# Logical Graphs, Iconicity, Interpretation

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### Jon Awbrey

Oct 3, 2021, 4:56:21 PM10/3/21
to Cybernetic Communications, Laws of Form, Ontolog Forum, Peirce List, Structural Modeling, SysSciWG
Cf: Logical Graphs, Iconicity, Interpretation • 1
https://inquiryintoinquiry.com/2021/10/03/logical-graphs-iconicity-interpretation-1/

<QUOTE Paul Ricoeur>
If exegesis raised a hermeneutic problem, that is, a problem
of interpretation, it is because every reading of a text always
takes place within a community, a tradition, or a living current
of thought, all of which display presuppositions and exigencies —
regardless of how closely a reading may be tied to the *quid*, to
“that in view of which” the text was written.

❧ Paul Ricoeur • The Conflict of Interpretations
https://oeis.org/wiki/Inquiry_Driven_Systems_%E2%80%A2_Part_9#Points_Forward
</QUOTE>

All,

If a picture is worth a thousand words, here’s my 48,000 words
worth on the periodically recurring question of logical graphs,
their iconicity, and their interpretation, at least so far as
Peirce’s alpha graphs interpreted for propositional logic go.
A few more actual words, literally speaking, may be called for.

Referring to the Table —

• Column 1 shows a conventional name fₙ and a venn diagram
for each of the sixteen boolean functions on two variables.

• Column 2 shows the logical graph canonically representing the
boolean function in Column 1 under the entitative interpretation.
This is the interpretation C.S. Peirce used in his earlier work
on entitative graphs and the one Spencer Brown used in his book
Laws of Form.

• Column 3 shows the logical graph canonically representing the
boolean function in Column 1 under the existential interpretation.
This is the interpretation C.S. Peirce used in his later work on
existential graphs.

Table 1. Boolean Functions and Logical Graphs on Two Variables
https://inquiryintoinquiry.files.wordpress.com/2021/10/boolean-functions-and-logical-graphs-on-two-variables.png

Resources
=========

• Logic Syllabus ( https://oeis.org/wiki/Logic_Syllabus )
• Logical Graphs ( https://oeis.org/wiki/Logical_Graphs )

Regards,

Jon
Boolean Functions and Logical Graphs on Two Variables.png

### Jon Awbrey

Oct 4, 2021, 5:20:24 PM10/4/21
to Cybernetic Communications, Laws of Form, Ontolog Forum, Peirce List, Structural Modeling, SysSciWG
Cf: Logical Graphs, Iconicity, Interpretation • 2
https://inquiryintoinquiry.com/2021/10/04/logical-graphs-iconicity-interpretation-2/

<QUOTE C.S. Peirce>

In the first place there are likenesses or copies — such as statues,
pictures, emblems, hieroglyphics, and the like. Such representations
stand for their objects only so far as they have an actual resemblance
to them — that is agree with them in some characters. The peculiarity
of such representations is that they do not determine their objects —
they stand for anything more or less; for they stand for whatever
they resemble and they resemble everything more or less.

The second kind of representations are such as are set up by
a convention of men or a decree of God. Such are tallies,
proper names, &c. The peculiarity of these conventional
signs is that they represent no character of their objects.
Likenesses denote nothing in particular; conventional signs
connote nothing in particular.

The third and last kind of representations are symbols or general
representations. They connote attributes and so connote them as
to determine what they denote. To this class belong all words
and all conceptions. Most combinations of words are also symbols.
A proposition, an argument, even a whole book may be, and should be,
a single symbol.

C.S. Peirce (1866), Lowell Lecture 7, CE 1, 467–468
( https://oeis.org/wiki/Semeiotic#Types_of_signs )
</QUOTE>

All,

The Table in the previous post can now be sorted to bring out the
“family resemblances”, likenesses, or symmetries among logical graphs
and the boolean functions they denote, where the “orbits” or similarity
classes are determined by the dual interpretation of logical graphs.

Performing the sort produces the following Table. As we have
seen in previous discussions, there are 10 orbits in all,
4 orbits of 1 point each and 6 orbits of 2 points each.

Table 2. Boolean Functions and Logical Graphs on Two Variables • Orbit Order
https://inquiryintoinquiry.files.wordpress.com/2021/10/boolean-functions-and-logical-graphs-on-two-variables-e280a2-orbit-order.png
Boolean Functions and Logical Graphs on Two Variables • Orbit Order.png

### Jon Awbrey

Oct 13, 2021, 12:40:17 PM10/13/21
to Cybernetic Communications, Laws of Form, Ontolog Forum, Peirce List, Structural Modeling, SysSciWG
Cf: Logical Graphs, Iconicity, Interpretation • Discussion 1
https://inquiryintoinquiry.com/2021/10/13/logical-graphs-iconicity-interpretation-discussion-1/

Re: Logical Graphs, Iconicity, Interpretation • 1
https://inquiryintoinquiry.com/2021/10/03/logical-graphs-iconicity-interpretation-1/
Re: Laws of Form
https://groups.io/g/lawsofform/topic/logical_graphs_iconicity/86051464
::: John Mingers ( https://groups.io/g/lawsofform/message/913 )

<QUOTE JM:>
I’m impressed that you have read Ricoeur — my impression is
that Americans don’t have much time for Continental philosophy
(a huge generalisation of course).

Have you looked at Habermas? He uses Peirce's work as well as
hermeneutics (mainly Gadamer) and critical theory to come up
with what he calls a theory of communicative action. He also
called it “universal pragmatics” at one time as a nod to both
Chomsky and semiotics.
</QUOTE>

Dear John,

That observation from Ricoeur’s Conflict of Interpretations comes
from a time when Susan Awbrey and I were exploring the synergies
of action research, critical thinking, classical and post-modern
hermeneutics, and Peirce’s triadic relational semiotics.

We benefited greatly from our study of Gadamer, Habermas, Ricoeur
and a little more from Derrida, Foucault, Lyotard, aided by the
lucid surveys of Richard J. Bernstein. All that culminated in a paper
we presented at a conference on Hermeneutics and the Human Sciences,
subsequently published as “Interpretation as Action : The Risk of Inquiry”.

I found Ricoeur’s comment fitting in the present connection because it
speaks to the way identical modulations of a medium may convey different
messages to different cultures and contexts of communication. Conversely,
conveying the same message to different cultures and contexts of communication
may require different modulations of the same medium.

That is precisely situation we observe in the Table from Episode 1,
for ease of reference repeated below. The objects to be conveyed
are the 16 boolean functions on 2 variables, whose venn diagrams
appear in Column 1. And we have the two cultures of interpreters,
Entitative and Existential, whose graphical and parenthetical forms
of expression for the boolean functions are shown in Column 2 and
Column 3, respectively.

Table 1. Boolean Functions and Logical Graphs on Two Variables
https://inquiryintoinquiry.files.wordpress.com/2021/10/boolean-functions-and-logical-graphs-on-two-variables.png

Have to break here ... gotta go get our booster shots ...

Regards,

Jon

References
===========

• Awbrey, J.L., and Awbrey, S.M. (Autumn 1995), “Interpretation as Action :
The Risk of Inquiry”, Inquiry : Critical Thinking Across the Disciplines 15(1),
40–52.
https://web.archive.org/web/20001210162300/http://chss.montclair.edu/inquiry/fall95/awbrey.html
https://www.pdcnet.org/inquiryct/content/inquiryct_1995_0015_0001_0040_0052

• Awbrey, J.L., and Awbrey, S.M. (June 1992), “Interpretation as Action :
The Risk of Inquiry”, The Eleventh International Human Science Research Conference,
Oakland University, Rochester, Michigan.

Boolean Functions and Logical Graphs on Two Variables.png

### Jon Awbrey

Oct 21, 2021, 1:24:35 PM10/21/21
to Cybernetic Communications, Laws of Form, Ontolog Forum, Peirce List, Structural Modeling, SysSciWG
Cf: Logical Graphs, Iconicity, Interpretation • Discussion 2
https://inquiryintoinquiry.com/2021/10/21/logical-graphs-iconicity-interpretation-discussion-2/

Re: Logical Graphs, Iconicity, Interpretation • 2
https://inquiryintoinquiry.com/2021/10/04/logical-graphs-iconicity-interpretation-2/
::: John Mingers ( https://groups.io/g/lawsofform/message/918 )

<QUOTE JM:>
The quote you have given does not match the standard Peircean trichotomy
of icon, index, symbol. See this quote from CP 4.448 […]
</QUOTE>

Dear John,

I hesitate to call any sketch Peirce gave of the big three sign types
a “standard Peircean trichotomy of icon, index, symbol”. Several
considerations give me pause on this point.

• Peirce gave so many instructive and useful characterizations
of the main sign types over the years I'd be hard-pressed to
declare any one text definitive. It is not that we have a
hermeneutic circle where every text is granted equal weight,
only that it takes more analysis to define the terms as yet
undefined and to sort all terms involved in order of their
mutual and sole dependencies.

• A cursory inspection of Peirce's sign types, from major to minor,
shows we rarely if ever have true k-tomies, in the sense of exhaustive
and mutually exclusive categories. True, we often speak of dichotomies
and trichotomies in loose terms, but now and again loose speech has led
to sinking ontologies.

Oops, more to say but need to break for midday sustenance …

Regards,

Jon