On 3 Oct 2021, at 21:56, Jon Awbrey <jawbrey@...> wrote:

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.
I’ll return to that anon.

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>