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Directory:Jon Awbrey/Papers/Differential Propositional Calculus (view source)
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, 14:20, 6 May 2008→Note 14: markup
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*<p>If we make the identifications:</p><p><math>\mathrm{resting} = \mathrm{true}\ (= \mathrm{indicated}),\!</math></p><p><math>\mathrm{charged} = \mathrm{false}\ (= \mathrm{otherwise}),\!</math></p><p>then the physical function <math>f : \mathbf{B} \times \mathbf{B} \to \mathbf{B}</math> is tantamount to the logical function that is commonly known as ''logical difference'', or ''exclusive disjunction'':</p>
<pre>
<pre>
Table 7. Difference Function
Table 7. Difference Function
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| true | true | false |
| true | true | false |
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Although the syntax of the cactus language modifies the
Although the syntax of the cactus language modifies the syntax of Peirce's graphical formalisms to some extent, the first interpretation corresponds to what he called the ''entitative graphs'' and the second interpretation corresponds to what he called the ''existential graphs''. In working through the present example, I have chosen the existential interpretation of cactus expressions, and so the form "<code>(jets , sharks)</code>" is interpreted as saying that everything in the universe of discourse is either a Jet or a Shark, but never both at once.
syntax of Peirce's graphical formalisms to some extent,
the first interpretation corresponds to what he called
the "entitative graphs" and the second interpretation
corresponds to what he called the "existential graphs".
In working through the present example, I have chosen
the existential interpretation of cactus expressions,
and so the form "(jets , sharks)" is interpreted as
saying that everything in the universe of discourse
is either a Jet or a Shark, but never both at once.
===Note 15===
===Note 15===