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: [email protected] <[email protected]>
Sent: Sunday, May 26, 2019 11:24:26 AM
To: [email protected]
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), but starting with this question from Jon:
JAS: What remains unclear to me is why you seem to think that such Collateral
Experience/Observation cannot be entirely mediated by other Signs. If even a
Percept is a Seme (Sign) that Retroductively produces a Perceptual Judgment,
which is a Proposition (Sign), how can we gain acquaintance with anything in a
way that is not entirely mediated by Signs?
GF: If we can’t, then there is no such thing as direct, unmediated experience
of anything. Would you really want to make that assertion? It would seem to
entail that there are no real relations as opposed to relations of reason:
[CSP:[ Relations are truly, though not very lucidly, said to be either
relations of reason or relations in re. The latter expression the more
obtrusively fails to hit its nail squarely on the head. It would be better to
say that relations are either dicible or surd. For the only kind of relation
which could be veritably described to a person who had no experience of it is a
relation of reason. A relation of reason is not purely dyadic: it is a relation
through a sign: that is why it is dicible. Consequently the relation involved
in duality is not dicible, but surd; and duality must contain as an ingredient
of it a surd disquiparance. ] EP2:382-3]
The quote from EP2:304 included in your post, Jon, refers to such a surd,
dyadic relation as an “experiential reaction,” the only source of “direct
knowledge of real objects.” As you said yourself, “Peirce required direct
experience for all knowledge. See http://gnusystems.ca/Peirce.htm#dirxp for
more of Peirce’s remarks on direct experience.
JAS: Both [common nouns and proper names] are represented in EGs by labeled
Spots, and therefore correspond to general concepts;
GF: I don’t think so; I think proper names are represented in EGs, if at all,
by Selectives. Spots represent rhemes, i.e. predicates, which are always
general, unlike the Selectives, which ‘name’ lines of identity when they need
to be distinguished from other lines.
Finally, Jon, your closing sentence quotes Peirce’s own statement of what I’ve
been saying all along, that the ultimate meaning of religious concepts consists
not in their conveying theoretical knowledge of an external Object but in their
influence on the conduct of their interpreters: “After all, he explicitly
considered his (Retroductive) Neglected Argument for the Reality of God to be
‘the First Stage of a scientific inquiry, resulting in a hypothesis of the very
highest Plausibility, whose ultimate test must lie in its value in the
self-controlled growth of man's conduct of life’ (CP 6.480, EP 2:446; 1908).
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 <[email protected]>
Sent: 20-May-19 23:58
To: [email protected]
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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