Cactus Language • Semantics

[Jon Awbrey]

Cactus Language • Semantics 1
• https://inquiryintoinquiry.com/2025/10/06/cactus-language-semantics-1/

❝Alas, and yet what are you, my written and painted thoughts! It is not
long ago that you were still so many‑coloured, young and malicious, so
full of thorns and hidden spices you made me sneeze and laugh — and now?
You have already taken off your novelty and some of you, I fear, are
on the point of becoming truths: they already look so immortal, so
pathetically righteous, so boring!❞

— Nietzsche • Beyond Good and Evil

The discussion to follow describes a particular semantics for painted
cactus languages, showing one way to link logical meanings with the
bare syntactic forms of linguistic expressions. Forging those links
between signs and intents gives the parametric family of formal
languages in question one of its principal “interpretations”.

We'll keep that interpretation in our sights for the time being but
it must be remembered it forms just one of many such interpretations
which may be conceivable and even viable in the long run. Indeed, the
distinction between the sign domain and the object domain can be observed
in the fact that many languages can be deployed to depict the same set of
objects while any language worth its salt is bound to give rise to a host
of salient interpretations.

Resources —

Cactus Language • Semantics
• https://oeis.org/wiki/Cactus_Language_%E2%80%A2_Part_3#Cactus_Language_%E2%80%A2_Semantics

Survey of Animated Logical Graphs
• https://inquiryintoinquiry.com/2025/05/02/survey-of-animated-logical-graphs-8/

Survey of Theme One Program
• https://inquiryintoinquiry.com/2025/05/06/survey-of-theme-one-program-7/

Regards,

Jon

cc: https://www.academia.edu/community/V0r38A
cc: https://www.researchgate.net/post/Cactus_Language_Semantics

[Jon Awbrey]

Cactus Language • Semantics 2
• https://inquiryintoinquiry.com/2025/10/08/cactus-language-semantics-2/

It is common in formal settings to speak of interpretation as if it created
a direct connection from the signs of a formal language to the objects of
the intended domain, in effect, as if it determined the denotative component
of a sign relation. But closer attention to what goes on reveals that the
process of interpretation is more indirect, that what it does is provide each
sign of a prospectively meaningful source language with a translation into
an already established target language, where “already established” means its
relationship to pragmatic objects is taken for granted at the moment in question.

With that in mind, it is clear interpretation is an affair of signs which
at best respects the objects of all the signs entering into it, and so it is
the connotative aspect of semiotics we find to embody the process. There is
nothing wrong with our saying we interpret expressions of a formal language
as signs referring to functions or propositions or other objects so long as
we understand the reference is generally achieved by way of more familiar
and perhaps less formal signs we already take to denote those objects.

Resources —

Cactus Language • Semantics
• https://oeis.org/wiki/Cactus_Language_%E2%80%A2_Part_3#Cactus_Language_%E2%80%A2_Semantics

Survey of Animated Logical Graphs
• https://inquiryintoinquiry.com/2025/05/02/survey-of-animated-logical-graphs-8/

Survey of Theme One Program
• https://inquiryintoinquiry.com/2025/05/06/survey-of-theme-one-program-7/

Regards,

Jon

cc: https://www.academia.edu/community/V9KEBE
cc: https://www.researchgate.net/post/Cactus_Language_Semantics