existential
> Graphs that I have ever undertaken to give, I laid it down, as a rule, that
> no graph could be partly in one area and partly in another; and this I said
> simply because I could attach no interpretation to a graph which should
> cross a cut. As soon, however, as I discovered that the *verso* of the
> sheet represents a universe of possibility, I saw clearly that such a graph
> was not only interpretable, but that it fills the great lacuna in all my
> previous developments of the logic of relatives. For although I have always
> recognized that a possibility may *be real*, that it is sheer insanity to
> deny the reality of the possibility of my raising my arm, even if, when the
> time comes, I do *not* raise it; and although, in all my attempts to
> classify relations, I have invariably recognized, as one great class of
> relations, the class of *references*, as I have called them, where one
> correlate is an existent, and another is a mere possibility; yet whenever I
> have undertaken to develop the logic of relations, I have always left these
> references out of account, notwithstanding their manifest importance,
> simply because the algebras or other forms of diagrammatization which I
> employed did not seem to afford me any means of representing them. I need
> hardly say that the moment I discovered in the *verso* of the sheet of
> Existential Graphs a representation of a universe of possibility, I
> perceived that a *reference* would be represented by a graph which should
> cross a cut, thus subduing a vast field of thought to the governance and
> control of exact logic. ]]
>
> This is the place where Peirce changed his mind about the rule (stated in
> the “Syllabus”) that a line of identity could not cross a cut. I’m still
> not sure I ‘get’ what he means by a *reference* in this context, although
> phaneroscopically it seems to be a relation between a First and a Second
> which is not simply a dyadic relation. I think the later Peirce text (which
> you quoted) about symmetrical vs. asymmetrical dyadic relations is highly
> relevant here, but I’m not sure I can explain why, just yet. (Maybe you
> can.) Anyway, in the Prolegomena he reverted to the rule that a *line of
> identity* could not cross a cut (because of the different modalities of
> the areas on either side, but a *ligature* can cross a cut by joining two
> lines of identity that meet at a common point on the cut itself. I suppose
> this was one of the adjustments Peirce had to make as he worked out the
> details of his April revelation.
>
> My reason for calling it a “revelation” should become clear as I quote the
> last two paragraphs in Peirce’s text. (I am skipping over a long section
> which deals with some rather abstruse points of logic using EGs, but this
> section has been dealt with in great detail both by Don Roberts in his book
> on EGs and by Frederik Stjernfelt in *Natural Propositions*, and I have
> nothing further to say about it here.)
>
> [[ 583. The System of Existential Graphs recognizes but one mode of
> combination of ideas, that by which two indefinite propositions define, or
> rather partially define, each other on the *recto* and by which two
> general propositions mutually limit each other upon the *verso*; or, in a
> unitary formula, by which two indeterminate propositions mutually determine
> each other in a measure. I say in a measure, for it is impossible that any
> sign whether mental or external should be perfectly determinate. If it were
> possible such sign must remain absolutely unconnected with any other. It
> would quite obviously be such a sign of its entire universe, as Leibniz and
> others have described the omniscience of God to be, an intuitive
> representation amounting to an indecomposable feeling of the whole in all
> its details, from which those details would not be separable. For no
> reasoning, and consequently no abstraction, could connect itself with such
> a sign. This consideration, which is obviously correct, is a strong
> argument to show that what the system of existential graphs represents to
> be true of propositions and which must be true of *them*, since every
> proposition can be analytically expressed in existential graphs, equally
> holds good of concepts that are *not* propositional; and this argument is
> supported by the evident truth that no sign of a thing or kind of thing —
> the ideas of signs to which concepts belong — can arise except in a
> proposition; and no logical operation upon a proposition can result in
> anything but a proposition; so that non-propositional signs can only exist
> as constituents of propositions. But it is not true, as ordinarily
> represented, that a proposition can be built up of non-propositional signs.
> The truth is that concepts are nothing but indefinite problematic
> judgments. The concept of *man* necessarily involves the thought of the
> possible being of a man; and thus it is precisely the judgment, “There may
> be a man.” Since no perfectly determinate proposition is possible, there is
> one more reform that needs to be made in the system of existential graphs.
> Namely, the line of identity must be totally abolished, or *rather* must
> be understood quite differently. We must hereafter understand it to be
> *potentially* the graph of *teridentity* by which means there always will
> virtually be at least one loose end in every graph. In fact, it will not be
> truly a graph of *teridentity* but a graph of indefinitely multiple
> identity.
>
> 584. We here reach a point at which novel considerations about the
> constitution of knowledge and therefore of the constitution of nature burst
> in upon the mind with cataclysmal multitude and resistlessness. It is that
> synthesis of tychism and of pragmatism for which I long ago proposed the
> name, Synechism, to which one thus returns; but this time with stronger
> reasons than ever before. But I cannot, consistently with my own
> convictions, ask the Academy to listen to a discourse upon Metaphysics.
> ]]
>
> There is so much to say about CP 4.583 and its implications that I won’t
> even start here, as that would probably double the length of this post, at
> least. There are some other Peirce texts that throw light on it as well.
> But as for me, I’ve had enough for one day. Maybe you (Jon) or someone else
> will pick up the torch before I get back to it … I hope so!
>
> Gary f.
>
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