Theme One • A Program Of Inquiry : 11
http://inquiryintoinquiry.com/2018/03/28/theme-one-%e2%80%a2-a-program-of-inquiry-11/
Peircers,
The portions of exposition just skipped over covered the
use of cactus graphs in the program's learning module to
learn sequences of characters called “words” or “strings”
and sequences of words called “sentences” or “strands”.
Leaving the matter of grammar to another time we turn to
the use of cactus graphs in the program's reasoning module
to represent logical propositions on the order of Peirce's
Alpha Graphs and Spencer Brown's calculus of indications.
(Please see the blog post linked above for the Tables mentioned below.)
Regards,
Jon
Logical Cacti
=============
Up till now we've been working to hammer out a two-edged sword of syntax, honing the syntax of cactus graphs and cactus
expressions and turning it to use in taming the syntax of two-level formal languages.
But the purpose of a logical syntax is to support a logical semantics, which means, for starters, to bear interpretation
as sentential signs capable of denoting objective propositions about a universe of objects.
One of the difficulties we face is that the words “interpretation”, “meaning”, “semantics”, and their ilk take on so
many different meanings from one moment to the next of their use. A dedicated neologician might be able to think up
distinctive names for all the aspects of meaning and all the approaches to them that concern us, but I will do the best
I can with the common lot of ambiguous terms, leaving it to context and intelligent interpreters to sort it out as much
as possible.
The formal language of cacti is formed at such a high level of abstraction that its graphs can bear at least two
distinct interpretations as logical propositions. The two interpretations that concern us here are descended from the
ones C.S. Peirce called the “entitative” and the “existential” interpretations of his systems of graphical logics.
Existential Interpretation
==========================
Table 1 illustrates the existential interpretation of cactus graphs and cactus expressions by providing English
translations for a few of the most basic and commonly occurring forms.
Entitative Interpretation
=========================
Table 2 illustrates the entitative interpretation of cactus graphs and cactus expressions by providing English
translations for a few of the most basic and commonly occurring forms.
Resources
=========
* Theme One Program • Documentation
http://intersci.ss.uci.edu/wiki/index.php/Theme_One_Program
* Theme One Program • Exposition
http://intersci.ss.uci.edu/wiki/index.php/Theme_One_Program_%E2%80%A2_Exposition
* Theme One Program • Expository Note 13
http://intersci.ss.uci.edu/wiki/index.php/Theme_One_Program_%E2%80%A2_Exposition#Expository_Note_13
* Theme One Program • User Guide
https://www.academia.edu/5211369/Theme_One_Program_User_Guide
--
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isw: http://intersci.ss.uci.edu/wiki/index.php/JLA
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