Cf: Inquiry Into Inquiry • In Medias Res
https://inquiryintoinquiry.com/2022/07/21/inquiry-into-inquiry-in-medias-re…
Re: Dan Everett
<QUOTE DE:>
I am trying to represent two readings of the three juxtaposed sentences in English. The first reading is that the judge
and the jury both know that Malcolm is guilty. The second is that the judge knows that the jury thinks that Malcolm is
guilty.
Figure 1
https://inquiryintoinquiry.files.wordpress.com/2022/07/daniel-everett-e280a…
Figure 2
https://inquiryintoinquiry.files.wordpress.com/2022/07/daniel-everett-e280a…
Do these purported EGs of mine seem correct to you?
</QUOTE>
Dear Dan,
Apologies for the delay in responding … I won't have much of use to say about those particular graphs as I've long been
following a different fork in Peirce's work about how to get from Alpha to Beta, from propositional to quantificational
logic via graphical syntax.
But the examples raise one of the oldest issues I've bothered about over the years, going back to the days when I read
PQR (Peirce, Quine, Russell) in tandem and many long discussions with my undergrad phil advisor. That is the question
of intentional contexts and ”referential opacity”. The thing is Peirce's pragmatic standpoint yields a radically
distinct analysis of belief, knowledge, and indeed truth from the way things have been handled down the line from
logical atomism and empiricism to analytic philosophy in general. As it happens, there was a critical branch point in
time when Russell almost got a clue but Wittgenstein bullied him into dropping it, at least so far as I could tell from
a scattered sample of texts.
At any rate, I fell down the Wayback Machine rabbit hole looking for things I wrote about all this on the Peirce List
and other places around the web at the turn of the millennium …
I'd almost be tempted to start a blog series on this, probably simulcast on the Facebook Peirce Matters page if you're
into discussing it online … I have enough off the cuff to start an anchor post or two, but it might be the middle of
August before I could do much more.
Regards,
Jon
Cf: Sign Relations • Anthesis
http://inquiryintoinquiry.com/2022/06/29/sign-relations-anthesis-2/
<QUOTE CSP:>
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
</QUOTE>
All,
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.
Resources —
• 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
http://inquiryintoinquiry.com/2022/06/24/theme-one-program-discussion-7/
Re: Ontolog Forum
https://groups.google.com/g/ontolog-forum/c/vlsQqvEiIkY
::: Alex Shkotin
https://groups.google.com/g/ontolog-forum/c/vlsQqvEiIkY/m/07uF-WTzDwAJ
<QUOTE AS:>
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,
* nonterminal,
** for syntactic nonterminal: rule id used for derivation,
** for lexical nonterminal: value taken from text.
</QUOTE>
Dear Alex,
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 )
Regards,
Jon
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:
Helmut, List,
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.
best
Jack
________________________________
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
*Warning*
This email originated from outside of Maynooth University's Mail System. Do not reply, click links or open attachments unless you recognise the sender and know the content is safe.
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.
Best Regards
Helmut
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.
John
_ _ _ _ _ _ _ _ _ _ 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
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.
John
Cf: Theme One Program • Exposition 4
https://inquiryintoinquiry.com/2022/06/20/theme-one-program-exposition-4/
All,
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
https://inquiryintoinquiry.files.wordpress.com/2022/06/theme-exposition-cac…
Figure 3. Parse Graph and Traverse String
https://inquiryintoinquiry.files.wordpress.com/2022/06/theme-exposition-par…
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.
Regards,
Jon
Cf: Theme One Program • Exposition 3
https://inquiryintoinquiry.com/2022/06/17/theme-one-program-exposition-3-2/
All,
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
generic examples.
Figure 1 shows a typical example of a painted and rooted cactus.
Figure 1. Painted And Rooted Cactus
https://inquiryintoinquiry.files.wordpress.com/2022/06/theme-exposition-pai…
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
https://inquiryintoinquiry.files.wordpress.com/2022/06/theme-exposition-cac…
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
this case.
• 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”.
Regards,
Jon
Cf: Theme One Program • Exposition 2
https://inquiryintoinquiry.com/2022/06/16/theme-one-program-exposition-2-2/
Re: Theme One Program • Exposition 1
https://inquiryintoinquiry.com/2022/06/15/theme-one-program-exposition-1-2/
All,
The previous post described the elementary data structure
used to represent nodes of graphs in the Theme One program.
This post describes the specific family of graphs employed
by the program.
Figure 1 shows a typical example of a “painted and rooted cactus”.
Figure 1. Painted And Rooted Cactus
https://inquiryintoinquiry.files.wordpress.com/2022/06/theme-exposition-pai…
The graph itself is a mathematical object and does not inhabit the
page or other medium before our eyes, and it must not be confused
with any picture or other representation of it, anymore than we’d
want someone to confuse us with a picture of ourselves, but it’s
a fair enough picture, once we understand the conventions of
representation involved.
Let V(G) be the set of nodes in a graph G and let L be a set of identifiers.
We often find ourselves in situations where we have to consider many different
ways of associating the nodes of G with the identifiers in L. Various manners
of associating nodes with identifiers have been given conventional names by
different schools of graph theorists. I will give one way of describing
a few of the most common patterns of association.
• A graph is “painted” if there is a relation between its node set
and a set of identifiers, in which case the relation is called
a “painting” and the identifiers are called “paints”.
• A graph is “colored” if there is a function from its node set
to a set of identifiers, in which case the function is called
a “coloring” and the identifiers are called “colors”.
• A graph is “labeled” if there is a one-to-one mapping between
its node set and a set of identifiers, in which case the mapping
is called a “labeling” and the identifiers are called “labels”.
• A graph is said to be “rooted” if it has a unique distinguished node,
in which case the distinguished node is called the “root” of the graph.
The graph in Figure 1 has a root node marked by the “at” sign or amphora
symbol “@”.
The graph in Figure 1 has eight nodes plus the five paints in the
set {a, b, c, d, e}. The painting of nodes is indicated by drawing
the paints of each node next to the node they paint. Observe that
some nodes may be painted with an empty set of paints.
The structure of a painted and rooted cactus may be encoded in the form of
a character string called a “painted and rooted cactus expression”. For the
remainder of this discussion the terms “cactus” and “cactus expression” will
be used to mean the painted and rooted varieties. A cactus expression is
formed on an alphabet consisting of the relevant set of identifiers, the
“paints”, together with three punctuation marks: the left parenthesis,
the comma, and the right parenthesis.
Regards,
Jon
Cf: Theme One Program • Exposition 1
https://inquiryintoinquiry.com/2018/06/08/theme-one-program-exposition-1/
All,
Theme One is a program for building and transforming a particular species
of graph-theoretic data structures, forms designed to support a variety of
fundamental learning and reasoning tasks.
The program evolved over the course of an exploration into the integration of
contrasting types of activities involved in learning and reasoning, especially
the types of algorithms and data structures capable of supporting a range of
inquiry processes, from everyday problem solving to scientific investigation.
In its current state, Theme One integrates over a common data structure
fundamental algorithms for one type of inductive learning and one type
of deductive reasoning.
We begin by describing the class of graph-theoretic data structures
used by the program, as determined by their local and global aspects.
It will be the usual practice to shift around and to view these graphs
at many different levels of detail, from their abstract definition to
their concrete implementation, and many points in between.
The main work of the Theme One program is achieved by building and
transforming a single species of graph-theoretic data structures.
In their abstract form these structures are closely related to the
graphs that are called “cacti” and “conifers” in graph theory,
so we'll generally refer to them under those names.
The graph-theoretic data structures used by the program are built up from
a basic data structure called an “idea-form flag”. That structure is defined
as a pair of Pascal data types by means of the following specifications.
Box 1. Type Idea = ^Form
https://inquiryintoinquiry.files.wordpress.com/2022/06/theme-exposition-typ…
An “idea” is a pointer to a “form”.
A “form” is a record consisting of:
A “sign” of type char;
Four pointers, as, up, on, by, of type idea;
A “code” of type numb, that is, an integer in [0, max integer].
Represented in terms of “digraphs”, or directed graphs, the combination
of an “idea” pointer and a “form” record is most easily pictured as an arc,
or directed edge, leading to a node that is labeled with the other data,
in this case, a letter and a number.
At the roughest but quickest level of detail, an idea of a form can be drawn like this.
Box 2. Idea^Form Node
https://inquiryintoinquiry.files.wordpress.com/2022/06/theme-exposition-ide…
When it is necessary to fill in more detail, the following schematic pattern can be used.
Box 3. Idea^Form Flag
https://inquiryintoinquiry.files.wordpress.com/2022/06/theme-exposition-ide…
The idea-form type definition determines the local structure of
the whole host of graphs used by the program, including a motley
array of ephemeral buffers, temporary scratch lists, and other
graph-theoretic data structures used for their transient utilities
at specific points in the program.
I will put off discussing these more incidental graph structures
until the points where they actually arise, focusing here on the
particular varieties and the specific variants of cactoid graphs
that constitute the main formal media of the program's operation.
Regards,
Jon
