Theme One Program • Exposition 8
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https://inquiryintoinquiry.com/2024/06/18/theme-one-program-exposition-8-b/
Re: Theme One Program • Exposition 7
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https://inquiryintoinquiry.com/2024/06/17/theme-one-program-exposition-7-b/
Mathematical Structure and Logical Interpretation —
The main things to take away from the previous post are
the following two ideas, one syntactic and one semantic.
• Syntax. The compositional structures of cactus graphs
and cactus expressions are constructed from two kinds
of connective operations.
• Semantics. There are two ways of mapping the compositional
structures of syntax into the compositional structures of
propositional sentences.
The two kinds of connective operations are described as follows.
The “node connective” joins a number of component cacti C₁, …, Cₖ
to a node, as shown below.
•
https://inquiryintoinquiry.files.wordpress.com/2018/04/theme-one-exposition…
The “lobe connective” joins a number of component cacti C₁, …, Cₖ
to a lobe, as shown below.
•
https://inquiryintoinquiry.files.wordpress.com/2018/04/theme-one-exposition…
The two ways of mapping cactus structures to logical meanings
are summarized in Table 3, which compares the entitative and
existential interpretations of the basic cactus structures,
in effect, the graphical constants and connectives.
Table 3. Logical Interpretations of Cactus Structures
•
https://inquiryintoinquiry.files.wordpress.com/2022/10/logical-interpretati…
Regards,
Jon
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