Jeff, Mary, Gary R, Lists,
Jeff wrote:
(012315-1)
"Instead of thinking of the relationship between recto and verso
extensionally as, "it is actually the case that this object x has this
property F," and "it is not the case that this object x does not have this
property F," we are thinking differently about how the two sides of the
sheet are related one to the other. As I mentioned in an earlier email,
Peirce is classifying the referential relation as a species of dyadic
relation proper (i.e., one that is genuine and not degenerate--as a
reference happens to be). In the movement to the Gamma Graphs, Peirce is
trying to find a way to represent--as iconically as possible--the
introduction of a triadic relation between reference to ground, reference
to object and reference to interpretant. All legisigns bring these three
functions together and binding them together--under a rule--as it were."
It seems to me that
"There are at least two distinct kinds of relations between the the recto
and the verso surfaces of Peirce's (012315-2)
Sheet of Assertion (SA) -- (i) OPPOSITION when viewed LOCALLY
(or synchronically) and (ii) COMPLEMENTARITY
when viewed GLOBALLY (or diachronically), assuming that SA can be
identified with a Moebius strip (or curved surface)
rather than as a flat surface as apparently assumed by Peirce."
To 'prove' the validity of Statement (012315-2), it is necessary only to
carry out the following simple imaginary experiment with a Moebius strip.
"Imagine a segment of a Moebius strip, one side of which is labeled as R
(recto) and the other side as V (verso). (012315-3)
This is a local view. Now leave the initial segment behind and move along
the surface, either to the left or to the
right, and you will find yourself passing through the V surface and by the
time you return to the original starting point
you are standing on a R surface. So the character of the surface changes
along your trajectory: R -----> V ------> R."
If you replace R and V in (012315-3) with A and B, the assertion, (6-40),
shown in the following excerpt from [1, p. 195] results:
*"6.3.5 The Principle of Mőbius Relations*
The Möbius strip is "a one-sided surface that is constructed from rectangle
by holding one end fixed, rotating the (012315-4)
opposite end through 180 degrees, and applying it to the first end"
[Webster's Ninth New College Dictionary]. The
essential geometric properties of the Möbius strip may be characterized in
terms of the following two propositions:
"The Möbius strip consists of two opposite surfaces, A and
B, (6-38)
when viewed
locally.”
"Surfaces, A and B, merge into one another when viewed globally."
(6-39)
Statements (6-38) and (6-39) may be combined into one:
"Locally A *or* B; globally A *and*
B." (6-40)
Statement (6-40) may be viewed as an alternative expression of what is
referred to as the *global-local complementarity*
(or the *forest-tree complementarity*). In all these statements, the
terms”local” and “global” may be replaced with “synchronic”
and “diachronic”, respectively. For the definitions of “synchronicity” and
“diachronicity”, see Sections 4.5 and 6.3.2."
Hence it may be concluded that
"By replacing the flat sheet of assertion of Peirce with a curved surface
of Moebius strip,
the logic of Peirce's existential graphs may be extended to accommodate the
complementarian logic
of quantum mechanics which has been characterized in terms of the following
three criteria [2]:
(1) EXCLUSIVITY
"A and B are mutually exclusive."
(012315-5)
(2) ESSENTIALITY
"A and B are essential for C."
(01234`15-6)
(3) TRANSCENDENTALITY
"C transcends the level where A and B have meanings."
(012315-7)
Finally, it may be possible to use the Moebius strip as a geometrical
representation of the Principle of Complementarity by assigning the two
opposite surfaces to A and B and the entire curved surface in the 3-D space
to C. If these speculations turn out to be right (in principle), it may be
justified to conclude that there are two kinds of logic used by the human
mind as indicated in Table 1.
________________________________________________________________________________________
Table 1. Two kinds of logic utilized by the human mind.
________________________________________________________________________________________
Logic
____________________________________________________________________
Manifestations in Classical
Complementarian
________________________________________________________________________________________
1. Geometry Euclidean geometry
No-Euclidean geometry
2. Physics Classical physics
Quantum physics
3. Diagrams Existential graphs on a flat sheet
Existential graphs on a curved sheet
________________________________________________________________________________________
With all the best.
Sung
Reference:
[1] Ji, S. (2012). Molecular Theory of the Living Cell: Concepts,
Molecular Mechanisms, and Biomedical Applications. Springer, New York.
[2] Ji, S. (2012). Complementarian Logic. in: Molecular Theory of
the Living Cell: Concepts, Molecular Mechanisms, and Biomedical
Applications. Springer, New York. Pp. 29-31. PDF available at
http://www.conformon.net under Publications > Book Chapters.
On Thu, Jan 22, 2015 at 3:39 PM, Jeffrey Brian Downard <
[email protected]> wrote:
> Lists,
>
> Ben has made a quick remark offlist, and I wanted to respond to the
> Lists. He says, "A surprising thing to me is that Peirce in the Gamma
> graphs treats possibility, necessity, etc. without mentionng that he is not
> starting like in probability theory from a set of given data parameters
> like in probability theory, but instead (somewhat like contemporary modal
> logic) supposing, for instance, unspecified conditions, or an unspecified
> state of information, in virtue of which which g is possible. Of course if
> one does it like probability theory, then the possibilities and necessities
> are merely logical possibilities and necessities and don't belong to a
> separate province within logic. The approach of leaving unspecified the
> data parameters, the states of information, etc., that one might like to
> specifically know, suggests to me the idea of devising deductive formalisms
> with special utility for inductive inquiries. But that's just an initial
> impression."
>
> Here is my response: interesting remarks, Ben, especially the "idea of
> devising deductive formalisms with special utility for inductive
> inquiries." One of the moves Peirce makes as he transitions from the Beta
> to the Gamma graphs is to think of the lines of identity as being really
> composed of branching relations--at least potentially. In the essay on the
> improvement of the Gamma Graphs, he says:
>
> "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." (CP, 4.583)
>
> This shouldn't be too surprising, I think, because the lines of identity
> in the Beta system are thought of extensionally as existing objects that
> are joined by actually having or not having specific qualities. As such,
> the lines are an iconic representation of the dyadic relation of an actual
> matter of fact. As Peirce says in his discussion of the nomenclature and
> division of dyadic relations: "The author's writings on the logic of
> relations were substantially restricted to existential relations; and the
> same restriction will be continued in the body of what here follows." (CP,
> 3.574)
>
> Once we move from the Beta to the Gamma system, we are connecting things
> with different modal characteristics, and we are connecting things across
> different universes of discourse. As such, the character of the connection
> between qualities that are present in an existing thing are being connected
> to the possible qualities that possible things might have --including the
> possible changes that might occur to this object if certain conditions were
> to obtain. Peirce sees that the specification of such possibilities is
> governed by some rule (i.e., either one in our understanding or one that is
> in the world). Connecting qualities, individuals and objects under rules
> requires some way of dealing with the generality of the rule itself and the
> way that it holds across different possible states of affairs.
>
> So, here is a suggestion for Gary F., as he thinks about the character of
> the sheet of assertion in the Beta and Gamma systems. In effect, the
> movement from the Beta to the Gamma graphs forces us to reinterpret the
> meaning of the empty spaces found on the recto side of the sheet of
> assertion, and the relationships between those empty spaces and those that
> are occupied on the verso side of that sheet. This gives new meaning to
> the boundaries between spaces and the connections between those spaces.
> Instead of thinking of the relationship between recto and verso
> extensionally as, "it is actually the case that this object x has this
> property F," and "it is not the case that this object x does not have this
> property F," we are thinking differently about how the two sides of the
> sheet are related one to the other. As I mentioned in an earlier email,
> Peirce is classifying the referential relation as a species of dyadic
> relation proper (i.e., one that is genuine and not degenerate--as a
> reference happens to be). In the movement to the Gamma Graphs, Peirce is
> trying to find a way to represent--as iconically as possible--the
> introduction of a triadic relation between reference to ground, reference
> to object and reference to interpretant. All legisigns bring these three
> functions together and binding them together--under a rule--as it were.
>
> One reason I find your last remark especially interesting, Ben, is that
> the leading principles of induction and abduction are rules of a special
> sort, and Peirce is trying to understand how we might clarify the
> relationship between the rules of synthetic inference and the leading rule
> that governs deductive inference. As a side remark, it is really
> interesting to see him explore the limits of what could and couldn't be
> done with Euler graphs in his entry on that subject. A comparison between
> Peirce's remarks on the limitations of the Euler system of diagrams and
> what is introduced--piece by piece--in the development of the Alpha, Beta
> and Gamma systems, is really quite instructive for thinking about these big
> questions about the leading principles of synthetic inference--and the
> grounds of the validity of these principles.
>
> Like you, I think that Peirce was very much motivated by these kinds of
> philosophical questions--and that they are helping him clarify many of the
> goals that are guiding him in the development of the existential graphs
> generally, and especially in the development of gamma graphs. Peirce is
> focusing on the question of how to understand the nature of different kinds
> of conditionals (and not just those that are conditional propositions de in
> esse) because we want to gain greater insight into what is involved in the
> illative transformation when the reasoning is synthetic and not just when
> the transformation is deductive. Consider, for instance, Peirce's remarks
> in the "Apology for Pragmatism" when he explains why he chose the scroll as
> an iconic representation that enables us to see what is going on when we
> draw inferences from a conditional proposition de inesse. (CP 4,564) Very
> quickly, he clarifies the permissions (one might label them postulates, if
> you are thinking like a geometer) called "the rule of deletion and
> insertion,"the rule of iteration and reiteration,"and " the rule of the
> double cut," etc.
>
> Let me close by saying that I place great weight on Peirce's conclusion
> that, ultimately, there are only three such permissions in the existential
> graphs that are needed to understand the nature of the illative
> transformation. Those are colligation, iteration and erasure. (CP, 5.579)
> My assumption is that he is making a point about any kind of illative
> transformation when he says this, and not just the transformation involved
> in a deductive inference. After all, his main point in this passage is
> that these three permissions are precisely what is needed in order to gain
> a deeper understanding of the self correcting character of any kind of
> inference--including inferences by induction and abduction.
>
> --Jeff
>
> Jeff Downard
> Associate Professor
> Department of Philosophy
> NAU
> (o) 523-8354
> ________________________________________
> From: Benjamin Udell [[email protected]]
> Sent: Thursday, January 22, 2015 11:19 AM
> To: Gary Fuhrman; Jeffrey Brian Downard
> Subject: Re: OFF-LIST Re: Contradictories, contraries, etc. WAS Re:
> [PEIRCE-L] Natural Propositions : Chapter 8 - On the philosophical nature
> of semiosis?
>
>
> ________________________________________
> From: Benjamin Udell [[email protected]]
> Sent: Tuesday, January 20, 2015 10:52 AM
> To: [email protected]; Peirce List
> Subject: Re: [PEIRCE-L] RE: NP 8.3 and the Improvement on the Gamma Graphs
>
> Mary, Gary F.,
>
> Gary F., thanks for changing the subject title. I had renamed it
> 'Contradictories, Contraries [etc]' and then it unexpectedly veered back
> toward the original subject, I should have changed the title when that
> happened.
>
> Mary, you did indeed write the starting post in this subthread. (You sent
> it only to the biosemiotics list, but Gary Richmond forwarded it peirce-l
> (I provide these links so everybody can peruse)
> (gmane) http://thread.gmane.org/gmane.science.philosophy.peirce/15394
> (IUPUI) https://list.iupui.edu/sympa/arc/peirce-l/2015-01/msg00102.html
> and replied to it:
> (gmane) http://thread.gmane.org/gmane.science.philosophy.peirce/15404
> (IUPUI) https://list.iupui.edu/sympa/arc/peirce-l/2015-01/msg00112.html
> and your text (originally in reply to Jeffrey Brian Downard) follows Gary
> R.'s reply.)
>
> I wasn't active in the subthread till a bit later but I did read your
> original post. As regards the questions that you posed there:
>
> 1. From your original post:
>
> > For example I, like many readers, relate the dicisign overall as
> Stjernfelt has presented it to his far-reaching cpt. 8: "Operational and
> Optimal Iconicity in Peirce¹s Diagrammatology.² How do the two kinds of
> iconicity (chapter 8) Optimal and Operational Icons), make sense when I
> relate them to or place them in dialogue with the dynamic and immediate
> objects of the index? I wonder, does a dicisign posit or ³say² that there
> exists (may exist, hypothetically exists) a written or spoken proposition
> SRO (Subject Relation Object)? Š that the whole proposition (seen completed
> after the fact or seen hypothetically completed before the fact of writing
> or utterance or action) is made up of two parts? To distinguish the object
> as optimal and operational in relation to the dicisign, I consider the
> index as it operates in an icon and the index as it operates as an index.
> (The node between the two, the index and icon, as they reach out and for
> that moment exist. Is Stjernfelt saying, in other words, that there (1)
> exists an object, undistributed in relation to the subject and that there
> (2) exists an object of this specific subject under discussion that is
> distributed (that are under discussion,that are being thought, that are
> coming into a realer or more iconic existence)? What and who have or will
> have placed these in discussion may be the Grapheus and the Graphist, the
> realist and the doubter, but the Universe.
> [End quote]
>
> I confess that I didn't understand it! I admit that I was feeling kind of
> obtuse. I was hoping that others' subsequent discussion would clarify it.
>
> 2. From your original post:
>
> > I find some loose ends in my thinking about Peirce, amplified somewhat
> by NP. Is the recto/verso Sheet of Discourse, the ³leaf² pointed to by
> Stjernfelt, boundless, and in what dimension? I always imagine it as a
> mobius strip when the sign is in process, but the boundaries of the
> Universe of Discourse that are discussed by linguists and others are
> raised. Just now I continue with the leaf (sheet of assertion) analogy and
> consider the node of life at the stem as it grows. I will continue to think
> through these icons.
> [End qote]
>
> I thought about the Mobius strip idea but I stopped because I was
> uncertain about whether existential graphs have chirality, but I think that
> they don't, and anyway it doesn't matter (I was wondering about a graph
> that locally seems on the verso, what happens to it when one moves it
> around the Mobius strip to what locally seems the recto). Shaping a sheet
> into a Mobius strip makes it all recto and no verso, as Gary F. said, and
> eliminates the ability to negate a graph. I think Peirce somewhere talks
> about logic without negation. Anyway it can have only particular
> affirmatives and conjunctive compounds of particular affirmatives, a
> one-sided logic so the Mobius strip is actually perfect for it. If you want
> it to be unbounded, the surface of a Klein bottle would do that
> https://people.math.osu.edu/fiedorowicz.1/math655/Klein2.html . Anyway I
> guessed that you were trying to think of a way for there to be a
> referential relation between a recto graph and a verso 'possibility' graph.
> I remember once trying to think of some topological trick for that.
>
> Best, Ben
>
> On 1/20/2015 10:36 AM, Gary Fuhrman wrote:
>
> Mary,
>
> The subject line got truncated in your post so I made up a new and shorter
> one to continue the thread.
>
> I can only speak for myself — I read your post carefully more than once,
> but left it to others to reply to it (which Gary R had already done,
> actually) because I had no answers to the questions you raised in it. I
> couldn't make a connection between your suggestion of “would-be
> hypothetical situations, such as the mobius strip” and Peirce's idea of
> using the verso of the sheet of assertion as the area inside a cut. In fact
> I still don't see a connection. A mobius strip, being a bounded surface
> with only one side, doesn't have a verso, and I don't see how it relates to
> Peirce's “discovery” that the verso of the sheet represents “a kind of
> possibility” and not just the negation of the graph within the cut. I also
> couldn't get a handle on your question “Would boundedness exist in a mobius
> strip?” or its relevance to the issue we’ve been discussing yesterday and
> today.
>
> Maybe it’s just my obtuseness, but you’ll need to explain what you were
> driving at before I can see its relevance to Jeff’s post that I did reply
> to. (I assume you want to be given credit for more than just mentioning the
> “verso” in your post, but I don’t yet see what else in it anticipates
> Jeff’s post).
>
> gary f.
>
> -----Original Message-----
> From: Libertin, Mary
> Sent: 20-Jan-15 8:36 AM
> To: [email protected]<mailto:[email protected]>
> Subject: [biosemiotics:7975] Re: Contradictories, contraries, etc. WAS
>
> Jeffrey, Gary R, Lists,
>
> I brought up significance of the verso side of the existential graphs in
> my most recent post last week, but have not been acknowledged as the
> initiator of this thread. Gary R. responded to my comment on the
> distributed and undistributed significance of the immediate and direct
> objects of the dicisign. I wrote:
>
> "I do think we should go on. Stjernfelt places his discussion of the
> dicisign in as large a Universe of Discourse as is practical for his
> audience. We need to be more tolerant of interdisciplinary analogies. I
> also think we need some instruction when we find it necessary, which means
> we should ask. Here are some of the questions that came to mind after the
> third time reading NP: how is the sheet of assertion, recto and verso
> sides, to be understood in various ³would¹be² hypothetical situations, such
> as the mobius strip. Would boundedness exist in a mobius strip? The
> concepts of in/out, the whole or the part of the universe of discourse are
> in chapter 8, along with many other important thoughts, juxtapositions,
> questions, and musings. . . ”
>
> I have been researching this area and find it surprising that my initial
> discussion has been overlooked. If this is the first time the issue has
> been discussed I wish to be given credit or acknowledged in the discussion.
>
> Mary Libertin
>
> Mary Libertin, PhD
> Professor of English
> Shippensburg University of PA
> Shippensburg PA 17257
> [email protected]<mailto:[email protected]>
>
> On 1/19/15, 11:16 PM, "Jeffrey Brian Downard" wrote:
>
>
> -----------------------------
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>
>
>
>
>
>
--
Sungchul Ji, Ph.D.
Associate Professor of Pharmacology and Toxicology
Department of Pharmacology and Toxicology
Ernest Mario School of Pharmacy
Rutgers University
Piscataway, N.J. 08855
732-445-4701
www.conformon.net
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