Jeff, Gary F., List:
I am not sure how much more I will have to say on this topic, but I thought
that it might be helpful to provide some context for the original excerpt.
GF: I feel I’m not explaining this very well, so maybe it would be better
for interested readers to just read again and ponder CP 2.230 as quoted by
Jeff (below). By the way, according to Cornelis de Waal (2014), that
passage is an excerpt from R 637, written in October 1909.
The passage is indeed from that manuscript (R 637:25-29[31-35]; 1909 Oct
12). Here is what comes immediately beforehand.
CSP: Now the unity of reasoning is simply the identity of the object
reasoned about. An argument is simply a constructure of premisses which
constitutes a *sign* of the truth *of the truth* of its conclusion, no
matter what kind of reasoning it uses; and the question of what its logic
is, is nothing but the question in what mode of representation those
premisses make up a sign of the substance of the conclusion. Now any
equivalent signs will be in the same relation to that conclusion; and the
preference among different forms of signs should be given that one which is
most easily examined, manipulated, preserved, and anatomized. If this be
admitted, logic will rarely consider judgments as they are in the mind but
will make choice of some form of external sign. This has been the writer's
method; and he has found so great a variety of kinds of signs to be
indispensible in reasoning of different kinds that it seems to him that in
the present state of science in which the study of the natures of the
broader classes of signs has been almost completely neglected, it would be
well for scientific logicians to recognize the whole field of general
semeiotic as consigned to their industry. Another book in which, if the
author's powers hold out to complete it, the results of those studies of
logic considered as semeiotic to which the only useful part of his days
have been consecrated, results which he believes will furnish any person of
intelligence who will examine them with clear ideas of how to find the
truth, as well as a sound basis for a truly religious life, will be
submitted in systematic form to the judgment of thoughtful men. Meantime,
this preliminary and unsystematic volume is put forth in the hopes that it
may, in some way or through some pen lead to thinking men generally being
made acquainted with the point of view in question, which the pragmatists
have not quite taken up.
To attain this view-point, it is requisite to know something of the nature
of Signs; and that feature of Signs which is particularly to be considered
in this volume is their *meaning*. In order that the reader may get a
little clearer idea of what this is than the word by itself is likely to
convey, it will be well to begin by explaining that the word Sign will be
used throughout this volume to denote an Object perceptible ... (R
637:23-25[30-31]; 1909 Oct 11-12)
It turns out that the CP editors omitted (without saying so) a footnote
that Peirce intended to accompany the sentence about the map of an island,
as well as some further text that comes between that and the statement, "A
sign may have more than one Object."
CSP: *If map and island were both ring-shaped it might not be so. This
example is introduced in order to correct an error (not the sole, nor the
most important one) in a certain book that is very well worth reading.
As to what is meant by saying the Object is *represented* by the Sign,
perhaps the best account that can be given of the matter is the following,
which may be preceded by the remark, that the mode of representation may be
by likeness or analogy, in which case, the sign may be called an *Icon*; or
it may be by a real connexion as a certain kind of rapid pulse is symptom
of a fever, in which case the sign may be called an indication, or *Index*;
or finally the only connexion may be in the fact that the Sign, (a word,
for example,) is sure to be interpreted as standing for the Object, in
which case the Sign may be called a *Symbol*; and these terms, *Icon*,
*Index*, and *Symbol*, will be so used throughout the volume.*
*This terminology was first introduced by the writer in the *Proceedings of
the American Academy of Arts and Sciences*, 1867 May 14. Vol. VII p. 294,
only Icons were, at first, called 'likenesses.' (R 637:27-28[33-34]; 1909
Oct 12)
I wonder what worthwhile but erroneous book Peirce had in mind. Anyway, it
also seems noteworthy that CP 2.231-232 are *not continuous* with CP 2.230
in the actual manuscript, but rather come from an alternate draft written
the next day (R 637:37-39[31-33]; 1909 Oct 13). The following comes
immediately after CP 2.232.
CSP: In this volume, something will be said about the relations of signs
to their Objects; but what is called on the Title page "Meaning" is that
which a sign communicates. This may be nothing but a Feeling or emotion,
which is all that a performance of instrumental music, for example,
commonly expresses. Or the Sign being a command, such as the order "Ground
Arms," its Meaning may be the impulse to obey, which the sign excites. A
question is a sort of command. Or the Sign may be an appeal to reason by
an argument consisting of known premisses, the synthesis of which, which
Synthesis will be its meaning, may be a new thought. Or the Sign may be an
assertion, or "Proposition," to use the logical term, when the Meaning is
the substance of an assent to it. Or it may be a mere suggestion to
imagination or memory, such as [a] single word may convey. Many
"Utterances," as all acts of using Signs will here be called, are
purposeless. But a serious Utterance is usually intended to influence
either a single act or the reasoned conduct of the Interpreter or
Interpreters, and its meaning is that general kind of conduct that it
virtually recommends. Such Signs are mostly Arguments; and the Conclusion
of an Argument, considered as matter for belief, is its Meaning; while a
secret purpose of an Utterance is the Meaning of some thinking, or "saying
to himself" on the part of the Utterer. It will thus be perceived that the
subject of this book is no trivial one. In the writer's opinion, it, or
rather Semeiotic, the science of Signs in general, ought to be regarded as
the foundation of a liberal education, whether for young men or young women.
There is no attempt in these pages to treat this vast subject
systematically: a few topics only which press upon the author are
considered. He has done his best to make the book clear and agreeable; but
it would hardly be possible for the most accomplished pen to produce the
latter effect; since the subject, of its very nature, requires the reader *to
think*, without which he cannot even know what it is all about; and there
is no occupation that the general herd of mankind find so intolerably
irksome as thinking. "I hate books," will often be heard in tones that
leave no doubt of the depth of the feeling; and one who hates books must
loathe thinking. So it must be acknowledged that it is only those who
enjoy the exercize of rational exertion who will have any patience with the
individual who has perpetrated these Essays, especially as he is far from
being a graceful writer; and because he is accustomed to take certain
points of view that happen to be much out of fashion, his modes of
expressing himself are likely to be thought even more *gauche* than they
really are; and they are bad enough at best.
Pretty much all he can do toward rendering this writing perspicuous, beyond
giving concrete examples whenever he can discover the need of them, is as
far as possible always to use each word in a single sense. (R
637:39-42[33-36]; 1909 Oct 13)
Regards,
Jon Alan Schmidt - Olathe, Kansas, USA
Professional Engineer, Amateur Philosopher, Lutheran Layman
www.LinkedIn.com/in/JonAlanSchmidt - twitter.com/JonAlanSchmidt
On Sun, May 26, 2019 at 6:27 PM Jeffrey Brian Downard <
jeffrey.down...@nau.edu> wrote:
> Gary F, List,
>
> Thank you for taking up the challenges involved in trying to interpret the
> difficult passage in "Meaning", (CP 2.230) and for clarifying the date of
> composition (1909 , R 637).
>
> I was not aware of the work by Arthur Koestler on complex systems that
> are organized as *holarchies*. It is helpful to me when folks point out
> such interesting references. I'll need to read more to see what he is
> saying about the relations of part/whole within complex systems. Thus far,
> the points you've made seem to fit with my still rather tentative
> understanding
> of what Peirce is suggesting in this passage.
>
> In one short remark, you make reference to Peirce's work on topology:
> GF: These systemic causal relations are quite complex, as Peirce
> explains in “New Elements” (EP2:315).
>
> Did you mean to make reference to the last page of a short piece on knots?
> If so, what is it that has caught your attention? Louis Kauffman has some
> interesting work on knots and logic. Many of his ideas appear to be
> inspired by Peirce's work on mathematical logic, including the EGs, and
> the semiotic theory. Without making any explicit reference to Peirce's or
> Kauffman's work on knots, I would like to draw out some ideas about
> continuity that seem to important for thinking about logical inferences
> that are synthetic in character--i.e., that have the peculiar properties of
> being (1) self-correcting and (2) capable of growth.
>
> In general, I think that Peirce is gaining considerable traction on the
> question of what makes some complex systems strongly nonlinear in their
> dynamics and self-organizing in their character by modeling them on logical
> systems.
> On his account, semiotic systems are probably the clearest case of such
> complex systems, and he takes them to be paradigmatic for this reason.
>
> Peirce seems to have seen--with remarkable lucidity--what most of us have
> only learned in the second half of the 20th century through the intensive
> mathematical study of complex systems. Simplifying matters somewhat, here are
> two
> features that appear to be essential for any such system to be strongly
> non-linear in its character. First, any such system must be capable of
> iteration. Second, it must have an operation in virtue of which the variables
> are multiplied by themselves.
>
> In the past few weeks, I've raised some questions about John Sowa's
> remarks about First Order Predicate Logic being paradigmatic as a formal
> system of logic. Like many who work in mathematical logic, John seems to be
> impressed by (1) the expressive power and (2) the stability of this
> system. Quite a number of mathematicians working today appear to have
> come to the conclusion that this system of formal logic should be taken as
> foundational for all of mathematics. I have numerous reservations about
> adopting this posture towards the predicate calculus. Note: I am not
> attributing this view to John. He can speak for himself.
>
> As a self-admitted student of the various systems of systems
> of mathematical logic (quite the beginner in many areas), one thing that
> appears to be essential to the predicate calculus being a first-order
> system is that it does not provide for the representation of hypostatic
> abstraction within the logical system itself. Other systems do, including
> symbolic systems having, for example, Hilbert operators or lambda
> operators. Systems having operators that represent hypostatic abstraction are
> what Peirce calls second intentional logics, which corresponds roughly to
> what we call second-order logical systems. The gamma system of the EGs
> was expressly intended to be a modal logic that is second intentional in
> character.
>
> Consider what Peirce says about the self-correcting character of reasoning
> generally and the role of iteration in such inferential processes:
>
> So it appears that this marvellous self-correcting property of Reason, which
> Hegel made so much of, belongs to every sort of science, although it
> appears as essential, intrinsic, and inevitable only in the highest type
> of reasoning, which is induction. But the logic of relatives shows that
> the other types of reasoning, Deduction and Retroduction, are not so
> thoroughly unlike Induction as they might be thought, and as Deduction,
> at least, always has been thought to be. Stuart Mill alone among the
> older logicians in his analysis of the *Pons Asinorum *came very near to
> the view which the logic of relatives forces us to take.†1 Namely, in the
> logic of relatives, treated let us say, in order to fix our ideas, by
> means of those existential graphs of which I gave a slight sketch in the
> last lecture, [we] begin a Deduction by writing down all the premisses.
> Those different premisses are then brought into one field of assertion,
> that is, are *colligated, *as Whewell would say, or joined into one copulative
> proposition. Thereupon, we proceed attentively to observe the graph. It is
> just
> as much an operation of *Observation *as is the observation of bees. This
> observation
> leads us to make an *experiment *upon the Graph. Namely, we first duplicate
> portions of it; and then we erase portions of it, that is, we put out of
> sight part of the assertion in order to see what the rest of it is. We
> observe the result of this experiment, and that is our deductive
> conclusion. Precisely those three things are all that enter into the
> experiment of any Deduction -- Colligation, Iteration, Erasure. The rest of
> the process consists of observing the result. It is not, however, in every
> Deduction
> that all the three possible elements of the Experiment take place. In
> particular,
> in ordinary syllogism the iteration may be said to be absent. And that is
> the reason that ordinary syllogism can be worked by a machine. There is
> but one conclusion of any consequence to be drawn by ordinary syllogism
> from given premisses. Hence, it is that we fall into the habit of talking
> of *the *conclusion. But in the logic of relatives there are conclusions
> of different orders, depending upon how much iteration takes place. What
> is *the *conclusion deducible from the very simple first principles of
> number? It is ridiculous to speak of *the *conclusion. *The *conclusion is
> no less than the aggregate of all the theorems of higher arithmetic that
> have been discovered or that ever will be discovered. Now let us turn to
> Induction. This mode of reasoning also begins by a colligation. In fact,
> it is precisely the colligation that gave induction its name, {epagein}
> with Socrates, {synagögé} with Plato, {epagögé} with Aristotle. It must,
> by the rule of predesignation, be a deliberate experiment. In ordinary
> induction we proceed to observe something about each instance. Relative
> induction is illustrated by the process of making out the law of the
> arrangement of the scales of a pine-cone. It is necessary to mark a scale
> taken as an instance, and counting in certain directions to come back to
> that marked scale. This double observation of the same instance corresponds
> to Iteration in deduction. Finally, we erase the particular instances and
> leave the class or system sampled directly connected with the characters,
> relative or otherwise, which have been found in the sample of it. CP 5.
> 579.
>
> The example drawn from the theory of number seems instructive. From the
> initial definitions, postulates and axioms, a remarkable set of theorems
> follows. What is more, the logic of relatives helps us see how richly
> systematic those theorems, taken together, really are. At the present
> time, those theorems form but a fragment of those that are yet to be
> discovered. Consider the Riemann hypothesis as an example. Can it be proven
> as a theorem? Recent advances seem to suggest that a remarkably simple set
> of ideas can be used to prove something that has eluded mathematicians for
> the last 150 years. If you are interested, see:
> https://www.sciencenews.org/article/mathematicians-progress-riemann-hypothesis-proof
>
> For the sake of understanding Peirce's remarks in "Meaning" about the
> explanation
> or argument or other context that is a part of every sign that is
> separate, in some sense from its object, I think the reference to possible
> future
> developments of a system of signs is just as important as those that
> refer to developments made in the past. Those future developments are, at
> any given time, part of that sign's potentiality.
>
> Yours,
>
> Jeff
> Jeffrey Downard
> Associate Professor
> Department of Philosophy
> Northern Arizona University
> (o) 928 523-8354
> ------------------------------
> *From:* g...@gnusystems.ca <g...@gnusystems.ca>
> *Sent:* Sunday, May 26, 2019 11:24:26 AM
> *To:* peirce-l@list.iupui.edu
> *Subject:* RE: [PEIRCE-L] Continuity of Semeiosis Revisited
>
>
> Jeff, JAS, Gary R, list,
>
> Having said all I have to say about theology and metaphysics, I’d like to
> focus here on semiotic questions, especially those raised by Jeff in his
> post of May 20 (copied below) ...
>
> Now to Jeff’s post, with its extended quote from Peirce that includes a
> plethora of important points about “Meaning.” Jeff has pointed out some of
> the implications; here I’ll only focus on one sentence: “If a Sign is
> other than its Object, there must exist, either in thought or in
> expression, some explanation or argument or other context, showing how,
> upon what system or for what reason the Sign represents the Object or set
> of Objects that it does.”
>
> If we consider signs as *systems*, we can view them as organized in
> *holarchies*, to use the term coined by Arthur Koestler. Every complex
> system can be analyzed into subsystems, but it also functions as a whole
> within the larger system which is its context. In Peirce’s scenario, this
> is an *explanatory* context, but as Jeff says, it raises questions about
> any case where a sign is part of another sign — which I would say is the
> *usual* situation if the sign is a *symbol* such as a proposition or an
> argument. The Universe as Sign, being a “text without a context” (as Thomas
> Berry says), would be an exception, maybe the *only* exception.
>
> In living holarchies at least, the various levels of the holarchy are
> discrete *in re* and not as *entia rationis*, as sign and object are when
> the one is external to the other. This makes them discontinuous — but when
> the holons are nested within one another, the causal/determinative
> *relations* between levels may very well be continuous. These systemic
> causal relations are quite complex, as Peirce explains in “New Elements”
> (EP2:315). Even when operating at the same level in a holarchy, like
> concepts represented on the recto of an EG, they may be *mutually*
> determinative, as Peirce observes in the conclusion of his 1906
> “Prolegomena” (CP 4.572). All of this suggests that the requirement for the
> Object to be necessarily *other* than the Sign is not only “perhaps
> arbitrary,” as Peirce says, but vastly oversimplified in the case of
> complex and recursive sign systems.
>
> I feel I’m not explaining this very well, so maybe it would be better for
> interested readers to just read again and ponder CP 2.230 as quoted by Jeff
> (below). By the way, according to Cornelis de Waal (2014), that passage is
> an excerpt from R 637, written in October 1909.
>
> Gary f.
>
>
>
> *From:* Jeffrey Brian Downard <jeffrey.down...@nau.edu>
> *Sent:* 20-May-19 23:58
> *To:* peirce-l@list.iupui.edu
> *Subject:* Re: [PEIRCE-L] Continuity of Semeiosis Revisited
>
> Jon S, Gary F, John S, Edwina, Gary R, List
>
> I'd like to raise some questions about the assertion that every sign has
> an object that is separate, in some sense, from that sign. The basis of the
> claim that the object must be *separate* from the sign, I am supposing,
> is that the object *determines* the sign. As a matter of principle, an
> object cannot be the kind of thing that determines a sign if that object is
> not separate from the sign.
>
> This assertion seems, at least to me, to be clearest in the case
> of the actual objects that determine indexical sinsigns--where the objects
> and signs stand in the relation of agent and patient. This type of relation
> is classified as a dynamical dyadic relation that is formally ordered. For
> this type of sign, the object, as agent, cannot determine the indexical
> sinsign, as patient, if the two are identical. Diversity is requisite for
> the relation to hold.
>
> If we can all agree on this much, then what shall we say about the case of
> a sign that is part of a sign? In order to anchor the discussion of this
> question about Peirce's semiotics in a text, l'd like to focus our
> attention on the following clarification that is offered in "Meaning" from
> 1910: "But in order that anything should be a Sign, it must "represent,"
> as we say, something else, called its *Object, *although the condition
> that a Sign must be other than its Object is perhaps arbitrary, since, if
> we insist upon it we must at least make an exception in the case of a
> Sign that is a part of a Sign."
>
> Here is the larger paragraph from which this sentence has been abstracted:
>
> SIGNS AND THEIR OBJECTS
>
> The word Sign will be used to denote an Object perceptible, or only
> imaginable,
> or even unimaginable in one sense--for the word "*fast*," which is a Sign, is
> not imaginable, since it is not *this word itself *that can be set down
> on paper or pronounced, but only *an instance *of it, and since it is the
> very same word when it is written as it is when it is pronounced, but is
> one word when it means "rapidly" and quite another when it means
> "immovable," and a third when it refers to abstinence. But in order that
> anything should be a Sign, it must "represent," as we say, something else,
> called its *Object, *although the condition that a Sign must be other
> than its Object is perhaps arbitrary, since, if we insist upon it we must
> at least make an exception in the case of a Sign that is a part of a
> Sign. Thus nothing prevents the actor who acts a character in an
> historical drama from carrying as a theatrical "property" the very relic that
> that article is supposed merely to represent, such as the crucifix that
> Bulwer's Richelieu holds up with such effect in his defiance. On a map of
> an island laid down upon the soil of that island there must, under all
> ordinary circumstances, be some position, some point, marked or not, that
> represents *qua *place on the map, the very same point *qua *place on the
> island. A sign may have more than one Object. Thus, the sentence "Cain
> killed Abel," which is a Sign, refers at least as much to Abel as to Cain,
> even if it be not regarded as it should, as having *"a killing" *as a
> third Object. But the set of objects may be regarded as making up one
> complex Object. In what follows and often elsewhere Signs will be treated
> as having but one object each for the sake of dividing difficulties of
> the study. If a Sign is other than its Object, there must exist, either
> in thought or in expression, some explanation or argument or other context,
> showing how--upon what system or for what reason the Sign represents the
> Object
> or set of Objects that it does. Now the Sign and the Explanation together
> make up another Sign, and since the explanation will be a Sign, it will
> probably require an additional explanation, which taken together with the
> already enlarged Sign will make up a still larger Sign; and proceeding in
> the same way, we shall, or should, ultimately reach a Sign of itself,
> containing its own explanation and those of all its significant parts;
> and according to this explanation each such part has some other part as its
> Object. According to this every Sign has, actually or virtually, what we
> may call a *Precept *of explanation according to which it is to be
> understood as a sort of emanation, so to speak, of its Object. (If the
> Sign be an Icon, a scholastic might say that the *"species" *of the
> Object emanating from it found its matter in the Icon. If the Sign be an
> Index, we may think of it as a fragment torn away from the Object, the two in
> their Existence being one whole or a part of such whole. If the Sign is a
> Symbol, we may think of it as embodying the *"ratio," *or reason, of the
> Object that has emanated from it. These, of course, are mere figures of
> speech; but that does not render them useless.) [CP 2.230]
>
> Consider the three examples Peirce offers to illustrate this point about a
> sign that is part of a sign:
>
> a) "Thus nothing prevents the actor who acts a character in an
> historical drama from carrying as a theatrical "property" the very relic that
> that article is supposed merely to represent, such as the crucifix that
> Bulwer's Richelieu holds up with such effect in his defiance." Bulwer is
> the author who penned the famous phrase "the pen is mightier than the
> sword" in the play *Richelieu**.* In this case, it is the crucifix and
> not the pen that is serving as the object of the proposition. How is that
> object also functioning as a sign (of itself)?
>
> b) "On a map of an island laid down upon the soil of that island there
> must, under all ordinary circumstances, be some position, some point,
> marked or not, that represents *qua *place on the map, the very same
> point *qua *place on the island." We've discussed this example earlier.
> The discussion following the three examples, seems to suggest that the
> point being made about the self-referential character of some signs is a
> rather general point.
>
> c) "A sign may have more than one Object. Thus, the sentence "Cain killed
> Abel," which is a Sign, refers at least as much to Abel as to Cain, even
> if it be not regarded as it should, as having *"a killing" *as a third
> Object. But the set of objects may be regarded as making up one complex
> Object." This example suggests that the relations that are represented as
> holding between subjects in a proposition are, themselves, also the objects
> of the proposition. Taken together, the two subjects and the relation may
> be regarded as one complex object. In saying that the object is *complex*,
> it appears that it is something more than a mere aggregate.
>
> How might these examples be used to clarify the following parts of
> Peirce's central claim?
>
> i) Now the Sign and the Explanation together make up another Sign, and
> since the explanation will be a Sign, it will probably require an additional
> explanation, which taken together with the already enlarged Sign will make
> up a still larger Sign;
>
> ii) and proceeding in the same way, we shall, or should, ultimately reach
> a Sign of itself, containing its own explanation and those of all its
> significant parts; and according to this explanation each such part has
> some other part as its Object.
>
> Yours,
>
> Jeff
>
> Jeffrey Downard
> Associate Professor
> Department of Philosophy
> Northern Arizona University
> (o) 928 523-8354
>
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