[CG] Re: Differential Propositional Calculus

Differential Propositional Calculus • 3 • https://inquiryintoinquiry.com/2023/11/17/differential-propositional-calcul… All, Casual Introduction (cont.) Figure 3 returns to the situation in Figure 1, but this time interpolates a new quality specifically tailored to account for the relation between Figure 1 and Figure 2. Figure 3. Back, To The Future • https://inquiryintoinquiry.files.wordpress.com/2023/11/differential-proposi… This new quality, dq, is an example of a “differential quality”, since its absence or presence qualifies the absence or presence of change occurring in another quality. As with any other quality, it is represented in the venn diagram by means of a “circle” distinguishing two halves of the universe of discourse, in this case, the portions of X outside and inside the region dQ. Figure 1 represents a universe of discourse, X, together with a basis of discussion, {q}, for expressing propositions about the contents of that universe. Once the quality q is given a name, say, the symbol “q”, we have the basis for a formal language specifically cut out for discussing X in terms of q. This language is more formally known as the propositional calculus with alphabet {“q”}. In the context marked by X and {q} there are just four distinct pieces of information which can be expressed in the corresponding propositional calculus, namely, the constant proposition False, the negative proposition ¬q, the positive proposition q, and the constant proposition True. For example, referring to the points in Figure 1, the constant proposition False holds of no points, the negative proposition ¬q holds of a and d, the positive proposition q holds of b and c, and the constant proposition True holds of all points in the sample. Figure 3 preserves the same universe of discourse and extends the basis of discussion to a set of two qualities, {q, dq}. In corresponding fashion, the initial propositional calculus is extended by means of the enlarged alphabet, {“q”, “dq”}. Regards, Jon cc: https://www.academia.edu/community/LZb2ZL