Cf: Theme One Program • Exposition 5
Lexical, Literal, Logical
Theme One puts cactus graphs to work in three distinct but related ways,
called their “lexical”, “literal”, and “logical” uses. Those three modes
of operation employ three distinct but overlapping subsets of the broader
species of cacti. Accordingly we find ourselves working with graphs, files,
and expressions of lexical, literal, and logical types, depending on the task
The logical class of cacti is the broadest, encompassing the whole species
described above, of which we have already seen a typical example in its
several avatars as abstract graph, pointer data structure, and string
of characters suitable for storage in a text file.
Being a “logical cactus” is not just a matter of syntactic form —
it means being subject to meaningful interpretations as a sign of
a logical proposition. To enter the logical arena cactus expressions
must express something, a proposition true or false of something.
Fully addressing the logical, interpretive, semantic aspect of cactus graphs
normally requires a mind-boggling mass of preliminary work on the details of
their syntactic structure. Practical, pragmatic, and especially computational
considerations will eventually make that unavoidable. For the sake of the
present discussion, however, let’s put a pin in it and fast forward to the
Cf: Sign Relations • Anthesis
Thus, if a sunflower, in turning towards the sun, becomes by that
very act fully capable, without further condition, of reproducing
a sunflower which turns in precisely corresponding ways toward the
sun, and of doing so with the same reproductive power, the sunflower
would become a Representamen of the sun.
— C.S. Peirce, Collected Papers, CP 2.274
In his picturesque illustration of a sign relation, along with his tracing
of a corresponding sign process, or “semiosis”, Peirce uses the technical term
“representamen” for his concept of a sign, but the shorter word is precise enough,
so long as one recognizes its meaning in a particular theory of signs is given by
a specific definition of what it means to be a sign.
• Semeiotic ( https://oeis.org/wiki/Semeiotic )
• Logic Syllabus ( https://inquiryintoinquiry.com/logic-syllabus/ )
• Sign Relations ( https://oeis.org/wiki/Sign_relation )
• Triadic Relations ( https://oeis.org/wiki/Triadic_relation )
• Relation Theory ( https://oeis.org/wiki/Relation_theory )
cc: Conceptual Graphs • Cybernetics • Laws of Form • Ontolog Forum
cc: FB | Semeiotics • Structural Modeling • Systems Science
Cf: Theme One Program • Discussion 7
Re: Ontolog Forum
::: Alex Shkotin
As we both like digraphs and looking at your way of rendering, let me
share my lazy way of using Graphviz ( https://graphviz.org/ ) on one of
the last pictures produced ( https://photos.app.goo.gl/pJEGBnNqJRBE7JUT9 ).
This is a picture of a derivation tree (aka AST) for the text of four
statements of context-free grammar of some kind. It is important that
this is a digraph with ordered children, and nodes have some attributes.
In your case attributes are “sign”, “code”. In my case attributes are:
* node id,
** for syntactic nonterminal: rule id used for derivation,
** for lexical nonterminal: value taken from text.
Many thanks, the Graphviz suite looks very nice and I will
spend some time looking through the docs. I kept a few samples
of my old ASCII graphics, mostly from a sense of nostalgia, but
I've reached a point in reworking my Theme One Exposition where
I need to upgrade the graphics. My original aim was to have the
program display its own visuals, but it doesn't look like I'll
be the one doing that. Visualizing proofs requires animation —
I used to have an app for that bundled with CorelDraw but it
quit working in a previous platform change and I haven't gotten
around to hunting up a new one. At any rate, there's a sampler
of animated proofs in logical graphs on the following page.
* Proof Animations
( https://oeis.org/wiki/User:Jon_Awbrey/ANIMATION#Proof_Animations )
just for clarity, the point I'm making is probably an old one but: Peirce conceives of the subject-less feeling as object. That, I think, is an impossibility.
From: peirce-l-request(a)list.iupui.edu <peirce-l-request(a)list.iupui.edu> on behalf of JACK ROBERT KELLY CODY <jack.cody.2015(a)mumail.ie>
Sent: Thursday, June 30, 2022 3:48 PM
To: sowa(a)bestweb.net <sowa(a)bestweb.net>; Helmut Raulien <H.Raulien(a)gmx.de>
Cc: Peirce List <PEIRCE-L(a)list.iupui.edu>; CG <cg(a)lists.iccs-conference.org>
Subject: Re: [PEIRCE-L] [EXTERNAL] Aw: meaning
A feeling is what it is, positively, regardless of anything else. Its being is in it alone, and it is a mere potentiality. A brute force, as, for example, an existent particle, on the other hand, is nothing for itself; whatever it is, it is for what it is attracting and what it is repelling:
Is this an example of Peirce being abstract again? Because by "feeling" he often meant "tone" if I recall correctly. The problem I have (although I think it only exists with regard to this short extract as Peirce explains it better in detail) is that a "feeling" cannot easily be disregarded from that which embodies it. That is, the being -- or essence -- of "feeling" is not in feeling alone but also (and this is an anthropocentric point) requires the body (as conduit) which embodies the feeling as such.
I don't remember disagreeing with Peirce re "feeling" the last time I read through his texts at length so likely just a result of much context ommitted.
From: peirce-l-request(a)list.iupui.edu <peirce-l-request(a)list.iupui.edu> on behalf of Helmut Raulien <H.Raulien(a)gmx.de>
Sent: Thursday, June 30, 2022 3:40 PM
To: sowa(a)bestweb.net <sowa(a)bestweb.net>
Cc: Peirce List <PEIRCE-L(a)list.iupui.edu>; CG <cg(a)lists.iccs-conference.org>
Subject: [EXTERNAL] Aw: [PEIRCE-L] meaning
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John, Gary F., List,
first, here again the part of Gary´s Peirce quote, in which Peirce tells the three modes of being:
So, then, there are these three modes of being: first, the being of a feeling, in itself, unattached to any subject, which is merely an atmospheric possibility, a possibility floating in vacuo, not rational yet capable of rationalization; secondly, there is the being that consists in arbitrary brute action upon other things, not only irrational but anti-rational, since to rationalize it would be to destroy its being; and thirdly, there is living intelligence from which all reality and all power are derived; which is rational necessity and necessitation.
A feeling is what it is, positively, regardless of anything else. Its being is in it alone, and it is a mere potentiality. A brute force, as, for example, an existent particle, on the other hand, is nothing for itself; whatever it is, it is for what it is attracting and what it is repelling: its being is actual, consists in action, is dyadic. That is what I call existence. A reason has its being in bringing other things into connexion with each other; its essence is to compose: it is triadic, and it alone has a real power.
As I said, I not merely want to talk about reality, which is always meant universally, but also about false, but for a system viable, narratives. In this more general matter, not only talking about reality, but about pseudoreality as well, the third mode is not only the universal intelligible force, but also a system´s intentional force, creating false but viable narratives. I think, it is for all agreeable, that such things exist, and that it would be helpful to uncover them? Examples are galore.
Peirce says of the third mode, that its essence is composition. I think, before composition comes classification. A system can only compose its organs, if they first are classified and so specified. Example: The castes system in India, other feudal classification of people, and also classification of acts as good or bad. If classification of acts is in accord with the universal system (I think, the ten commandments mostly are), this is good at first glance, but if the system does not adress their origin as the universe´s nature, but as an act of its own, this is hijacking. Example: Liberal christians admit, that in Mahayana-Buddhism too similar values like compassion exist, but illiberal christians perhaps say, that good values only exist in the christian context, and since their prophets have declareded them.
Gesendet: Mittwoch, 29. Juni 2022 um 21:44 Uhr
Von: "John F Sowa" <sowa(a)bestweb.net>
An: "Peirce List" <PEIRCE-L(a)list.iupui.edu>
Cc: "CG" <cg(a)lists.iccs-conference.org>
Betreff: RE: [PEIRCE-L] meaning
Helmut, Gary F, List
The many complex issues in this thread would require a lengthy commentary. But I'll just make a few remarks on the word myth.
In classical Greek, the basic meaning of mythos is (1) word or speech; (2) public speech; (3) conversation; (4) thing said, fact, matter; (5) thing thought, unspoken word, purpose, design. (Liddell & Scott, 9th edition)
From those basic meanings, it came to be applied to tales, stories, and narratives. Since many of those stories contained a mixture of fact and fiction and sometimes more fiction than fact, critics such as Plato condemned them as false.
But the same criticism could be made of any scientific theories of any time past, present, or future. The goal of science is a deeper understanding of experience, but any theory is at best a good generalization of certain kinds of experience. And all scientific theories are eventually recognized as inadequate in one or more ways. Furthermore, many of the old myths still embody deep insights into human nature and experience -- many of them are still good guides for new scientific theories (abductions).
Summary: Science and myth represent insights (abductions) obtained through a deep analysis of experience. We should recognize them for what they contribute, but realize that they have limitations which may be clarified and extended by further analysis, and testing against new observations.
_ _ _ _ _ _ _ _ _ _ â–º PEIRCE-L subscribers: Click on "Reply List" or "Reply All" to REPLY ON PEIRCE-L to this message. PEIRCE-L posts should go to peirce-L(a)list.iupui.edu . â–º To UNSUBSCRIBE, send a message NOT to PEIRCE-L but to list(a)list.iupui.edu with UNSUBSCRIBE PEIRCE-L in the SUBJECT LINE of the message and nothing in the body. More at https://list.iupui.edu/sympa/help/user-signoff.html . â–º PEIRCE-L is owned by THE PEIRCE GROUP; moderated by Gary Richmond; and co-managed by him and Ben Udell.
Helmut, Gary F, List
The many complex issues in this thread would require a lengthy commentary.
But I'll just make a few remarks on the word myth.
In classical Greek, the basic meaning of mythos is (1) word or speech; (2)
public speech; (3) conversation; (4) thing said, fact, matter; (5) thing
thought, unspoken word, purpose, design. (Liddell & Scott, 9th edition)
From those basic meanings, it came to be applied to tales, stories, and
narratives. Since many of those stories contained a mixture of fact and
fiction and sometimes more fiction than fact, critics such as Plato
condemned them as false.
But the same criticism could be made of any scientific theories of any
time past, present, or future. The goal of science is a deeper
understanding of experience, but any theory is at best a good
generalization of certain kinds of experience. And all scientific theories
are eventually recognized as inadequate in one or more ways. Furthermore,
many of the old myths still embody deep insights into human nature and
experience -- many of them are still good guides for new scientific
Summary: Science and myth represent insights (abductions) obtained
through a deep analysis of experience. We should recognize them for what
they contribute, but realize that they have limitations which may be
clarified and extended by further analysis, and testing against new
Cf: Theme One Program • Exposition 4
It is possible to write a program that parses cactus expressions
into reasonable facsimiles of cactus graphs as pointer structures
in computer memory, making edges correspond to addresses and nodes
correspond to records. I did just that in the early forerunners of
the present program, but it turned out to be a more robust strategy
in the long run, despite the need for additional nodes at the outset,
to implement a more articulate but more indirect parsing algorithm,
one in which the punctuation marks are not just tacitly converted
to addresses in passing, but instead recorded as nodes in roughly
the same way as the ordinary identifiers, or “paints”.
Figure 3 illustrates the type of parsing paradigm used by the program,
showing the pointer graph obtained by parsing the cactus expression in
Figure 2. A traversal of this graph naturally reconstructs the cactus
string that parses into it.
Figure 2. Cactus Graph and Cactus Expression
Figure 3. Parse Graph and Traverse String
The pointer graph in Figure 3, namely, the parse graph of a cactus
expression, is the sort of thing we'll probably not be able to resist
calling a “cactus graph”, for all the looseness of that manner of speaking,
but we should keep in mind its level of abstraction lies a step further in
the direction of a concrete implementation than the last thing we called by
that name. While we have them before our mind's eyes, there are several other
distinctive features of cactus parse graphs we ought to notice before moving on.
In terms of idea-form structures, a cactus parse graph begins with a root idea
pointing into a “by”‑cycle of forms, each of whose “sign” fields bears either
a “paint”, in other words, a direct or indirect identifier reference, or an
opening left parenthesis indicating a link to a subtended lobe of the cactus.
A lobe springs from a form whose “sign” field bears a left parenthesis.
That stem form has an “on” idea pointing into a “by”‑cycle of forms,
exactly one of which has a “sign” field bearing a right parenthesis.
That last form has an “on” idea pointing back to the form bearing
the initial left parenthesis.
In the case of a lobe, aside from the single form bearing the closing
right parenthesis, the “by”‑cycle of a lobe may list any number of forms,
each of whose “sign” fields bears either a comma, a paint, or an opening
left parenthesis signifying a link to a more deeply subtended lobe.
Just to draw out one of the implications of this characterization and to
stress the point of it, the root node can be painted and bear many lobes,
but it cannot be segmented, that is, the “by”‑cycle corresponding to the
root node can bear no commas.
Cf: Theme One Program • Exposition 3
My earliest experiments coding logical graphs as dynamic “pointer”
data structures taught me conceptual and computational efficiencies
of a critical sort could be achieved by generalizing their abstract
graphs from trees to the variety graph theorists know as “cacti”.
The genesis of that generalization is a tale worth telling another
time, but for now it's best to jump right in and proceed by way of
Figure 1 shows a typical example of a painted and rooted cactus.
Figure 1. Painted And Rooted Cactus
Figure 2 shows a way to visualize the correspondence between
cactus graphs and cactus strings, demonstrated on the cactus
from Figure 1. By way of convenient terminology, the polygons
of a cactus graph are called its “lobes”. An edge not part of
a larger polygon is called a “2-gon” or a “bi-gon”. A terminal
bi-gon is called a “spike”.
Figure 2. Cactus Graph and Cactus Expression
The correspondence between a cactus graph and a cactus string is
obtained by an operation called “traversing” the graph in question.
• One traverses a cactus graph by beginning at the left hand side
of the root node, reading off the list of paints one encounters
at that point. Since the order of elements at any node is not
significant, one may start the cactus string with that list of
paints or save them for the end. We have done the latter in
• One continues by climbing up the left hand side of the leftmost lobe,
marking the ascent by means of a left parenthesis, traversing whatever
cactus one happens to reach at the first node above the root, that done,
proceeding from left to right along the top side of the lobe, marking each
interlobal span by means of a comma, traversing each cactus in turn one meets
along the way, on completing the last of them climbing down the right hand side
of the lobe, marking the descent by means of a right parenthesis, then traversing
each cactus in turn, in left to right order, that is incident with the root node.
The string of letters, parentheses, and commas one obtains by this procedure
is called the “traversal string” of the graph, in this case, a “cactus string”.